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Diffstat (limited to 'dom/webgpu/tests/cts/checkout/src/unittests/floating_point.spec.ts')
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1 files changed, 8238 insertions, 0 deletions
diff --git a/dom/webgpu/tests/cts/checkout/src/unittests/floating_point.spec.ts b/dom/webgpu/tests/cts/checkout/src/unittests/floating_point.spec.ts new file mode 100644 index 0000000000..e8f8525d7f --- /dev/null +++ b/dom/webgpu/tests/cts/checkout/src/unittests/floating_point.spec.ts @@ -0,0 +1,8238 @@ +export const description = ` +Floating Point unit tests. +`; + +import { makeTestGroup } from '../common/framework/test_group.js'; +import { objectEquals, unreachable } from '../common/util/util.js'; +import { kValue } from '../webgpu/util/constants.js'; +import { FP, FPInterval, FPIntervalParam, IntervalBounds } from '../webgpu/util/floating_point.js'; +import { map2DArray, oneULPF32, oneULPF16, oneULPF64 } from '../webgpu/util/math.js'; +import { + reinterpretU16AsF16, + reinterpretU32AsF32, + reinterpretU64AsF64, +} from '../webgpu/util/reinterpret.js'; + +import { UnitTest } from './unit_test.js'; + +export const g = makeTestGroup(UnitTest); + +/** + * For ULP purposes, abstract float behaves like f32, so need to swizzle it in + * for expectations. + */ +const kFPTraitForULP = { + abstract: 'f32', + f32: 'f32', + f16: 'f16', +} as const; + +/** Bounds indicating an expectation of unbounded error */ +const kUnboundedBounds: IntervalBounds = [Number.NEGATIVE_INFINITY, Number.POSITIVE_INFINITY]; + +/** Interval from kUnboundedBounds */ +const kUnboundedInterval = { + f32: FP.f32.toParam(kUnboundedBounds), + f16: FP.f16.toParam(kUnboundedBounds), + abstract: FP.abstract.toParam(kUnboundedBounds), +}; + +/** @returns a number N * ULP greater than the provided number */ +const kPlusNULPFunctions = { + f32: (x: number, n: number) => { + return x + n * oneULPF32(x); + }, + f16: (x: number, n: number) => { + return x + n * oneULPF16(x); + }, + abstract: (x: number, n: number) => { + return x + n * oneULPF64(x); + }, +}; + +/** @returns a number one ULP greater than the provided number */ +const kPlusOneULPFunctions = { + f32: (x: number): number => { + return kPlusNULPFunctions['f32'](x, 1); + }, + f16: (x: number): number => { + return kPlusNULPFunctions['f16'](x, 1); + }, + abstract: (x: number): number => { + return kPlusNULPFunctions['abstract'](x, 1); + }, +}; + +/** @returns a number N * ULP less than the provided number */ +const kMinusNULPFunctions = { + f32: (x: number, n: number) => { + return x - n * oneULPF32(x); + }, + f16: (x: number, n: number) => { + return x - n * oneULPF16(x); + }, + abstract: (x: number, n: number) => { + return x - n * oneULPF64(x); + }, +}; + +/** @returns a number one ULP less than the provided number */ +const kMinusOneULPFunctions = { + f32: (x: number): number => { + return kMinusNULPFunctions['f32'](x, 1); + }, + f16: (x: number): number => { + return kMinusNULPFunctions['f16'](x, 1); + }, + abstract: (x: number): number => { + return kMinusNULPFunctions['abstract'](x, 1); + }, +}; + +/** @returns the expected IntervalBounds adjusted by the given error function + * + * @param expected the bounds to be adjusted + * @param error error function to adjust the bounds via + */ +function applyError( + expected: number | IntervalBounds, + error: (n: number) => number +): IntervalBounds { + // Avoiding going through FPInterval to avoid tying this to a specific kind + const unpack = (n: number | IntervalBounds): [number, number] => { + if (expected instanceof Array) { + switch (expected.length) { + case 1: + return [expected[0], expected[0]]; + case 2: + return [expected[0], expected[1]]; + } + unreachable(`Tried to unpack an IntervalBounds with length other than 1 or 2`); + } else { + // TS doesn't narrow this to number automatically + return [n as number, n as number]; + } + }; + + let [begin, end] = unpack(expected); + + begin -= error(begin); + end += error(end); + + if (begin === end) { + return [begin]; + } + return [begin, end]; +} + +// FPInterval + +interface ConstructorCase { + input: IntervalBounds; + expected: IntervalBounds; +} + +g.test('constructor') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ConstructorCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + const cases: ConstructorCase[] = [ + // Common cases + { input: [0, 10], expected: [0, 10] }, + { input: [-5, 0], expected: [-5, 0] }, + { input: [-5, 10], expected: [-5, 10] }, + { input: [0], expected: [0] }, + { input: [10], expected: [10] }, + { input: [-5], expected: [-5] }, + { input: [2.5], expected: [2.5] }, + { input: [-1.375], expected: [-1.375] }, + { input: [-1.375, 2.5], expected: [-1.375, 2.5] }, + + // Edges + { input: [0, constants.positive.max], expected: [0, constants.positive.max] }, + { input: [constants.negative.min, 0], expected: [constants.negative.min, 0] }, + { input: [constants.negative.min, constants.positive.max], expected: [constants.negative.min, constants.positive.max] }, + + // Infinities + { input: [0, constants.positive.infinity], expected: [0, Number.POSITIVE_INFINITY] }, + { input: [constants.negative.infinity, 0], expected: [Number.NEGATIVE_INFINITY, 0] }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + ]; + + // Note: Out of range values are limited to infinities for abstract float, due to abstract + // float and 'number' both being f64. So there are no separate OOR tests for abstract float, + // otherwise the testing framework will consider them duplicated. + if (p.trait !== 'abstract') { + // prettier-ignore + cases.push(...[ + // Out of range + { input: [0, 2 * constants.positive.max], expected: [0, 2 * constants.positive.max] }, + { input: [2 * constants.negative.min, 0], expected: [2 * constants.negative.min, 0] }, + { input: [2 * constants.negative.min, 2 * constants.positive.max], expected: [2 * constants.negative.min, 2 * constants.positive.max] }, + ] as ConstructorCase[]); + } + + return cases; + }) + ) + .fn(t => { + const i = new FPInterval(t.params.trait, ...t.params.input); + t.expect( + objectEquals(i.bounds(), t.params.expected), + `new FPInterval('${t.params.trait}', [${t.params.input}]) returned ${i}. Expected [${t.params.expected}]` + ); + }); + +interface ContainsNumberCase { + bounds: number | IntervalBounds; + value: number; + expected: boolean; +} + +g.test('contains_number') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ContainsNumberCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + const cases: ContainsNumberCase[] = [ + // Common usage + { bounds: [0, 10], value: 0, expected: true }, + { bounds: [0, 10], value: 10, expected: true }, + { bounds: [0, 10], value: 5, expected: true }, + { bounds: [0, 10], value: -5, expected: false }, + { bounds: [0, 10], value: 50, expected: false }, + { bounds: [0, 10], value: Number.NaN, expected: false }, + { bounds: [-5, 10], value: 0, expected: true }, + { bounds: [-5, 10], value: 10, expected: true }, + { bounds: [-5, 10], value: 5, expected: true }, + { bounds: [-5, 10], value: -5, expected: true }, + { bounds: [-5, 10], value: -6, expected: false }, + { bounds: [-5, 10], value: 50, expected: false }, + { bounds: [-5, 10], value: -10, expected: false }, + { bounds: [-1.375, 2.5], value: -10, expected: false }, + { bounds: [-1.375, 2.5], value: 0.5, expected: true }, + { bounds: [-1.375, 2.5], value: 10, expected: false }, + + // Point + { bounds: 0, value: 0, expected: true }, + { bounds: 0, value: 10, expected: false }, + { bounds: 0, value: -1000, expected: false }, + { bounds: 10, value: 10, expected: true }, + { bounds: 10, value: 0, expected: false }, + { bounds: 10, value: -10, expected: false }, + { bounds: 10, value: 11, expected: false }, + + // Upper infinity + { bounds: [0, constants.positive.infinity], value: constants.positive.min, expected: true }, + { bounds: [0, constants.positive.infinity], value: constants.positive.max, expected: true }, + { bounds: [0, constants.positive.infinity], value: constants.positive.infinity, expected: true }, + { bounds: [0, constants.positive.infinity], value: constants.negative.min, expected: false }, + { bounds: [0, constants.positive.infinity], value: constants.negative.max, expected: false }, + { bounds: [0, constants.positive.infinity], value: constants.negative.infinity, expected: false }, + + // Lower infinity + { bounds: [constants.negative.infinity, 0], value: constants.positive.min, expected: false }, + { bounds: [constants.negative.infinity, 0], value: constants.positive.max, expected: false }, + { bounds: [constants.negative.infinity, 0], value: constants.positive.infinity, expected: false }, + { bounds: [constants.negative.infinity, 0], value: constants.negative.min, expected: true }, + { bounds: [constants.negative.infinity, 0], value: constants.negative.max, expected: true }, + { bounds: [constants.negative.infinity, 0], value: constants.negative.infinity, expected: true }, + + // Full infinity + { bounds: [constants.negative.infinity, constants.positive.infinity], value: constants.positive.min, expected: true }, + { bounds: [constants.negative.infinity, constants.positive.infinity], value: constants.positive.max, expected: true }, + { bounds: [constants.negative.infinity, constants.positive.infinity], value: constants.positive.infinity, expected: true }, + { bounds: [constants.negative.infinity, constants.positive.infinity], value: constants.negative.min, expected: true }, + { bounds: [constants.negative.infinity, constants.positive.infinity], value: constants.negative.max, expected: true }, + { bounds: [constants.negative.infinity, constants.positive.infinity], value: constants.negative.infinity, expected: true }, + { bounds: [constants.negative.infinity, constants.positive.infinity], value: Number.NaN, expected: true }, + + // Maximum f32 boundary + { bounds: [0, constants.positive.max], value: constants.positive.min, expected: true }, + { bounds: [0, constants.positive.max], value: constants.positive.max, expected: true }, + { bounds: [0, constants.positive.max], value: constants.positive.infinity, expected: false }, + { bounds: [0, constants.positive.max], value: constants.negative.min, expected: false }, + { bounds: [0, constants.positive.max], value: constants.negative.max, expected: false }, + { bounds: [0, constants.positive.max], value: constants.negative.infinity, expected: false }, + + // Minimum f32 boundary + { bounds: [constants.negative.min, 0], value: constants.positive.min, expected: false }, + { bounds: [constants.negative.min, 0], value: constants.positive.max, expected: false }, + { bounds: [constants.negative.min, 0], value: constants.positive.infinity, expected: false }, + { bounds: [constants.negative.min, 0], value: constants.negative.min, expected: true }, + { bounds: [constants.negative.min, 0], value: constants.negative.max, expected: true }, + { bounds: [constants.negative.min, 0], value: constants.negative.infinity, expected: false }, + + // Subnormals + { bounds: [0, constants.positive.min], value: constants.positive.subnormal.min, expected: true }, + { bounds: [0, constants.positive.min], value: constants.positive.subnormal.max, expected: true }, + { bounds: [0, constants.positive.min], value: constants.negative.subnormal.min, expected: false }, + { bounds: [0, constants.positive.min], value: constants.negative.subnormal.max, expected: false }, + { bounds: [constants.negative.max, 0], value: constants.positive.subnormal.min, expected: false }, + { bounds: [constants.negative.max, 0], value: constants.positive.subnormal.max, expected: false }, + { bounds: [constants.negative.max, 0], value: constants.negative.subnormal.min, expected: true }, + { bounds: [constants.negative.max, 0], value: constants.negative.subnormal.max, expected: true }, + { bounds: [0, constants.positive.subnormal.min], value: constants.positive.subnormal.min, expected: true }, + { bounds: [0, constants.positive.subnormal.min], value: constants.positive.subnormal.max, expected: false }, + { bounds: [0, constants.positive.subnormal.min], value: constants.negative.subnormal.min, expected: false }, + { bounds: [0, constants.positive.subnormal.min], value: constants.negative.subnormal.max, expected: false }, + { bounds: [constants.negative.subnormal.max, 0], value: constants.positive.subnormal.min, expected: false }, + { bounds: [constants.negative.subnormal.max, 0], value: constants.positive.subnormal.max, expected: false }, + { bounds: [constants.negative.subnormal.max, 0], value: constants.negative.subnormal.min, expected: false }, + { bounds: [constants.negative.subnormal.max, 0], value: constants.negative.subnormal.max, expected: true }, + ]; + + // Note: Out of range values are limited to infinities for abstract float, due to abstract + // float and 'number' both being f64. So there are no separate OOR tests for abstract float, + // otherwise the testing framework will consider them duplicated. + if (p.trait !== 'abstract') { + // prettier-ignore + cases.push(...[ + // Out of range high + { bounds: [0, 2 * constants.positive.max], value: constants.positive.min, expected: true }, + { bounds: [0, 2 * constants.positive.max], value: constants.positive.max, expected: true }, + { bounds: [0, 2 * constants.positive.max], value: constants.positive.infinity, expected: false }, + { bounds: [0, 2 * constants.positive.max], value: constants.negative.min, expected: false }, + { bounds: [0, 2 * constants.positive.max], value: constants.negative.max, expected: false }, + { bounds: [0, 2 * constants.positive.max], value: constants.negative.infinity, expected: false }, + + // Out of range low + { bounds: [2 * constants.negative.min, 0], value: constants.positive.min, expected: false }, + { bounds: [2 * constants.negative.min, 0], value: constants.positive.max, expected: false }, + { bounds: [2 * constants.negative.min, 0], value: constants.positive.infinity, expected: false }, + { bounds: [2 * constants.negative.min, 0], value: constants.negative.min, expected: true }, + { bounds: [2 * constants.negative.min, 0], value: constants.negative.max, expected: true }, + { bounds: [2 * constants.negative.min, 0], value: constants.negative.infinity, expected: false }, + ] as ContainsNumberCase[]); + } + + return cases; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const i = trait.toInterval(t.params.bounds); + const value = t.params.value; + const expected = t.params.expected; + + const got = i.contains(value); + t.expect(expected === got, `${i}.contains(${value}) returned ${got}. Expected ${expected}`); + }); + +interface ContainsIntervalCase { + lhs: number | IntervalBounds; + rhs: number | IntervalBounds; + expected: boolean; +} + +g.test('contains_interval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ContainsIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + const cases: ContainsIntervalCase[] = [ + // Common usage + { lhs: [-10, 10], rhs: 0, expected: true }, + { lhs: [-10, 10], rhs: [-1, 0], expected: true }, + { lhs: [-10, 10], rhs: [0, 2], expected: true }, + { lhs: [-10, 10], rhs: [-1, 2], expected: true }, + { lhs: [-10, 10], rhs: [0, 10], expected: true }, + { lhs: [-10, 10], rhs: [-10, 2], expected: true }, + { lhs: [-10, 10], rhs: [-10, 10], expected: true }, + { lhs: [-10, 10], rhs: [-100, 10], expected: false }, + + // Upper infinity + { lhs: [0, constants.positive.infinity], rhs: 0, expected: true }, + { lhs: [0, constants.positive.infinity], rhs: [-1, 0], expected: false }, + { lhs: [0, constants.positive.infinity], rhs: [0, 1], expected: true }, + { lhs: [0, constants.positive.infinity], rhs: [0, constants.positive.max], expected: true }, + { lhs: [0, constants.positive.infinity], rhs: [0, constants.positive.infinity], expected: true }, + { lhs: [0, constants.positive.infinity], rhs: [100, constants.positive.infinity], expected: true }, + { lhs: [0, constants.positive.infinity], rhs: [Number.NEGATIVE_INFINITY, constants.positive.infinity], expected: false }, + + // Lower infinity + { lhs: [constants.negative.infinity, 0], rhs: 0, expected: true }, + { lhs: [constants.negative.infinity, 0], rhs: [-1, 0], expected: true }, + { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.min, 0], expected: true }, + { lhs: [constants.negative.infinity, 0], rhs: [0, 1], expected: false }, + { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.infinity, 0], expected: true }, + { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.infinity, -100 ], expected: true }, + { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, + + // Full infinity + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: 0, expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [-1, 0], expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [0, 1], expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [0, constants.positive.infinity], expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [100, constants.positive.infinity], expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [constants.negative.infinity, 0], expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [constants.negative.infinity, -100 ], expected: true }, + { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [constants.negative.infinity, constants.positive.infinity], expected: true }, + + // Maximum boundary + { lhs: [0, constants.positive.max], rhs: 0, expected: true }, + { lhs: [0, constants.positive.max], rhs: [-1, 0], expected: false }, + { lhs: [0, constants.positive.max], rhs: [0, 1], expected: true }, + { lhs: [0, constants.positive.max], rhs: [0, constants.positive.max], expected: true }, + { lhs: [0, constants.positive.max], rhs: [0, constants.positive.infinity], expected: false }, + { lhs: [0, constants.positive.max], rhs: [100, constants.positive.infinity], expected: false }, + { lhs: [0, constants.positive.max], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, + + // Minimum boundary + { lhs: [constants.negative.min, 0], rhs: [0, 0], expected: true }, + { lhs: [constants.negative.min, 0], rhs: [-1, 0], expected: true }, + { lhs: [constants.negative.min, 0], rhs: [constants.negative.min, 0], expected: true }, + { lhs: [constants.negative.min, 0], rhs: [0, 1], expected: false }, + { lhs: [constants.negative.min, 0], rhs: [constants.negative.infinity, 0], expected: false }, + { lhs: [constants.negative.min, 0], rhs: [constants.negative.infinity, -100 ], expected: false }, + { lhs: [constants.negative.min, 0], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, + ]; + + // Note: Out of range values are limited to infinities for abstract float, due to abstract + // float and 'number' both being f64. So there are no separate OOR tests for abstract float, + // otherwise the testing framework will consider them duplicated. + if (p.trait !== 'abstract') { + // prettier-ignore + cases.push(...[ + // Out of range high + { lhs: [0, 2 * constants.positive.max], rhs: 0, expected: true }, + { lhs: [0, 2 * constants.positive.max], rhs: [-1, 0], expected: false }, + { lhs: [0, 2 * constants.positive.max], rhs: [0, 1], expected: true }, + { lhs: [0, 2 * constants.positive.max], rhs: [0, constants.positive.max], expected: true }, + { lhs: [0, 2 * constants.positive.max], rhs: [0, constants.positive.infinity], expected: false }, + { lhs: [0, 2 * constants.positive.max], rhs: [100, constants.positive.infinity], expected: false }, + { lhs: [0, 2 * constants.positive.max], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, + + // Out of range low + { lhs: [2 * constants.negative.min, 0], rhs: 0, expected: true }, + { lhs: [2 * constants.negative.min, 0], rhs: [-1, 0], expected: true }, + { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.min, 0], expected: true }, + { lhs: [2 * constants.negative.min, 0], rhs: [0, 1], expected: false }, + { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.infinity, 0], expected: false }, + { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.infinity, -100 ], expected: false }, + { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, + ] as ContainsIntervalCase[]); + } + + return cases; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const lhs = trait.toInterval(t.params.lhs); + const rhs = trait.toInterval(t.params.rhs); + const expected = t.params.expected; + + const got = lhs.contains(rhs); + t.expect(expected === got, `${lhs}.contains(${rhs}) returned ${got}. Expected ${expected}`); + }); + +// Utilities + +interface SpanIntervalsCase { + intervals: (number | IntervalBounds)[]; + expected: number | IntervalBounds; +} + +g.test('spanIntervals') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<SpanIntervalsCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // Single Intervals + { intervals: [[0, 10]], expected: [0, 10] }, + { intervals: [[0, constants.positive.max]], expected: [0, constants.positive.max] }, + { intervals: [[0, constants.positive.nearest_max]], expected: [0, constants.positive.nearest_max] }, + { intervals: [[0, constants.positive.infinity]], expected: [0, Number.POSITIVE_INFINITY] }, + { intervals: [[constants.negative.min, 0]], expected: [constants.negative.min, 0] }, + { intervals: [[constants.negative.nearest_min, 0]], expected: [constants.negative.nearest_min, 0] }, + { intervals: [[constants.negative.infinity, 0]], expected: [Number.NEGATIVE_INFINITY, 0] }, + + // Double Intervals + { intervals: [[0, 1], [2, 5]], expected: [0, 5] }, + { intervals: [[2, 5], [0, 1]], expected: [0, 5] }, + { intervals: [[0, 2], [1, 5]], expected: [0, 5] }, + { intervals: [[0, 5], [1, 2]], expected: [0, 5] }, + { intervals: [[constants.negative.infinity, 0], [0, constants.positive.infinity]], expected: kUnboundedBounds }, + + // Multiple Intervals + { intervals: [[0, 1], [2, 3], [4, 5]], expected: [0, 5] }, + { intervals: [[0, 1], [4, 5], [2, 3]], expected: [0, 5] }, + { intervals: [[0, 1], [0, 1], [0, 1]], expected: [0, 1] }, + + // Point Intervals + { intervals: [1], expected: 1 }, + { intervals: [1, 2], expected: [1, 2] }, + { intervals: [-10, 2], expected: [-10, 2] }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const intervals = t.params.intervals.map(i => trait.toInterval(i)); + const expected = trait.toInterval(t.params.expected); + + const got = trait.spanIntervals(...intervals); + t.expect( + objectEquals(got, expected), + `${t.params.trait}.span({${intervals}}) returned ${got}. Expected ${expected}` + ); + }); + +interface isVectorCase { + input: (number | IntervalBounds | FPIntervalParam)[]; + expected: boolean; +} + +g.test('isVector') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<isVectorCase>(p => { + const trait = FP[p.trait]; + return [ + // numbers + { input: [1, 2], expected: false }, + { input: [1, 2, 3], expected: false }, + { input: [1, 2, 3, 4], expected: false }, + + // IntervalBounds + { input: [[1], [2]], expected: false }, + { input: [[1], [2], [3]], expected: false }, + { input: [[1], [2], [3], [4]], expected: false }, + { + input: [ + [1, 2], + [2, 3], + ], + expected: false, + }, + { + input: [ + [1, 2], + [2, 3], + [3, 4], + ], + expected: false, + }, + { + input: [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + expected: false, + }, + + // FPInterval, valid dimensions + { input: [trait.toParam([1]), trait.toParam([2])], expected: true }, + { input: [trait.toParam([1, 2]), trait.toParam([2, 3])], expected: true }, + { + input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3])], + expected: true, + }, + { + input: [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + expected: true, + }, + { + input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3]), trait.toParam([4])], + expected: true, + }, + { + input: [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + expected: true, + }, + + // FPInterval, invalid dimensions + { input: [trait.toParam([1])], expected: false }, + { + input: [ + trait.toParam([1]), + trait.toParam([2]), + trait.toParam([3]), + trait.toParam([4]), + trait.toParam([5]), + ], + expected: false, + }, + + // Mixed + { input: [1, [2]], expected: false }, + { input: [1, [2], trait.toParam([3])], expected: false }, + { input: [1, trait.toParam([2]), [3], 4], expected: false }, + { input: [trait.toParam(1), 2], expected: false }, + { input: [trait.toParam(1), [2]], expected: false }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const input = t.params.input.map(e => trait.fromParam(e)); + const expected = t.params.expected; + + const got = trait.isVector(input); + t.expect( + got === expected, + `${t.params.trait}.isVector([${input}]) returned ${got}. Expected ${expected}` + ); + }); + +interface toVectorCase { + input: (number | IntervalBounds | FPIntervalParam)[]; + expected: (number | IntervalBounds)[]; +} + +g.test('toVector') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<toVectorCase>(p => { + const trait = FP[p.trait]; + return [ + // numbers + { input: [1, 2], expected: [1, 2] }, + { input: [1, 2, 3], expected: [1, 2, 3] }, + { input: [1, 2, 3, 4], expected: [1, 2, 3, 4] }, + + // IntervalBounds + { input: [[1], [2]], expected: [1, 2] }, + { input: [[1], [2], [3]], expected: [1, 2, 3] }, + { input: [[1], [2], [3], [4]], expected: [1, 2, 3, 4] }, + { + input: [ + [1, 2], + [2, 3], + ], + expected: [ + [1, 2], + [2, 3], + ], + }, + { + input: [ + [1, 2], + [2, 3], + [3, 4], + ], + expected: [ + [1, 2], + [2, 3], + [3, 4], + ], + }, + { + input: [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + expected: [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + }, + + // FPInterval + { input: [trait.toParam([1]), trait.toParam([2])], expected: [1, 2] }, + { + input: [trait.toParam([1, 2]), trait.toParam([2, 3])], + expected: [ + [1, 2], + [2, 3], + ], + }, + { + input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3])], + expected: [1, 2, 3], + }, + { + input: [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + expected: [ + [1, 2], + [2, 3], + [3, 4], + ], + }, + { + input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3]), trait.toParam([4])], + expected: [1, 2, 3, 4], + }, + { + input: [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + expected: [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + }, + + // Mixed + { input: [1, [2]], expected: [1, 2] }, + { input: [1, [2], trait.toParam([3])], expected: [1, 2, 3] }, + { input: [1, trait.toParam([2]), [3], 4], expected: [1, 2, 3, 4] }, + { + input: [1, [2], [2, 3], kUnboundedInterval[p.trait]], + expected: [1, 2, [2, 3], kUnboundedBounds], + }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const input = t.params.input.map(e => trait.fromParam(e)); + const expected = t.params.expected.map(e => trait.toInterval(e)); + + const got = trait.toVector(input); + t.expect( + objectEquals(got, expected), + `${t.params.trait}.toVector([${input}]) returned [${got}]. Expected [${expected}]` + ); + }); + +interface isMatrixCase { + input: (number | IntervalBounds | FPIntervalParam)[][]; + expected: boolean; +} + +g.test('isMatrix') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<isMatrixCase>(p => { + const trait = FP[p.trait]; + return [ + // numbers + { + input: [ + [1, 2], + [3, 4], + ], + expected: false, + }, + { + input: [ + [1, 2], + [3, 4], + [5, 6], + ], + expected: false, + }, + { + input: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + expected: false, + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + ], + expected: false, + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + expected: false, + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + expected: false, + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + expected: false, + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + expected: false, + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + expected: false, + }, + + // IntervalBounds + { + input: [ + [[1], [2]], + [[3], [4]], + ], + expected: false, + }, + { + input: [ + [[1], [2]], + [[3], [4]], + [[5], [6]], + ], + expected: false, + }, + { + input: [ + [[1], [2]], + [[3], [4]], + [[5], [6]], + [[7], [8]], + ], + expected: false, + }, + { + input: [ + [[1], [2], [3]], + [[4], [5], [6]], + ], + expected: false, + }, + { + input: [ + [[1], [2], [3]], + [[4], [5], [6]], + [[7], [8], [9]], + ], + expected: false, + }, + { + input: [ + [[1], [2], [3]], + [[4], [5], [6]], + [[7], [8], [9]], + [[10], [11], [12]], + ], + expected: false, + }, + { + input: [ + [[1], [2], [3], [4]], + [[5], [6], [7], [8]], + ], + expected: false, + }, + { + input: [ + [[1], [2], [3], [4]], + [[5], [6], [7], [8]], + [[9], [10], [11], [12]], + ], + expected: false, + }, + { + input: [ + [[1], [2], [3], [4]], + [[5], [6], [7], [8]], + [[9], [10], [11], [12]], + [[13], [14], [15], [16]], + ], + expected: false, + }, + + // FPInterval, valid dimensions + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3)], + [trait.toParam(4), trait.toParam(5), trait.toParam(6)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3)], + [trait.toParam(4), trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8), trait.toParam(9)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3)], + [trait.toParam(4), trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8), trait.toParam(9)], + [trait.toParam(10), trait.toParam(11), trait.toParam(12)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], + [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], + ], + expected: true, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], + [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], + [trait.toParam(13), trait.toParam(14), trait.toParam(15), trait.toParam(16)], + ], + expected: true, + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3])], + [trait.toParam([3, 4]), trait.toParam([4, 5])], + ], + expected: true, + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3])], + [trait.toParam([3, 4]), trait.toParam([4, 5])], + [trait.toParam([5, 6]), trait.toParam([6, 7])], + ], + expected: true, + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3])], + [trait.toParam([3, 4]), trait.toParam([4, 5])], + [trait.toParam([5, 6]), trait.toParam([6, 7])], + [trait.toParam([7, 8]), trait.toParam([8, 9])], + ], + expected: true, + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], + ], + expected: true, + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], + [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], + ], + expected: true, + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], + [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], + [trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13])], + ], + expected: true, + }, + { + input: [ + [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + [ + trait.toParam([5, 6]), + trait.toParam([6, 7]), + trait.toParam([7, 8]), + trait.toParam([8, 9]), + ], + ], + expected: true, + }, + { + input: [ + [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + [ + trait.toParam([5, 6]), + trait.toParam([6, 7]), + trait.toParam([7, 8]), + trait.toParam([8, 9]), + ], + [ + trait.toParam([9, 10]), + trait.toParam([10, 11]), + trait.toParam([11, 12]), + trait.toParam([12, 13]), + ], + ], + expected: true, + }, + { + input: [ + [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + [ + trait.toParam([5, 6]), + trait.toParam([6, 7]), + trait.toParam([7, 8]), + trait.toParam([8, 9]), + ], + [ + trait.toParam([9, 10]), + trait.toParam([10, 11]), + trait.toParam([11, 12]), + trait.toParam([12, 13]), + ], + [ + trait.toParam([13, 14]), + trait.toParam([14, 15]), + trait.toParam([15, 16]), + trait.toParam([16, 17]), + ], + ], + expected: true, + }, + + // FPInterval, invalid dimensions + { input: [[trait.toParam(1)]], expected: false }, + { + input: [[trait.toParam(1)], [trait.toParam(3), trait.toParam(4)]], + expected: false, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4), trait.toParam(5)], + ], + expected: false, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + [trait.toParam(5)], + ], + expected: false, + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8)], + [trait.toParam(9), trait.toParam(10)], + ], + expected: false, + }, + + // Mixed + { + input: [ + [1, [2]], + [3, 4], + ], + expected: false, + }, + { + input: [ + [[1], [2]], + [[3], 4], + ], + expected: false, + }, + { + input: [ + [1, 2], + [trait.toParam([3]), 4], + ], + expected: false, + }, + { + input: [ + [[1], trait.toParam([2])], + [trait.toParam([3]), trait.toParam([4])], + ], + expected: false, + }, + { + input: [ + [trait.toParam(1), [2]], + [3, 4], + ], + expected: false, + }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const input = t.params.input.map(a => a.map(e => trait.fromParam(e))); + const expected = t.params.expected; + + const got = trait.isMatrix(input); + t.expect( + got === expected, + `${t.params.trait}.isMatrix([${input}]) returned ${got}. Expected ${expected}` + ); + }); + +interface toMatrixCase { + input: (number | IntervalBounds | FPIntervalParam)[][]; + expected: (number | IntervalBounds)[][]; +} + +g.test('toMatrix') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<toMatrixCase>(p => { + const trait = FP[p.trait]; + return [ + // numbers + { + input: [ + [1, 2], + [3, 4], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + { + input: [ + [1, 2], + [3, 4], + [5, 6], + ], + expected: [ + [1, 2], + [3, 4], + [5, 6], + ], + }, + { + input: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + expected: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + ], + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + }, + + // IntervalBounds + { + input: [ + [[1], [2]], + [[3], [4]], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + { + input: [ + [[1], [2]], + [[3], [4]], + [[5], [6]], + ], + expected: [ + [1, 2], + [3, 4], + [5, 6], + ], + }, + { + input: [ + [[1], [2]], + [[3], [4]], + [[5], [6]], + [[7], [8]], + ], + expected: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + }, + { + input: [ + [[1], [2], [3]], + [[4], [5], [6]], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + ], + }, + { + input: [ + [[1], [2], [3]], + [[4], [5], [6]], + [[7], [8], [9]], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + }, + { + input: [ + [[1], [2], [3]], + [[4], [5], [6]], + [[7], [8], [9]], + [[10], [11], [12]], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + }, + { + input: [ + [[1], [2], [3], [4]], + [[5], [6], [7], [8]], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + }, + { + input: [ + [[1], [2], [3], [4]], + [[5], [6], [7], [8]], + [[9], [10], [11], [12]], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + }, + { + input: [ + [[1], [2], [3], [4]], + [[5], [6], [7], [8]], + [[9], [10], [11], [12]], + [[13], [14], [15], [16]], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + }, + + // FPInterval + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6)], + ], + expected: [ + [1, 2], + [3, 4], + [5, 6], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2)], + [trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8)], + ], + expected: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3)], + [trait.toParam(4), trait.toParam(5), trait.toParam(6)], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3)], + [trait.toParam(4), trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8), trait.toParam(9)], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3)], + [trait.toParam(4), trait.toParam(5), trait.toParam(6)], + [trait.toParam(7), trait.toParam(8), trait.toParam(9)], + [trait.toParam(10), trait.toParam(11), trait.toParam(12)], + ], + expected: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], + [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + }, + { + input: [ + [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], + [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], + [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], + [trait.toParam(13), trait.toParam(14), trait.toParam(15), trait.toParam(16)], + ], + expected: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + }, + + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3])], + [trait.toParam([3, 4]), trait.toParam([4, 5])], + ], + expected: [ + [ + [1, 2], + [2, 3], + ], + [ + [3, 4], + [4, 5], + ], + ], + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3])], + [trait.toParam([3, 4]), trait.toParam([4, 5])], + [trait.toParam([5, 6]), trait.toParam([6, 7])], + ], + expected: [ + [ + [1, 2], + [2, 3], + ], + [ + [3, 4], + [4, 5], + ], + [ + [5, 6], + [6, 7], + ], + ], + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3])], + [trait.toParam([3, 4]), trait.toParam([4, 5])], + [trait.toParam([5, 6]), trait.toParam([6, 7])], + [trait.toParam([7, 8]), trait.toParam([8, 9])], + ], + expected: [ + [ + [1, 2], + [2, 3], + ], + [ + [3, 4], + [4, 5], + ], + [ + [5, 6], + [6, 7], + ], + [ + [7, 8], + [8, 9], + ], + ], + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], + ], + expected: [ + [ + [1, 2], + [2, 3], + [3, 4], + ], + [ + [4, 5], + [5, 6], + [6, 7], + ], + ], + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], + [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], + ], + expected: [ + [ + [1, 2], + [2, 3], + [3, 4], + ], + [ + [4, 5], + [5, 6], + [6, 7], + ], + [ + [7, 8], + [8, 9], + [9, 10], + ], + ], + }, + { + input: [ + [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], + [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], + [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], + [trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13])], + ], + expected: [ + [ + [1, 2], + [2, 3], + [3, 4], + ], + [ + [4, 5], + [5, 6], + [6, 7], + ], + [ + [7, 8], + [8, 9], + [9, 10], + ], + [ + [10, 11], + [11, 12], + [12, 13], + ], + ], + }, + { + input: [ + [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + [ + trait.toParam([5, 6]), + trait.toParam([6, 7]), + trait.toParam([7, 8]), + trait.toParam([8, 9]), + ], + ], + expected: [ + [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + [ + [5, 6], + [6, 7], + [7, 8], + [8, 9], + ], + ], + }, + { + input: [ + [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + [ + trait.toParam([5, 6]), + trait.toParam([6, 7]), + trait.toParam([7, 8]), + trait.toParam([8, 9]), + ], + [ + trait.toParam([9, 10]), + trait.toParam([10, 11]), + trait.toParam([11, 12]), + trait.toParam([12, 13]), + ], + ], + expected: [ + [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + [ + [5, 6], + [6, 7], + [7, 8], + [8, 9], + ], + [ + [9, 10], + [10, 11], + [11, 12], + [12, 13], + ], + ], + }, + { + input: [ + [ + trait.toParam([1, 2]), + trait.toParam([2, 3]), + trait.toParam([3, 4]), + trait.toParam([4, 5]), + ], + [ + trait.toParam([5, 6]), + trait.toParam([6, 7]), + trait.toParam([7, 8]), + trait.toParam([8, 9]), + ], + [ + trait.toParam([9, 10]), + trait.toParam([10, 11]), + trait.toParam([11, 12]), + trait.toParam([12, 13]), + ], + [ + trait.toParam([13, 14]), + trait.toParam([14, 15]), + trait.toParam([15, 16]), + trait.toParam([16, 17]), + ], + ], + expected: [ + [ + [1, 2], + [2, 3], + [3, 4], + [4, 5], + ], + [ + [5, 6], + [6, 7], + [7, 8], + [8, 9], + ], + [ + [9, 10], + [10, 11], + [11, 12], + [12, 13], + ], + [ + [13, 14], + [14, 15], + [15, 16], + [16, 17], + ], + ], + }, + + // Mixed + { + input: [ + [1, [2]], + [3, 4], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + { + input: [ + [[1], [2]], + [[3], 4], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + { + input: [ + [1, 2], + [trait.toParam([3]), 4], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + { + input: [ + [[1], trait.toParam([2])], + [trait.toParam([3]), trait.toParam([4])], + ], + expected: [ + [1, 2], + [3, 4], + ], + }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const input = map2DArray(t.params.input, e => trait.fromParam(e)); + const expected = map2DArray(t.params.expected, e => trait.toInterval(e)); + + const got = trait.toMatrix(input); + t.expect( + objectEquals(got, expected), + `${t.params.trait}.toMatrix([${input}]) returned [${got}]. Expected [${expected}]` + ); + }); + +// API - Fundamental Error Intervals + +interface AbsoluteErrorCase { + value: number; + error: number; + expected: number | IntervalBounds; +} + +// Special values used for testing absolute error interval +// A small absolute error value is a representable value x that much smaller than 1.0, +// but 1.0 +/- x is still exactly representable. +const kSmallAbsoluteErrorValue = { + f32: 2 ** -11, // Builtin cos and sin has a absolute error 2**-11 for f32 + f16: 2 ** -7, // Builtin cos and sin has a absolute error 2**-7 for f16 +} as const; +// A large absolute error value is a representable value x that much smaller than maximum +// positive, but positive.max - x is still exactly representable. +const kLargeAbsoluteErrorValue = { + f32: 2 ** 110, // f32.positive.max - 2**110 = 3.4028104e+38 = 0x7f7fffbf in f32 + f16: 2 ** 10, // f16.positive.max - 2**10 = 64480 = 0x7bdf in f16 +} as const; +// A subnormal absolute error value is a subnormal representable value x of kind, which ensures +// that positive.subnormal.min +/- x is still exactly representable. +const kSubnormalAbsoluteErrorValue = { + f32: 2 ** -140, // f32 0x00000200 + f16: 2 ** -20, // f16 0x0010 +} as const; + +g.test('absoluteErrorInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<AbsoluteErrorCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + const smallErr = kSmallAbsoluteErrorValue[p.trait]; + const largeErr = kLargeAbsoluteErrorValue[p.trait]; + const subnormalErr = kSubnormalAbsoluteErrorValue[p.trait]; + // prettier-ignore + return [ + // Edge Cases + // 1. Interval around infinity would be kUnboundedBounds + { value: constants.positive.infinity, error: 0, expected: kUnboundedBounds }, + { value: constants.positive.infinity, error: largeErr, expected: kUnboundedBounds }, + { value: constants.positive.infinity, error: 1, expected: kUnboundedBounds }, + { value: constants.negative.infinity, error: 0, expected: kUnboundedBounds }, + { value: constants.negative.infinity, error: largeErr, expected: kUnboundedBounds }, + { value: constants.negative.infinity, error: 1, expected: kUnboundedBounds }, + // 2. Interval around largest finite positive/negative + { value: constants.positive.max, error: 0, expected: constants.positive.max }, + { value: constants.positive.max, error: largeErr, expected: kUnboundedBounds}, + { value: constants.positive.max, error: constants.positive.max, expected: kUnboundedBounds}, + { value: constants.negative.min, error: 0, expected: constants.negative.min }, + { value: constants.negative.min, error: largeErr, expected: kUnboundedBounds}, + { value: constants.negative.min, error: constants.positive.max, expected: kUnboundedBounds}, + // 3. Interval around small but normal center, center should not get flushed. + { value: constants.positive.min, error: 0, expected: constants.positive.min }, + { value: constants.positive.min, error: smallErr, expected: [constants.positive.min - smallErr, constants.positive.min + smallErr]}, + { value: constants.positive.min, error: 1, expected: [constants.positive.min - 1, constants.positive.min + 1]}, + { value: constants.negative.max, error: 0, expected: constants.negative.max }, + { value: constants.negative.max, error: smallErr, expected: [constants.negative.max - smallErr, constants.negative.max + smallErr]}, + { value: constants.negative.max, error: 1, expected: [constants.negative.max - 1, constants.negative.max + 1] }, + // 4. Subnormals, center can be flushed to 0.0 + { value: constants.positive.subnormal.max, error: 0, expected: [0, constants.positive.subnormal.max] }, + { value: constants.positive.subnormal.max, error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.max + subnormalErr]}, + { value: constants.positive.subnormal.max, error: smallErr, expected: [-smallErr, constants.positive.subnormal.max + smallErr]}, + { value: constants.positive.subnormal.max, error: 1, expected: [-1, constants.positive.subnormal.max + 1]}, + { value: constants.positive.subnormal.min, error: 0, expected: [0, constants.positive.subnormal.min] }, + { value: constants.positive.subnormal.min, error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.min + subnormalErr]}, + { value: constants.positive.subnormal.min, error: smallErr, expected: [-smallErr, constants.positive.subnormal.min + smallErr]}, + { value: constants.positive.subnormal.min, error: 1, expected: [-1, constants.positive.subnormal.min + 1] }, + { value: constants.negative.subnormal.min, error: 0, expected: [constants.negative.subnormal.min, 0] }, + { value: constants.negative.subnormal.min, error: subnormalErr, expected: [constants.negative.subnormal.min - subnormalErr, subnormalErr] }, + { value: constants.negative.subnormal.min, error: smallErr, expected: [constants.negative.subnormal.min - smallErr, smallErr] }, + { value: constants.negative.subnormal.min, error: 1, expected: [constants.negative.subnormal.min - 1, 1] }, + { value: constants.negative.subnormal.max, error: 0, expected: [constants.negative.subnormal.max, 0] }, + { value: constants.negative.subnormal.max, error: subnormalErr, expected: [constants.negative.subnormal.max - subnormalErr, subnormalErr] }, + { value: constants.negative.subnormal.max, error: smallErr, expected: [constants.negative.subnormal.max - smallErr, smallErr] }, + { value: constants.negative.subnormal.max, error: 1, expected: [constants.negative.subnormal.max - 1, 1] }, + + // 64-bit subnormals, expected to be treated as 0.0 or smallest subnormal of kind. + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), error: 0, expected: [0, constants.positive.subnormal.min] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.min + subnormalErr] }, + // Note that f32 minimum subnormal is so smaller than 1.0, adding them together may result in the f64 results 1.0. + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), error: 1, expected: [-1, constants.positive.subnormal.min + 1] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), error: 0, expected: [0, constants.positive.subnormal.min] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.min + subnormalErr] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), error: 1, expected: [-1, constants.positive.subnormal.min + 1] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), error: 0, expected: [constants.negative.subnormal.max, 0] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), error: subnormalErr, expected: [constants.negative.subnormal.max - subnormalErr, subnormalErr] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), error: 1, expected: [constants.negative.subnormal.max - 1, 1] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), error: 0, expected: [constants.negative.subnormal.max, 0] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), error: subnormalErr, expected: [constants.negative.subnormal.max - subnormalErr, subnormalErr] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), error: 1, expected: [constants.negative.subnormal.max - 1, 1] }, + + // Zero + { value: 0, error: 0, expected: 0 }, + { value: 0, error: smallErr, expected: [-smallErr, smallErr] }, + { value: 0, error: 1, expected: [-1, 1] }, + + // Two + { value: 2, error: 0, expected: 2 }, + { value: 2, error: smallErr, expected: [2 - smallErr, 2 + smallErr] }, + { value: 2, error: 1, expected: [1, 3] }, + { value: -2, error: 0, expected: -2 }, + { value: -2, error: smallErr, expected: [-2 - smallErr, -2 + smallErr] }, + { value: -2, error: 1, expected: [-3, -1] }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.absoluteErrorInterval(t.params.value, t.params.error); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.absoluteErrorInterval(${t.params.value}, ${ + t.params.error + }) returned ${got} (${got.begin.toExponential()}, ${got.end.toExponential()}). Expected ${expected}` + ); + }); + +interface CorrectlyRoundedCase { + value: number; + expected: number | IntervalBounds; +} + +// Correctly rounded cases that input values are exactly representable normal values of target type +// prettier-ignore +const kCorrectlyRoundedNormalCases = { + f32: [ + { value: 0, expected: [0, 0] }, + { value: reinterpretU32AsF32(0x03800000), expected: reinterpretU32AsF32(0x03800000) }, + { value: reinterpretU32AsF32(0x03800001), expected: reinterpretU32AsF32(0x03800001) }, + { value: reinterpretU32AsF32(0x83800000), expected: reinterpretU32AsF32(0x83800000) }, + { value: reinterpretU32AsF32(0x83800001), expected: reinterpretU32AsF32(0x83800001) }, + ] as CorrectlyRoundedCase[], + f16: [ + { value: 0, expected: [0, 0] }, + { value: reinterpretU16AsF16(0x0c00), expected: reinterpretU16AsF16(0x0c00) }, + { value: reinterpretU16AsF16(0x0c01), expected: reinterpretU16AsF16(0x0c01) }, + { value: reinterpretU16AsF16(0x8c00), expected: reinterpretU16AsF16(0x8c00) }, + { value: reinterpretU16AsF16(0x8c01), expected: reinterpretU16AsF16(0x8c01) }, + ] as CorrectlyRoundedCase[], +} as const; + +// 64-bit normals that fall between two conjunction normal values in target type +const kCorrectlyRoundedF64NormalCases = [ + { + value: reinterpretU64AsF64(0x3ff0_0000_0000_0001n), + expected: { + f32: [reinterpretU32AsF32(0x3f800000), reinterpretU32AsF32(0x3f800001)], + f16: [reinterpretU16AsF16(0x3c00), reinterpretU16AsF16(0x3c01)], + }, + }, + { + value: reinterpretU64AsF64(0x3ff0_0000_0000_0002n), + expected: { + f32: [reinterpretU32AsF32(0x3f800000), reinterpretU32AsF32(0x3f800001)], + f16: [reinterpretU16AsF16(0x3c00), reinterpretU16AsF16(0x3c01)], + }, + }, + { + value: reinterpretU64AsF64(0x3ff0_0800_0000_0010n), + expected: { + f32: [reinterpretU32AsF32(0x3f804000), reinterpretU32AsF32(0x3f804001)], + f16: [reinterpretU16AsF16(0x3c02), reinterpretU16AsF16(0x3c03)], + }, + }, + { + value: reinterpretU64AsF64(0x3ff0_1000_0000_0020n), + expected: { + f32: [reinterpretU32AsF32(0x3f808000), reinterpretU32AsF32(0x3f808001)], + f16: [reinterpretU16AsF16(0x3c04), reinterpretU16AsF16(0x3c05)], + }, + }, + { + value: reinterpretU64AsF64(0xbff0_0000_0000_0001n), + expected: { + f32: [reinterpretU32AsF32(0xbf800001), reinterpretU32AsF32(0xbf800000)], + f16: [reinterpretU16AsF16(0xbc01), reinterpretU16AsF16(0xbc00)], + }, + }, + { + value: reinterpretU64AsF64(0xbff0_0000_0000_0002n), + expected: { + f32: [reinterpretU32AsF32(0xbf800001), reinterpretU32AsF32(0xbf800000)], + f16: [reinterpretU16AsF16(0xbc01), reinterpretU16AsF16(0xbc00)], + }, + }, + { + value: reinterpretU64AsF64(0xbff0_0800_0000_0010n), + expected: { + f32: [reinterpretU32AsF32(0xbf804001), reinterpretU32AsF32(0xbf804000)], + f16: [reinterpretU16AsF16(0xbc03), reinterpretU16AsF16(0xbc02)], + }, + }, + { + value: reinterpretU64AsF64(0xbff0_1000_0000_0020n), + expected: { + f32: [reinterpretU32AsF32(0xbf808001), reinterpretU32AsF32(0xbf808000)], + f16: [reinterpretU16AsF16(0xbc05), reinterpretU16AsF16(0xbc04)], + }, + }, +] as const; + +g.test('correctlyRoundedInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<CorrectlyRoundedCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // Edge Cases + { value: constants.positive.infinity, expected: kUnboundedBounds }, + { value: constants.negative.infinity, expected: kUnboundedBounds }, + { value: constants.positive.max, expected: constants.positive.max }, + { value: constants.negative.min, expected: constants.negative.min }, + { value: constants.positive.min, expected: constants.positive.min }, + { value: constants.negative.max, expected: constants.negative.max }, + + // Subnormals + { value: constants.positive.subnormal.min, expected: [0, constants.positive.subnormal.min] }, + { value: constants.positive.subnormal.max, expected: [0, constants.positive.subnormal.max] }, + { value: constants.negative.subnormal.min, expected: [constants.negative.subnormal.min, 0] }, + { value: constants.negative.subnormal.max, expected: [constants.negative.subnormal.max, 0] }, + + // 64-bit subnormals should be rounded down to 0 or up to smallest subnormal + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), expected: [0, constants.positive.subnormal.min] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), expected: [0, constants.positive.subnormal.min] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), expected: [constants.negative.subnormal.max, 0] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), expected: [constants.negative.subnormal.max, 0] }, + + // Normals + ...kCorrectlyRoundedNormalCases[p.trait], + + // 64-bit normals that fall between two conjunction normal values in target type + ...kCorrectlyRoundedF64NormalCases.map(t => { return {value: t.value, expected: t.expected[p.trait]} as CorrectlyRoundedCase;}), + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.correctlyRoundedInterval(t.params.value); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.correctlyRoundedInterval(${t.params.value}) returned ${got}. Expected ${expected}` + ); + }); + +interface ULPCase { + value: number; + num_ulp: number; + expected: number | IntervalBounds; +} + +// Special values used for testing ULP error interval +const kULPErrorValue = { + f32: 4096, // 4096 ULP is required for atan accuracy on f32 + f16: 5, // 5 ULP is required for atan accuracy on f16 +}; + +g.test('ulpInterval') + .params(u => + u + .combine('trait', ['abstract', 'f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ULPCase>(p => { + const trait = kFPTraitForULP[p.trait]; + const constants = FP[trait].constants(); + const ULPValue = kULPErrorValue[trait]; + const plusOneULP = kPlusOneULPFunctions[trait]; + const plusNULP = kPlusNULPFunctions[trait]; + const minusOneULP = kMinusOneULPFunctions[trait]; + const minusNULP = kMinusNULPFunctions[trait]; + // prettier-ignore + return [ + // Edge Cases + { value: constants.positive.infinity, num_ulp: 0, expected: kUnboundedBounds }, + { value: constants.positive.infinity, num_ulp: 1, expected: kUnboundedBounds }, + { value: constants.positive.infinity, num_ulp: ULPValue, expected: kUnboundedBounds }, + { value: constants.negative.infinity, num_ulp: 0, expected: kUnboundedBounds }, + { value: constants.negative.infinity, num_ulp: 1, expected: kUnboundedBounds }, + { value: constants.negative.infinity, num_ulp: ULPValue, expected: kUnboundedBounds }, + { value: constants.positive.max, num_ulp: 0, expected: constants.positive.max }, + { value: constants.positive.max, num_ulp: 1, expected: kUnboundedBounds }, + { value: constants.positive.max, num_ulp: ULPValue, expected: kUnboundedBounds }, + { value: constants.positive.min, num_ulp: 0, expected: constants.positive.min }, + { value: constants.positive.min, num_ulp: 1, expected: [0, plusOneULP(constants.positive.min)] }, + { value: constants.positive.min, num_ulp: ULPValue, expected: [0, plusNULP(constants.positive.min, ULPValue)] }, + { value: constants.negative.min, num_ulp: 0, expected: constants.negative.min }, + { value: constants.negative.min, num_ulp: 1, expected: kUnboundedBounds }, + { value: constants.negative.min, num_ulp: ULPValue, expected: kUnboundedBounds }, + { value: constants.negative.max, num_ulp: 0, expected: constants.negative.max }, + { value: constants.negative.max, num_ulp: 1, expected: [minusOneULP(constants.negative.max), 0] }, + { value: constants.negative.max, num_ulp: ULPValue, expected: [minusNULP(constants.negative.max, ULPValue), 0] }, + + // Subnormals + { value: constants.positive.subnormal.max, num_ulp: 0, expected: [0, constants.positive.subnormal.max] }, + { value: constants.positive.subnormal.max, num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.max)] }, + { value: constants.positive.subnormal.max, num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.max, ULPValue)] }, + { value: constants.positive.subnormal.min, num_ulp: 0, expected: [0, constants.positive.subnormal.min] }, + { value: constants.positive.subnormal.min, num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.min)] }, + { value: constants.positive.subnormal.min, num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.min, ULPValue)] }, + { value: constants.negative.subnormal.min, num_ulp: 0, expected: [constants.negative.subnormal.min, 0] }, + { value: constants.negative.subnormal.min, num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.min), plusOneULP(0)] }, + { value: constants.negative.subnormal.min, num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.min, ULPValue), plusNULP(0, ULPValue)] }, + { value: constants.negative.subnormal.max, num_ulp: 0, expected: [constants.negative.subnormal.max, 0] }, + { value: constants.negative.subnormal.max, num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.max), plusOneULP(0)] }, + { value: constants.negative.subnormal.max, num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.max, ULPValue), plusNULP(0, ULPValue)] }, + + // 64-bit subnormals + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), num_ulp: 0, expected: [0, constants.positive.subnormal.min] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.min)] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.min, ULPValue)] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), num_ulp: 0, expected: [0, constants.positive.subnormal.min] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.min)] }, + { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.min, ULPValue)] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), num_ulp: 0, expected: [constants.negative.subnormal.max, 0] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.max), plusOneULP(0)] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.max, ULPValue), plusNULP(0, ULPValue)] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), num_ulp: 0, expected: [constants.negative.subnormal.max, 0] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.max), plusOneULP(0)] }, + { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.max, ULPValue), plusNULP(0, ULPValue)] }, + + // Zero + { value: 0, num_ulp: 0, expected: 0 }, + { value: 0, num_ulp: 1, expected: [minusOneULP(0), plusOneULP(0)] }, + { value: 0, num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(0, ULPValue)] }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.ulpInterval(t.params.value, t.params.num_ulp); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.ulpInterval(${t.params.value}, ${t.params.num_ulp}) returned ${got}. Expected ${expected}` + ); + }); + +// API - Acceptance Intervals +// List of frequently used JS number in test cases, which are not exactly representable in f32 or f16. +type ConstantNumberFrequentlyUsedInCases = '0.1' | '-0.1' | '1.9' | '-1.9'; + +// Correctly rounded expectation of frequently used JS Number value in test cases +const kConstantCorrectlyRoundedExpectation = { + f32: { + // 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD + '0.1': [reinterpretU32AsF32(0x3dcccccc), reinterpretU32AsF32(0x3dcccccd)], + // -0.1 falls between f32 0xBDCCCCCD and 0xBDCCCCCC + '-0.1': [reinterpretU32AsF32(0xbdcccccd), reinterpretU32AsF32(0xbdcccccc)], + // 1.9 falls between f32 0x3FF33333 and 0x3FF33334 + '1.9': [reinterpretU32AsF32(0x3ff33333), reinterpretU32AsF32(0x3ff33334)], + // -1.9 falls between f32 0xBFF33334 and 0xBFF33333 + '-1.9': [reinterpretU32AsF32(0xbff33334), reinterpretU32AsF32(0xbff33333)], + } as { [value in ConstantNumberFrequentlyUsedInCases]: IntervalBounds }, + f16: { + // 0.1 falls between f16 0x2E66 and 0x2E67 + '0.1': [reinterpretU16AsF16(0x2e66), reinterpretU16AsF16(0x2e67)], + // -0.1 falls between f16 0xAE67 and 0xAE66 + '-0.1': [reinterpretU16AsF16(0xae67), reinterpretU16AsF16(0xae66)], + // 1.9 falls between f16 0x3F99 and 0x3F9A + '1.9': [reinterpretU16AsF16(0x3f99), reinterpretU16AsF16(0x3f9a)], + // 1.9 falls between f16 0xBF9A and 0xBF99 + '-1.9': [reinterpretU16AsF16(0xbf9a), reinterpretU16AsF16(0xbf99)], + } as { [value in ConstantNumberFrequentlyUsedInCases]: IntervalBounds }, + // Since abstract is actually f64 and JS number is also f64, the JS number value will map to + // identical abstracty value without rounded. + abstract: { + '0.1': 0.1, + '-0.1': -0.1, + '1.9': 1.9, + '-1.9': -1.9, + } as { [value in ConstantNumberFrequentlyUsedInCases]: number }, +} as const; + +interface ScalarToIntervalCase { + input: number; + expected: number | IntervalBounds; +} + +g.test('absInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // Common usages + { input: 1, expected: 1 }, + { input: -1, expected: 1 }, + // abs(+/-0.1) is correctly rounded interval of 0.1 + { input: 0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, + { input: -0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, + // abs(+/-1.9) is correctly rounded interval of 1.9 + { input: 1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['1.9']}, + { input: -1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['1.9']}, + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: constants.positive.max }, + { input: constants.positive.min, expected: constants.positive.min }, + { input: constants.negative.min, expected: constants.positive.max }, + { input: constants.negative.max, expected: constants.positive.min }, + + // Subnormals + { input: constants.positive.subnormal.max, expected: [0, constants.positive.subnormal.max] }, + { input: constants.positive.subnormal.min, expected: [0, constants.positive.subnormal.min] }, + { input: constants.negative.subnormal.min, expected: [0, constants.positive.subnormal.max] }, + { input: constants.negative.subnormal.max, expected: [0, constants.positive.subnormal.min] }, + + // Zero + { input: 0, expected: 0 }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.absInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.absInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Acos expectation intervals are bounded by both inherited atan2(sqrt(1.0 - x*x), x) and absolute error. +// Atan2 introduce 4096ULP for f32 and 5ULP for f16, and sqrt inherited from 1.0/inverseSqrt. +// prettier-ignore +const kAcosIntervalCases = { + f32: [ + { input: kPlusOneULPFunctions['f32'](-1), expected: [reinterpretU32AsF32(0x4048fa32), reinterpretU32AsF32(0x40491bdb)] }, // ~π + { input: -1/2, expected: [reinterpretU32AsF32(0x4005fa90), reinterpretU32AsF32(0x40061a93)] }, // ~2π/3 + { input: 1/2, expected: [reinterpretU32AsF32(0x3f85fa8f), reinterpretU32AsF32(0x3f861a94)] }, // ~π/3 + // Input case to get smallest well-defined expected result, the expectation interval is bounded + // by ULP (lower boundary) and absolute error (upper boundary). + // f32 1.0-1ULP=0x3F7FFFFF=0.9999999403953552, + // acos(0.9999999403953552)=3.4526698478747995220159699019994e-4 rounded to f32 0x39B504F3 or 0x39B504F4, + // absolute error interval upper boundary 0x39B504F4+6.77e-5=0.00041296700619608164 i.e. f64 0x3F3B_106F_C933_4FB9. + { input: kMinusOneULPFunctions['f32'](1), expected: [reinterpretU64AsF64(0x3f2f_fdff_6000_0000n), reinterpretU64AsF64(0x3f3b_106f_c933_4fb9n)] }, // ~0.0003 + ] as ScalarToIntervalCase[], + f16: [ + { input: kPlusOneULPFunctions['f16'](-1), expected: [reinterpretU16AsF16(0x4233), reinterpretU16AsF16(0x4243)] }, // ~π + { input: -1/2, expected: [reinterpretU16AsF16(0x402a), reinterpretU16AsF16(0x4037)] }, // ~2π/3 + { input: 1/2, expected: [reinterpretU16AsF16(0x3c29), reinterpretU16AsF16(0x3c38)] }, // ~π/3 + // Input case to get smallest well-defined expected result, the expectation interval is bounded + // by ULP (lower boundary) and absolute error (upper boundary). + // f16 1.0-1ULP=0x3BFF=0.99951171875, + // acos(0.99951171875)=0.03125127170547389912035676677648 rounded to f16 0x2800 or 0x2801, + // absolute error interval upper boundary 0x2801+3.91e-3=0.035190517578125 i.e. f64 0x3FA2_047D_D441_3554. + { input: kMinusOneULPFunctions['f16'](1), expected: [reinterpretU16AsF16(0x259d), reinterpretU64AsF64(0x3fa2_047d_d441_3554n)] }, // ~0.03 + ] as ScalarToIntervalCase[], +} as const; + +g.test('acosInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // The acceptance interval @ x = -1 and 1 is kUnboundedBounds, because + // sqrt(1 - x*x) = sqrt(0), and sqrt is defined in terms of inverseqrt + // The acceptance interval @ x = 0 is kUnboundedBounds, because atan2 is not + // well-defined/implemented at 0. + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: 1, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + + // Cases that bounded by absolute error and inherited from atan2(sqrt(1-x*x), x). Note that + // even x is very close to 1.0 and the expected result is close to 0.0, the expected + // interval is still bounded by ULP as well as absolute error, specifically lower boundary + // comes from ULP error and upper boundary comes from absolute error in those cases. + ...kAcosIntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.acosInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.acosInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kAcoshAlternativeIntervalCases = { + f32: [ + { input: 1.1, expected: [reinterpretU64AsF64(0x3fdc_6368_8000_0000n), reinterpretU64AsF64(0x3fdc_636f_2000_0000n)] }, // ~0.443..., differs from the primary in the later digits + { input: 10, expected: [reinterpretU64AsF64(0x4007_f21e_4000_0000n), reinterpretU64AsF64(0x4007_f21f_6000_0000n)] }, // ~2.993... + ] as ScalarToIntervalCase[], + f16: [ + { input: 1.1, expected: [reinterpretU64AsF64(0x3fdb_bc00_0000_0000n), reinterpretU64AsF64(0x3fdd_1000_0000_0000n)] }, // ~0.443..., differs from the primary in the later digits + { input: 10, expected: [reinterpretU64AsF64(0x4007_e000_0000_0000n), reinterpretU64AsF64(0x4008_0400_0000_0000n)] }, // ~2.993... + ] as ScalarToIntervalCase[], +} as const; + +g.test('acoshAlternativeInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kAcoshAlternativeIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: 1, expected: kUnboundedBounds }, // 1/0 occurs in inverseSqrt in this formulation + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.acoshAlternativeInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.acoshAlternativeInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kAcoshPrimaryIntervalCases = { + f32: [ + { input: 1.1, expected: [reinterpretU64AsF64(0x3fdc_6368_2000_0000n), reinterpretU64AsF64(0x3fdc_636f_8000_0000n)] }, // ~0.443..., differs from the alternative in the later digits + { input: 10, expected: [reinterpretU64AsF64(0x4007_f21e_4000_0000n), reinterpretU64AsF64(0x4007_f21f_6000_0000n)] }, // ~2.993... + ] as ScalarToIntervalCase[], + f16: [ + { input: 1.1, expected: [reinterpretU64AsF64(0x3fdb_bc00_0000_0000n), reinterpretU64AsF64(0x3fdd_1c00_0000_0000n)] }, // ~0.443..., differs from the primary in the later digits + { input: 10, expected: [reinterpretU64AsF64(0x4007_e000_0000_0000n), reinterpretU64AsF64(0x4008_0400_0000_0000n)] }, // ~2.993... + ] as ScalarToIntervalCase[], +} as const; + +g.test('acoshPrimaryInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kAcoshPrimaryIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: 1, expected: kUnboundedBounds }, // 1/0 occurs in inverseSqrt in this formulation + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.acoshPrimaryInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.acoshPrimaryInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Asin cases that bounded by inherited atan2(x, sqrt(1.0 - x*x)) rather than absolute error. +// Atan2 introduce 4096ULP for f32 and 5ULP for f16, and sqrt inherited from 1.0/inverseSqrt. +// prettier-ignore +const kAsinIntervalInheritedCases = { + f32: [ + { input: -1/2, expected: [reinterpretU32AsF32(0xbf061a96), reinterpretU32AsF32(0xbf05fa8e)] }, // ~-π/6 + { input: 1/2, expected: [reinterpretU32AsF32(0x3f05fa8e), reinterpretU32AsF32(0x3f061a96)] }, // ~π/6 + ] as ScalarToIntervalCase[], + f16: [ + { input: -1/2, expected: [reinterpretU16AsF16(0xb83a), reinterpretU16AsF16(0xb827)] }, // ~-π/6 + { input: 1/2, expected: [reinterpretU16AsF16(0x3827), reinterpretU16AsF16(0x383a)] }, // ~π/6 + ] as ScalarToIntervalCase[], +} as const; + +g.test('asinInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + const abs_error = p.trait === 'f32' ? 6.77e-5 : 3.91e-3; + // prettier-ignore + return [ + // The acceptance interval @ x = -1 and 1 is kUnboundedBounds, because + // sqrt(1 - x*x) = sqrt(0), and sqrt is defined in terms of inversqrt. + // The acceptance interval @ x = 0 is kUnboundedBounds, because atan2 is not + // well-defined/implemented at 0. + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: -1, expected: kUnboundedBounds }, + // Subnormal input may get flushed to 0, and result in kUnboundedBounds. + { input: constants.negative.subnormal.min, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: constants.positive.subnormal.max, expected: kUnboundedBounds }, + { input: 1, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + + // When input near 0, the expected result is bounded by absolute error rather than ULP + // error. Away from 0 the atan2 inherited error should be larger. + { input: constants.negative.max, expected: trait.absoluteErrorInterval(Math.asin(constants.negative.max), abs_error).bounds() }, // ~0 + { input: constants.positive.min, expected: trait.absoluteErrorInterval(Math.asin(constants.positive.min), abs_error).bounds() }, // ~0 + + // Cases that inherited from atan2(x, sqrt(1-x*x)) + ...kAsinIntervalInheritedCases[p.trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.asinInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.asinInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kAsinhIntervalCases = { + f32: [ + { input: -1, expected: [reinterpretU64AsF64(0xbfec_343a_8000_0000n), reinterpretU64AsF64(0xbfec_3432_8000_0000n)] }, // ~-0.88137... + { input: 0, expected: [reinterpretU64AsF64(0xbeaa_0000_2000_0000n), reinterpretU64AsF64(0x3eb1_ffff_d000_0000n)] }, // ~0 + { input: 1, expected: [reinterpretU64AsF64(0x3fec_3435_4000_0000n), reinterpretU64AsF64(0x3fec_3437_8000_0000n)] }, // ~0.88137... + ] as ScalarToIntervalCase[], + f16: [ + { input: -1, expected: [reinterpretU64AsF64(0xbfec_b800_0000_0000n), reinterpretU64AsF64(0xbfeb_b800_0000_0000n)] }, // ~-0.88137... + { input: 0, expected: [reinterpretU64AsF64(0xbf85_0200_0000_0000n), reinterpretU64AsF64(0x3f89_fa00_0000_0000n)] }, // ~0 + { input: 1, expected: [reinterpretU64AsF64(0x3fec_1000_0000_0000n), reinterpretU64AsF64(0x3fec_5400_0000_0000n)] }, // ~0.88137... + ] as ScalarToIntervalCase[], +} as const; + +g.test('asinhInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kAsinhIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.asinhInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.asinhInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kAtanIntervalCases = { + f32: [ + // x=-√3=-1.7320508... quantized to f32 0xBFDDB3D7, + // atan(0xBFDDB3D7)=-1.0471975434247854181546378047331 ~ -pi/3 rounded to f32 0xBF860A92 or 0xBF860A91, + // kValue.f32.negative.pi.third is 0xBF860A92. + { input: reinterpretU32AsF32(0xbfddb3d7), expected: [kValue.f32.negative.pi.third, kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.third)] }, + // atan(-1)=-0.78539816339744830961566084581988 ~ -pi/4 rounded to f32 0xBF490FDB or 0xBF490FDA, + // kValue.f32.negative.pi.quarter is 0xBF490FDB. + { input: -1, expected: [kValue.f32.negative.pi.quarter, kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.quarter)] }, + // x=-1/√3=-0.577350269... quantized to f32 0xBF13CD3A, + // atan(0xBF13CD3A)=-0.52359876782648663982267459646249 ~ -pi/6 rounded to f32 0xBF060A92 or 0xBF060A91, + // kValue.f32.negative.pi.sixth is 0xBF060A92. + { input: reinterpretU32AsF32(0xbf13cd3a), expected: [kValue.f32.negative.pi.sixth, kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.sixth)] }, + // x=1/√3=0.577350269... quantized to f32 0x3F13CD3A. + { input: reinterpretU32AsF32(0x3f13cd3a), expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.sixth), kValue.f32.positive.pi.sixth] }, + { input: 1, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.quarter), kValue.f32.positive.pi.quarter] }, + // x=√3=1.7320508... quantized to f32 0x3FDDB3D7. + { input: reinterpretU32AsF32(0x3fddb3d7), expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.third), kValue.f32.positive.pi.third] }, + ] as ScalarToIntervalCase[], + f16: [ + // x=-√3=-1.7320508... quantized to f16 0xBEED, + // atan(0xBEED)=-1.0470461377318847079113932677171 ~ -pi/3 rounded to f16 0xBC31 or 0xBC30, + // kValue.f16.negative.pi.third is 0xBC30. + { input: reinterpretU16AsF16(0xbeed), expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.third), kValue.f16.negative.pi.third] }, + // atan(-1)=-0.78539816339744830961566084581988 ~ -pi/4 rounded to f16 0xBA49 or 0xBA48. + // kValue.f16.negative.pi.quarter is 0xBA48. + { input: -1, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.quarter), kValue.f16.negative.pi.quarter] }, + // x=-1/√3=-0.577350269... quantized to f16 0xB89E, + // atan(0xB89E)=-0.52344738860166563645762619364966 ~ -pi/6 rounded to f16 0xB831 or 0xB830, + // kValue.f16.negative.pi.sixth is 0xB830. + { input: reinterpretU16AsF16(0xb89e), expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.sixth), kValue.f16.negative.pi.sixth] }, + // x=1/√3=0.577350269... quantized to f16 0x389E + { input: reinterpretU16AsF16(0x389e), expected: [kValue.f16.positive.pi.sixth, kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.sixth)] }, + { input: 1, expected: [kValue.f16.positive.pi.quarter, kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.quarter)] }, + // x=√3=1.7320508... quantized to f16 0x3EED + { input: reinterpretU16AsF16(0x3eed), expected: [kValue.f16.positive.pi.third, kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.third)] }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('atanInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + { input: 0, expected: 0 }, + ...kAtanIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + + const ulp_error = t.params.trait === 'f32' ? 4096 : 5; + const error = (n: number): number => { + return ulp_error * trait.oneULP(n); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.atanInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.atanInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kAtanhIntervalCases = { + f32: [ + { input: -0.1, expected: [reinterpretU64AsF64(0xbfb9_af9a_6000_0000n), reinterpretU64AsF64(0xbfb9_af8c_c000_0000n)] }, // ~-0.1003... + { input: 0, expected: [reinterpretU64AsF64(0xbe96_0000_2000_0000n), reinterpretU64AsF64(0x3e98_0000_0000_0000n)] }, // ~0 + { input: 0.1, expected: [reinterpretU64AsF64(0x3fb9_af8b_8000_0000n), reinterpretU64AsF64(0x3fb9_af9b_0000_0000n)] }, // ~0.1003... + ] as ScalarToIntervalCase[], + f16: [ + { input: -0.1, expected: [reinterpretU64AsF64(0xbfbb_0c00_0000_0000n), reinterpretU64AsF64(0xbfb8_5800_0000_0000n)] }, // ~-0.1003... + { input: 0, expected: [reinterpretU64AsF64(0xbf73_0400_0000_0000n), reinterpretU64AsF64(0x3f74_0000_0000_0000n)] }, // ~0 + { input: 0.1, expected: [reinterpretU64AsF64(0x3fb8_3800_0000_0000n), reinterpretU64AsF64(0x3fbb_2400_0000_0000n)] }, // ~0.1003... + ] as ScalarToIntervalCase[], +} as const; + +g.test('atanhInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kAtanhIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: -1, expected: kUnboundedBounds }, + { input: 1, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.atanhInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.atanhInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Large but still representable integer +const kCeilIntervalCases = { + f32: [ + { input: 2 ** 30, expected: 2 ** 30 }, + { input: -(2 ** 30), expected: -(2 ** 30) }, + { input: 0x80000000, expected: 0x80000000 }, // https://github.com/gpuweb/cts/issues/2766 + ], + f16: [ + { input: 2 ** 14, expected: 2 ** 14 }, + { input: -(2 ** 14), expected: -(2 ** 14) }, + { input: 0x8000, expected: 0x8000 }, // https://github.com/gpuweb/cts/issues/2766 + ], +} as const; + +g.test('ceilInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + { input: 0, expected: 0 }, + { input: 0.1, expected: 1 }, + { input: 0.9, expected: 1 }, + { input: 1.0, expected: 1 }, + { input: 1.1, expected: 2 }, + { input: 1.9, expected: 2 }, + { input: -0.1, expected: 0 }, + { input: -0.9, expected: 0 }, + { input: -1.0, expected: -1 }, + { input: -1.1, expected: -1 }, + { input: -1.9, expected: -1 }, + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: constants.positive.max }, + { input: constants.positive.min, expected: 1 }, + { input: constants.negative.min, expected: constants.negative.min }, + { input: constants.negative.max, expected: 0 }, + ...kCeilIntervalCases[p.trait], + + // 32-bit subnormals + { input: constants.positive.subnormal.max, expected: [0, 1] }, + { input: constants.positive.subnormal.min, expected: [0, 1] }, + { input: constants.negative.subnormal.min, expected: 0 }, + { input: constants.negative.subnormal.max, expected: 0 }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.ceilInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.ceilInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Cos interval cases on x=π/3, the result of f32 and f16 is different because π/3 quantized to +// different direction for two types. +const kCosIntervalThirdPiCases = { + // prettier-ignore + f32: [ + // cos(-1.0471975803375244) = 0.499999974763 + { input: kValue.f32.negative.pi.third, expected: [kMinusOneULPFunctions['f32'](1/2), 1/2] }, + // cos(1.0471975803375244) = 0.499999974763 + { input: kValue.f32.positive.pi.third, expected: [kMinusOneULPFunctions['f32'](1/2), 1/2] }, + ], + f16: [ + // cos(-1.046875) = 0.50027931 + { + input: kValue.f16.negative.pi.third, + expected: FP['f16'].correctlyRoundedInterval(0.50027931).bounds(), + }, + // cos(1.046875) = 0.50027931 + { + input: kValue.f16.positive.pi.third, + expected: FP['f16'].correctlyRoundedInterval(0.50027931).bounds(), + }, + ], +}; + +g.test('cosInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // This test does not include some common cases. i.e. f(x = π/2) = 0, + // because the difference between true x and x as a f32 is sufficiently + // large, such that the high slope of f @ x causes the results to be + // substantially different, so instead of getting 0 you get a value on the + // order of 10^-8 away from 0, thus difficult to express in a + // human-readable manner. + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.negative.pi.whole, expected: [-1, kPlusOneULPFunctions[p.trait](-1)] }, + { input: 0, expected: [1, 1] }, + { input: constants.positive.pi.whole, expected: [-1, kPlusOneULPFunctions[p.trait](-1)] }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + + ...(kCosIntervalThirdPiCases[p.trait] as ScalarToIntervalCase[]), + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + + const error = (_: number): number => { + return t.params.trait === 'f32' ? 2 ** -11 : 2 ** -7; + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.cosInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.cosInterval(${t.params.input}) returned ${got}. Expected ${expected}, ===${t.params.expected}===` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kCoshIntervalCases = { + f32: [ + { input: -1, expected: [reinterpretU32AsF32(0x3fc583a4), reinterpretU32AsF32(0x3fc583b1)] }, // ~1.1543... + { input: 0, expected: [reinterpretU32AsF32(0x3f7ffffd), reinterpretU32AsF32(0x3f800002)] }, // ~1 + { input: 1, expected: [reinterpretU32AsF32(0x3fc583a4), reinterpretU32AsF32(0x3fc583b1)] }, // ~1.1543... + ] as ScalarToIntervalCase[], + f16: [ + { input: -1, expected: [reinterpretU16AsF16(0x3e27), reinterpretU16AsF16(0x3e30)] }, // ~1.1543... + { input: 0, expected: [reinterpretU16AsF16(0x3bff), reinterpretU16AsF16(0x3c01)] }, // ~1 + { input: 1, expected: [reinterpretU16AsF16(0x3e27), reinterpretU16AsF16(0x3e30)] }, // ~1.1543... + ] as ScalarToIntervalCase[], +} as const; + +g.test('coshInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kCoshIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.coshInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.coshInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kDegreesIntervalCases = { + f32: [ + { input: kValue.f32.negative.pi.whole, expected: [kMinusOneULPFunctions['f32'](-180), kPlusOneULPFunctions['f32'](-180)] }, + { input: kValue.f32.negative.pi.three_quarters, expected: [kMinusOneULPFunctions['f32'](-135), kPlusOneULPFunctions['f32'](-135)] }, + { input: kValue.f32.negative.pi.half, expected: [kMinusOneULPFunctions['f32'](-90), kPlusOneULPFunctions['f32'](-90)] }, + { input: kValue.f32.negative.pi.third, expected: [kMinusOneULPFunctions['f32'](-60), kPlusOneULPFunctions['f32'](-60)] }, + { input: kValue.f32.negative.pi.quarter, expected: [kMinusOneULPFunctions['f32'](-45), kPlusOneULPFunctions['f32'](-45)] }, + { input: kValue.f32.negative.pi.sixth, expected: [kMinusOneULPFunctions['f32'](-30), kPlusOneULPFunctions['f32'](-30)] }, + { input: kValue.f32.positive.pi.sixth, expected: [kMinusOneULPFunctions['f32'](30), kPlusOneULPFunctions['f32'](30)] }, + { input: kValue.f32.positive.pi.quarter, expected: [kMinusOneULPFunctions['f32'](45), kPlusOneULPFunctions['f32'](45)] }, + { input: kValue.f32.positive.pi.third, expected: [kMinusOneULPFunctions['f32'](60), kPlusOneULPFunctions['f32'](60)] }, + { input: kValue.f32.positive.pi.half, expected: [kMinusOneULPFunctions['f32'](90), kPlusOneULPFunctions['f32'](90)] }, + { input: kValue.f32.positive.pi.three_quarters, expected: [kMinusOneULPFunctions['f32'](135), kPlusOneULPFunctions['f32'](135)] }, + { input: kValue.f32.positive.pi.whole, expected: [kMinusOneULPFunctions['f32'](180), kPlusOneULPFunctions['f32'](180)] }, + ] as ScalarToIntervalCase[], + f16: [ + { input: kValue.f16.negative.pi.whole, expected: [-180, kPlusOneULPFunctions['f16'](-180)] }, + { input: kValue.f16.negative.pi.three_quarters, expected: [-135, kPlusOneULPFunctions['f16'](-135)] }, + { input: kValue.f16.negative.pi.half, expected: [-90, kPlusOneULPFunctions['f16'](-90)] }, + { input: kValue.f16.negative.pi.third, expected: [-60, kPlusNULPFunctions['f16'](-60, 2)] }, + { input: kValue.f16.negative.pi.quarter, expected: [-45, kPlusOneULPFunctions['f16'](-45)] }, + { input: kValue.f16.negative.pi.sixth, expected: [-30, kPlusNULPFunctions['f16'](-30, 2)] }, + { input: kValue.f16.positive.pi.sixth, expected: [kMinusNULPFunctions['f16'](30, 2), 30] }, + { input: kValue.f16.positive.pi.quarter, expected: [kMinusOneULPFunctions['f16'](45), 45] }, + { input: kValue.f16.positive.pi.third, expected: [kMinusNULPFunctions['f16'](60, 2), 60] }, + { input: kValue.f16.positive.pi.half, expected: [kMinusOneULPFunctions['f16'](90), 90] }, + { input: kValue.f16.positive.pi.three_quarters, expected: [kMinusOneULPFunctions['f16'](135), 135] }, + { input: kValue.f16.positive.pi.whole, expected: [kMinusOneULPFunctions['f16'](180), 180] }, + ] as ScalarToIntervalCase[], + abstract: [ + { input: kValue.f64.negative.pi.whole, expected: -180 }, + { input: kValue.f64.negative.pi.three_quarters, expected: -135 }, + { input: kValue.f64.negative.pi.half, expected: -90 }, + { input: kValue.f64.negative.pi.third, expected: kPlusOneULPFunctions['abstract'](-60) }, + { input: kValue.f64.negative.pi.quarter, expected: -45 }, + { input: kValue.f64.negative.pi.sixth, expected: kPlusOneULPFunctions['abstract'](-30) }, + { input: kValue.f64.positive.pi.sixth, expected: kMinusOneULPFunctions['abstract'](30) }, + { input: kValue.f64.positive.pi.quarter, expected: 45 }, + { input: kValue.f64.positive.pi.third, expected: kMinusOneULPFunctions['abstract'](60) }, + { input: kValue.f64.positive.pi.half, expected: 90 }, + { input: kValue.f64.positive.pi.three_quarters, expected: 135 }, + { input: kValue.f64.positive.pi.whole, expected: 180 }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('degreesInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = p.trait; + const constants = FP[trait].constants(); + // prettier-ignore + return [ + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: 0, expected: 0 }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + ...kDegreesIntervalCases[trait] + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.degreesInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.degreesInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kExpIntervalCases = { + f32: [ + { input: 1, expected: [kValue.f32.positive.e, kPlusOneULPFunctions['f32'](kValue.f32.positive.e)] }, + // exp(88) = 1.6516362549940018555283297962649e+38 = 0x7ef882b6/7. + { input: 88, expected: [reinterpretU32AsF32(0x7ef882b6), reinterpretU32AsF32(0x7ef882b7)] }, + // exp(89) overflow f32. + { input: 89, expected: kUnboundedBounds }, + ] as ScalarToIntervalCase[], + f16: [ + { input: 1, expected: [kValue.f16.positive.e, kPlusOneULPFunctions['f16'](kValue.f16.positive.e)] }, + // exp(11) = 59874.141715197818455326485792258 = 0x7b4f/0x7b50. + { input: 11, expected: [reinterpretU16AsF16(0x7b4f), reinterpretU16AsF16(0x7b50)] }, + // exp(12) = 162754.79141900392080800520489849 overflow f16. + { input: 12, expected: kUnboundedBounds }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('expInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = p.trait; + const constants = FP[trait].constants(); + // prettier-ignore + return [ + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: 0, expected: 1 }, + ...kExpIntervalCases[trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const error = (x: number): number => { + let ulp_error; + switch (t.params.trait) { + case 'f32': { + ulp_error = 3 + 2 * Math.abs(t.params.input); + break; + } + case 'f16': { + ulp_error = 1 + 2 * Math.abs(t.params.input); + break; + } + } + return ulp_error * trait.oneULP(x); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + const got = trait.expInterval(t.params.input); + + t.expect( + objectEquals(expected, got), + `${t.params.trait}.expInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kExp2IntervalCases = { + f32: [ + // exp2(127) = 1.7014118346046923173168730371588e+38 = 0x7f000000, 3 + 2 * 127 = 258 ulps. + { input: 127, expected: reinterpretU32AsF32(0x7f000000) }, + // exp2(128) overflow f32. + { input: 128, expected: kUnboundedBounds }, + ] as ScalarToIntervalCase[], + f16: [ + // exp2(15) = 32768 = 0x7800, 1 + 2 * 15 = 31 ulps + { input: 15, expected: reinterpretU16AsF16(0x7800) }, + // exp2(16) = 65536 overflow f16. + { input: 16, expected: kUnboundedBounds }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('exp2Interval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = p.trait; + const constants = FP[trait].constants(); + // prettier-ignore + return [ + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: 0, expected: 1 }, + { input: 1, expected: 2 }, + ...kExp2IntervalCases[trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const error = (x: number): number => { + let ulp_error; + switch (t.params.trait) { + case 'f32': { + ulp_error = 3 + 2 * Math.abs(t.params.input); + break; + } + case 'f16': { + ulp_error = 1 + 2 * Math.abs(t.params.input); + break; + } + } + return ulp_error * trait.oneULP(x); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.exp2Interval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.exp2Interval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Large but still representable integer +const kFloorIntervalCases = { + f32: [ + { input: 2 ** 30, expected: 2 ** 30 }, + { input: -(2 ** 30), expected: -(2 ** 30) }, + { input: 0x80000000, expected: 0x80000000 }, // https://github.com/gpuweb/cts/issues/2766 + ], + f16: [ + { input: 2 ** 14, expected: 2 ** 14 }, + { input: -(2 ** 14), expected: -(2 ** 14) }, + { input: 0x8000, expected: 0x8000 }, // https://github.com/gpuweb/cts/issues/2766 + ], + abstract: [ + { input: 2 ** 62, expected: 2 ** 62 }, + { input: -(2 ** 62), expected: -(2 ** 62) }, + { + input: 0x8000_0000_0000_0000, + expected: 0x8000_0000_0000_0000, + }, // https://github.com/gpuweb/cts/issues/2766 + ], +} as const; + +g.test('floorInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + { input: 0, expected: 0 }, + { input: 0.1, expected: 0 }, + { input: 0.9, expected: 0 }, + { input: 1.0, expected: 1 }, + { input: 1.1, expected: 1 }, + { input: 1.9, expected: 1 }, + { input: -0.1, expected: -1 }, + { input: -0.9, expected: -1 }, + { input: -1.0, expected: -1 }, + { input: -1.1, expected: -2 }, + { input: -1.9, expected: -2 }, + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: constants.positive.max }, + { input: constants.positive.min, expected: 0 }, + { input: constants.negative.min, expected: constants.negative.min }, + { input: constants.negative.max, expected: -1 }, + ...kFloorIntervalCases[p.trait], + + // Subnormals + { input: constants.positive.subnormal.max, expected: 0 }, + { input: constants.positive.subnormal.min, expected: 0 }, + { input: constants.negative.subnormal.min, expected: [-1, 0] }, + { input: constants.negative.subnormal.max, expected: [-1, 0] }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.floorInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.floorInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kFractIntervalCases = { + f32: [ + { input: 0.1, expected: [kMinusOneULPFunctions['f32'](reinterpretU32AsF32(0x3dcccccd)), reinterpretU32AsF32(0x3dcccccd)] }, // ~0.1 + { input: 0.9, expected: [reinterpretU32AsF32(0x3f666666), kPlusOneULPFunctions['f32'](reinterpretU32AsF32(0x3f666666))] }, // ~0.9 + { input: 1.1, expected: [reinterpretU32AsF32(0x3dccccc0), reinterpretU32AsF32(0x3dccccd0)] }, // ~0.1 + { input: -0.1, expected: [reinterpretU32AsF32(0x3f666666), kPlusOneULPFunctions['f32'](reinterpretU32AsF32(0x3f666666))] }, // ~0.9 + { input: -0.9, expected: [reinterpretU32AsF32(0x3dccccc8), reinterpretU32AsF32(0x3dccccd0)] }, // ~0.1 + { input: -1.1, expected: [reinterpretU32AsF32(0x3f666666), reinterpretU32AsF32(0x3f666668)] }, // ~0.9 + + // https://github.com/gpuweb/cts/issues/2766 + { input: 0x80000000, expected: 0 }, + ] as ScalarToIntervalCase[], + f16: [ + { input: 0.1, expected: [reinterpretU16AsF16(0x2e66), reinterpretU16AsF16(0x2e67)] }, // ~0.1 + { input: 0.9, expected: [reinterpretU16AsF16(0x3b33), reinterpretU16AsF16(0x3b34)] }, // ~0.9 + { input: 1.1, expected: [reinterpretU16AsF16(0x2e60), reinterpretU16AsF16(0x2e70)] }, // ~0.1 + { input: -0.1, expected: [reinterpretU16AsF16(0x3b33), reinterpretU16AsF16(0x3b34)] }, // ~0.9 + { input: -0.9, expected: [reinterpretU16AsF16(0x2e60), reinterpretU16AsF16(0x2e68)] }, // ~0.1 + { input: -1.1, expected: [reinterpretU16AsF16(0x3b32), reinterpretU16AsF16(0x3b34)] }, // ~0.9 + { input: 658.5, expected: 0.5 }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('fractInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + { input: 0, expected: 0 }, + { input: 1.0, expected: 0 }, + { input: -1.0, expected: 0 }, + + ...kFractIntervalCases[p.trait], + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: 0 }, + { input: constants.positive.min, expected: constants.positive.min }, + { input: constants.negative.min, expected: 0 }, + { input: constants.negative.max, expected: [constants.positive.less_than_one, 1.0] }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.fractInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.fractInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kInverseSqrtIntervalCases = { + f32: [ + // 0.04 rounded to f32 0x3D23D70A or 0x3D23D70B, + // 1/sqrt(0x3D23D70B)=4.9999998230487200185270893769213 rounded to f32 0x409FFFFF or 0x40A00000, + // 1/sqrt(0x3D23D70A)=5.0000000558793553117506910583908 rounded to f32 0x40A00000 or 0x40A00001. + { input: 0.04, expected: [reinterpretU32AsF32(0x409FFFFF), reinterpretU32AsF32(0x40A00001)] }, // ~5.0 + // Maximium f32 0x7F7FFFFF = 3.4028234663852886e+38, + // 1/sqrt(0x7F7FFFFF)=5.4210110239862427800382690921791e-20 rounded to f32 0x1F800000 or 0x1F800001 + { input: kValue.f32.positive.max, expected: [reinterpretU32AsF32(0x1f800000), reinterpretU32AsF32(0x1f800001)] }, // ~5.421...e-20 + ] as ScalarToIntervalCase[], + f16: [ + // 0.04 rounded to f16 0x291E or 0x291F, + // 1/sqrt(0x291F)=4.9994660279328446295684795818427 rounded to f16 0x44FF or 0x4500, + // 1/sqrt(0x291E)=5.001373857053206453045376503367 rounded to f16 0x4500 or 0x4501. + { input: 0.04, expected: [reinterpretU16AsF16(0x44FF), reinterpretU16AsF16(0x4501)] }, // ~5.0 + // Maximium f16 0x7BFF = 65504, + // 1/sqrt(0x7BFF)=0.00390720402370454101997160826062 rounded to f16 0x1C00 or 0x1C01 + { input: kValue.f16.positive.max, expected: [reinterpretU16AsF16(0x1c00), reinterpretU16AsF16(0x1c01)] }, // ~3.9072...e-3 + ] as ScalarToIntervalCase[], +} as const; + +g.test('inverseSqrtInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // Note that the 2 ULP error is not included here. + // prettier-ignore + return [ + // Exactly representable cases + { input: 1, expected: 1 }, + { input: 0.25, expected: 2 }, + { input: 64, expected: 0.125 }, + + // Cases that input and/or result not exactly representable + ...kInverseSqrtIntervalCases[p.trait], + // 1/sqrt(100.0)=0.1, rounded to corresponding trait + { input: 100, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + + // Out of definition domain + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + + const error = (n: number): number => { + return 2 * trait.oneULP(n); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.inverseSqrtInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.inverseSqrtInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Expectation interval of 1/inverseSqrt(sum(x[i]^2)) on some special values array x for certain +// float traits, used as expectation for `length` and `distance`. +// These cases are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kRootSumSquareExpectionInterval = { + f32: { + '[0.1]': [reinterpretU64AsF64(0x3fb9_9998_9000_0000n), reinterpretU64AsF64(0x3fb9_999a_7000_0000n)], // ~0.1 + '[1.0]' : [reinterpretU64AsF64(0x3fef_ffff_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_9000_0000n)], // ~1.0 + '[10]' : [reinterpretU64AsF64(0x4023_ffff_7000_0000n), reinterpretU64AsF64(0x4024_0000_b000_0000n)], // ~10 + '[1.0, 1.0]' : [reinterpretU64AsF64(0x3ff6_a09d_b000_0000n), reinterpretU64AsF64(0x3ff6_a09f_1000_0000n)], // ~√2 + '[1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3ffb_b67a_1000_0000n), reinterpretU64AsF64(0x3ffb_b67b_b000_0000n)], // ~√3 + '[1.0, 1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3fff_ffff_7000_0000n), reinterpretU64AsF64(0x4000_0000_9000_0000n)], // ~2 + } as {[s: string]: IntervalBounds}, + f16: { + '[0.1]': [reinterpretU64AsF64(0x3fb9_7e00_0000_0000n), reinterpretU64AsF64(0x3fb9_b600_0000_0000n)], // ~0.1 + '[1.0]' : [reinterpretU64AsF64(0x3fef_ee00_0000_0000n), reinterpretU64AsF64(0x3ff0_1200_0000_0000n)], // ~1.0 + '[10]' : [reinterpretU64AsF64(0x4023_ea00_0000_0000n), reinterpretU64AsF64(0x4024_1200_0000_0000n)], // ~10 + '[1.0, 1.0]' : [reinterpretU64AsF64(0x3ff6_8a00_0000_0000n), reinterpretU64AsF64(0x3ff6_b600_0000_0000n)], // ~√2 + '[1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3ffb_9a00_0000_0000n), reinterpretU64AsF64(0x3ffb_d200_0000_0000n)], // ~√3 + '[1.0, 1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3fff_ee00_0000_0000n), reinterpretU64AsF64(0x4000_1200_0000_0000n)], // ~2 + } as {[s: string]: IntervalBounds}, +} as const; + +g.test('lengthIntervalScalar') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + {input: 1.0, expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: -1.0, expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: 0.1, expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + {input: -0.1, expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + {input: 10.0, expected: kRootSumSquareExpectionInterval[p.trait]['[10]'] }, // ~10 + {input: -10.0, expected: kRootSumSquareExpectionInterval[p.trait]['[10]'] }, // ~10 + + // length(0) = kUnboundedBounds, because length uses sqrt, which is defined as 1/inversesqrt + {input: 0, expected: kUnboundedBounds }, + + // Subnormal Cases + { input: constants.negative.subnormal.min, expected: kUnboundedBounds }, + { input: constants.negative.subnormal.max, expected: kUnboundedBounds }, + { input: constants.positive.subnormal.min, expected: kUnboundedBounds }, + { input: constants.positive.subnormal.max, expected: kUnboundedBounds }, + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.negative.max, expected: kUnboundedBounds }, + { input: constants.positive.min, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.lengthInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.lengthInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kLogIntervalCases = { + f32: [ + // kValue.f32.positive.e is 0x402DF854 = 2.7182817459106445, + // log(0x402DF854) = 0.99999996963214000677592342891704 rounded to f32 0x3F7FFFFF or 0x3F800000 = 1.0 + { input: kValue.f32.positive.e, expected: [kMinusOneULPFunctions['f32'](1.0), 1.0] }, + // kValue.f32.positive.max is 0x7F7FFFFF = 3.4028234663852886e+38, + // log(0x7F7FFFFF) = 88.72283905206835305421152826479 rounded to f32 0x42B17217 or 0x42B17218. + { input: kValue.f32.positive.max, expected: [kMinusOneULPFunctions['f32'](reinterpretU32AsF32(0x42b17218)), reinterpretU32AsF32(0x42b17218)] }, + ] as ScalarToIntervalCase[], + f16: [ + // kValue.f16.positive.e is 0x416F = 2.716796875, + // log(0x416F) = 0.99945356688393512460279716546501 rounded to f16 0x3BFE or 0x3BFF. + { input: kValue.f16.positive.e, expected: [reinterpretU16AsF16(0x3bfe), reinterpretU16AsF16(0x3bff)] }, + // kValue.f16.positive.max is 0x7BFF = 65504, + // log(0x7BFF) = 11.089866488461016076210728979771 rounded to f16 0x498B or 0x498C. + { input: kValue.f16.positive.max, expected: [reinterpretU16AsF16(0x498b), reinterpretU16AsF16(0x498c)] }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('logInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + // prettier-ignore + return [ + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: 1, expected: 0 }, + ...kLogIntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const abs_error = t.params.trait === 'f32' ? 2 ** -21 : 2 ** -7; + const error = (n: number): number => { + if (t.params.input >= 0.5 && t.params.input <= 2.0) { + return abs_error; + } + return 3 * trait.oneULP(n); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.logInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.logInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kLog2IntervalCases = { + f32: [ + // kValue.f32.positive.max is 0x7F7FFFFF = 3.4028234663852886e+38, + // log2(0x7F7FFFFF) = 127.99999991400867200665269600978 rounded to f32 0x42FFFFFF or 0x43000000 = 128.0 + { input: kValue.f32.positive.max, expected: [kMinusOneULPFunctions['f32'](128.0), 128.0] }, + ] as ScalarToIntervalCase[], + f16: [ + // kValue.f16.positive.max is 0x7BFF = 65504, + // log2(0x7BFF) = 15.999295387023410627258428389903 rounded to f16 0x4BFF or 0x4C00 = 16.0 + { input: kValue.f16.positive.max, expected: [kMinusOneULPFunctions['f16'](16.0), 16.0] }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('log2Interval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + // prettier-ignore + return [ + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: 1, expected: 0 }, + { input: 2, expected: 1 }, + { input: 16, expected: 4 }, + ...kLog2IntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const abs_error = t.params.trait === 'f32' ? 2 ** -21 : 2 ** -7; + const error = (n: number): number => { + if (t.params.input >= 0.5 && t.params.input <= 2.0) { + return abs_error; + } + return 3 * trait.oneULP(n); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.log2Interval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.log2Interval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('negationInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: constants.negative.min }, + { input: constants.positive.min, expected: constants.negative.max }, + { input: constants.negative.min, expected: constants.positive.max }, + { input: constants.negative.max, expected: constants.positive.min }, + + // Normals + { input: 0, expected: 0 }, + { input: 1.0, expected: -1.0 }, + { input: -1.0, expected: 1 }, + { input: 0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + { input: 1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['-1.9'] }, // ~-1.9 + { input: -0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: -1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['1.9'] }, // ~1.9 + + // Subnormals + { input: constants.positive.subnormal.max, expected: [constants.negative.subnormal.min, 0] }, + { input: constants.positive.subnormal.min, expected: [constants.negative.subnormal.max, 0] }, + { input: constants.negative.subnormal.min, expected: [0, constants.positive.subnormal.max] }, + { input: constants.negative.subnormal.max, expected: [0, constants.positive.subnormal.min] }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.negationInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.negationInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('quantizeToF16Interval') + .paramsSubcasesOnly<ScalarToIntervalCase>( + // prettier-ignore + [ + { input: kValue.f32.negative.infinity, expected: kUnboundedBounds }, + { input: kValue.f32.negative.min, expected: kUnboundedBounds }, + { input: kValue.f16.negative.min, expected: kValue.f16.negative.min }, + { input: -1.9, expected: kConstantCorrectlyRoundedExpectation['f16']['-1.9'] }, // ~-1.9 + { input: -1, expected: -1 }, + { input: -0.1, expected: kConstantCorrectlyRoundedExpectation['f16']['-0.1'] }, // ~-0.1 + { input: kValue.f16.negative.max, expected: kValue.f16.negative.max }, + { input: kValue.f16.negative.subnormal.min, expected: [kValue.f16.negative.subnormal.min, 0] }, + { input: kValue.f16.negative.subnormal.max, expected: [kValue.f16.negative.subnormal.max, 0] }, + { input: kValue.f32.negative.subnormal.max, expected: [kValue.f16.negative.subnormal.max, 0] }, + { input: 0, expected: 0 }, + { input: kValue.f32.positive.subnormal.min, expected: [0, kValue.f16.positive.subnormal.min] }, + { input: kValue.f16.positive.subnormal.min, expected: [0, kValue.f16.positive.subnormal.min] }, + { input: kValue.f16.positive.subnormal.max, expected: [0, kValue.f16.positive.subnormal.max] }, + { input: kValue.f16.positive.min, expected: kValue.f16.positive.min }, + { input: 0.1, expected: kConstantCorrectlyRoundedExpectation['f16']['0.1'] }, // ~0.1 + { input: 1, expected: 1 }, + { input: 1.9, expected: kConstantCorrectlyRoundedExpectation['f16']['1.9'] }, // ~1.9 + { input: kValue.f16.positive.max, expected: kValue.f16.positive.max }, + { input: kValue.f32.positive.max, expected: kUnboundedBounds }, + { input: kValue.f32.positive.infinity, expected: kUnboundedBounds }, + ] + ) + .fn(t => { + const expected = FP.f32.toInterval(t.params.expected); + + const got = FP.f32.quantizeToF16Interval(t.params.input); + t.expect( + objectEquals(expected, got), + `f32.quantizeToF16Interval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kRadiansIntervalCases = { + f32: [ + { input: -180, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.whole), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.whole)] }, + { input: -135, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.three_quarters), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.three_quarters)] }, + { input: -90, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.half), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.half)] }, + { input: -60, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.third), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.third)] }, + { input: -45, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.quarter), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.quarter)] }, + { input: -30, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.sixth), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.sixth)] }, + { input: 30, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.sixth), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.sixth)] }, + { input: 45, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.quarter), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.quarter)] }, + { input: 60, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.third), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.third)] }, + { input: 90, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.half), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.half)] }, + { input: 135, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.three_quarters), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.three_quarters)] }, + { input: 180, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.whole), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.whole)] }, + ] as ScalarToIntervalCase[], + f16: [ + { input: -180, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.whole), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.whole)] }, + { input: -135, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.three_quarters), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.three_quarters)] }, + { input: -90, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.half), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.half)] }, + { input: -60, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.third), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.third)] }, + { input: -45, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.quarter), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.quarter)] }, + { input: -30, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.sixth), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.sixth)] }, + { input: 30, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.sixth), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.sixth)] }, + { input: 45, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.quarter), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.quarter)] }, + { input: 60, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.third), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.third)] }, + { input: 90, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.half), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.half)] }, + { input: 135, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.three_quarters), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.three_quarters)] }, + { input: 180, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.whole), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.whole)] }, + ] as ScalarToIntervalCase[], + abstract: [ + { input: -180, expected: kValue.f64.negative.pi.whole }, + { input: -135, expected: kValue.f64.negative.pi.three_quarters }, + { input: -90, expected: kValue.f64.negative.pi.half }, + { input: -60, expected: kValue.f64.negative.pi.third }, + { input: -45, expected: kValue.f64.negative.pi.quarter }, + { input: -30, expected: kValue.f64.negative.pi.sixth }, + { input: 30, expected: kValue.f64.positive.pi.sixth }, + { input: 45, expected: kValue.f64.positive.pi.quarter }, + { input: 60, expected: kValue.f64.positive.pi.third }, + { input: 90, expected: kValue.f64.positive.pi.half }, + { input: 135, expected: kValue.f64.positive.pi.three_quarters }, + { input: 180, expected: kValue.f64.positive.pi.whole }, + ] as ScalarToIntervalCase[], +} as const; + +g.test('radiansInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = p.trait; + const constants = FP[trait].constants(); + // prettier-ignore + return [ + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: 0, expected: 0 }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + ...kRadiansIntervalCases[trait] + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.radiansInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.radiansInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Large but still representable integer +const kRoundIntervalCases = { + f32: [ + { input: 2 ** 30, expected: 2 ** 30 }, + { input: -(2 ** 30), expected: -(2 ** 30) }, + { input: 0x80000000, expected: 0x80000000 }, // https://github.com/gpuweb/cts/issues/2766 + ], + f16: [ + { input: 2 ** 14, expected: 2 ** 14 }, + { input: -(2 ** 14), expected: -(2 ** 14) }, + { input: 0x8000, expected: 0x8000 }, // https://github.com/gpuweb/cts/issues/2766 + ], +} as const; + +g.test('roundInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + { input: 0, expected: 0 }, + { input: 0.1, expected: 0 }, + { input: 0.5, expected: 0 }, // Testing tie breaking + { input: 0.9, expected: 1 }, + { input: 1.0, expected: 1 }, + { input: 1.1, expected: 1 }, + { input: 1.5, expected: 2 }, // Testing tie breaking + { input: 1.9, expected: 2 }, + { input: -0.1, expected: 0 }, + { input: -0.5, expected: 0 }, // Testing tie breaking + { input: -0.9, expected: -1 }, + { input: -1.0, expected: -1 }, + { input: -1.1, expected: -1 }, + { input: -1.5, expected: -2 }, // Testing tie breaking + { input: -1.9, expected: -2 }, + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: constants.positive.max }, + { input: constants.positive.min, expected: 0 }, + { input: constants.negative.min, expected: constants.negative.min }, + { input: constants.negative.max, expected: 0 }, + ...kRoundIntervalCases[p.trait], + + // 32-bit subnormals + { input: constants.positive.subnormal.max, expected: 0 }, + { input: constants.positive.subnormal.min, expected: 0 }, + { input: constants.negative.subnormal.min, expected: 0 }, + { input: constants.negative.subnormal.max, expected: 0 }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.roundInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.roundInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('saturateInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // Normals + { input: 0, expected: 0 }, + { input: 0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + { input: 1, expected: 1.0 }, + { input: -0.1, expected: 0 }, + { input: -1, expected: 0 }, + { input: -10, expected: 0 }, + { input: 10, expected: 1.0 }, + { input: 11.1, expected: 1.0 }, + { input: constants.positive.max, expected: 1.0 }, + { input: constants.positive.min, expected: constants.positive.min }, + { input: constants.negative.max, expected: 0.0 }, + { input: constants.negative.min, expected: 0.0 }, + + // Subnormals + { input: constants.positive.subnormal.max, expected: [0.0, constants.positive.subnormal.max] }, + { input: constants.positive.subnormal.min, expected: [0.0, constants.positive.subnormal.min] }, + { input: constants.negative.subnormal.min, expected: [constants.negative.subnormal.min, 0.0] }, + { input: constants.negative.subnormal.max, expected: [constants.negative.subnormal.max, 0.0] }, + + // Infinities + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.saturateInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.saturationInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('signInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: -1 }, + { input: -10, expected: -1 }, + { input: -1, expected: -1 }, + { input: -0.1, expected: -1 }, + { input: constants.negative.max, expected: -1 }, + { input: constants.negative.subnormal.min, expected: [-1, 0] }, + { input: constants.negative.subnormal.max, expected: [-1, 0] }, + { input: 0, expected: 0 }, + { input: constants.positive.subnormal.max, expected: [0, 1] }, + { input: constants.positive.subnormal.min, expected: [0, 1] }, + { input: constants.positive.min, expected: 1 }, + { input: 0.1, expected: 1 }, + { input: 1, expected: 1 }, + { input: 10, expected: 1 }, + { input: constants.positive.max, expected: 1 }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.signInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.signInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('sinInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // This test does not include some common cases, i.e. f(x = -π|π) = 0, + // because the difference between true x and x as a f32 is sufficiently + // large, such that the high slope of f @ x causes the results to be + // substantially different, so instead of getting 0 you get a value on the + // order of 10^-8 away from it, thus difficult to express in a + // human-readable manner. + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.negative.pi.half, expected: [-1, kPlusOneULPFunctions[p.trait](-1)] }, + { input: 0, expected: 0 }, + { input: constants.positive.pi.half, expected: [kMinusOneULPFunctions[p.trait](1), 1] }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + + const error = (_: number): number => { + return t.params.trait === 'f32' ? 2 ** -11 : 2 ** -7; + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.sinInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.sinInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kSinhIntervalCases = { + f32: [ + { input: -1, expected: [reinterpretU32AsF32(0xbf966d05), reinterpretU32AsF32(0xbf966cf8)] }, // ~-1.175... + { input: 0, expected: [reinterpretU32AsF32(0xb4600000), reinterpretU32AsF32(0x34600000)] }, // ~0 + { input: 1, expected: [reinterpretU32AsF32(0x3f966cf8), reinterpretU32AsF32(0x3f966d05)] }, // ~1.175... + ] as ScalarToIntervalCase[], + f16: [ + { input: -1, expected: [reinterpretU16AsF16(0xbcb8), reinterpretU16AsF16(0xbcaf)] }, // ~-1.175... + { input: 0, expected: [reinterpretU16AsF16(0x9200), reinterpretU16AsF16(0x1200)] }, // ~0 + { input: 1, expected: [reinterpretU16AsF16(0x3caf), reinterpretU16AsF16(0x3cb8)] }, // ~1.175... + ] as ScalarToIntervalCase[], +} as const; + +g.test('sinhInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kSinhIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.sinhInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.sinhInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// For sqrt interval inherited from 1.0 / inverseSqrt(x), errors come from: +// 1. Rounding of input x, if any; +// 2. 2 ULP from inverseSqrt; +// 3. And 2.5 ULP from division. +// The last 2.5ULP is handled in test and not included in the expected values here. +// prettier-ignore +const kSqrtIntervalCases = { + f32: [ + // 0.01 rounded to f32 0x3C23D70A or 0x3C23D70B. + // For inverseSqrt interval, floor_f32(1.0/sqrt(0x3C23D70B))-2ULP=0x411FFFFD, + // ceil_f32(1.0/sqrt(0x3C23D70A))+2ULP=0x41200003. + // For division, 1.0/0x41200003=0.09999997138977868544997855067803 rounded to f32 0x3DCCCCC8 or 0x3DCCCCC9, + // 1.0/0x411FFFFD=0.100000028610237685454662304067 rounded to f32 0x3DCCCCD0 or 0x3DCCCCD1. + { input: 0.01, expected: [reinterpretU32AsF32(0x3DCCCCC8), reinterpretU32AsF32(0x3DCCCCD1)] }, // ~0.1 + // For inverseSqrt interval, 1.0/sqrt(1.0)-2ULP=0x3F7FFFFE, 1.0/sqrt(1.0)+2ULP=0x3F800001. + // For division, 1.0/0x3F800001=0.9999998807907246108530328709735 rounded to f32 0x3F7FFFFE or 0x3F7FFFFF, + // 1.0/0x3F7FFFFE=1.0000001192093038108564210027667 rounded to f32 0x3F800001 or 0x3F800002. + { input: 1, expected: [reinterpretU32AsF32(0x3F7FFFFE), reinterpretU32AsF32(0x3F800002)] }, // ~1 + // For inverseSqrt interval, 1.0/sqrt(4.0)-2ULP=0x3EFFFFFE, 1.0/sqrt(4.0)+2ULP=0x3F000001. + // For division, 1.0/0x3F000001=1.999999761581449221706065741947 rounded to f32 0x3FFFFFFE or 0x3FFFFFFF, + // 1.0/0x3EFFFFFE=2.0000002384186076217128420055334 rounded to f32 0x40000001 or 0x40000002. + { input: 4, expected: [reinterpretU32AsF32(0x3FFFFFFE), reinterpretU32AsF32(0x40000002)] }, // ~2 + // For inverseSqrt interval, floor_f32(1.0/sqrt(100.0))-2ULP=0x3DCCCCCA, + // ceil_f32(1.0/sqrt(100.0))+2ULP=0x3DCCCCCF. + // For division, 1.0/0x3DCCCCCF=9.9999983608725376739278142322684 rounded to f32 0x411FFFFE or 0x411FFFFF, + // 1.0/0x3DCCCCCA=10.000002086163002207516386565905 rounded to f32 0x41200002 or 0x41200003. + { input: 100, expected: [reinterpretU32AsF32(0x411FFFFE), reinterpretU32AsF32(0x41200003)] }, // ~10 + ] as ScalarToIntervalCase[], + f16: [ + // 0.01 rounded to f16 0x211E or 0x211F. + // For inverseSqrt interval, floor_f16(1.0/sqrt(0x211F))-2ULP=0x48FD, + // ceil_f16(1.0/sqrt(0x211E))+2ULP=0x4903. + // For division, 1.0/0x4903=0.09976617303195635229929851909587 rounded to f16 0x2E62 or 0x2E63, + // 1.0/0x48FD=0.10023492560689115113547376664056 rounded to f16 0x2E6A or 0x2E6B. + { input: 0.01, expected: [reinterpretU16AsF16(0x2E62), reinterpretU16AsF16(0x2E6B)] }, // ~0.1 + // For inverseSqrt interval, 1.0/sqrt(1.0)-2ULP=0x3BFE, 1.0/sqrt(1.0)+2ULP=0x3C01. + // For division, 1.0/0x3C01=0.99902439024390243902439024390244 rounded to f16 0x3BFE or 0x3BFF, + // 1.0/0x3BFE=1.000977517106549364613880742913 rounded to f16 0x3C01 or 0x3C02. + { input: 1, expected: [reinterpretU16AsF16(0x3BFE), reinterpretU16AsF16(0x3C02)] }, // ~1 + // For inverseSqrt interval, 1.0/sqrt(4.0)-2ULP=0x37FE, 1.0/sqrt(4.0)+2ULP=0x3801. + // For division, 1.0/0x3801=1.9980487804878048780487804878049 rounded to f16 0x3FFE or 0x3FFF, + // 1.0/0x37FE=2.001955034213098729227761485826 rounded to f16 0x4001 or 0x4002. + { input: 4, expected: [reinterpretU16AsF16(0x3FFE), reinterpretU16AsF16(0x4002)] }, // ~2 + // For inverseSqrt interval, floor_f16(1.0/sqrt(100.0))-2ULP=0x2E64, + // ceil_f16(1.0/sqrt(100.0))+2ULP=0x2E69. + // For division, 1.0/0x2E69=9.9841560024374942258493264279108 rounded to f16 0x48FD or 0x48FE, + // 1.0/0x2E64=10.014669926650366748166259168704 rounded to f16 0x4901 or 0x4902. + { input: 100, expected: [reinterpretU16AsF16(0x48FD), reinterpretU16AsF16(0x4902)] }, // ~10 + ] as ScalarToIntervalCase[], +} as const; + +g.test('sqrtInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Cases that input and/or result not exactly representable + ...kSqrtIntervalCases[p.trait], + + // Cases out of definition domain + { input: -1, expected: kUnboundedBounds }, + { input: 0, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + + // The expected error interval is inherited from 1.0 / inverseSqrt(x), the 2.5ULP for division + // is handled here. + const error = (n: number): number => { + return 2.5 * trait.oneULP(n); + }; + + const expected = trait.toInterval(applyError(t.params.expected, error)); + + const got = trait.sqrtInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `FP.${t.params.trait}.sqrtInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// All of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form. +// Some easy looking cases like f(x = -π|π) = 0 are actually quite difficult. This is because the +// interval is calculated from the results of sin(x)/cos(x), which becomes very messy at x = -π|π, +// since π is irrational, thus does not have an exact representation as a float. +// +// Even at 0, which has a precise f32/f16 value, there is still the problem that result of sin(0) +// and cos(0) will be intervals due to the inherited nature of errors, so the proper interval will +// be an interval calculated from dividing an interval by another interval and applying an error +// function to that. +// +// This complexity is why the entire interval framework was developed. +// +// The examples here have been manually traced to confirm the expectation values are correct. +// prettier-ignore +const kTanIntervalCases = { + f32: [ + { input: kValue.f32.negative.pi.whole, expected: [reinterpretU64AsF64(0xbf40_02bc_9000_0000n), reinterpretU64AsF64(0x3f40_0144_f000_0000n)] }, // ~0.0 + { input: kValue.f32.negative.pi.three_quarters, expected: [reinterpretU64AsF64(0x3fef_f4b1_3000_0000n), reinterpretU64AsF64(0x3ff0_05a9_9000_0000n)] }, // ~1.0 + { input: kValue.f32.negative.pi.third, expected: [reinterpretU64AsF64(0xbffb_c16b_d000_0000n), reinterpretU64AsF64(0xbffb_ab8f_9000_0000n)] }, // ~-√3 + { input: kValue.f32.negative.pi.quarter, expected: [reinterpretU64AsF64(0xbff0_05a9_b000_0000n), reinterpretU64AsF64(0xbfef_f4b1_5000_0000n)] }, // ~-1.0 + { input: kValue.f32.negative.pi.sixth, expected: [reinterpretU64AsF64(0xbfe2_80f1_f000_0000n), reinterpretU64AsF64(0xbfe2_725e_d000_0000n)] }, // ~-1/√3 + { input: 0, expected: [reinterpretU64AsF64(0xbf40_0200_b000_0000n), reinterpretU64AsF64(0x3f40_0200_b000_0000n)] }, // ~0.0 + { input: kValue.f32.positive.pi.sixth, expected: [reinterpretU64AsF64(0x3fe2_725e_d000_0000n), reinterpretU64AsF64(0x3fe2_80f1_f000_0000n)] }, // ~1/√3 + { input: kValue.f32.positive.pi.quarter, expected: [reinterpretU64AsF64(0x3fef_f4b1_5000_0000n), reinterpretU64AsF64(0x3ff0_05a9_b000_0000n)] }, // ~1.0 + { input: kValue.f32.positive.pi.third, expected: [reinterpretU64AsF64(0x3ffb_ab8f_9000_0000n), reinterpretU64AsF64(0x3ffb_c16b_d000_0000n)] }, // ~√3 + { input: kValue.f32.positive.pi.three_quarters, expected: [reinterpretU64AsF64(0xbff0_05a9_9000_0000n), reinterpretU64AsF64(0xbfef_f4b1_3000_0000n)] }, // ~-1.0 + { input: kValue.f32.positive.pi.whole, expected: [reinterpretU64AsF64(0xbf40_0144_f000_0000n), reinterpretU64AsF64(0x3f40_02bc_9000_0000n)] }, // ~0.0 + ] as ScalarToIntervalCase[], + f16: [ + { input: kValue.f16.negative.pi.whole, expected: [reinterpretU64AsF64(0xbf7c_5600_0000_0000n), reinterpretU64AsF64(0x3f82_2e00_0000_0000n)] }, // ~0.0 + { input: kValue.f16.negative.pi.three_quarters, expected: [reinterpretU64AsF64(0x3fef_4600_0000_0000n), reinterpretU64AsF64(0x3ff0_7200_0000_0000n)] }, // ~1.0 + { input: kValue.f16.negative.pi.third, expected: [reinterpretU64AsF64(0xbffc_7600_0000_0000n), reinterpretU64AsF64(0xbffa_f600_0000_0000n)] }, // ~-√3 + { input: kValue.f16.negative.pi.quarter, expected: [reinterpretU64AsF64(0xbff0_6600_0000_0000n), reinterpretU64AsF64(0xbfef_3600_0000_0000n)] }, // ~-1.0 + { input: kValue.f16.negative.pi.sixth, expected: [reinterpretU64AsF64(0xbfe2_fe00_0000_0000n), reinterpretU64AsF64(0xbfe1_f600_0000_0000n)] }, // ~-1/√3 + { input: 0, expected: [reinterpretU64AsF64(0xbf80_2e00_0000_0000n), reinterpretU64AsF64(0x3f80_2e00_0000_0000n)] }, // ~0.0 + { input: kValue.f16.positive.pi.sixth, expected: [reinterpretU64AsF64(0x3fe1_f600_0000_0000n), reinterpretU64AsF64(0x3fe2_fe00_0000_0000n)] }, // ~1/√3 + { input: kValue.f16.positive.pi.quarter, expected: [reinterpretU64AsF64(0x3fef_3600_0000_0000n), reinterpretU64AsF64(0x3ff0_6600_0000_0000n)] }, // ~1.0 + { input: kValue.f16.positive.pi.third, expected: [reinterpretU64AsF64(0x3ffa_f600_0000_0000n), reinterpretU64AsF64(0x3ffc_7600_0000_0000n)] }, // ~√3 + { input: kValue.f16.positive.pi.three_quarters, expected: [reinterpretU64AsF64(0xbff0_7200_0000_0000n), reinterpretU64AsF64(0xbfef_4600_0000_0000n)] }, // ~-1.0 + { input: kValue.f16.positive.pi.whole, expected: [reinterpretU64AsF64(0xbf82_2e00_0000_0000n), reinterpretU64AsF64(0x3f7c_5600_0000_0000n)] }, // ~0.0 + ] as ScalarToIntervalCase[], +} as const; + +g.test('tanInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kTanIntervalCases[p.trait], + + // Cases that result in unbounded interval. + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.negative.pi.half, expected: kUnboundedBounds }, + { input: constants.positive.pi.half, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.tanInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.tanInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kTanhIntervalCases = { + f32: [ + { input: -1, expected: [reinterpretU64AsF64(0xbfe8_5efd_1000_0000n), reinterpretU64AsF64(0xbfe8_5ef8_9000_0000n)] }, // ~-0.7615... + { input: 0, expected: [reinterpretU64AsF64(0xbe8c_0000_b000_0000n), reinterpretU64AsF64(0x3e8c_0000_b000_0000n)] }, // ~0 + { input: 1, expected: [reinterpretU64AsF64(0x3fe8_5ef8_9000_0000n), reinterpretU64AsF64(0x3fe8_5efd_1000_0000n)] }, // ~0.7615... + ] as ScalarToIntervalCase[], + f16: [ + { input: -1, expected: [reinterpretU64AsF64(0xbfe8_9600_0000_0000n), reinterpretU64AsF64(0xbfe8_2e00_0000_0000n)] }, // ~-0.7615... + { input: 0, expected: [reinterpretU64AsF64(0xbf48_0e00_0000_0000n), reinterpretU64AsF64(0x3f48_0e00_0000_0000n)] }, // ~0 + { input: 1, expected: [reinterpretU64AsF64(0x3fe8_2e00_0000_0000n), reinterpretU64AsF64(0x3fe8_9600_0000_0000n)] }, // ~0.7615... + ] as ScalarToIntervalCase[], +} as const; + +g.test('tanhInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kTanhIntervalCases[p.trait], + + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.negative.min, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: kUnboundedBounds }, + { input: constants.positive.infinity, expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.tanhInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.tanhInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('truncInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Normals + { input: 0, expected: 0 }, + { input: 0.1, expected: 0 }, + { input: 0.9, expected: 0 }, + { input: 1.0, expected: 1 }, + { input: 1.1, expected: 1 }, + { input: 1.9, expected: 1 }, + { input: -0.1, expected: 0 }, + { input: -0.9, expected: 0 }, + { input: -1.0, expected: -1 }, + { input: -1.1, expected: -1 }, + { input: -1.9, expected: -1 }, + + // Subnormals + { input: constants.positive.subnormal.max, expected: 0 }, + { input: constants.positive.subnormal.min, expected: 0 }, + { input: constants.negative.subnormal.min, expected: 0 }, + { input: constants.negative.subnormal.max, expected: 0 }, + + // Edge cases + { input: constants.positive.infinity, expected: kUnboundedBounds }, + { input: constants.negative.infinity, expected: kUnboundedBounds }, + { input: constants.positive.max, expected: constants.positive.max }, + { input: constants.positive.min, expected: 0 }, + { input: constants.negative.min, expected: constants.negative.min }, + { input: constants.negative.max, expected: 0 }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.truncInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `FP.${t.params.trait}.truncInterval(${t.params.input}) returned ${got}. Expected ${expected}` + ); + }); + +interface ScalarPairToIntervalCase { + // input is a pair of independent values, not a range, so should not be + // converted to a FPInterval. + input: [number, number]; + expected: number | IntervalBounds; +} + +// prettier-ignore +const kAdditionInterval64BitsNormalCases = { + f32: [ + // 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD, -0.1 falls between f32 0xBDCCCCCD and 0xBDCCCCCC + // f32 0x3DCCCCCC+0x3DCCCCCC=0x3E4CCCCC, 0x3DCCCCCD+0x3DCCCCCD=0x3E4CCCCD + { input: [0.1, 0.1], expected: [reinterpretU32AsF32(0x3e4ccccc), reinterpretU32AsF32(0x3e4ccccd)] }, // ~0.2 + // f32 0xBDCCCCCD+0xBDCCCCCD=0xBE4CCCCD, 0xBDCCCCCC+0xBDCCCCCC=0xBE4CCCCD + { input: [-0.1, -0.1], expected: [reinterpretU32AsF32(0xbe4ccccd), reinterpretU32AsF32(0xbe4ccccc)] }, // ~-0.2 + // 0.1+(-0.1) expect f32 interval [0x3DCCCCCC+0xBDCCCCCD, 0x3DCCCCCD+0xBDCCCCCC] + { input: [0.1, -0.1], expected: [reinterpretU32AsF32(0x3dcccccc)+reinterpretU32AsF32(0xbdcccccd), reinterpretU32AsF32(0x3dcccccd)+reinterpretU32AsF32(0xbdcccccc)] }, // ~0.0 + // -0.1+0.1 expect f32 interval [0xBDCCCCCD+0x3DCCCCCC, 0xBDCCCCCC+0x3DCCCCCD] + { input: [-0.1, 0.1], expected: [reinterpretU32AsF32(0xbdcccccd)+reinterpretU32AsF32(0x3dcccccc), reinterpretU32AsF32(0xbdcccccc)+reinterpretU32AsF32(0x3dcccccd)] }, // ~0.0 + ] as ScalarPairToIntervalCase[], + f16: [ + // 0.1 falls between f16 0x2E66 and 0x2E67, -0.1 falls between f16 0xAE67 and 0xAE66 + // f16 0x2E66+0x2E66=0x3266, 0x2E67+0x2E67=0x3267 + { input: [0.1, 0.1], expected: [reinterpretU16AsF16(0x3266), reinterpretU16AsF16(0x3267)] }, // ~0.2 + // f16 0xAE67+0xAE67=0xB267, 0xAE66+0xAE66=0xB266 + { input: [-0.1, -0.1], expected: [reinterpretU16AsF16(0xb267), reinterpretU16AsF16(0xb266)] }, // ~-0.2 + // 0.1+(-0.1) expect f16 interval [0x2E66+0xAE67, 0x2E67+0xAE66] + { input: [0.1, -0.1], expected: [reinterpretU16AsF16(0x2e66)+reinterpretU16AsF16(0xae67), reinterpretU16AsF16(0x2e67)+reinterpretU16AsF16(0xae66)] }, // ~0.0 + // -0.1+0.1 expect f16 interval [0xAE67+0x2E66, 0xAE66+0x2E67] + { input: [-0.1, 0.1], expected: [reinterpretU16AsF16(0xae67)+reinterpretU16AsF16(0x2e66), reinterpretU16AsF16(0xae66)+reinterpretU16AsF16(0x2e67)] }, // ~0.0 + ] as ScalarPairToIntervalCase[], + abstract: [ + // 0.1 isn't exactly representable in f64, but will be quantized to an + // exact value when storing to a 'number' (0x3FB999999999999A). + // This is why below the expectations are not intervals. + // f64 0x3FB999999999999A+0x3FB999999999999A = 0x3FC999999999999A + { input: [0.1, 0.1], expected: reinterpretU64AsF64(0x3FC999999999999An) }, // ~0.2 + // f64 0xBFB999999999999A+0xBFB999999999999A = 0xBFC999999999999A + { input: [-0.1, -0.1], expected: reinterpretU64AsF64(0xBFC999999999999An) }, // ~-0.2 + { input: [0.1, -0.1], expected: 0 }, + { input: [-0.1, 0.1], expected: 0 }, + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('additionInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Representable normals + { input: [0, 0], expected: 0 }, + { input: [1, 0], expected: 1 }, + { input: [0, 1], expected: 1 }, + { input: [-1, 0], expected: -1 }, + { input: [0, -1], expected: -1 }, + { input: [1, 1], expected: 2 }, + { input: [1, -1], expected: 0 }, + { input: [-1, 1], expected: 0 }, + { input: [-1, -1], expected: -2 }, + + // 0.1 should be correctly rounded + { input: [0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + { input: [0, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + // -0.1 should be correctly rounded + { input: [-0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, + { input: [0, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, + + // 64-bit normals that can not be exactly represented + ...kAdditionInterval64BitsNormalCases[p.trait], + + // Subnormals + { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, + { input: [0, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, + { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, + { input: [0, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, + { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, + { input: [0, constants.negative.subnormal.min], expected: [constants.negative.subnormal.min, 0] }, + + // Infinities + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.additionInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.additionInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +// Cases for Atan2Interval. The positive x & y quadrant is tested in more detail, and the other +// quadrants are spot checked that values are pointing in the right direction. +// Note: atan2's parameters are labelled (y, x) instead of (x, y) +// prettier-ignore +const kAtan2IntervalCases = { + // atan has 4096ULP error boundary for f32. + f32: [ + // positive y, positive x + // √3 rounded to f32 0x3FDDB3D7, atan2(1, 0x3FDDB3D7)=0.52359877749051820266056630237827 ~ pi/6 rounded to f32 0x3F060A91 or 0x3F060A92, + // kValue.f32.positive.pi.sixth is 0x3F060A92. + { input: [1, reinterpretU32AsF32(0x3fddb3d7)], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.sixth, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.sixth, 4096)] }, + // atan2(1, 1)=0.78539816339744830961566084581988 ~ pi/4 rounded to f32 0x3F490FDA or 0x3F490FDB, + // kValue.f32.positive.pi.quarter is 0x3F490FDB. + { input: [1, 1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.quarter, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.quarter, 4096)] }, + // √3 rounded to f32 0x3FDDB3D7, atan2(0x3FDDB3D7, 1) = 1.0471975493043784165707553892615 ~ pi/3 rounded to f32 0x3F860A91 or 0x3F860A92, + // kValue.f32.positive.pi.third is 0x3F860A92. + { input: [reinterpretU32AsF32(0x3fddb3d7), 1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.third, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.third, 4096)] }, + + // positive y, negative x + // atan2(1, -1)=pi*3/4=2.3561944901923449288469825374591 rounded to f32 0x4016CBE3 or 0x4016CBE4, + // kValue.f32.positive.pi.three_quarters is 0x4016CBE4. + { input: [1, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.three_quarters, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.three_quarters, 4096)] }, + + // negative y, negative x + // atan2(-1, -1)=-pi*3/4=-2.3561944901923449288469825374591 rounded to f32 0xC016CBE4 or 0xC016CBE3, + // kValue.f32.negative.pi.three_quarters is 0xC016CBE4. + { input: [-1, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.negative.pi.three_quarters, 4096), kPlusNULPFunctions['f32'](kValue.f32.negative.pi.three_quarters, 4097)] }, + + // negative y, positive x + // atan2(-1, 1)=-pi/4=-0.78539816339744830961566084581988 rounded to f32 0xBF490FDB or 0xBF490FDA, + // kValue.f32.negative.pi.quarter is 0xBF490FDB. + { input: [-1, 1], expected: [kMinusNULPFunctions['f32'](kValue.f32.negative.pi.quarter, 4096), kPlusNULPFunctions['f32'](kValue.f32.negative.pi.quarter, 4097)] }, + + // When y/x ~ 0, test that ULP applied to result of atan2, not the intermediate y/x value. + // y/x ~ 0, y<0, x<0, atan2(y,x) ~ -pi rounded to f32 0xC0490FDB or 0xC0490FDA, + // kValue.f32.negative.pi.whole is 0xC0490FDB. + {input: [kValue.f32.negative.max, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.negative.pi.whole, 4096), kPlusNULPFunctions['f32'](kValue.f32.negative.pi.whole, 4097)] }, + // y/x ~ 0, y>0, x<0, atan2(y,x) ~ pi rounded to f32 0x40490FDA or 0x40490FDB, + // kValue.f32.positive.pi.whole is 0x40490FDB. + {input: [kValue.f32.positive.min, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.whole, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.whole, 4096)] }, + ] as ScalarPairToIntervalCase[], + // atan has 5ULP error boundary for f16. + f16: [ + // positive y, positive x + // √3 rounded to f16 0x3EED, atan2(1, 0x3EED)=0.52375018906301191131992842392268 ~ pi/6 rounded to f16 0x3830 or 0x3831, + // kValue.f16.positive.pi.sixth is 0x3830. + { input: [1, reinterpretU16AsF16(0x3eed)], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.sixth, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.sixth, 6)] }, + // atan2(1, 1)=0.78539816339744830961566084581988 ~ pi/4 rounded to f16 0x3A48 or 0x3A49, + // kValue.f16.positive.pi.quarter is 0x3A48. + { input: [1, 1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.quarter, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.quarter, 6)] }, + // √3 rounded to f16 0x3EED, atan2(0x3EED, 1) = 1.0470461377318847079113932677171 ~ pi/3 rounded to f16 0x3C30 or 0x3C31, + // kValue.f16.positive.pi.third is 0x3C30. + { input: [reinterpretU16AsF16(0x3eed), 1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.third, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.third, 6)] }, + + // positive y, negative x + // atan2(1, -1)=pi*3/4=2.3561944901923449288469825374591 rounded to f16 0x40B6 or 0x40B7, + // kValue.f16.positive.pi.three_quarters is 0x40B6. + { input: [1, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.three_quarters, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.three_quarters, 6)] }, + + // negative y, negative x + // atan2(-1, -1)=-pi*3/4=-2.3561944901923449288469825374591 rounded to f16 0xC0B7 or 0xC0B6, + // kValue.f16.negative.pi.three_quarters is 0xC0B6. + { input: [-1, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.negative.pi.three_quarters, 6), kPlusNULPFunctions['f16'](kValue.f16.negative.pi.three_quarters, 5)] }, + + // negative y, positive x + // atan2(-1, 1)=-pi/4=-0.78539816339744830961566084581988 rounded to f16 0xBA49 or 0xBA48, + // kValue.f16.negative.pi.quarter is 0xBA48. + { input: [-1, 1], expected: [kMinusNULPFunctions['f16'](kValue.f16.negative.pi.quarter, 6), kPlusNULPFunctions['f16'](kValue.f16.negative.pi.quarter, 5)] }, + + // When y/x ~ 0, test that ULP applied to result of atan2, not the intermediate y/x value. + // y/x ~ 0, y<0, x<0, atan2(y,x) ~ -pi rounded to f16 0xC249 or 0xC248, + // kValue.f16.negative.pi.whole is 0xC248. + {input: [kValue.f16.negative.max, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.negative.pi.whole, 6), kPlusNULPFunctions['f16'](kValue.f16.negative.pi.whole, 5)] }, + // y/x ~ 0, y>0, x<0, atan2(y,x) ~ pi rounded to f16 0x4248 or 0x4249, + // kValue.f16.positive.pi.whole is 0x4248. + {input: [kValue.f16.positive.min, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.whole, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.whole, 6)] }, + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('atan2Interval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + ...kAtan2IntervalCases[p.trait], + + // Cases that y out of bound. + // positive y, positive x + { input: [Number.POSITIVE_INFINITY, 1], expected: kUnboundedBounds }, + // positive y, negative x + { input: [Number.POSITIVE_INFINITY, -1], expected: kUnboundedBounds }, + // negative y, negative x + { input: [Number.NEGATIVE_INFINITY, -1], expected: kUnboundedBounds }, + // negative y, positive x + { input: [Number.NEGATIVE_INFINITY, 1], expected: kUnboundedBounds }, + + // Discontinuity @ origin (0,0) + { input: [0, 0], expected: kUnboundedBounds }, + { input: [0, constants.positive.subnormal.max], expected: kUnboundedBounds }, + { input: [0, constants.negative.subnormal.min], expected: kUnboundedBounds }, + { input: [0, constants.positive.min], expected: kUnboundedBounds }, + { input: [0, constants.negative.max], expected: kUnboundedBounds }, + { input: [0, constants.positive.max], expected: kUnboundedBounds }, + { input: [0, constants.negative.min], expected: kUnboundedBounds }, + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [0, 1], expected: kUnboundedBounds }, + { input: [constants.positive.subnormal.max, 1], expected: kUnboundedBounds }, + { input: [constants.negative.subnormal.min, 1], expected: kUnboundedBounds }, + + // Very large |x| values should cause kUnboundedBounds to be returned, due to the restrictions on division + { input: [1, constants.positive.max], expected: kUnboundedBounds }, + { input: [1, constants.positive.nearest_max], expected: kUnboundedBounds }, + { input: [1, constants.negative.min], expected: kUnboundedBounds }, + { input: [1, constants.negative.nearest_min], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const [y, x] = t.params.input; + const expected = trait.toInterval(t.params.expected); + const got = trait.atan2Interval(y, x); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.atan2Interval(${y}, ${x}) returned ${got}]. Expected ${expected}` + ); + }); + +g.test('distanceIntervalScalar') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + { input: [1.0, 0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [0.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [-0.0, -1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [0.0, -1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [0.1, 0], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + { input: [0, 0.1], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + { input: [-0.1, 0], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + { input: [0, -0.1], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + { input: [10.0, 0], expected: kRootSumSquareExpectionInterval[p.trait]['[10]'] }, // ~10 + { input: [0, 10.0], expected: kRootSumSquareExpectionInterval[p.trait]['[10]'] }, // ~10 + { input: [-10.0, 0], expected: kRootSumSquareExpectionInterval[p.trait]['[10]'] }, // ~10 + { input: [0, -10.0], expected: kRootSumSquareExpectionInterval[p.trait]['[10]'] }, // ~10 + + // distance(x, y), where x - y = 0 has an acceptance interval of kUnboundedBounds, + // because distance(x, y) = length(x - y), and length(0) = kUnboundedBounds + { input: [0, 0], expected: kUnboundedBounds }, + { input: [1.0, 1.0], expected: kUnboundedBounds }, + { input: [-1.0, -1.0], expected: kUnboundedBounds }, + + // Subnormal Cases + { input: [constants.negative.subnormal.min, 0], expected: kUnboundedBounds }, + { input: [constants.negative.subnormal.max, 0], expected: kUnboundedBounds }, + { input: [constants.positive.subnormal.min, 0], expected: kUnboundedBounds }, + { input: [constants.positive.subnormal.max, 0], expected: kUnboundedBounds }, + + // Edge cases + { input: [constants.positive.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.min, 0], expected: kUnboundedBounds }, + { input: [constants.negative.max, 0], expected: kUnboundedBounds }, + { input: [constants.positive.min, 0], expected: kUnboundedBounds }, + { input: [constants.positive.max, 0], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.distanceInterval(...t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.distanceInterval(${t.params.input[0]}, ${t.params.input[1]}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kDivisionInterval64BitsNormalCases = { + f32: [ + // Zero divided by any non-zero finite value results in zero. + { input: [0, 0.1], expected: 0 }, + { input: [0, -0.1], expected: 0 }, + // 0.1 rounded to f32 0x3DCCCCCC or 0x3DCCCCCD, + // 1.0/0x3DCCCCCD = 9.9999998509883902204460179966303 rounded to f32 0x411FFFFF or 0x41200000, + // 1.0/0x3DCCCCCC = 10.000000596046483527138934924167 rounded to f32 0x41200000 or 0x41200001. + { input: [1, 0.1], expected: [reinterpretU32AsF32(0x411fffff), reinterpretU32AsF32(0x41200001)] }, // ~10.0 + // The same for -1/-0.1 + { input: [-1, -0.1], expected: [reinterpretU32AsF32(0x411fffff), reinterpretU32AsF32(0x41200001)] }, // ~10.0 + // -10.000000596046483527138934924167 rounded to f32 0xC1200001 or 0xC1200000, + // -9.9999998509883902204460179966303 rounded to f32 0xC1200000 or 0xC11FFFFF. + { input: [-1, 0.1], expected: [reinterpretU32AsF32(0xc1200001), reinterpretU32AsF32(0xc11fffff)] }, // ~-10.0 + { input: [1, -0.1], expected: [reinterpretU32AsF32(0xc1200001), reinterpretU32AsF32(0xc11fffff)] }, // ~-10.0 + // Cases that expected interval larger than +-1ULP. + // 0.000001 rounded to f32 0x358637BD or 0x358637BE, + // 1.0/0x358637BE = 999999.88883793195700674522548684 rounded to f32 0x497423FE or 0x497423FF, + // 1.0/0x358637BD = 1000000.0025247573063743994399971 rounded to f32 0x49742400 or 0x49742401. + { input: [1, 0.000001], expected: [reinterpretU32AsF32(0x497423fe), reinterpretU32AsF32(0x49742401)] }, // ~1000000.0 + { input: [1, -0.000001], expected: [reinterpretU32AsF32(0xc9742401), reinterpretU32AsF32(0xc97423fe)] }, // ~-1000000.0 + ] as ScalarPairToIntervalCase[], + f16: [ + // Zero divided by any non-zero finite value results in zero. + { input: [0, 0.1], expected: 0 }, + { input: [0, -0.1], expected: 0 }, + // 0.1 rounded to f16 0x2E66 or 0x2E67, + // 1.0/0x2E67 = 9.9963392312385600976205003050641 rounded to f16 0x48FF or 0x4900, + // 1.0/0x2E66 = 10.002442002442002442002442002442 rounded to f16 0x4900 or 0x4901. + { input: [1, 0.1], expected: [reinterpretU16AsF16(0x48ff), reinterpretU16AsF16(0x4901)] }, // ~10.0 + // The same for -1/-0.1 + { input: [-1, -0.1], expected: [reinterpretU16AsF16(0x48ff), reinterpretU16AsF16(0x4901)] }, // ~10.0 + // -10.002442002442002442002442002442 rounded to f16 0xC901 or 0xC900, + // -9.9963392312385600976205003050641 rounded to f16 0xC900 or 0xC8FF. + { input: [-1, 0.1], expected: [reinterpretU16AsF16(0xc901), reinterpretU16AsF16(0xc8ff)] }, // ~-10.0 + { input: [1, -0.1], expected: [reinterpretU16AsF16(0xc901), reinterpretU16AsF16(0xc8ff)] }, // ~-10.0 + // Cases that expected interval larger than +-1ULP. + // 0.001 rounded to f16 0x1418 or 0x1419, + // 1.0/0x1419 = 999.59580552907535977846384072716 rounded to f16 0x63CF or 0x63D0, + // 1.0/0x1418 = 1000.5496183206106870229007633588 rounded to f16 0x63D1 or 0x63D2. + { input: [1, 0.001], expected: [reinterpretU16AsF16(0x63cf), reinterpretU16AsF16(0x63d2)] }, // ~1000.0 + { input: [1, -0.001], expected: [reinterpretU16AsF16(0xe3d2), reinterpretU16AsF16(0xe3cf)] }, // ~-1000.0 + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('divisionInterval') + .params(u => + u + .combine('trait', ['abstract', 'f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + // This is a ULP based interval, so abstract should behave like f32, so + // swizzling the trait as needed. + const trait = p.trait === 'abstract' ? 'f32' : p.trait; + const fp = FP[trait]; + const constants = fp.constants(); + // prettier-ignore + return [ + // Representable normals + { input: [0, 1], expected: 0 }, + { input: [0, -1], expected: 0 }, + { input: [1, 1], expected: 1 }, + { input: [1, -1], expected: -1 }, + { input: [-1, 1], expected: -1 }, + { input: [-1, -1], expected: 1 }, + { input: [4, 2], expected: 2 }, + { input: [-4, 2], expected: -2 }, + { input: [4, -2], expected: -2 }, + { input: [-4, -2], expected: 2 }, + + // 64-bit normals that can not be exactly represented + ...kDivisionInterval64BitsNormalCases[trait], + + // Denominator out of range + { input: [1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [1, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [1, constants.positive.max], expected: kUnboundedBounds }, + { input: [1, constants.negative.min], expected: kUnboundedBounds }, + { input: [1, 0], expected: kUnboundedBounds }, + { input: [1, constants.positive.subnormal.max], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + // This is a ULP based interval, so abstract should behave like f32, so + // swizzling the trait as needed for calculating the expected result. + const trait = t.params.trait === 'abstract' ? 'f32' : t.params.trait; + const fp = FP[trait]; + + const error = (n: number): number => { + return 2.5 * fp.oneULP(n); + }; + + const [x, y] = t.params.input; + + // Do not swizzle here, so the correct implementation under test is called. + const expected = FP[t.params.trait].toInterval(applyError(t.params.expected, error)); + const got = FP[t.params.trait].divisionInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.divisionInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +const kLdexpIntervalCases = { + f32: [ + // 64-bit normals + { input: [1.0000000001, 1], expected: [2, kPlusNULPFunctions['f32'](2, 2)] }, // ~2, additional ULP error due to first param not being f32 precise + { input: [-1.0000000001, 1], expected: [kMinusNULPFunctions['f32'](-2, 2), -2] }, // ~-2, additional ULP error due to first param not being f32 precise + // Edge Cases + // f32 0b0_01111111_11111111111111111111111 = 1.9999998807907104, + // 1.9999998807907104 * 2 ** 127 = f32.positive.max + { input: [1.9999998807907104, 127], expected: kValue.f32.positive.max }, + // f32.positive.min = 1 * 2 ** -126 + { input: [1, -126], expected: kValue.f32.positive.min }, + // f32.positive.subnormal.max = 0.9999998807907104 * 2 ** -126 + { input: [0.9999998807907104, -126], expected: [0, kValue.f32.positive.subnormal.max] }, + // f32.positive.subnormal.min = 1.1920928955078125e-07 * 2 ** -126 + { input: [1.1920928955078125e-7, -126], expected: [0, kValue.f32.positive.subnormal.min] }, + { input: [-1.1920928955078125e-7, -126], expected: [kValue.f32.negative.subnormal.max, 0] }, + { input: [-0.9999998807907104, -126], expected: [kValue.f32.negative.subnormal.min, 0] }, + { input: [-1, -126], expected: kValue.f32.negative.max }, + { input: [-1.9999998807907104, 127], expected: kValue.f32.negative.min }, + // e2 + bias <= 0, expect correctly rounded intervals. + { input: [2 ** 120, -130], expected: 2 ** -10 }, + // Out of Bounds + { input: [1, 128], expected: kUnboundedBounds }, + { input: [-1, 128], expected: kUnboundedBounds }, + { input: [100, 126], expected: kUnboundedBounds }, + { input: [-100, 126], expected: kUnboundedBounds }, + { input: [2 ** 100, 100], expected: kUnboundedBounds }, + ] as ScalarPairToIntervalCase[], + f16: [ + // 64-bit normals + { input: [1.0000000001, 1], expected: [2, kPlusNULPFunctions['f16'](2, 2)] }, // ~2, additional ULP error due to first param not being f16 precise + { input: [-1.0000000001, 1], expected: [kMinusNULPFunctions['f16'](-2, 2), -2] }, // ~-2, additional ULP error due to first param not being f16 precise + // Edge Cases + // f16 0b0_01111_1111111111 = 1.9990234375, 1.9990234375 * 2 ** 15 = f16.positive.max + { input: [1.9990234375, 15], expected: kValue.f16.positive.max }, + // f16.positive.min = 1 * 2 ** -14 + { input: [1, -14], expected: kValue.f16.positive.min }, + // f16.positive.subnormal.max = 0.9990234375 * 2 ** -14 + { input: [0.9990234375, -14], expected: [0, kValue.f16.positive.subnormal.max] }, + // f16.positive.subnormal.min = 1 * 2 ** -10 * 2 ** -14 = 0.0009765625 * 2 ** -14 + { input: [0.0009765625, -14], expected: [0, kValue.f16.positive.subnormal.min] }, + { input: [-0.0009765625, -14], expected: [kValue.f16.negative.subnormal.max, 0] }, + { input: [-0.9990234375, -14], expected: [kValue.f16.negative.subnormal.min, 0] }, + { input: [-1, -14], expected: kValue.f16.negative.max }, + { input: [-1.9990234375, 15], expected: kValue.f16.negative.min }, + // e2 + bias <= 0, expect correctly rounded intervals. + { input: [2 ** 12, -18], expected: 2 ** -6 }, + // Out of Bounds + { input: [1, 16], expected: kUnboundedBounds }, + { input: [-1, 16], expected: kUnboundedBounds }, + { input: [100, 14], expected: kUnboundedBounds }, + { input: [-100, 14], expected: kUnboundedBounds }, + { input: [2 ** 10, 10], expected: kUnboundedBounds }, + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('ldexpInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // always exactly represeantable cases + { input: [0, 0], expected: 0 }, + { input: [0, 1], expected: 0 }, + { input: [0, -1], expected: 0 }, + { input: [1, 1], expected: 2 }, + { input: [1, -1], expected: 0.5 }, + { input: [-1, 1], expected: -2 }, + { input: [-1, -1], expected: -0.5 }, + + ...kLdexpIntervalCases[p.trait], + + // Extremely negative e2, any float value should be scale to 0.0 as the ground truth + // f64 e1 * 2 ** e2 would be 0.0 for e2 = -2147483648. + { input: [constants.positive.max, kValue.i32.negative.min], expected: 0 }, + { input: [constants.negative.min, kValue.i32.negative.min], expected: 0 }, + // Out of Bounds + { input: [constants.positive.max, kValue.i32.positive.max], expected: kUnboundedBounds }, + { input: [constants.negative.min, kValue.i32.positive.max], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.ldexpInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.ldexpInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('maxInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Representable normals + { input: [0, 0], expected: 0 }, + { input: [1, 0], expected: 1 }, + { input: [0, 1], expected: 1 }, + { input: [-1, 0], expected: 0 }, + { input: [0, -1], expected: 0 }, + { input: [1, 1], expected: 1 }, + { input: [1, -1], expected: 1 }, + { input: [-1, 1], expected: 1 }, + { input: [-1, -1], expected: -1 }, + + // 0.1 and -0.1 should be correctly rounded + { input: [-0.1, 0], expected: 0 }, + { input: [0, -0.1], expected: 0 }, + { input: [0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: [0, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: [0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: [0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: [-0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: [-0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + + // Representable subnormals + { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, + { input: [0, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, + { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, + { input: [0, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, + { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, + { input: [0, constants.negative.subnormal.min], expected: [constants.negative.subnormal.min, 0] }, + { input: [1, constants.positive.subnormal.max], expected: 1 }, + { input: [constants.negative.subnormal.min, constants.positive.subnormal.max], expected: [constants.negative.subnormal.min, constants.positive.subnormal.max] }, + + // Infinities + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const [x, y] = t.params.input; + const expected = trait.toInterval(t.params.expected); + const got = trait.maxInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.maxInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('minInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Representable normals + { input: [0, 0], expected: 0 }, + { input: [1, 0], expected: 0 }, + { input: [0, 1], expected: 0 }, + { input: [-1, 0], expected: -1 }, + { input: [0, -1], expected: -1 }, + { input: [1, 1], expected: 1 }, + { input: [1, -1], expected: -1 }, + { input: [-1, 1], expected: -1 }, + { input: [-1, -1], expected: -1 }, + + // 64-bit normals that not exactly representable + { input: [0.1, 0], expected: 0 }, + { input: [0, 0.1], expected: 0 }, + { input: [-0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + { input: [0, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + { input: [0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 + { input: [0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + { input: [-0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + { input: [-0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 + + // Representable subnormals + { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, + { input: [0, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, + { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, + { input: [0, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, + { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, + { input: [0, constants.negative.subnormal.min], expected: [constants.negative.subnormal.min, 0] }, + { input: [-1, constants.positive.subnormal.max], expected: -1 }, + { input: [constants.negative.subnormal.min, constants.positive.subnormal.max], expected: [constants.negative.subnormal.min, constants.positive.subnormal.max] }, + + // Infinities + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const [x, y] = t.params.input; + const expected = trait.toInterval(t.params.expected); + const got = trait.minInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.minInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kMultiplicationInterval64BitsNormalCases = { + f32: [ + // 0.1*0.1, 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD, + // min result 0x3DCCCCCC*0x3DCCCCCC=0.00999999880790713952713681734167 rounded to f32 0x3C23D708 or 0x3C23D709, + // max result 0x3DCCCCCD*0x3DCCCCCD=0.01000000029802322622044605108385 rounded to f32 0x3C23D70A or 0x3C23D70B. + { input: [0.1, 0.1], expected: [reinterpretU32AsF32(0x3c23d708), reinterpretU32AsF32(0x3c23d70b)] }, // ~0.01 + { input: [-0.1, -0.1], expected: [reinterpretU32AsF32(0x3c23d708), reinterpretU32AsF32(0x3c23d70b)] }, // ~0.01 + // -0.01000000029802322622044605108385 rounded to f32 0xBC23D70B or 0xBC23D70A, + // -0.00999999880790713952713681734167 rounded to f32 0xBC23D709 or 0xBC23D708. + { input: [0.1, -0.1], expected: [reinterpretU32AsF32(0xbc23d70b), reinterpretU32AsF32(0xbc23d708)] }, // ~-0.01 + { input: [-0.1, 0.1], expected: [reinterpretU32AsF32(0xbc23d70b), reinterpretU32AsF32(0xbc23d708)] }, // ~-0.01 + ] as ScalarPairToIntervalCase[], + f16: [ + // 0.1*0.1, 0.1 falls between f16 0x2E66 and 0x2E67, + // min result 0x2E66*0x2E66=0.00999511778354644775390625 rounded to f16 0x211E or 0x211F, + // max result 0x2E67*0x2E67=0.0100073255598545074462890625 rounded to f16 0x211F or 0x2120. + { input: [0.1, 0.1], expected: [reinterpretU16AsF16(0x211e), reinterpretU16AsF16(0x2120)] }, // ~0.01 + { input: [-0.1, -0.1], expected: [reinterpretU16AsF16(0x211e), reinterpretU16AsF16(0x2120)] }, // ~0.01 + // -0.0100073255598545074462890625 rounded to f16 0xA120 or 0xA11F, + // -0.00999511778354644775390625 rounded to f16 0xA11F or 0xA11E. + { input: [0.1, -0.1], expected: [reinterpretU16AsF16(0xa120), reinterpretU16AsF16(0xa11e)] }, // ~-0.01 + { input: [-0.1, 0.1], expected: [reinterpretU16AsF16(0xa120), reinterpretU16AsF16(0xa11e)] }, // ~-0.01 + ] as ScalarPairToIntervalCase[], + abstract: [ + // 0.1 isn't exactly representable in f64, but will be quantized to an + // exact value when storing to a 'number' (0x3FB999999999999A). + // This is why below the expectations are not intervals. + // f64 0.1 * 0.1 = 0x3f847ae147ae147c, + { input: [0.1, 0.1], expected: reinterpretU64AsF64(0x3f847ae147ae147cn) }, // ~0.01 + { input: [-0.1, -0.1], expected: reinterpretU64AsF64(0x3f847ae147ae147cn) }, // ~0.01 + { input: [0.1, -0.1], expected: reinterpretU64AsF64(0xbf847ae147ae147cn) }, // ~-0.01 + { input: [-0.1, 0.1], expected: reinterpretU64AsF64(0xbf847ae147ae147cn) }, // ~-0.01 + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('multiplicationInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Representable normals + { input: [0, 0], expected: 0 }, + { input: [1, 0], expected: 0 }, + { input: [0, 1], expected: 0 }, + { input: [-1, 0], expected: 0 }, + { input: [0, -1], expected: 0 }, + { input: [1, 1], expected: 1 }, + { input: [1, -1], expected: -1 }, + { input: [-1, 1], expected: -1 }, + { input: [-1, -1], expected: 1 }, + { input: [2, 1], expected: 2 }, + { input: [1, -2], expected: -2 }, + { input: [-2, 1], expected: -2 }, + { input: [-2, -1], expected: 2 }, + { input: [2, 2], expected: 4 }, + { input: [2, -2], expected: -4 }, + { input: [-2, 2], expected: -4 }, + { input: [-2, -2], expected: 4 }, + + // 64-bit normals that can not be exactly represented + // Finite values multiply zero result in zero + { input: [0.1, 0], expected: 0 }, + { input: [0, 0.1], expected: 0 }, + { input: [-0.1, 0], expected: 0 }, + { input: [0, -0.1], expected: 0 }, + // Finite value multiply +/-1.0 + { input: [0.1, 1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + { input: [-1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + { input: [-0.1, 1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, + { input: [-1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, + // Other cases + ...kMultiplicationInterval64BitsNormalCases[p.trait], + + // Infinities + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [-1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [1, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [-1, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + + // Edges + { input: [constants.positive.max, constants.positive.max], expected: kUnboundedBounds }, + { input: [constants.negative.min, constants.negative.min], expected: kUnboundedBounds }, + { input: [constants.positive.max, constants.negative.min], expected: kUnboundedBounds }, + { input: [constants.negative.min, constants.positive.max], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.multiplicationInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.multiplicationInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kPowIntervalCases = { + f32 : [ + { input: [1, 0], expected: [kMinusNULPFunctions['f32'](1, 3), reinterpretU64AsF64(0x3ff0_0000_3000_0000n)] }, // ~1 + { input: [2, 0], expected: [kMinusNULPFunctions['f32'](1, 3), reinterpretU64AsF64(0x3ff0_0000_3000_0000n)] }, // ~1 + { input: [kValue.f32.positive.max, 0], expected: [kMinusNULPFunctions['f32'](1, 3), reinterpretU64AsF64(0x3ff0_0000_3000_0000n)] }, // ~1 + { input: [1, 1], expected: [reinterpretU64AsF64(0x3fef_fffe_dfff_fe00n), reinterpretU64AsF64(0x3ff0_0000_c000_0200n)] }, // ~1 + { input: [1, 100], expected: [reinterpretU64AsF64(0x3fef_ffba_3fff_3800n), reinterpretU64AsF64(0x3ff0_0023_2000_c800n)] }, // ~1 + { input: [2, 1], expected: [reinterpretU64AsF64(0x3fff_fffe_a000_0200n), reinterpretU64AsF64(0x4000_0001_0000_0200n)] }, // ~2 + { input: [2, 2], expected: [reinterpretU64AsF64(0x400f_fffd_a000_0400n), reinterpretU64AsF64(0x4010_0001_a000_0400n)] }, // ~4 + { input: [10, 10], expected: [reinterpretU64AsF64(0x4202_a04f_51f7_7000n), reinterpretU64AsF64(0x4202_a070_ee08_e000n)] }, // ~10000000000 + { input: [10, 1], expected: [reinterpretU64AsF64(0x4023_fffe_0b65_8b00n), reinterpretU64AsF64(0x4024_0002_149a_7c00n)] }, // ~10 + ] as ScalarPairToIntervalCase[], + f16 : [ + { input: [1, 0], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0200_0000_0000n)] }, // ~1 + { input: [2, 0], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0200_0000_0000n)] }, // ~1 + { input: [kValue.f16.positive.max, 0], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0200_0000_0000n)] }, // ~1 + { input: [1, 1], expected: [reinterpretU64AsF64(0x3fef_cbf0_0000_0000n), reinterpretU64AsF64(0x3ff0_1c10_0000_0000n)] }, // ~1 + { input: [1, 100], expected: [reinterpretU64AsF64(0x3fe2_91c0_0000_0000n), reinterpretU64AsF64(0x3ffb_8a40_0000_0000n)] }, // ~1 + { input: [2, 1], expected: [reinterpretU64AsF64(0x3fff_c410_0000_0000n), reinterpretU64AsF64(0x4000_2410_0000_0000n)] }, // ~2 + { input: [2, 2], expected: [reinterpretU64AsF64(0x400f_9020_0000_0000n), reinterpretU64AsF64(0x4010_4420_0000_0000n)] }, // ~4 + { input: [5, 5], expected: [reinterpretU64AsF64(0x40a7_5f70_0000_0000n), reinterpretU64AsF64(0x40a9_5520_0000_0000n)] }, // ~3125 + { input: [10, 1], expected: [reinterpretU64AsF64(0x4023_c57c_0000_0000n), reinterpretU64AsF64(0x4024_36a0_0000_0000n)] }, // ~10 + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('powInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + { input: [-1, 0], expected: kUnboundedBounds }, + { input: [0, 0], expected: kUnboundedBounds }, + { input: [0, 1], expected: kUnboundedBounds }, + { input: [1, constants.positive.max], expected: kUnboundedBounds }, + { input: [constants.positive.max, 1], expected: kUnboundedBounds }, + + ...kPowIntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.powInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.powInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kRemainderCases = { + f32: [ + { input: [1, 0.1], expected: [reinterpretU32AsF32(0xb4000000), reinterpretU32AsF32(0x3dccccd8)] }, // ~[0, 0.1] + { input: [-1, 0.1], expected: [reinterpretU32AsF32(0xbdccccd8), reinterpretU32AsF32(0x34000000)] }, // ~[-0.1, 0] + { input: [1, -0.1], expected: [reinterpretU32AsF32(0xb4000000), reinterpretU32AsF32(0x3dccccd8)] }, // ~[0, 0.1] + { input: [-1, -0.1], expected: [reinterpretU32AsF32(0xbdccccd8), reinterpretU32AsF32(0x34000000)] }, // ~[-0.1, 0] + ] as ScalarPairToIntervalCase[], + f16: [ + { input: [1, 0.1], expected: [reinterpretU16AsF16(0x9400), reinterpretU16AsF16(0x2e70)] }, // ~[0, 0.1] + { input: [-1, 0.1], expected: [reinterpretU16AsF16(0xae70), reinterpretU16AsF16(0x1400)] }, // ~[-0.1, 0] + { input: [1, -0.1], expected: [reinterpretU16AsF16(0x9400), reinterpretU16AsF16(0x2e70)] }, // ~[0, 0.1] + { input: [-1, -0.1], expected: [reinterpretU16AsF16(0xae70), reinterpretU16AsF16(0x1400)] }, // ~[-0.1, 0] + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('remainderInterval') + .params(u => + u + .combine('trait', ['abstract', 'f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = kFPTraitForULP[p.trait]; + const constants = FP[trait].constants(); + + // prettier-ignore + return [ + ...kRemainderCases[trait], + // Normals + { input: [0, 1], expected: 0 }, + { input: [0, -1], expected: 0 }, + { input: [1, 1], expected: [0, 1] }, + { input: [1, -1], expected: [0, 1] }, + { input: [-1, 1], expected: [-1, 0] }, + { input: [-1, -1], expected: [-1, 0] }, + { input: [4, 2], expected: [0, 2] }, + { input: [-4, 2], expected: [-2, 0] }, + { input: [4, -2], expected: [0, 2] }, + { input: [-4, -2], expected: [-2, 0] }, + { input: [2, 4], expected: [2, 2] }, + { input: [-2, 4], expected: -2 }, + { input: [2, -4], expected: 2 }, + { input: [-2, -4], expected: [-2, -2] }, + { input: [0, 0.1], expected: 0 }, + { input: [0, -0.1], expected: 0 }, + { input: [8.5, 2], expected: 0.5 }, + { input: [1.125, 1], expected: 0.125 }, + + // Denominator out of range + { input: [1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [1, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [1, constants.positive.max], expected: kUnboundedBounds }, + { input: [1, constants.negative.min], expected: kUnboundedBounds }, + { input: [1, 0], expected: kUnboundedBounds }, + { input: [1, constants.positive.subnormal.max], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const [x, y] = t.params.input; + const expected = trait.toInterval(t.params.expected); + const got = trait.remainderInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.remainderInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('stepInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // 32-bit normals + { input: [0, 0], expected: 1 }, + { input: [1, 1], expected: 1 }, + { input: [0, 1], expected: 1 }, + { input: [1, 0], expected: 0 }, + { input: [-1, -1], expected: 1 }, + { input: [0, -1], expected: 0 }, + { input: [-1, 0], expected: 1 }, + { input: [-1, 1], expected: 1 }, + { input: [1, -1], expected: 0 }, + + // 64-bit normals + { input: [0.1, 0.1], expected: [0, 1] }, + { input: [0, 0.1], expected: 1 }, + { input: [0.1, 0], expected: 0 }, + { input: [0.1, 1], expected: 1 }, + { input: [1, 0.1], expected: 0 }, + { input: [-0.1, -0.1], expected: [0, 1] }, + { input: [0, -0.1], expected: 0 }, + { input: [-0.1, 0], expected: 1 }, + { input: [-0.1, -1], expected: 0 }, + { input: [-1, -0.1], expected: 1 }, + + // Subnormals + { input: [0, constants.positive.subnormal.max], expected: 1 }, + { input: [0, constants.positive.subnormal.min], expected: 1 }, + { input: [0, constants.negative.subnormal.max], expected: [0, 1] }, + { input: [0, constants.negative.subnormal.min], expected: [0, 1] }, + { input: [1, constants.positive.subnormal.max], expected: 0 }, + { input: [1, constants.positive.subnormal.min], expected: 0 }, + { input: [1, constants.negative.subnormal.max], expected: 0 }, + { input: [1, constants.negative.subnormal.min], expected: 0 }, + { input: [-1, constants.positive.subnormal.max], expected: 1 }, + { input: [-1, constants.positive.subnormal.min], expected: 1 }, + { input: [-1, constants.negative.subnormal.max], expected: 1 }, + { input: [-1, constants.negative.subnormal.min], expected: 1 }, + { input: [constants.positive.subnormal.max, 0], expected: [0, 1] }, + { input: [constants.positive.subnormal.min, 0], expected: [0, 1] }, + { input: [constants.negative.subnormal.max, 0], expected: 1 }, + { input: [constants.negative.subnormal.min, 0], expected: 1 }, + { input: [constants.positive.subnormal.max, 1], expected: 1 }, + { input: [constants.positive.subnormal.min, 1], expected: 1 }, + { input: [constants.negative.subnormal.max, 1], expected: 1 }, + { input: [constants.negative.subnormal.min, 1], expected: 1 }, + { input: [constants.positive.subnormal.max, -1], expected: 0 }, + { input: [constants.positive.subnormal.min, -1], expected: 0 }, + { input: [constants.negative.subnormal.max, -1], expected: 0 }, + { input: [constants.negative.subnormal.min, -1], expected: 0 }, + { input: [constants.negative.subnormal.min, constants.positive.subnormal.max], expected: 1 }, + { input: [constants.positive.subnormal.max, constants.negative.subnormal.min], expected: [0, 1] }, + + // Infinities + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const [edge, x] = t.params.input; + const expected = trait.toInterval(t.params.expected); + const got = trait.stepInterval(edge, x); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.stepInterval(${edge}, ${x}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kSubtractionInterval64BitsNormalCases = { + f32: [ + // 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD, -0.1 falls between f32 0xBDCCCCCD and 0xBDCCCCCC + // Expect f32 interval [0x3DCCCCCC-0x3DCCCCCD, 0x3DCCCCCD-0x3DCCCCCC] + { input: [0.1, 0.1], expected: [reinterpretU32AsF32(0x3dcccccc)-reinterpretU32AsF32(0x3dcccccd), reinterpretU32AsF32(0x3dcccccd)-reinterpretU32AsF32(0x3dcccccc)] }, + // Expect f32 interval [0xBDCCCCCD-0xBDCCCCCC, 0xBDCCCCCC-0xBDCCCCCD] + { input: [-0.1, -0.1], expected: [reinterpretU32AsF32(0xbdcccccd)-reinterpretU32AsF32(0xbdcccccc), reinterpretU32AsF32(0xbdcccccc)-reinterpretU32AsF32(0xbdcccccd)] }, + // Expect f32 interval [0x3DCCCCCC-0xBDCCCCCC, 0x3DCCCCCD-0xBDCCCCCD] + { input: [0.1, -0.1], expected: [reinterpretU32AsF32(0x3dcccccc)-reinterpretU32AsF32(0xbdcccccc), reinterpretU32AsF32(0x3dcccccd)-reinterpretU32AsF32(0xbdcccccd)] }, + // Expect f32 interval [0xBDCCCCCD-0x3DCCCCCD, 0xBDCCCCCC-0x3DCCCCCC] + { input: [-0.1, 0.1], expected: [reinterpretU32AsF32(0xbdcccccd)-reinterpretU32AsF32(0x3dcccccd), reinterpretU32AsF32(0xbdcccccc)-reinterpretU32AsF32(0x3dcccccc)] }, + ] as ScalarPairToIntervalCase[], + f16: [ + // 0.1 falls between f16 0x2E66 and 0x2E67, -0.1 falls between f16 0xAE67 and 0xAE66 + // Expect f16 interval [0x2E66-0x2E67, 0x2E67-0x2E66] + { input: [0.1, 0.1], expected: [reinterpretU16AsF16(0x2e66)-reinterpretU16AsF16(0x2e67), reinterpretU16AsF16(0x2e67)-reinterpretU16AsF16(0x2e66)] }, + // Expect f16 interval [0xAE67-0xAE66, 0xAE66-0xAE67] + { input: [-0.1, -0.1], expected: [reinterpretU16AsF16(0xae67)-reinterpretU16AsF16(0xae66), reinterpretU16AsF16(0xae66)-reinterpretU16AsF16(0xae67)] }, + // Expect f16 interval [0x2E66-0xAE66, 0x2E67-0xAE67] + { input: [0.1, -0.1], expected: [reinterpretU16AsF16(0x2e66)-reinterpretU16AsF16(0xae66), reinterpretU16AsF16(0x2e67)-reinterpretU16AsF16(0xae67)] }, + // Expect f16 interval [0xAE67-0x2E67, 0xAE66-0x2E66] + { input: [-0.1, 0.1], expected: [reinterpretU16AsF16(0xae67)-reinterpretU16AsF16(0x2e67), reinterpretU16AsF16(0xae66)-reinterpretU16AsF16(0x2e66)] }, + ] as ScalarPairToIntervalCase[], + abstract: [ + // 0.1 isn't exactly representable in f64, but will be quantized to an + // exact value when storing to a 'number' (0x3FB999999999999A). + // This is why below the expectations are not intervals. + { input: [0.1, 0.1], expected: 0 }, + { input: [-0.1, -0.1], expected: 0 }, + // f64 0x3FB999999999999A - 0xBFB999999999999A = 0x3FC999999999999A + { input: [0.1, -0.1], expected: reinterpretU64AsF64(0x3fc999999999999an) }, // ~0.2 + // f64 0xBFB999999999999A - 0x3FB999999999999A = 0xBFC999999999999A + { input: [-0.1, 0.1], expected: reinterpretU64AsF64(0xbfc999999999999an) }, // ~-0.2, + ] as ScalarPairToIntervalCase[], +} as const; + +g.test('subtractionInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Representable normals + { input: [0, 0], expected: 0 }, + { input: [1, 0], expected: 1 }, + { input: [0, 1], expected: -1 }, + { input: [-1, 0], expected: -1 }, + { input: [0, -1], expected: 1 }, + { input: [1, 1], expected: 0 }, + { input: [1, -1], expected: 2 }, + { input: [-1, 1], expected: -2 }, + { input: [-1, -1], expected: 0 }, + + // 64-bit normals that can not be exactly represented in f32/f16 + { input: [0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + { input: [0, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, + { input: [-0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, + { input: [0, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, + ...kSubtractionInterval64BitsNormalCases[p.trait], + + // Subnormals + { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max], expected: [constants.negative.subnormal.min, 0] }, + { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, + { input: [0, constants.positive.subnormal.min], expected: [constants.negative.subnormal.max, 0] }, + { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, + { input: [0, constants.negative.subnormal.max], expected: [0, constants.positive.subnormal.min] }, + { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, + { input: [0, constants.negative.subnormal.min], expected: [0, constants.positive.subnormal.max] }, + + // Infinities + { input: [0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 0], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.subtractionInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.subtractionInterval(${x}, ${y}) returned ${got}. Expected ${expected}` + ); + }); + +interface ScalarTripleToIntervalCase { + input: [number, number, number]; + expected: number | IntervalBounds; +} + +g.test('clampMedianInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarTripleToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Normals + { input: [0, 0, 0], expected: 0 }, + { input: [1, 0, 0], expected: 0 }, + { input: [0, 1, 0], expected: 0 }, + { input: [0, 0, 1], expected: 0 }, + { input: [1, 0, 1], expected: 1 }, + { input: [1, 1, 0], expected: 1 }, + { input: [0, 1, 1], expected: 1 }, + { input: [1, 1, 1], expected: 1 }, + { input: [1, 10, 100], expected: 10 }, + { input: [10, 1, 100], expected: 10 }, + { input: [100, 1, 10], expected: 10 }, + { input: [-10, 1, 100], expected: 1 }, + { input: [10, 1, -100], expected: 1 }, + { input: [-10, 1, -100], expected: -10 }, + { input: [-10, -10, -10], expected: -10 }, + + // Subnormals + { input: [constants.positive.subnormal.max, 0, 0], expected: 0 }, + { input: [0, constants.positive.subnormal.max, 0], expected: 0 }, + { input: [0, 0, constants.positive.subnormal.max], expected: 0 }, + { input: [constants.positive.subnormal.max, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.positive.subnormal.min, constants.negative.subnormal.max], expected: [0, constants.positive.subnormal.min] }, + { input: [constants.positive.subnormal.max, constants.negative.subnormal.min, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, + { input: [constants.positive.max, constants.positive.max, constants.positive.subnormal.min], expected: constants.positive.max }, + + // Infinities + { input: [0, 1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y, z] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.clampMedianInterval(x, y, z); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.clampMedianInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` + ); + }); + +g.test('clampMinMaxInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarTripleToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Normals + { input: [0, 0, 0], expected: 0 }, + { input: [1, 0, 0], expected: 0 }, + { input: [0, 1, 0], expected: 0 }, + { input: [0, 0, 1], expected: 0 }, + { input: [1, 0, 1], expected: 1 }, + { input: [1, 1, 0], expected: 0 }, + { input: [0, 1, 1], expected: 1 }, + { input: [1, 1, 1], expected: 1 }, + { input: [1, 10, 100], expected: 10 }, + { input: [10, 1, 100], expected: 10 }, + { input: [100, 1, 10], expected: 10 }, + { input: [-10, 1, 100], expected: 1 }, + { input: [10, 1, -100], expected: -100 }, + { input: [-10, 1, -100], expected: -100 }, + { input: [-10, -10, -10], expected: -10 }, + + // Subnormals + { input: [constants.positive.subnormal.max, 0, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.positive.subnormal.min, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, constants.negative.subnormal.min, constants.negative.subnormal.max], expected: [constants.negative.subnormal.min, constants.positive.subnormal.max] }, + { input: [constants.positive.max, constants.positive.max, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, + + // Infinities + { input: [0, 1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y, z] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.clampMinMaxInterval(x, y, z); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.clampMinMaxInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kFmaIntervalCases = { + f32: [ + // positive.subnormal.max * positive.subnormal.max is much smaller than positive.subnormal.min but larger than 0, rounded to [0, positive.subnormal.min] + { input: [kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.max, 0], expected: [0, kValue.f32.positive.subnormal.min] }, + // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, + // 0 + constants.positive.subnormal.max rounded to [0, constants.positive.subnormal.max], + // positive.subnormal.min + constants.positive.subnormal.max = constants.positive.min. + { input: [kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.max], expected: [0, kValue.f32.positive.min] }, + // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, + // negative.subnormal.max may flushed to 0, + // minimum case: 0 + negative.subnormal.max rounded to [negative.subnormal.max, 0], + // maximum case: positive.subnormal.min + 0 rounded to [0, positive.subnormal.min]. + { input: [kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.min, kValue.f32.negative.subnormal.max], expected: [kValue.f32.negative.subnormal.max, kValue.f32.positive.subnormal.min] }, + // positive.subnormal.max * negative.subnormal.min rounded to -0.0 or negative.subnormal.max = -1 * [subnormal ulp], + // negative.subnormal.max = -1 * [subnormal ulp] may flushed to -0.0, + // minimum case: -1 * [subnormal ulp] + -1 * [subnormal ulp] rounded to [-2 * [subnormal ulp], 0], + // maximum case: -0.0 + -0.0 = 0. + { input: [kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.min, kValue.f32.negative.subnormal.max], expected: [-2 * FP['f32'].oneULP(0, 'no-flush'), 0] }, + ] as ScalarTripleToIntervalCase[], + f16: [ + // positive.subnormal.max * positive.subnormal.max is much smaller than positive.subnormal.min but larger than 0, rounded to [0, positive.subnormal.min] + { input: [kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.max, 0], expected: [0, kValue.f16.positive.subnormal.min] }, + // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, + // 0 + constants.positive.subnormal.max rounded to [0, constants.positive.subnormal.max], + // positive.subnormal.min + constants.positive.subnormal.max = constants.positive.min. + { input: [kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.max], expected: [0, kValue.f16.positive.min] }, + // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, + // negative.subnormal.max may flushed to 0, + // minimum case: 0 + negative.subnormal.max rounded to [negative.subnormal.max, 0], + // maximum case: positive.subnormal.min + 0 rounded to [0, positive.subnormal.min]. + { input: [kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.min, kValue.f16.negative.subnormal.max], expected: [kValue.f16.negative.subnormal.max, kValue.f16.positive.subnormal.min] }, + // positive.subnormal.max * negative.subnormal.min rounded to -0.0 or negative.subnormal.max = -1 * [subnormal ulp], + // negative.subnormal.max = -1 * [subnormal ulp] may flushed to -0.0, + // minimum case: -1 * [subnormal ulp] + -1 * [subnormal ulp] rounded to [-2 * [subnormal ulp], 0], + // maximum case: -0.0 + -0.0 = 0. + { input: [kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.min, kValue.f16.negative.subnormal.max], expected: [-2 * FP['f16'].oneULP(0, 'no-flush'), 0] }, ] as ScalarTripleToIntervalCase[], + abstract: [ + // These operations break down in the CTS, because `number` is a f64 under the hood, so precision is sometimes lost + // if intermediate results are closer to 0 than the smallest subnormal will be precisely 0. + // See https://github.com/gpuweb/cts/issues/2993 for details + { input: [kValue.f64.positive.subnormal.max, kValue.f64.positive.subnormal.max, 0], expected: 0 }, + { input: [kValue.f64.positive.subnormal.max, kValue.f64.positive.subnormal.max, kValue.f64.positive.subnormal.max], expected: [0, kValue.f64.positive.subnormal.max] }, + { input: [kValue.f64.positive.subnormal.max, kValue.f64.positive.subnormal.min, kValue.f64.negative.subnormal.max], expected: [kValue.f64.negative.subnormal.max, 0] }, + { input: [kValue.f64.positive.subnormal.max, kValue.f64.negative.subnormal.min, kValue.f64.negative.subnormal.max], expected: [kValue.f64.negative.subnormal.max, 0] }, + ] as ScalarTripleToIntervalCase[], +} as const; + +g.test('fmaInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ScalarTripleToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // Normals + { input: [0, 0, 0], expected: 0 }, + { input: [1, 0, 0], expected: 0 }, + { input: [0, 1, 0], expected: 0 }, + { input: [0, 0, 1], expected: 1 }, + { input: [1, 0, 1], expected: 1 }, + { input: [1, 1, 0], expected: 1 }, + { input: [0, 1, 1], expected: 1 }, + { input: [1, 1, 1], expected: 2 }, + { input: [1, 10, 100], expected: 110 }, + { input: [10, 1, 100], expected: 110 }, + { input: [100, 1, 10], expected: 110 }, + { input: [-10, 1, 100], expected: 90 }, + { input: [10, 1, -100], expected: -90 }, + { input: [-10, 1, -100], expected: -110 }, + { input: [-10, -10, -10], expected: 90 }, + + // Subnormals + { input: [constants.positive.subnormal.max, 0, 0], expected: 0 }, + { input: [0, constants.positive.subnormal.max, 0], expected: 0 }, + { input: [0, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [constants.positive.subnormal.max, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + { input: [0, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, + + // Infinities + { input: [0, 1, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.max, constants.positive.max, constants.positive.subnormal.min], expected: kUnboundedBounds }, + ...kFmaIntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.fmaInterval(...t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.fmaInterval(${t.params.input.join( + ',' + )}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kMixImpreciseIntervalCases = { + f32: [ + // [0.0, 1.0] cases + { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9999_8000_0000n), reinterpretU64AsF64(0x3fb9_9999_a000_0000n)] }, // ~0.1 + { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 + // [1.0, 0.0] cases + { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 + { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_9999_0000_0000n), reinterpretU64AsF64(0x3fb9_999a_0000_0000n)] }, // ~0.1 + // [0.0, 10.0] cases + { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_ffff_e000_0000n), reinterpretU64AsF64(0x3ff0_0000_2000_0000n)] }, // ~1 + { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_ffff_e000_0000n), reinterpretU64AsF64(0x4022_0000_2000_0000n)] }, // ~9 + // [2.0, 10.0] cases + { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6666_6000_0000n), reinterpretU64AsF64(0x4006_6666_8000_0000n)] }, // ~2.8 + { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6666_6000_0000n), reinterpretU64AsF64(0x4022_6666_8000_0000n)] }, // ~9.2 + // [-1.0, 1.0] cases + { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_9999_a000_0000n), reinterpretU64AsF64(0xbfe9_9999_8000_0000n)] }, // ~-0.8 + { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9999_8000_0000n), reinterpretU64AsF64(0x3fe9_9999_c000_0000n)] }, // ~0.8 + + // Showing how precise and imprecise versions diff + // Note that this expectation is 0 only in f32 as 10.0 is much smaller that f32.negative.min, + // So that 10 - f32.negative.min == f32.negative.min even in f64. But for f16, there is not + // a exactly-represenatble f16 value v that make v - f16.negative.min == f16.negative.min + // in f64, in fact that require v being smaller than 2**-37. + { input: [kValue.f32.negative.min, 10.0, 1.0], expected: 0.0 }, + // -10.0 is the same, much smaller than f32.negative.min + { input: [kValue.f32.negative.min, -10.0, 1.0], expected: 0.0 }, + ] as ScalarTripleToIntervalCase[], + f16: [ + // [0.0, 1.0] cases + { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9800_0000_0000n), reinterpretU64AsF64(0x3fb9_9c00_0000_0000n)] }, // ~0.1 + { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 + // [1.0, 0.0] cases + { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 + { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_8000_0000_0000n), reinterpretU64AsF64(0x3fb9_a000_0000_0000n)] }, // ~0.1 + // [0.0, 10.0] cases + { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0400_0000_0000n)] }, // ~1 + { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_fc00_0000_0000n), reinterpretU64AsF64(0x4022_0400_0000_0000n)] }, // ~9 + // [2.0, 10.0] cases + { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6400_0000_0000n), reinterpretU64AsF64(0x4006_6800_0000_0000n)] }, // ~2.8 + { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6400_0000_0000n), reinterpretU64AsF64(0x4022_6800_0000_0000n)] }, // ~9.2 + // [-1.0, 1.0] cases + { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_9c00_0000_0000n), reinterpretU64AsF64(0xbfe9_9800_0000_0000n)] }, // ~-0.8 + { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9800_0000_0000n), reinterpretU64AsF64(0x3fe9_a000_0000_0000n)] }, // ~0.8 + + // Showing how precise and imprecise versions diff + // In imprecise version, we compute (y - x), where y = 10 and x = -65504, the result is 65514 + // and cause an overflow in f16. + { input: [kValue.f16.negative.min, 10.0, 1.0], expected: kUnboundedBounds }, + // (y - x) * 1.0, where y = -10 and x = -65504, the result is 65494 rounded to 65472 or 65504. + // The result is -65504 + 65472 = -32 or -65504 + 65504 = 0. + { input: [kValue.f16.negative.min, -10.0, 1.0], expected: [-32, 0] }, + ] as ScalarTripleToIntervalCase[], +} as const; + +g.test('mixImpreciseInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarTripleToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kMixImpreciseIntervalCases[p.trait], + + // [0.0, 1.0] cases + { input: [0.0, 1.0, -1.0], expected: -1.0 }, + { input: [0.0, 1.0, 0.0], expected: 0.0 }, + { input: [0.0, 1.0, 0.5], expected: 0.5 }, + { input: [0.0, 1.0, 1.0], expected: 1.0 }, + { input: [0.0, 1.0, 2.0], expected: 2.0 }, + + // [1.0, 0.0] cases + { input: [1.0, 0.0, -1.0], expected: 2.0 }, + { input: [1.0, 0.0, 0.0], expected: 1.0 }, + { input: [1.0, 0.0, 0.5], expected: 0.5 }, + { input: [1.0, 0.0, 1.0], expected: 0.0 }, + { input: [1.0, 0.0, 2.0], expected: -1.0 }, + + // [0.0, 10.0] cases + { input: [0.0, 10.0, -1.0], expected: -10.0 }, + { input: [0.0, 10.0, 0.0], expected: 0.0 }, + { input: [0.0, 10.0, 0.5], expected: 5.0 }, + { input: [0.0, 10.0, 1.0], expected: 10.0 }, + { input: [0.0, 10.0, 2.0], expected: 20.0 }, + + // [2.0, 10.0] cases + { input: [2.0, 10.0, -1.0], expected: -6.0 }, + { input: [2.0, 10.0, 0.0], expected: 2.0 }, + { input: [2.0, 10.0, 0.5], expected: 6.0 }, + { input: [2.0, 10.0, 1.0], expected: 10.0 }, + { input: [2.0, 10.0, 2.0], expected: 18.0 }, + + // [-1.0, 1.0] cases + { input: [-1.0, 1.0, -2.0], expected: -5.0 }, + { input: [-1.0, 1.0, 0.0], expected: -1.0 }, + { input: [-1.0, 1.0, 0.5], expected: 0.0 }, + { input: [-1.0, 1.0, 1.0], expected: 1.0 }, + { input: [-1.0, 1.0, 2.0], expected: 3.0 }, + + // Infinities + { input: [0.0, constants.positive.infinity, 0.5], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0.0, 0.5], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 1.0, 0.5], expected: kUnboundedBounds }, + { input: [1.0, constants.negative.infinity, 0.5], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, 0.5], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity, 0.5], expected: kUnboundedBounds }, + { input: [0.0, 1.0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [1.0, 0.0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [0.0, 1.0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [1.0, 0.0, constants.positive.infinity], expected: kUnboundedBounds }, + + // The [negative.min, +/-10.0, 1.0] cases has different result for different trait on + // imprecise version. + ]; + }) + ) + .fn(t => { + const [x, y, z] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.mixImpreciseInterval(x, y, z); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.mixImpreciseInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kMixPreciseIntervalCases = { + f32: [ + // [0.0, 1.0] cases + { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9999_8000_0000n), reinterpretU64AsF64(0x3fb9_9999_a000_0000n)] }, // ~0.1 + { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 + // [1.0, 0.0] cases + { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 + { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_9999_0000_0000n), reinterpretU64AsF64(0x3fb9_999a_0000_0000n)] }, // ~0.1 + // [0.0, 10.0] cases + { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_ffff_e000_0000n), reinterpretU64AsF64(0x3ff0_0000_2000_0000n)] }, // ~1 + { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_ffff_e000_0000n), reinterpretU64AsF64(0x4022_0000_2000_0000n)] }, // ~9 + // [2.0, 10.0] cases + { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6666_4000_0000n), reinterpretU64AsF64(0x4006_6666_8000_0000n)] }, // ~2.8 + { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6666_4000_0000n), reinterpretU64AsF64(0x4022_6666_a000_0000n)] }, // ~9.2 + // [-1.0, 1.0] cases + { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_9999_c000_0000n), reinterpretU64AsF64(0xbfe9_9999_8000_0000n)] }, // ~-0.8 + { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9999_8000_0000n), reinterpretU64AsF64(0x3fe9_9999_c000_0000n)] }, // ~0.8 + ] as ScalarTripleToIntervalCase[], + f16: [ + // [0.0, 1.0] cases + { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9800_0000_0000n), reinterpretU64AsF64(0x3fb9_9c00_0000_0000n)] }, // ~0.1 + { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 + // [1.0, 0.0] cases + { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 + { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_8000_0000_0000n), reinterpretU64AsF64(0x3fb9_a000_0000_0000n)] }, // ~0.1 + // [0.0, 10.0] cases + { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0400_0000_0000n)] }, // ~1 + { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_fc00_0000_0000n), reinterpretU64AsF64(0x4022_0400_0000_0000n)] }, // ~9 + // [2.0, 10.0] cases + { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6400_0000_0000n), reinterpretU64AsF64(0x4006_6c00_0000_0000n)] }, // ~2.8 + { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6000_0000_0000n), reinterpretU64AsF64(0x4022_6c00_0000_0000n)] }, // ~9.2 + // [-1.0, 1.0] cases + { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_a000_0000_0000n), reinterpretU64AsF64(0xbfe9_9800_0000_0000n)] }, // ~-0.8 + { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9800_0000_0000n), reinterpretU64AsF64(0x3fe9_a000_0000_0000n)] }, // ~0.8 + ] as ScalarTripleToIntervalCase[], +} as const; + +g.test('mixPreciseInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarTripleToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kMixPreciseIntervalCases[p.trait], + + // [0.0, 1.0] cases + { input: [0.0, 1.0, -1.0], expected: -1.0 }, + { input: [0.0, 1.0, 0.0], expected: 0.0 }, + { input: [0.0, 1.0, 0.5], expected: 0.5 }, + { input: [0.0, 1.0, 1.0], expected: 1.0 }, + { input: [0.0, 1.0, 2.0], expected: 2.0 }, + + // [1.0, 0.0] cases + { input: [1.0, 0.0, -1.0], expected: 2.0 }, + { input: [1.0, 0.0, 0.0], expected: 1.0 }, + { input: [1.0, 0.0, 0.5], expected: 0.5 }, + { input: [1.0, 0.0, 1.0], expected: 0.0 }, + { input: [1.0, 0.0, 2.0], expected: -1.0 }, + + // [0.0, 10.0] cases + { input: [0.0, 10.0, -1.0], expected: -10.0 }, + { input: [0.0, 10.0, 0.0], expected: 0.0 }, + { input: [0.0, 10.0, 0.5], expected: 5.0 }, + { input: [0.0, 10.0, 1.0], expected: 10.0 }, + { input: [0.0, 10.0, 2.0], expected: 20.0 }, + + // [2.0, 10.0] cases + { input: [2.0, 10.0, -1.0], expected: -6.0 }, + { input: [2.0, 10.0, 0.0], expected: 2.0 }, + { input: [2.0, 10.0, 0.5], expected: 6.0 }, + { input: [2.0, 10.0, 1.0], expected: 10.0 }, + { input: [2.0, 10.0, 2.0], expected: 18.0 }, + + // [-1.0, 1.0] cases + { input: [-1.0, 1.0, -2.0], expected: -5.0 }, + { input: [-1.0, 1.0, 0.0], expected: -1.0 }, + { input: [-1.0, 1.0, 0.5], expected: 0.0 }, + { input: [-1.0, 1.0, 1.0], expected: 1.0 }, + { input: [-1.0, 1.0, 2.0], expected: 3.0 }, + + // Infinities + { input: [0.0, constants.positive.infinity, 0.5], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 0.0, 0.5], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 1.0, 0.5], expected: kUnboundedBounds }, + { input: [1.0, constants.negative.infinity, 0.5], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, constants.positive.infinity, 0.5], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, constants.negative.infinity, 0.5], expected: kUnboundedBounds }, + { input: [0.0, 1.0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [1.0, 0.0, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [0.0, 1.0, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [1.0, 0.0, constants.positive.infinity], expected: kUnboundedBounds }, + + // Showing how precise and imprecise versions diff + { input: [constants.negative.min, 10.0, 1.0], expected: 10.0 }, + { input: [constants.negative.min, -10.0, 1.0], expected: -10.0 }, + ]; + }) + ) + .fn(t => { + const [x, y, z] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.mixPreciseInterval(x, y, z); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.mixPreciseInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` + ); + }); + +// Some of these are hard coded, since the error intervals are difficult to express in a closed +// human-readable form due to the inherited nature of the errors. +// prettier-ignore +const kSmoothStepIntervalCases = { + f32: [ + // Normals + { input: [0, 1, 0], expected: [0, kValue.f32.positive.subnormal.min] }, + { input: [0, 1, 1], expected: [reinterpretU32AsF32(0x3f7ffffa), reinterpretU32AsF32(0x3f800003)] }, // ~1 + { input: [0, 2, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [0, 2, 0.5], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... + { input: [2, 0, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [2, 0, 1.5], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... + { input: [0, 100, 50], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [0, 100, 25], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... + { input: [0, -2, -1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [0, -2, -0.5], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... + // Subnormals + { input: [kValue.f32.positive.subnormal.max, 2, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [kValue.f32.positive.subnormal.min, 2, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [kValue.f32.negative.subnormal.max, 2, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [kValue.f32.negative.subnormal.min, 2, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 + { input: [0, 2, kValue.f32.positive.subnormal.max], expected: [0, kValue.f32.positive.subnormal.min] }, + { input: [0, 2, kValue.f32.positive.subnormal.min], expected: [0, kValue.f32.positive.subnormal.min] }, + { input: [0, 2, kValue.f32.negative.subnormal.max], expected: [0, kValue.f32.positive.subnormal.min] }, + { input: [0, 2, kValue.f32.negative.subnormal.min], expected: [0, kValue.f32.positive.subnormal.min] }, + ] as ScalarTripleToIntervalCase[], + f16: [ + // Normals + { input: [0, 1, 0], expected: [0, reinterpretU16AsF16(0x0002)] }, + { input: [0, 1, 1], expected: [reinterpretU16AsF16(0x3bfa), reinterpretU16AsF16(0x3c03)] }, // ~1 + { input: [0, 2, 1], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 + { input: [0, 2, 0.5], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... + { input: [2, 0, 1], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 + { input: [2, 0, 1.5], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... + { input: [0, 100, 50], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 + { input: [0, 100, 25], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... + { input: [0, -2, -1], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 + { input: [0, -2, -0.5], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... + // Subnormals + { input: [kValue.f16.positive.subnormal.max, 2, 1], expected: [reinterpretU16AsF16(0x37f4), reinterpretU16AsF16(0x380b)] }, // ~0.5 + { input: [kValue.f16.positive.subnormal.min, 2, 1], expected: [reinterpretU16AsF16(0x37f4), reinterpretU16AsF16(0x380b)] }, // ~0.5 + { input: [kValue.f16.negative.subnormal.max, 2, 1], expected: [reinterpretU16AsF16(0x37f2), reinterpretU16AsF16(0x380c)] }, // ~0.5 + { input: [kValue.f16.negative.subnormal.min, 2, 1], expected: [reinterpretU16AsF16(0x37f2), reinterpretU16AsF16(0x380c)] }, // ~0.5 + { input: [0, 2, kValue.f16.positive.subnormal.max], expected: [0, reinterpretU16AsF16(0x0002)] }, + { input: [0, 2, kValue.f16.positive.subnormal.min], expected: [0, reinterpretU16AsF16(0x0002)] }, + { input: [0, 2, kValue.f32.negative.subnormal.max], expected: [0, reinterpretU16AsF16(0x0002)] }, + { input: [0, 2, kValue.f32.negative.subnormal.min], expected: [0, reinterpretU16AsF16(0x0002)] }, + ] as ScalarTripleToIntervalCase[], +} as const; + +g.test('smoothStepInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<ScalarTripleToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kSmoothStepIntervalCases[p.trait], + + // Normals + { input: [0, 1, 10], expected: 1 }, + { input: [0, 1, -10], expected: 0 }, + + // Subnormals + { input: [0, constants.positive.subnormal.max, 1], expected: kUnboundedBounds }, + { input: [0, constants.positive.subnormal.min, 1], expected: kUnboundedBounds }, + { input: [0, constants.negative.subnormal.max, 1], expected: kUnboundedBounds }, + { input: [0, constants.negative.subnormal.min, 1], expected: kUnboundedBounds }, + + // Infinities + { input: [0, 2, constants.positive.infinity], expected: kUnboundedBounds }, + { input: [0, 2, constants.negative.infinity], expected: kUnboundedBounds }, + { input: [constants.positive.infinity, 2, 1], expected: kUnboundedBounds }, + { input: [constants.negative.infinity, 2, 1], expected: kUnboundedBounds }, + { input: [0, constants.positive.infinity, 1], expected: kUnboundedBounds }, + { input: [0, constants.negative.infinity, 1], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [low, high, x] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.smoothStepInterval(low, high, x); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.smoothStepInterval(${low}, ${high}, ${x}) returned ${got}. Expected ${expected}` + ); + }); + +interface ScalarToVectorCase { + input: number; + expected: (number | IntervalBounds)[]; +} + +g.test('unpack2x16floatInterval') + .paramsSubcasesOnly<ScalarToVectorCase>( + // prettier-ignore + [ + // f16 normals + { input: 0x00000000, expected: [0, 0] }, + { input: 0x80000000, expected: [0, 0] }, + { input: 0x00008000, expected: [0, 0] }, + { input: 0x80008000, expected: [0, 0] }, + { input: 0x00003c00, expected: [1, 0] }, + { input: 0x3c000000, expected: [0, 1] }, + { input: 0x3c003c00, expected: [1, 1] }, + { input: 0xbc00bc00, expected: [-1, -1] }, + { input: 0x49004900, expected: [10, 10] }, + { input: 0xc900c900, expected: [-10, -10] }, + + // f16 subnormals + { input: 0x000003ff, expected: [[0, kValue.f16.positive.subnormal.max], 0] }, + { input: 0x000083ff, expected: [[kValue.f16.negative.subnormal.min, 0], 0] }, + + // f16 out of bounds + { input: 0x7c000000, expected: [kUnboundedBounds, kUnboundedBounds] }, + { input: 0xffff0000, expected: [kUnboundedBounds, kUnboundedBounds] }, + ] + ) + .fn(t => { + const expected = FP.f32.toVector(t.params.expected); + const got = FP.f32.unpack2x16floatInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `unpack2x16floatInterval(${t.params.input}) returned [${got}]. Expected [${expected}]` + ); + }); + +// Scope for unpack2x16snormInterval tests so that they can have constants for +// magic numbers that don't pollute the global namespace or have unwieldy long +// names. +{ + const kZeroBounds: IntervalBounds = [ + reinterpretU32AsF32(0x81400000), + reinterpretU32AsF32(0x01400000), + ]; + const kOneBoundsSnorm: IntervalBounds = [ + reinterpretU64AsF64(0x3fef_ffff_a000_0000n), + reinterpretU64AsF64(0x3ff0_0000_3000_0000n), + ]; + const kNegOneBoundsSnorm: IntervalBounds = [ + reinterpretU64AsF64(0xbff0_0000_3000_0000n), + reinterpretU64AsF64(0xbfef_ffff_a000_0000n), + ]; + + const kHalfBounds2x16snorm: IntervalBounds = [ + reinterpretU64AsF64(0x3fe0_001f_a000_0000n), + reinterpretU64AsF64(0x3fe0_0020_8000_0000n), + ]; // ~0.5..., due to lack of precision in i16 + const kNegHalfBounds2x16snorm: IntervalBounds = [ + reinterpretU64AsF64(0xbfdf_ffc0_6000_0000n), + reinterpretU64AsF64(0xbfdf_ffbf_8000_0000n), + ]; // ~-0.5..., due to lack of precision in i16 + + g.test('unpack2x16snormInterval') + .paramsSubcasesOnly<ScalarToVectorCase>( + // prettier-ignore + [ + { input: 0x00000000, expected: [kZeroBounds, kZeroBounds] }, + { input: 0x00007fff, expected: [kOneBoundsSnorm, kZeroBounds] }, + { input: 0x7fff0000, expected: [kZeroBounds, kOneBoundsSnorm] }, + { input: 0x7fff7fff, expected: [kOneBoundsSnorm, kOneBoundsSnorm] }, + { input: 0x80018001, expected: [kNegOneBoundsSnorm, kNegOneBoundsSnorm] }, + { input: 0x40004000, expected: [kHalfBounds2x16snorm, kHalfBounds2x16snorm] }, + { input: 0xc001c001, expected: [kNegHalfBounds2x16snorm, kNegHalfBounds2x16snorm] }, + ] + ) + .fn(t => { + const expected = FP.f32.toVector(t.params.expected); + const got = FP.f32.unpack2x16snormInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `unpack2x16snormInterval(${t.params.input}) returned [${got}]. Expected [${expected}]` + ); + }); +} + +// Scope for unpack2x16unormInterval tests so that they can have constants for +// magic numbers that don't pollute the global namespace or have unwieldy long +// names. +{ + const kZeroBounds: IntervalBounds = [ + reinterpretU32AsF32(0x8140_0000), + reinterpretU32AsF32(0x0140_0000), + ]; // ~0 + const kOneBounds: IntervalBounds = [ + reinterpretU64AsF64(0x3fef_ffff_a000_0000n), + reinterpretU64AsF64(0x3ff0_0000_3000_0000n), + ]; // ~1 + const kHalfBounds: IntervalBounds = [ + reinterpretU64AsF64(0x3fe0_000f_a000_0000n), + reinterpretU64AsF64(0x3fe0_0010_8000_0000n), + ]; // ~0.5..., due to the lack of accuracy in u16 + + g.test('unpack2x16unormInterval') + .paramsSubcasesOnly<ScalarToVectorCase>( + // prettier-ignore + [ + { input: 0x00000000, expected: [kZeroBounds, kZeroBounds] }, + { input: 0x0000ffff, expected: [kOneBounds, kZeroBounds] }, + { input: 0xffff0000, expected: [kZeroBounds, kOneBounds] }, + { input: 0xffffffff, expected: [kOneBounds, kOneBounds] }, + { input: 0x80008000, expected: [kHalfBounds, kHalfBounds] }, + ] + ) + .fn(t => { + const expected = FP.f32.toVector(t.params.expected); + const got = FP.f32.unpack2x16unormInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `unpack2x16unormInterval(${t.params.input})\n\tReturned [${got}]\n\tExpected [${expected}]` + ); + }); +} + +// Scope for unpack4x8snormInterval tests so that they can have constants for +// magic numbers that don't pollute the global namespace or have unwieldy long +// names. +{ + const kZeroBounds: IntervalBounds = [ + reinterpretU32AsF32(0x8140_0000), + reinterpretU32AsF32(0x0140_0000), + ]; // ~0 + const kOneBounds: IntervalBounds = [ + reinterpretU64AsF64(0x3fef_ffff_a000_0000n), + reinterpretU64AsF64(0x3ff0_0000_3000_0000n), + ]; // ~1 + const kNegOneBounds: IntervalBounds = [ + reinterpretU64AsF64(0xbff0_0000_3000_0000n), + reinterpretU64AsF64(0xbfef_ffff_a0000_000n), + ]; // ~-1 + const kHalfBounds: IntervalBounds = [ + reinterpretU64AsF64(0x3fe0_2040_2000_0000n), + reinterpretU64AsF64(0x3fe0_2041_0000_0000n), + ]; // ~0.50196..., due to lack of precision in i8 + const kNegHalfBounds: IntervalBounds = [ + reinterpretU64AsF64(0xbfdf_bf7f_6000_0000n), + reinterpretU64AsF64(0xbfdf_bf7e_8000_0000n), + ]; // ~-0.49606..., due to lack of precision in i8 + + g.test('unpack4x8snormInterval') + .paramsSubcasesOnly<ScalarToVectorCase>( + // prettier-ignore + [ + { input: 0x00000000, expected: [kZeroBounds, kZeroBounds, kZeroBounds, kZeroBounds] }, + { input: 0x0000007f, expected: [kOneBounds, kZeroBounds, kZeroBounds, kZeroBounds] }, + { input: 0x00007f00, expected: [kZeroBounds, kOneBounds, kZeroBounds, kZeroBounds] }, + { input: 0x007f0000, expected: [kZeroBounds, kZeroBounds, kOneBounds, kZeroBounds] }, + { input: 0x7f000000, expected: [kZeroBounds, kZeroBounds, kZeroBounds, kOneBounds] }, + { input: 0x00007f7f, expected: [kOneBounds, kOneBounds, kZeroBounds, kZeroBounds] }, + { input: 0x7f7f0000, expected: [kZeroBounds, kZeroBounds, kOneBounds, kOneBounds] }, + { input: 0x7f007f00, expected: [kZeroBounds, kOneBounds, kZeroBounds, kOneBounds] }, + { input: 0x007f007f, expected: [kOneBounds, kZeroBounds, kOneBounds, kZeroBounds] }, + { input: 0x7f7f7f7f, expected: [kOneBounds, kOneBounds, kOneBounds, kOneBounds] }, + { + input: 0x81818181, + expected: [kNegOneBounds, kNegOneBounds, kNegOneBounds, kNegOneBounds] + }, + { + input: 0x40404040, + expected: [kHalfBounds, kHalfBounds, kHalfBounds, kHalfBounds] + }, + { + input: 0xc1c1c1c1, + expected: [kNegHalfBounds, kNegHalfBounds, kNegHalfBounds, kNegHalfBounds] + }, + ] + ) + .fn(t => { + const expected = FP.f32.toVector(t.params.expected); + const got = FP.f32.unpack4x8snormInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `unpack4x8snormInterval(${t.params.input})\n\tReturned [${got}]\n\tExpected [${expected}]` + ); + }); +} + +// Scope for unpack4x8unormInterval tests so that they can have constants for +// magic numbers that don't pollute the global namespace or have unwieldy long +// names. +{ + const kZeroBounds: IntervalBounds = [ + reinterpretU32AsF32(0x8140_0000), + reinterpretU32AsF32(0x0140_0000), + ]; // ~0 + const kOneBounds: IntervalBounds = [ + reinterpretU64AsF64(0x3fef_ffff_a000_0000n), + reinterpretU64AsF64(0x3ff0_0000_3000_0000n), + ]; // ~1 + const kHalfBounds: IntervalBounds = [ + reinterpretU64AsF64(0x3fe0_100f_a000_0000n), + reinterpretU64AsF64(0x3fe0_1010_8000_0000n), + ]; // ~0.50196..., due to lack of precision in u8 + + g.test('unpack4x8unormInterval') + .paramsSubcasesOnly<ScalarToVectorCase>( + // prettier-ignore + [ + { input: 0x00000000, expected: [kZeroBounds, kZeroBounds, kZeroBounds, kZeroBounds] }, + { input: 0x000000ff, expected: [kOneBounds, kZeroBounds, kZeroBounds, kZeroBounds] }, + { input: 0x0000ff00, expected: [kZeroBounds, kOneBounds, kZeroBounds, kZeroBounds] }, + { input: 0x00ff0000, expected: [kZeroBounds, kZeroBounds, kOneBounds, kZeroBounds] }, + { input: 0xff000000, expected: [kZeroBounds, kZeroBounds, kZeroBounds, kOneBounds] }, + { input: 0x0000ffff, expected: [kOneBounds, kOneBounds, kZeroBounds, kZeroBounds] }, + { input: 0xffff0000, expected: [kZeroBounds, kZeroBounds, kOneBounds, kOneBounds] }, + { input: 0xff00ff00, expected: [kZeroBounds, kOneBounds, kZeroBounds, kOneBounds] }, + { input: 0x00ff00ff, expected: [kOneBounds, kZeroBounds, kOneBounds, kZeroBounds] }, + { input: 0xffffffff, expected: [kOneBounds, kOneBounds, kOneBounds, kOneBounds] }, + { + input: 0x80808080, + expected: [kHalfBounds, kHalfBounds, kHalfBounds, kHalfBounds] + }, + ] + ) + .fn(t => { + const expected = FP.f32.toVector(t.params.expected); + const got = FP.f32.unpack4x8unormInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `unpack4x8unormInterval(${t.params.input})\n\tReturned [${got}]\n\tExpected [${expected}]` + ); + }); +} + +interface VectorToIntervalCase { + input: number[]; + expected: number | IntervalBounds; +} + +g.test('lengthIntervalVector') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<VectorToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // vec2 + {input: [1.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [0.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [1.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 + {input: [-1.0, -1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 + {input: [-1.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 + {input: [0.1, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + + // vec3 + {input: [1.0, 0.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [0.0, 1.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [0.0, 0.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [1.0, 1.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + {input: [-1.0, -1.0, -1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + {input: [1.0, -1.0, -1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + {input: [0.1, 0.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + + // vec4 + {input: [1.0, 0.0, 0.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [0.0, 1.0, 0.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [0.0, 0.0, 1.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [0.0, 0.0, 0.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + {input: [1.0, 1.0, 1.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + {input: [-1.0, -1.0, -1.0, -1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + {input: [-1.0, 1.0, -1.0, 1.0], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + {input: [0.1, 0.0, 0.0, 0.0], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + + // Test that dot going OOB bounds in the intermediate calculations propagates + { input: [constants.positive.nearest_max, constants.positive.max, constants.negative.min], expected: kUnboundedBounds }, + { input: [constants.positive.max, constants.positive.nearest_max, constants.negative.min], expected: kUnboundedBounds }, + { input: [constants.negative.min, constants.positive.max, constants.positive.nearest_max], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.lengthInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.lengthInterval([${t.params.input}]) returned ${got}. Expected ${expected}` + ); + }); + +interface VectorPairToIntervalCase { + input: [number[], number[]]; + expected: number | IntervalBounds; +} + +g.test('distanceIntervalVector') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<VectorPairToIntervalCase>(p => { + // prettier-ignore + return [ + // distance(x, y), where x - y = 0 has an acceptance interval of kUnboundedBounds, + // because distance(x, y) = length(x - y), and length(0) = kUnboundedBounds. + + // vec2 + { input: [[1.0, 0.0], [1.0, 0.0]], expected: kUnboundedBounds }, + { input: [[1.0, 0.0], [0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0], [1.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[-1.0, 0.0], [0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0], [-1.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 1.0], [-1.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 + { input: [[0.1, 0.0], [0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + + // vec3 + { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: kUnboundedBounds }, + { input: [[1.0, 0.0, 0.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 1.0, 0.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 1.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0], [0.0, 1.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0], [0.0, 0.0, 1.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[1.0, 1.0, 1.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + { input: [[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + { input: [[-1.0, -1.0, -1.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + { input: [[0.0, 0.0, 0.0], [-1.0, -1.0, -1.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 + { input: [[0.1, 0.0, 0.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + { input: [[0.0, 0.0, 0.0], [0.1, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + + // vec4 + { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: kUnboundedBounds }, + { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0]'] }, // ~1 + { input: [[1.0, 1.0, 1.0, 1.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + { input: [[0.0, 0.0, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + { input: [[-1.0, 1.0, -1.0, 1.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + { input: [[0.0, 0.0, 0.0, 0.0], [1.0, -1.0, 1.0, -1.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 + { input: [[0.1, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + { input: [[0.0, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectionInterval[p.trait]['[0.1]'] }, // ~0.1 + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.distanceInterval(...t.params.input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.lengthInterval([${t.params.input[0]}, ${t.params.input[1]}]) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kDotIntervalCases = { + f32: [ + // Inputs with large values but cancel out to finite result. In these cases, 2.0*2.0 = 4.0 and + // 3.0*3.0 = 9.0 is much smaller than kValue.f32.positive.max, as a result + // kValue.f32.positive.max + 9.0 = kValue.f32.positive.max in f32 and even f64. So, if the + // positive and negative large number cancel each other first, the result would be + // 2.0*2.0+3.0*3.0 = 13. Otherwise, the resule would be 0.0 or 4.0 or 9.0. + // https://github.com/gpuweb/cts/issues/2155 + { input: [[kValue.f32.positive.max, 1.0, 2.0, 3.0], [-1.0, kValue.f32.positive.max, -2.0, -3.0]], expected: [-13, 0] }, + { input: [[kValue.f32.positive.max, 1.0, 2.0, 3.0], [1.0, kValue.f32.negative.min, 2.0, 3.0]], expected: [0, 13] }, + ] as VectorPairToIntervalCase[], + f16: [ + // Inputs with large values but cancel out to finite result. In these cases, 2.0*2.0 = 4.0 and + // 3.0*3.0 = 9.0 is not small enough comparing to kValue.f16.positive.max = 65504, as a result + // kValue.f16.positive.max + 9.0 = 65513 is exactly representable in f32 and f64. So, if the + // positive and negative large number don't cancel each other first, the computation will + // overflow f16 and result in unbounded bounds. + // https://github.com/gpuweb/cts/issues/2155 + { input: [[kValue.f16.positive.max, 1.0, 2.0, 3.0], [-1.0, kValue.f16.positive.max, -2.0, -3.0]], expected: kUnboundedBounds }, + { input: [[kValue.f16.positive.max, 1.0, 2.0, 3.0], [1.0, kValue.f16.negative.min, 2.0, 3.0]], expected: kUnboundedBounds }, + ] as VectorPairToIntervalCase[], +} as const; + +g.test('dotInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<VectorPairToIntervalCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // vec2 + { input: [[1.0, 0.0], [1.0, 0.0]], expected: 1.0 }, + { input: [[0.0, 1.0], [0.0, 1.0]], expected: 1.0 }, + { input: [[1.0, 1.0], [1.0, 1.0]], expected: 2.0 }, + { input: [[-1.0, -1.0], [-1.0, -1.0]], expected: 2.0 }, + { input: [[-1.0, 1.0], [1.0, -1.0]], expected: -2.0 }, + { input: [[0.1, 0.0], [1.0, 0.0]], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // correclt rounded of 0.1 + + // vec3 + { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: 1.0 }, + { input: [[0.0, 1.0, 0.0], [0.0, 1.0, 0.0]], expected: 1.0 }, + { input: [[0.0, 0.0, 1.0], [0.0, 0.0, 1.0]], expected: 1.0 }, + { input: [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], expected: 3.0 }, + { input: [[-1.0, -1.0, -1.0], [-1.0, -1.0, -1.0]], expected: 3.0 }, + { input: [[1.0, -1.0, -1.0], [-1.0, 1.0, -1.0]], expected: -1.0 }, + { input: [[0.1, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // correclt rounded of 0.1 + + // vec4 + { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: 1.0 }, + { input: [[0.0, 1.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]], expected: 1.0 }, + { input: [[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 1.0, 0.0]], expected: 1.0 }, + { input: [[0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 1.0]], expected: 1.0 }, + { input: [[1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0]], expected: 4.0 }, + { input: [[-1.0, -1.0, -1.0, -1.0], [-1.0, -1.0, -1.0, -1.0]], expected: 4.0 }, + { input: [[-1.0, 1.0, -1.0, 1.0], [1.0, -1.0, 1.0, -1.0]], expected: -4.0 }, + { input: [[0.1, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // correclt rounded of 0.1 + + ...kDotIntervalCases[p.trait], + + // Test that going out of bounds in the intermediate calculations is caught correctly. + { input: [[constants.positive.nearest_max, constants.positive.max, constants.negative.min], [1.0, 1.0, 1.0]], expected: kUnboundedBounds }, + { input: [[constants.positive.nearest_max, constants.negative.min, constants.positive.max], [1.0, 1.0, 1.0]], expected: kUnboundedBounds }, + { input: [[constants.positive.max, constants.positive.nearest_max, constants.negative.min], [1.0, 1.0, 1.0]], expected: kUnboundedBounds }, + { input: [[constants.negative.min, constants.positive.nearest_max, constants.positive.max], [1.0, 1.0, 1.0]], expected: kUnboundedBounds }, + { input: [[constants.positive.max, constants.negative.min, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: kUnboundedBounds }, + { input: [[constants.negative.min, constants.positive.max, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: kUnboundedBounds }, + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.dotInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.dotInterval([${x}], [${y}]) returned ${got}. Expected ${expected}` + ); + }); + +interface VectorToVectorCase { + input: number[]; + expected: (number | IntervalBounds)[]; +} + +// prettier-ignore +const kNormalizeIntervalCases = { + f32: [ + // vec2 + {input: [1.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0] + {input: [0.0, 1.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)]] }, // [ ~0.0, ~1.0] + {input: [-1.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_0000_b000_0000n), reinterpretU64AsF64(0xbfef_fffe_7000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0] + {input: [1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe6_a09d_5000_0000n), reinterpretU64AsF64(0x3fe6_a09f_9000_0000n)], [reinterpretU64AsF64(0x3fe6_a09d_5000_0000n), reinterpretU64AsF64(0x3fe6_a09f_9000_0000n)]] }, // [ ~1/√2, ~1/√2] + + // vec3 + {input: [1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0] + {input: [0.0, 1.0, 0.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~0.0, ~1.0, ~0.0] + {input: [0.0, 0.0, 1.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)]] }, // [ ~0.0, ~0.0, ~1.0] + {input: [-1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_0000_b000_0000n), reinterpretU64AsF64(0xbfef_fffe_7000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0] + {input: [1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe2_79a6_5000_0000n), reinterpretU64AsF64(0x3fe2_79a8_5000_0000n)], [reinterpretU64AsF64(0x3fe2_79a6_5000_0000n), reinterpretU64AsF64(0x3fe2_79a8_5000_0000n)], [reinterpretU64AsF64(0x3fe2_79a6_5000_0000n), reinterpretU64AsF64(0x3fe2_79a8_5000_0000n)]] }, // [ ~1/√3, ~1/√3, ~1/√3] + + // vec4 + {input: [1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] + {input: [0.0, 1.0, 0.0, 0.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~0.0, ~1.0, ~0.0, ~0.0] + {input: [0.0, 0.0, 1.0, 0.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~0.0, ~0.0, ~1.0, ~0.0] + {input: [0.0, 0.0, 0.0, 1.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)]] }, // [ ~0.0, ~0.0, ~0.0, ~1.0] + {input: [-1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_0000_b000_0000n), reinterpretU64AsF64(0xbfef_fffe_7000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] + {input: [1.0, 1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)], [reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)], [reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)], [reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)]] }, // [ ~1/√4, ~1/√4, ~1/√4] + ] as VectorToVectorCase[], + f16: [ + // vec2 + {input: [1.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0] + {input: [0.0, 1.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)]] }, // [ ~0.0, ~1.0] + {input: [-1.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_1600_0000_0000n), reinterpretU64AsF64(0xbfef_ce00_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0] + {input: [1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe6_7e00_0000_0000n), reinterpretU64AsF64(0x3fe6_c600_0000_0000n)], [reinterpretU64AsF64(0x3fe6_7e00_0000_0000n), reinterpretU64AsF64(0x3fe6_c600_0000_0000n)]] }, // [ ~1/√2, ~1/√2] + + // vec3 + {input: [1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0] + {input: [0.0, 1.0, 0.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~0.0, ~1.0, ~0.0] + {input: [0.0, 0.0, 1.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)]] }, // [ ~0.0, ~0.0, ~1.0] + {input: [-1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_1600_0000_0000n), reinterpretU64AsF64(0xbfef_ce00_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0] + {input: [1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe2_5a00_0000_0000n), reinterpretU64AsF64(0x3fe2_9a00_0000_0000n)], [reinterpretU64AsF64(0x3fe2_5a00_0000_0000n), reinterpretU64AsF64(0x3fe2_9a00_0000_0000n)], [reinterpretU64AsF64(0x3fe2_5a00_0000_0000n), reinterpretU64AsF64(0x3fe2_9a00_0000_0000n)]] }, // [ ~1/√3, ~1/√3, ~1/√3] + + // vec4 + {input: [1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] + {input: [0.0, 1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~0.0, ~1.0, ~0.0, ~0.0] + {input: [0.0, 0.0, 1.0, 0.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~0.0, ~0.0, ~1.0, ~0.0] + {input: [0.0, 0.0, 0.0, 1.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)]] }, // [ ~0.0, ~0.0, ~0.0, ~1.0] + {input: [-1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_1600_0000_0000n), reinterpretU64AsF64(0xbfef_ce00_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] + {input: [1.0, 1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)], [reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)], [reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)], [reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)]] }, // [ ~1/√4, ~1/√4, ~1/√4] + ] as VectorToVectorCase[], +} as const; + +g.test('normalizeInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<VectorToVectorCase>(p => kNormalizeIntervalCases[p.trait]) + ) + .fn(t => { + const x = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toVector(t.params.expected); + const got = trait.normalizeInterval(x); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.normalizeInterval([${x}]) returned ${got}. Expected ${expected}` + ); + }); + +interface VectorPairToVectorCase { + input: [number[], number[]]; + expected: (number | IntervalBounds)[]; +} + +// prettier-ignore +const kCrossIntervalCases = { + f32: [ + { input: [ + [kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max, kValue.f32.negative.subnormal.min], + [kValue.f32.negative.subnormal.min, kValue.f32.positive.subnormal.min, kValue.f32.negative.subnormal.max] + ], + expected: [ + [0.0, reinterpretU32AsF32(0x00000002)], // ~0 + [0.0, reinterpretU32AsF32(0x00000002)], // ~0 + [kValue.f32.negative.subnormal.max, kValue.f32.positive.subnormal.min] // ~0 + ] + }, + { input: [ + [0.1, -0.1, -0.1], + [-0.1, 0.1, -0.1] + ], + expected: [ + [reinterpretU32AsF32(0x3ca3d708), reinterpretU32AsF32(0x3ca3d70b)], // ~0.02 + [reinterpretU32AsF32(0x3ca3d708), reinterpretU32AsF32(0x3ca3d70b)], // ~0.02 + [reinterpretU32AsF32(0xb1400000), reinterpretU32AsF32(0x31400000)], // ~0 + ] + }, + ] as VectorPairToVectorCase[], + f16: [ + { input: [ + [kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max, kValue.f16.negative.subnormal.min], + [kValue.f16.negative.subnormal.min, kValue.f16.positive.subnormal.min, kValue.f16.negative.subnormal.max] + ], + expected: [ + [0.0, reinterpretU16AsF16(0x0002)], // ~0 + [0.0, reinterpretU16AsF16(0x0002)], // ~0 + [kValue.f16.negative.subnormal.max, kValue.f16.positive.subnormal.min] // ~0 + ] + }, + { input: [ + [0.1, -0.1, -0.1], + [-0.1, 0.1, -0.1] + ], + expected: [ + [reinterpretU16AsF16(0x251e), reinterpretU16AsF16(0x2520)], // ~0.02 + [reinterpretU16AsF16(0x251e), reinterpretU16AsF16(0x2520)], // ~0.02 + [reinterpretU16AsF16(0x8100), reinterpretU16AsF16(0x0100)] // ~0 + ] + }, + ] as VectorPairToVectorCase[], + abstract: [ + { input: [ + [kValue.f64.positive.subnormal.max, kValue.f64.negative.subnormal.max, kValue.f64.negative.subnormal.min], + [kValue.f64.negative.subnormal.min, kValue.f64.positive.subnormal.min, kValue.f64.negative.subnormal.max] + ], + expected: [0.0, 0.0, 0.0] + }, + { input: [ + [0.1, -0.1, -0.1], + [-0.1, 0.1, -0.1] + ], + expected: [ + reinterpretU64AsF64(0x3f94_7ae1_47ae_147cn), // ~0.02 + reinterpretU64AsF64(0x3f94_7ae1_47ae_147cn), // ~0.02 + 0.0 + ] + }, + ] as VectorPairToVectorCase[], +} as const; + +g.test('crossInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<VectorPairToVectorCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // parallel vectors, AXB == 0 + { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0] }, + { input: [[0.0, 1.0, 0.0], [0.0, 1.0, 0.0]], expected: [0.0, 0.0, 0.0] }, + { input: [[0.0, 0.0, 1.0], [0.0, 0.0, 1.0]], expected: [0.0, 0.0, 0.0] }, + { input: [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], expected: [0.0, 0.0, 0.0] }, + { input: [[-1.0, -1.0, -1.0], [-1.0, -1.0, -1.0]], expected: [0.0, 0.0, 0.0] }, + { input: [[0.1, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0] }, + { input: [[constants.positive.subnormal.max, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0] }, + + // non-parallel vectors, AXB != 0 + { input: [[1.0, -1.0, -1.0], [-1.0, 1.0, -1.0]], expected: [2.0, 2.0, 0.0] }, + { input: [[1.0, 2, 3], [1.0, 5.0, 7.0]], expected: [-1, -4, 3] }, + ...kCrossIntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toVector(t.params.expected); + const got = trait.crossInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.crossInterval([${x}], [${y}]) returned ${got}. Expected ${expected}` + ); + }); + +// prettier-ignore +const kReflectIntervalCases = { + f32: [ + // vec2s + { input: [[0.1, 0.1], [1.0, 1.0]], expected: [[reinterpretU32AsF32(0xbe99999a), reinterpretU32AsF32(0xbe999998)], [reinterpretU32AsF32(0xbe99999a), reinterpretU32AsF32(0xbe999998)]] }, // [~-0.3, ~-0.3] + { input: [[kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max], [1.0, 1.0]], expected: [[reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00800001)], [reinterpretU32AsF32(0x80ffffff), reinterpretU32AsF32(0x00000002)]] }, // [~0.0, ~0.0] + // vec3s + { input: [[0.1, 0.1, 0.1], [1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0xbf000001), reinterpretU32AsF32(0xbefffffe)], [reinterpretU32AsF32(0xbf000001), reinterpretU32AsF32(0xbefffffe)], [reinterpretU32AsF32(0xbf000001), reinterpretU32AsF32(0xbefffffe)]] }, // [~-0.5, ~-0.5, ~-0.5] + { input: [[kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max, 0.0], [1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00800001)], [reinterpretU32AsF32(0x80ffffff), reinterpretU32AsF32(0x00000002)], [reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00000002)]] }, // [~0.0, ~0.0, ~0.0] + // vec4s + { input: [[0.1, 0.1, 0.1, 0.1], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)], [reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)], [reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)], [reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)]] }, // [~-0.7, ~-0.7, ~-0.7, ~-0.7] + { input: [[kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00800001)], [reinterpretU32AsF32(0x80ffffff), reinterpretU32AsF32(0x00000002)], [reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00000002)], [reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00000002)]] }, // [~0.0, ~0.0, ~0.0, ~0.0] + ] as VectorPairToVectorCase[], + f16: [ + // vec2s + { input: [[0.1, 0.1], [1.0, 1.0]], expected: [[reinterpretU16AsF16(0xb4ce), reinterpretU16AsF16(0xb4cc)], [reinterpretU16AsF16(0xb4ce), reinterpretU16AsF16(0xb4cc)]] }, // [~-0.3, ~-0.3] + { input: [[kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max], [1.0, 1.0]], expected: [[reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0401)], [reinterpretU16AsF16(0x87ff), reinterpretU16AsF16(0x0002)]] }, // [~0.0, ~0.0] + // vec3s + { input: [[0.1, 0.1, 0.1], [1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0xb802), reinterpretU16AsF16(0xb7fe)], [reinterpretU16AsF16(0xb802), reinterpretU16AsF16(0xb7fe)], [reinterpretU16AsF16(0xb802), reinterpretU16AsF16(0xb7fe)]] }, // [~-0.5, ~-0.5, ~-0.5] + { input: [[kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max, 0.0], [1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0401)], [reinterpretU16AsF16(0x87ff), reinterpretU16AsF16(0x0002)], [reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0002)]] }, // [~0.0, ~0.0, ~0.0] + // vec4s + { input: [[0.1, 0.1, 0.1, 0.1], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)], [reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)], [reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)], [reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)]] }, // [~-0.7, ~-0.7, ~-0.7, ~-0.7] + { input: [[kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0401)], [reinterpretU16AsF16(0x87ff), reinterpretU16AsF16(0x0002)], [reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0002)], [reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0002)]] }, // [~0.0, ~0.0, ~0.0, ~0.0] + ] as VectorPairToVectorCase[], +} as const; + +g.test('reflectInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<VectorPairToVectorCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kReflectIntervalCases[p.trait], + + // vec2s + { input: [[1.0, 0.0], [1.0, 0.0]], expected: [-1.0, 0.0] }, + { input: [[1.0, 0.0], [0.0, 1.0]], expected: [1.0, 0.0] }, + { input: [[0.0, 1.0], [0.0, 1.0]], expected: [0.0, -1.0] }, + { input: [[0.0, 1.0], [1.0, 0.0]], expected: [0.0, 1.0] }, + { input: [[1.0, 1.0], [1.0, 1.0]], expected: [-3.0, -3.0] }, + { input: [[-1.0, -1.0], [1.0, 1.0]], expected: [3.0, 3.0] }, + // vec3s + { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [-1.0, 0.0, 0.0] }, + { input: [[0.0, 1.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 1.0, 0.0] }, + { input: [[0.0, 0.0, 1.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 1.0] }, + { input: [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]], expected: [1.0, 0.0, 0.0] }, + { input: [[1.0, 0.0, 0.0], [0.0, 0.0, 1.0]], expected: [1.0, 0.0, 0.0] }, + { input: [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], expected: [-5.0, -5.0, -5.0] }, + { input: [[-1.0, -1.0, -1.0], [1.0, 1.0, 1.0]], expected: [5.0, 5.0, 5.0] }, + // vec4s + { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [-1.0, 0.0, 0.0, 0.0] }, + { input: [[0.0, 1.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [0.0, 1.0, 0.0, 0.0] }, + { input: [[0.0, 0.0, 1.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [0.0, 0.0, 1.0, 0.0] }, + { input: [[0.0, 0.0, 0.0, 1.0], [1.0, 0.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0, 1.0] }, + { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]], expected: [1.0, 0.0, 0.0, 0.0] }, + { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]], expected: [1.0, 0.0, 0.0, 0.0] }, + { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]], expected: [1.0, 0.0, 0.0, 0.0] }, + { input: [[-1.0, -1.0, -1.0, -1.0], [1.0, 1.0, 1.0, 1.0]], expected: [7.0, 7.0, 7.0, 7.0] }, + // Test that dot going OOB bounds in the intermediate calculations propagates + { input: [[constants.positive.nearest_max, constants.positive.max, constants.negative.min], [1.0, 1.0, 1.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.positive.nearest_max, constants.negative.min, constants.positive.max], [1.0, 1.0, 1.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.positive.max, constants.positive.nearest_max, constants.negative.min], [1.0, 1.0, 1.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.negative.min, constants.positive.nearest_max, constants.positive.max], [1.0, 1.0, 1.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.positive.max, constants.negative.min, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.negative.min, constants.positive.max, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + + // Test that post-dot going OOB propagates + { input: [[constants.positive.max, 1.0, 2.0, 3.0], [-1.0, constants.positive.max, -2.0, -3.0]], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + ]; + }) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toVector(t.params.expected); + const got = trait.reflectInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.reflectInterval([${x}], [${y}]) returned ${JSON.stringify( + got + )}. Expected ${JSON.stringify(expected)}` + ); + }); + +interface MatrixToScalarCase { + input: number[][]; + expected: number | IntervalBounds; +} + +g.test('determinantInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .combineWithParams<MatrixToScalarCase>([ + // Extreme values, i.e. subnormals, very large magnitudes, and those lead to + // non-precise products, are intentionally not tested, since the accuracy of + // determinant is restricted to well behaving inputs. Handling all cases + // requires ~23! options to be calculated in the 4x4 case, so is not + // feasible. + { + input: [ + [1, 2], + [3, 4], + ], + expected: -2, + }, + { + input: [ + [-1, 2], + [-3, 4], + ], + expected: 2, + }, + { + input: [ + [11, 22], + [33, 44], + ], + expected: -242, + }, + { + input: [ + [5, 6], + [8, 9], + ], + expected: -3, + }, + { + input: [ + [4, 6], + [7, 9], + ], + expected: -6, + }, + { + input: [ + [4, 5], + [7, 8], + ], + expected: -3, + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + expected: 0, + }, + { + input: [ + [-1, 2, 3], + [-4, 5, 6], + [-7, 8, 9], + ], + expected: 0, + }, + { + input: [ + [4, 1, -1], + [-3, 0, 5], + [5, 3, 2], + ], + expected: -20, + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + expected: 0, + }, + { + input: [ + [4, 0, 0, 0], + [3, 1, -1, 3], + [2, -3, 3, 1], + [2, 3, 3, 1], + ], + expected: -240, + }, + ]) + ) + .fn(t => { + const input = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toInterval(t.params.expected); + const got = trait.determinantInterval(input); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.determinantInterval([${JSON.stringify( + input + )}]) returned '${got}. Expected '${expected}'` + ); + }); + +interface MatrixToMatrixCase { + input: number[][]; + expected: (number | IntervalBounds)[][]; +} + +g.test('transposeInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<MatrixToMatrixCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + return [ + { + input: [ + [1, 2], + [3, 4], + ], + expected: [ + [1, 3], + [2, 4], + ], + }, + { + input: [ + [1, 2], + [3, 4], + [5, 6], + ], + expected: [ + [1, 3, 5], + [2, 4, 6], + ], + }, + { + input: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + expected: [ + [1, 3, 5, 7], + [2, 4, 6, 8], + ], + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + ], + expected: [ + [1, 4], + [2, 5], + [3, 6], + ], + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + expected: [ + [1, 4, 7], + [2, 5, 8], + [3, 6, 9], + ], + }, + { + input: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + expected: [ + [1, 4, 7, 10], + [2, 5, 8, 11], + [3, 6, 9, 12], + ], + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + expected: [ + [1, 5], + [2, 6], + [3, 7], + [4, 8], + ], + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + expected: [ + [1, 5, 9], + [2, 6, 10], + [3, 7, 11], + [4, 8, 12], + ], + }, + { + input: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + expected: [ + [1, 5, 9, 13], + [2, 6, 10, 14], + [3, 7, 11, 15], + [4, 8, 12, 16], + ], + }, + { + input: [ + [constants.positive.subnormal.max, constants.positive.subnormal.min], + [constants.negative.subnormal.min, constants.negative.subnormal.max], + ], + expected: [ + [ + [0, constants.positive.subnormal.max], + [constants.negative.subnormal.min, 0], + ], + [ + [0, constants.positive.subnormal.min], + [constants.negative.subnormal.max, 0], + ], + ], + }, + ]; + }) + ) + .fn(t => { + const input = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toMatrix(t.params.expected); + const got = trait.transposeInterval(input); + t.expect( + objectEquals(expected, got), + `FP.${t.params.trait}.transposeInterval([${JSON.stringify( + input + )}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` + ); + }); + +interface MatrixPairToMatrixCase { + input: [number[][], number[][]]; + expected: (number | IntervalBounds)[][]; +} + +g.test('additionMatrixMatrixInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .combineWithParams<MatrixPairToMatrixCase>([ + // Only testing that different shapes of matrices are handled correctly + // here, to reduce test duplication. + // additionMatrixMatrixInterval uses AdditionIntervalOp for calculating intervals, + // so the testing for additionInterval covers the actual interval + // calculations. + { + input: [ + [ + [1, 2], + [3, 4], + ], + [ + [10, 20], + [30, 40], + ], + ], + expected: [ + [11, 22], + [33, 44], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + ], + [ + [10, 20], + [30, 40], + [50, 60], + ], + ], + expected: [ + [11, 22], + [33, 44], + [55, 66], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + [ + [10, 20], + [30, 40], + [50, 60], + [70, 80], + ], + ], + expected: [ + [11, 22], + [33, 44], + [55, 66], + [77, 88], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + ], + [ + [10, 20, 30], + [40, 50, 60], + ], + ], + expected: [ + [11, 22, 33], + [44, 55, 66], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + [ + [10, 20, 30], + [40, 50, 60], + [70, 80, 90], + ], + ], + expected: [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + [ + [10, 20, 30], + [40, 50, 60], + [70, 80, 90], + [1000, 1100, 1200], + ], + ], + expected: [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + [1010, 1111, 1212], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + [ + [10, 20, 30, 40], + [50, 60, 70, 80], + ], + ], + expected: [ + [11, 22, 33, 44], + [55, 66, 77, 88], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + [ + [10, 20, 30, 40], + [50, 60, 70, 80], + [90, 1000, 1100, 1200], + ], + ], + expected: [ + [11, 22, 33, 44], + [55, 66, 77, 88], + [99, 1010, 1111, 1212], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + [ + [10, 20, 30, 40], + [50, 60, 70, 80], + [90, 1000, 1100, 1200], + [1300, 1400, 1500, 1600], + ], + ], + expected: [ + [11, 22, 33, 44], + [55, 66, 77, 88], + [99, 1010, 1111, 1212], + [1313, 1414, 1515, 1616], + ], + }, + ]) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toMatrix(t.params.expected); + const got = trait.additionMatrixMatrixInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.additionMatrixMatrixInterval([${JSON.stringify(x)}], [${JSON.stringify( + y + )}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` + ); + }); + +g.test('subtractionMatrixMatrixInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .combineWithParams<MatrixPairToMatrixCase>([ + // Only testing that different shapes of matrices are handled correctly + // here, to reduce test duplication. + // subtractionMatrixMatrixInterval uses AdditionIntervalOp for calculating intervals, + // so the testing for subtractionInterval covers the actual interval + // calculations. + { + input: [ + [ + [1, 2], + [3, 4], + ], + [ + [-10, -20], + [-30, -40], + ], + ], + expected: [ + [11, 22], + [33, 44], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + ], + [ + [-10, -20], + [-30, -40], + [-50, -60], + ], + ], + expected: [ + [11, 22], + [33, 44], + [55, 66], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + [ + [-10, -20], + [-30, -40], + [-50, -60], + [-70, -80], + ], + ], + expected: [ + [11, 22], + [33, 44], + [55, 66], + [77, 88], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + ], + [ + [-10, -20, -30], + [-40, -50, -60], + ], + ], + expected: [ + [11, 22, 33], + [44, 55, 66], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + [ + [-10, -20, -30], + [-40, -50, -60], + [-70, -80, -90], + ], + ], + expected: [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + [ + [-10, -20, -30], + [-40, -50, -60], + [-70, -80, -90], + [-1000, -1100, -1200], + ], + ], + expected: [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + [1010, 1111, 1212], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + [ + [-10, -20, -30, -40], + [-50, -60, -70, -80], + ], + ], + expected: [ + [11, 22, 33, 44], + [55, 66, 77, 88], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + [ + [-10, -20, -30, -40], + [-50, -60, -70, -80], + [-90, -1000, -1100, -1200], + ], + ], + expected: [ + [11, 22, 33, 44], + [55, 66, 77, 88], + [99, 1010, 1111, 1212], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + [ + [-10, -20, -30, -40], + [-50, -60, -70, -80], + [-90, -1000, -1100, -1200], + [-1300, -1400, -1500, -1600], + ], + ], + expected: [ + [11, 22, 33, 44], + [55, 66, 77, 88], + [99, 1010, 1111, 1212], + [1313, 1414, 1515, 1616], + ], + }, + ]) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toMatrix(t.params.expected); + const got = trait.subtractionMatrixMatrixInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.subtractionMatrixMatrixInterval([${JSON.stringify(x)}], [${JSON.stringify( + y + )}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` + ); + }); + +g.test('multiplicationMatrixMatrixInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .combineWithParams<MatrixPairToMatrixCase>([ + // Only testing that different shapes of matrices are handled correctly + // here, to reduce test duplication. + // multiplicationMatrixMatrixInterval uses and transposeInterval & + // dotInterval for calculating intervals, so the testing for those functions + // will cover the actual interval calculations. + // Keep all expected result integer no larger than 2047 to ensure that all result is exactly + // represeantable in both f32 and f16. + { + input: [ + [ + [1, 2], + [3, 4], + ], + [ + [11, 22], + [33, 44], + ], + ], + expected: [ + [77, 110], + [165, 242], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + ], + [ + [11, 22], + [33, 44], + [55, 66], + ], + ], + expected: [ + [77, 110], + [165, 242], + [253, 374], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + ], + [ + [11, 22], + [33, 44], + [55, 66], + [77, 88], + ], + ], + expected: [ + [77, 110], + [165, 242], + [253, 374], + [341, 506], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + ], + [ + [11, 22], + [33, 44], + ], + ], + expected: [ + [99, 132, 165], + [209, 286, 363], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + ], + [ + [11, 22], + [33, 44], + [55, 66], + ], + ], + expected: [ + [99, 132, 165], + [209, 286, 363], + [319, 440, 561], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + ], + [ + [11, 22], + [33, 44], + [55, 66], + [77, 88], + ], + ], + expected: [ + [99, 132, 165], + [209, 286, 363], + [319, 440, 561], + [429, 594, 759], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + [ + [11, 22], + [33, 44], + ], + ], + expected: [ + [121, 154, 187, 220], + [253, 330, 407, 484], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + [ + [11, 22], + [33, 44], + [55, 66], + ], + ], + expected: [ + [121, 154, 187, 220], + [253, 330, 407, 484], + [385, 506, 627, 748], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + [ + [11, 22], + [33, 44], + [55, 66], + [77, 88], + ], + ], + expected: [ + [121, 154, 187, 220], + [253, 330, 407, 484], + [385, 506, 627, 748], + [517, 682, 847, 1012], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + ], + [ + [11, 22, 33], + [44, 55, 66], + ], + ], + expected: [ + [242, 308], + [539, 704], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + ], + [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + ], + ], + expected: [ + [242, 308], + [539, 704], + [836, 1100], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + ], + [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + [10, 11, 12], + ], + ], + expected: [ + [242, 308], + [539, 704], + [836, 1100], + [103, 136], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + [ + [11, 22, 33], + [44, 55, 66], + ], + ], + expected: [ + [330, 396, 462], + [726, 891, 1056], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + ], + ], + expected: [ + [330, 396, 462], + [726, 891, 1056], + [1122, 1386, 1650], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + [ + [11, 22, 33], + [44, 55, 66], + [77, 88, 99], + [10, 11, 12], + ], + ], + expected: [ + [330, 396, 462], + [726, 891, 1056], + [1122, 1386, 1650], + [138, 171, 204], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + [ + [11, 12, 13], + [21, 22, 23], + ], + ], + expected: [ + [188, 224, 260, 296], + [338, 404, 470, 536], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + [ + [11, 12, 13], + [21, 22, 23], + [31, 32, 33], + ], + ], + expected: [ + [188, 224, 260, 296], + [338, 404, 470, 536], + [488, 584, 680, 776], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + [ + [11, 12, 13], + [21, 22, 23], + [31, 32, 33], + [41, 42, 43], + ], + ], + expected: [ + [188, 224, 260, 296], + [338, 404, 470, 536], + [488, 584, 680, 776], + [638, 764, 890, 1016], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + [ + [11, 22, 33, 44], + [55, 66, 77, 88], + ], + ], + expected: [ + [550, 660], + [1254, 1540], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + ], + ], + expected: [ + [210, 260], + [370, 460], + [530, 660], + ], + }, + { + input: [ + [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + [41, 42, 43, 44], + ], + ], + expected: [ + [210, 260], + [370, 460], + [530, 660], + [690, 860], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + ], + ], + expected: [ + [290, 340, 390], + [510, 600, 690], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + ], + ], + expected: [ + [290, 340, 390], + [510, 600, 690], + [730, 860, 990], + ], + }, + { + input: [ + [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + [41, 42, 43, 44], + ], + ], + expected: [ + [290, 340, 390], + [510, 600, 690], + [730, 860, 990], + [950, 1120, 1290], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + ], + ], + expected: [ + [370, 420, 470, 520], + [650, 740, 830, 920], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + ], + ], + expected: [ + [370, 420, 470, 520], + [650, 740, 830, 920], + [930, 1060, 1190, 1320], + ], + }, + { + input: [ + [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + [41, 42, 43, 44], + ], + ], + expected: [ + [370, 420, 470, 520], + [650, 740, 830, 920], + [930, 1060, 1190, 1320], + [1210, 1380, 1550, 1720], + ], + }, + ]) + ) + .fn(t => { + const [x, y] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toMatrix(t.params.expected); + const got = trait.multiplicationMatrixMatrixInterval(x, y); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.multiplicationMatrixMatrixInterval([${JSON.stringify( + x + )}], [${JSON.stringify(y)}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify( + expected + )}]'` + ); + }); + +interface MatrixScalarToMatrixCase { + matrix: number[][]; + scalar: number; + expected: (number | IntervalBounds)[][]; +} + +const kMultiplicationMatrixScalarIntervalCases = { + f32: [ + // From https://github.com/gpuweb/cts/issues/3044 + { + matrix: [ + [kValue.f32.negative.min, 0], + [0, 0], + ], + scalar: kValue.f32.negative.subnormal.min, + expected: [ + [[0, reinterpretU32AsF32(0x407ffffe)], 0], // [[0, 3.9999995...], 0], + [0, 0], + ], + }, + ] as MatrixScalarToMatrixCase[], + f16: [ + // From https://github.com/gpuweb/cts/issues/3044 + { + matrix: [ + [kValue.f16.negative.min, 0], + [0, 0], + ], + scalar: kValue.f16.negative.subnormal.min, + expected: [ + [[0, reinterpretU16AsF16(0x43fe)], 0], // [[0, 3.99609375], 0] + [0, 0], + ], + }, + ] as MatrixScalarToMatrixCase[], +} as const; + +g.test('multiplicationMatrixScalarInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<MatrixScalarToMatrixCase>(p => { + // Primarily testing that different shapes of matrices are handled correctly + // here, to reduce test duplication. Additional testing for edge case + // discovered in https://github.com/gpuweb/cts/issues/3044. + // + // multiplicationMatrixScalarInterval uses for calculating intervals, + // so the testing for multiplicationInterval covers the actual interval + // calculations. + return [ + { + matrix: [ + [1, 2], + [3, 4], + ], + scalar: 10, + expected: [ + [10, 20], + [30, 40], + ], + }, + { + matrix: [ + [1, 2], + [3, 4], + [5, 6], + ], + scalar: 10, + expected: [ + [10, 20], + [30, 40], + [50, 60], + ], + }, + { + matrix: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + scalar: 10, + expected: [ + [10, 20], + [30, 40], + [50, 60], + [70, 80], + ], + }, + { + matrix: [ + [1, 2, 3], + [4, 5, 6], + ], + scalar: 10, + expected: [ + [10, 20, 30], + [40, 50, 60], + ], + }, + { + matrix: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + scalar: 10, + expected: [ + [10, 20, 30], + [40, 50, 60], + [70, 80, 90], + ], + }, + { + matrix: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + scalar: 10, + expected: [ + [10, 20, 30], + [40, 50, 60], + [70, 80, 90], + [100, 110, 120], + ], + }, + { + matrix: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + scalar: 10, + expected: [ + [10, 20, 30, 40], + [50, 60, 70, 80], + ], + }, + { + matrix: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + scalar: 10, + expected: [ + [10, 20, 30, 40], + [50, 60, 70, 80], + [90, 100, 110, 120], + ], + }, + { + matrix: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + scalar: 10, + expected: [ + [10, 20, 30, 40], + [50, 60, 70, 80], + [90, 100, 110, 120], + [130, 140, 150, 160], + ], + }, + ...kMultiplicationMatrixScalarIntervalCases[p.trait], + ]; + }) + ) + .fn(t => { + const matrix = t.params.matrix; + const scalar = t.params.scalar; + const trait = FP[t.params.trait]; + const expected = trait.toMatrix(t.params.expected); + const got = trait.multiplicationMatrixScalarInterval(matrix, scalar); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.multiplicationMatrixScalarInterval([${JSON.stringify( + matrix + )}], ${scalar}) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` + ); + }); + +// There are no explicit tests for multiplicationScalarMatrixInterval, since it +// is just a pass-through to multiplicationMatrixScalarInterval + +interface MatrixVectorToVectorCase { + matrix: number[][]; + vector: number[]; + expected: (number | IntervalBounds)[]; +} + +g.test('multiplicationMatrixVectorInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .combineWithParams<MatrixVectorToVectorCase>([ + // Only testing that different shapes of matrices are handled correctly + // here, to reduce test duplication. + // multiplicationMatrixVectorInterval uses DotIntervalOp & + // TransposeIntervalOp for calculating intervals, so the testing for + // dotInterval & transposeInterval covers the actual interval + // calculations. + { + matrix: [ + [1, 2], + [3, 4], + ], + vector: [11, 22], + expected: [77, 110], + }, + { + matrix: [ + [1, 2, 3], + [4, 5, 6], + ], + vector: [11, 22], + expected: [99, 132, 165], + }, + { + matrix: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + ], + vector: [11, 22], + expected: [121, 154, 187, 220], + }, + { + matrix: [ + [1, 2], + [3, 4], + [5, 6], + ], + vector: [11, 22, 33], + expected: [242, 308], + }, + { + matrix: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + ], + vector: [11, 22, 33], + expected: [330, 396, 462], + }, + { + matrix: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + ], + vector: [11, 22, 33], + expected: [418, 484, 550, 616], + }, + { + matrix: [ + [1, 2], + [3, 4], + [5, 6], + [7, 8], + ], + vector: [11, 22, 33, 44], + expected: [550, 660], + }, + { + matrix: [ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + ], + vector: [11, 22, 33, 44], + expected: [770, 880, 990], + }, + { + matrix: [ + [1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16], + ], + vector: [11, 22, 33, 44], + expected: [990, 1100, 1210, 1320], + }, + ]) + ) + .fn(t => { + const matrix = t.params.matrix; + const vector = t.params.vector; + const trait = FP[t.params.trait]; + const expected = trait.toVector(t.params.expected); + const got = trait.multiplicationMatrixVectorInterval(matrix, vector); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.multiplicationMatrixVectorInterval([${JSON.stringify( + matrix + )}], [${JSON.stringify(vector)}]) returned '[${JSON.stringify( + got + )}]'. Expected '[${JSON.stringify(expected)}]'` + ); + }); + +interface VectorMatrixToVectorCase { + vector: number[]; + matrix: number[][]; + expected: (number | IntervalBounds)[]; +} + +g.test('multiplicationVectorMatrixInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .combineWithParams<VectorMatrixToVectorCase>([ + // Only testing that different shapes of matrices are handled correctly + // here, to reduce test duplication. + // multiplicationVectorMatrixInterval uses DotIntervalOp for calculating + // intervals, so the testing for dotInterval covers the actual interval + // calculations. + // Keep all expected result integer no larger than 2047 to ensure that all result is exactly + // represeantable in both f32 and f16. + { + vector: [1, 2], + matrix: [ + [11, 22], + [33, 44], + ], + expected: [55, 121], + }, + { + vector: [1, 2], + matrix: [ + [11, 22], + [33, 44], + [55, 66], + ], + expected: [55, 121, 187], + }, + { + vector: [1, 2], + matrix: [ + [11, 22], + [33, 44], + [55, 66], + [77, 88], + ], + expected: [55, 121, 187, 253], + }, + { + vector: [1, 2, 3], + matrix: [ + [11, 12, 13], + [21, 22, 23], + ], + expected: [74, 134], + }, + { + vector: [1, 2, 3], + matrix: [ + [11, 12, 13], + [21, 22, 23], + [31, 32, 33], + ], + expected: [74, 134, 194], + }, + { + vector: [1, 2, 3], + matrix: [ + [11, 12, 13], + [21, 22, 23], + [31, 32, 33], + [41, 42, 43], + ], + expected: [74, 134, 194, 254], + }, + { + vector: [1, 2, 3, 4], + matrix: [ + [11, 12, 13, 14], + [21, 22, 23, 24], + ], + expected: [130, 230], + }, + { + vector: [1, 2, 3, 4], + matrix: [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + ], + expected: [130, 230, 330], + }, + { + vector: [1, 2, 3, 4], + matrix: [ + [11, 12, 13, 14], + [21, 22, 23, 24], + [31, 32, 33, 34], + [41, 42, 43, 44], + ], + expected: [130, 230, 330, 430], + }, + ]) + ) + .fn(t => { + const vector = t.params.vector; + const matrix = t.params.matrix; + const trait = FP[t.params.trait]; + const expected = trait.toVector(t.params.expected); + const got = trait.multiplicationVectorMatrixInterval(vector, matrix); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.multiplicationVectorMatrixInterval([${JSON.stringify( + vector + )}], [${JSON.stringify(matrix)}]) returned '[${JSON.stringify( + got + )}]'. Expected '[${JSON.stringify(expected)}]'` + ); + }); + +// API - Acceptance Intervals w/ bespoke implementations + +interface FaceForwardCase { + input: [number[], number[], number[]]; + expected: ((number | IntervalBounds)[] | undefined)[]; +} + +g.test('faceForwardIntervals') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<FaceForwardCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + // vec2 + { input: [[1.0, 0.0], [1.0, 0.0], [1.0, 0.0]], expected: [[-1.0, 0.0]] }, + { input: [[-1.0, 0.0], [1.0, 0.0], [1.0, 0.0]], expected: [[1.0, 0.0]] }, + { input: [[1.0, 0.0], [-1.0, 1.0], [1.0, -1.0]], expected: [[1.0, 0.0]] }, + { input: [[-1.0, 0.0], [-1.0, 1.0], [1.0, -1.0]], expected: [[-1.0, 0.0]] }, + { input: [[10.0, 0.0], [10.0, 0.0], [10.0, 0.0]], expected: [[-10.0, 0.0]] }, + { input: [[-10.0, 0.0], [10.0, 0.0], [10.0, 0.0]], expected: [[10.0, 0.0]] }, + { input: [[10.0, 0.0], [-10.0, 10.0], [10.0, -10.0]], expected: [[10.0, 0.0]] }, + { input: [[-10.0, 0.0], [-10.0, 10.0], [10.0, -10.0]], expected: [[-10.0, 0.0]] }, + { input: [[0.1, 0.0], [0.1, 0.0], [0.1, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0]] }, + { input: [[-0.1, 0.0], [0.1, 0.0], [0.1, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0]] }, + { input: [[0.1, 0.0], [-0.1, 0.1], [0.1, -0.1]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0]] }, + { input: [[-0.1, 0.0], [-0.1, 0.1], [0.1, -0.1]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0]] }, + + // vec3 + { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [[-1.0, 0.0, 0.0]] }, + { input: [[-1.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [[1.0, 0.0, 0.0]] }, + { input: [[1.0, 0.0, 0.0], [-1.0, 1.0, 0.0], [1.0, -1.0, 0.0]], expected: [[1.0, 0.0, 0.0]] }, + { input: [[-1.0, 0.0, 0.0], [-1.0, 1.0, 0.0], [1.0, -1.0, 0.0]], expected: [[-1.0, 0.0, 0.0]] }, + { input: [[10.0, 0.0, 0.0], [10.0, 0.0, 0.0], [10.0, 0.0, 0.0]], expected: [[-10.0, 0.0, 0.0]] }, + { input: [[-10.0, 0.0, 0.0], [10.0, 0.0, 0.0], [10.0, 0.0, 0.0]], expected: [[10.0, 0.0, 0.0]] }, + { input: [[10.0, 0.0, 0.0], [-10.0, 10.0, 0.0], [10.0, -10.0, 0.0]], expected: [[10.0, 0.0, 0.0]] }, + { input: [[-10.0, 0.0, 0.0], [-10.0, 10.0, 0.0], [10.0, -10.0, 0.0]], expected: [[-10.0, 0.0, 0.0]] }, + { input: [[0.1, 0.0, 0.0], [0.1, 0.0, 0.0], [0.1, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0]] }, + { input: [[-0.1, 0.0, 0.0], [0.1, 0.0, 0.0], [0.1, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0]] }, + { input: [[0.1, 0.0, 0.0], [-0.1, 0.0, 0.0], [0.1, -0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0]] }, + { input: [[-0.1, 0.0, 0.0], [-0.1, 0.0, 0.0], [0.1, -0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0]] }, + + // vec4 + { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [[-1.0, 0.0, 0.0, 0.0]] }, + { input: [[-1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [[1.0, 0.0, 0.0, 0.0]] }, + { input: [[1.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 0.0], [1.0, -1.0, 0.0, 0.0]], expected: [[1.0, 0.0, 0.0, 0.0]] }, + { input: [[-1.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 0.0], [1.0, -1.0, 0.0, 0.0]], expected: [[-1.0, 0.0, 0.0, 0.0]] }, + { input: [[10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0]], expected: [[-10.0, 0.0, 0.0, 0.0]] }, + { input: [[-10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0]], expected: [[10.0, 0.0, 0.0, 0.0]] }, + { input: [[10.0, 0.0, 0.0, 0.0], [-10.0, 10.0, 0.0, 0.0], [10.0, -10.0, 0.0, 0.0]], expected: [[10.0, 0.0, 0.0, 0.0]] }, + { input: [[-10.0, 0.0, 0.0, 0.0], [-10.0, 10.0, 0.0, 0.0], [10.0, -10.0, 0.0, 0.0]], expected: [[-10.0, 0.0, 0.0, 0.0]] }, + { input: [[0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0, 0.0]] }, + { input: [[-0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0, 0.0]] }, + { input: [[0.1, 0.0, 0.0, 0.0], [-0.1, 0.0, 0.0, 0.0], [0.1, -0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0, 0.0]] }, + { input: [[-0.1, 0.0, 0.0, 0.0], [-0.1, 0.0, 0.0, 0.0], [0.1, -0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0, 0.0]] }, + + // dot(y, z) === 0 + { input: [[1.0, 1.0], [1.0, 0.0], [0.0, 1.0]], expected: [[-1.0, -1.0]] }, + + // subnormals, also dot(y, z) spans 0 + { input: [[constants.positive.subnormal.max, 0.0], [constants.positive.subnormal.min, 0.0], [constants.negative.subnormal.min, 0.0]], expected: [[[0.0, constants.positive.subnormal.max], 0.0], [[constants.negative.subnormal.min, 0], 0.0]] }, + + // dot going OOB returns [undefined, x, -x] + { input: [[1.0, 1.0], [constants.positive.max, constants.positive.max], [constants.positive.max, constants.positive.max]], expected: [undefined, [1, 1], [-1, -1]] }, + ]; + }) + ) + .fn(t => { + const [x, y, z] = t.params.input; + const trait = FP[t.params.trait]; + const expected = t.params.expected.map(e => (e !== undefined ? trait.toVector(e) : undefined)); + const got = trait.faceForwardIntervals(x, y, z); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.faceForwardInterval([${x}], [${y}], [${z}]) returned [${got}]. Expected [${expected}]` + ); + }); + +interface ModfCase { + input: number; + fract: number | IntervalBounds; + whole: number | IntervalBounds; +} + +g.test('modfInterval') + .params(u => + u + .combine('trait', ['f32', 'f16', 'abstract'] as const) + .beginSubcases() + .expandWithParams<ModfCase>(p => { + const constants = FP[p.trait].constants(); + // prettier-ignore + return [ + // Normals + { input: 0, fract: 0, whole: 0 }, + { input: 1, fract: 0, whole: 1 }, + { input: -1, fract: 0, whole: -1 }, + { input: 0.5, fract: 0.5, whole: 0 }, + { input: -0.5, fract: -0.5, whole: 0 }, + { input: 2.5, fract: 0.5, whole: 2 }, + { input: -2.5, fract: -0.5, whole: -2 }, + { input: 10.0, fract: 0, whole: 10 }, + { input: -10.0, fract: 0, whole: -10 }, + + // Subnormals + { input: constants.positive.subnormal.min, fract: [0, constants.positive.subnormal.min], whole: 0 }, + { input: constants.positive.subnormal.max, fract: [0, constants.positive.subnormal.max], whole: 0 }, + { input: constants.negative.subnormal.min, fract: [constants.negative.subnormal.min, 0], whole: 0 }, + { input: constants.negative.subnormal.max, fract: [constants.negative.subnormal.max, 0], whole: 0 }, + + // Boundaries + { input: constants.negative.min, fract: 0, whole: constants.negative.min }, + { input: constants.negative.max, fract: constants.negative.max, whole: 0 }, + { input: constants.positive.min, fract: constants.positive.min, whole: 0 }, + { input: constants.positive.max, fract: 0, whole: constants.positive.max }, + ]; + }) + ) + .fn(t => { + const trait = FP[t.params.trait]; + const expected = { + fract: trait.toInterval(t.params.fract), + whole: trait.toInterval(t.params.whole), + }; + + const got = trait.modfInterval(t.params.input); + t.expect( + objectEquals(expected, got), + `${trait}.modfInterval([${t.params.input}) returned { fract: [${got.fract}], whole: [${got.whole}] }. Expected { fract: [${expected.fract}], whole: [${expected.whole}] }` + ); + }); + +interface RefractCase { + input: [number[], number[], number]; + expected: (number | IntervalBounds)[]; +} + +// Scope for refractInterval tests so that they can have constants for magic +// numbers that don't pollute the global namespace or have unwieldy long names. +{ + const kNegativeOneBounds = { + f32: [ + reinterpretU64AsF64(0xbff0_0000_c000_0000n), + reinterpretU64AsF64(0xbfef_ffff_4000_0000n), + ] as IntervalBounds, + f16: [reinterpretU16AsF16(0xbc06), reinterpretU16AsF16(0xbbfa)] as IntervalBounds, + } as const; + + // prettier-ignore + const kRefractIntervalCases = { + f32: [ + // k > 0 + // vec2 + { input: [[1, -2], [3, 4], 5], expected: [[reinterpretU32AsF32(0x40ce87a4), reinterpretU32AsF32(0x40ce8840)], // ~6.454... + [reinterpretU32AsF32(0xc100fae8), reinterpretU32AsF32(0xc100fa80)]] }, // ~-8.061... + // vec3 + { input: [[1, -2, 3], [-4, 5, -6], 7], expected: [[reinterpretU32AsF32(0x40d24480), reinterpretU32AsF32(0x40d24c00)], // ~6.571... + [reinterpretU32AsF32(0xc1576f80), reinterpretU32AsF32(0xc1576ad0)], // ~-13.464... + [reinterpretU32AsF32(0x41a2d9b0), reinterpretU32AsF32(0x41a2dc80)]] }, // ~20.356... + // vec4 + { input: [[1, -2, 3, -4], [-5, 6, -7, 8], 9], expected: [[reinterpretU32AsF32(0x410ae480), reinterpretU32AsF32(0x410af240)], // ~8.680... + [reinterpretU32AsF32(0xc18cf7c0), reinterpretU32AsF32(0xc18cef80)], // ~-17.620... + [reinterpretU32AsF32(0x41d46cc0), reinterpretU32AsF32(0x41d47660)], // ~26.553... + [reinterpretU32AsF32(0xc20dfa80), reinterpretU32AsF32(0xc20df500)]] }, // ~-35.494... + ] as RefractCase[], + f16: [ + // k > 0 + // vec2 + { input: [[1, -2], [3, 4], 5], expected: [[reinterpretU16AsF16(0x4620), reinterpretU16AsF16(0x46bc)], // ~6.454... + [reinterpretU16AsF16(0xc840), reinterpretU16AsF16(0xc7b0)]] }, // ~-8.061... + // vec3 + { input: [[1, -2, 3], [-4, 5, -6], 7], expected: [[reinterpretU16AsF16(0x4100), reinterpretU16AsF16(0x4940)], // ~6.571... + [reinterpretU16AsF16(0xcc98), reinterpretU16AsF16(0xc830)], // ~-13.464... + [reinterpretU16AsF16(0x4b20), reinterpretU16AsF16(0x4e90)]] }, // ~20.356... + // vec4 + // x = [1, -2, 3, -4], y = [-5, 6, -7, 8], z = 9, + // dot(y, x) = -71, k = 1.0 - 9 * 9 * (1.0 - 71 * 71) = 408241 overflow f16. + { input: [[1, -2, 3, -4], [-5, 6, -7, 8], 9], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + // x = [1, -2, 3, -4], y = [-5, 4, -3, 2], z = 2.5, + // dot(y, x) = -30, k = 1.0 - 2.5 * 2.5 * (1.0 - 30 * 30) = 5619.75. + // a = z * dot(y, x) + sqrt(k) = ~-0.035, result is about z * x - a * y = [~2.325, ~-4.86, ~7.4025, ~-9.93] + { input: [[1, -2, 3, -4], [-5, 4, -3, 2], 2.5], expected: [[reinterpretU16AsF16(0x3900), reinterpretU16AsF16(0x4410)], // ~2.325 + [reinterpretU16AsF16(0xc640), reinterpretU16AsF16(0xc300)], // ~-4.86 + [reinterpretU16AsF16(0x4660), reinterpretU16AsF16(0x4838)], // ~7.4025 + [reinterpretU16AsF16(0xc950), reinterpretU16AsF16(0xc8a0)]] }, // ~-9.93 + ] as RefractCase[], + } as const; + + g.test('refractInterval') + .params(u => + u + .combine('trait', ['f32', 'f16'] as const) + .beginSubcases() + .expandWithParams<RefractCase>(p => { + const trait = FP[p.trait]; + const constants = trait.constants(); + // prettier-ignore + return [ + ...kRefractIntervalCases[p.trait], + + // k < 0 + { input: [[1, 1], [0.1, 0], 10], expected: [0, 0] }, + + // k contains 0 + { input: [[1, 1], [0.1, 0], 1.005038], expected: [kUnboundedBounds, kUnboundedBounds] }, + + // k > 0 + // vec2 + { input: [[1, 1], [1, 0], 1], expected: [kNegativeOneBounds[p.trait], 1] }, + // vec3 + { input: [[1, 1, 1], [1, 0, 0], 1], expected: [kNegativeOneBounds[p.trait], 1, 1] }, + // vec4 + { input: [[1, 1, 1, 1], [1, 0, 0, 0], 1], expected: [kNegativeOneBounds[p.trait], 1, 1, 1] }, + + // Test that dot going OOB bounds in the intermediate calculations propagates + { input: [[constants.positive.nearest_max, constants.positive.max, constants.negative.min], [1.0, 1.0, 1.0], 1], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.positive.nearest_max, constants.negative.min, constants.positive.max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.positive.max, constants.positive.nearest_max, constants.negative.min], [1.0, 1.0, 1.0], 1], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.negative.min, constants.positive.nearest_max, constants.positive.max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.positive.max, constants.negative.min, constants.positive.nearest_max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + { input: [[constants.negative.min, constants.positive.max, constants.positive.nearest_max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedBounds, kUnboundedBounds, kUnboundedBounds] }, + ]; + }) + ) + .fn(t => { + const [i, s, r] = t.params.input; + const trait = FP[t.params.trait]; + const expected = trait.toVector(t.params.expected); + const got = trait.refractInterval(i, s, r); + t.expect( + objectEquals(expected, got), + `${t.params.trait}.refractIntervals([${i}], [${s}], ${r}) returned [${got}]. Expected [${expected}]` + ); + }); +} |