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Diffstat (limited to '')
| -rw-r--r-- | test/float_lit2.go | 164 |
1 files changed, 164 insertions, 0 deletions
diff --git a/test/float_lit2.go b/test/float_lit2.go new file mode 100644 index 0000000..901698f --- /dev/null +++ b/test/float_lit2.go @@ -0,0 +1,164 @@ +// run + +// Check conversion of constant to float32/float64 near min/max boundaries. + +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package main + +import ( + "fmt" + "math" +) + +// The largest exact float32 is f₁ = (1+1-1/2²³)×2¹²⁷ = (2-2⁻²³)×2¹²⁷ = 2¹²⁸ - 2¹⁰⁴. +// The next float32 would be f₂ = (1+1)×2¹²⁷ = 1×2¹²⁸, except that exponent is out of range. +// Float32 conversion rounds to the nearest float32, rounding to even mantissa: +// between f₁ and f₂, values closer to f₁ round to f₁ and values closer to f₂ are rejected as out of range. +// f₁ is an odd mantissa, so the halfway point (f₁+f₂)/2 rounds to f₂ and is rejected. +// The halfway point is (f₁+f₂)/2 = 2¹²⁸ - 2¹⁰³. +// +// The same is true of float64, with different constants: s/24/53/ and s/128/1024/. + +const ( + two24 = 1.0 * (1 << 24) + two53 = 1.0 * (1 << 53) + two64 = 1.0 * (1 << 64) + two128 = two64 * two64 + two256 = two128 * two128 + two512 = two256 * two256 + two768 = two512 * two256 + two1024 = two512 * two512 + + ulp32 = two128 / two24 + max32 = two128 - ulp32 + + ulp64 = two1024 / two53 + max64 = two1024 - ulp64 +) + +var cvt = []struct { + bits uint64 // keep us honest + exact interface{} + approx interface{} + text string +}{ + // 0 + {0x7f7ffffe, float32(max32 - ulp32), float32(max32 - ulp32 - ulp32/2), "max32 - ulp32 - ulp32/2"}, + {0x7f7ffffe, float32(max32 - ulp32), float32(max32 - ulp32), "max32 - ulp32"}, + {0x7f7ffffe, float32(max32 - ulp32), float32(max32 - ulp32/2), "max32 - ulp32/2"}, + {0x7f7ffffe, float32(max32 - ulp32), float32(max32 - ulp32 + ulp32/2), "max32 - ulp32 + ulp32/2"}, + {0x7f7fffff, float32(max32), float32(max32 - ulp32 + ulp32/2 + ulp32/two64), "max32 - ulp32 + ulp32/2 + ulp32/two64"}, + {0x7f7fffff, float32(max32), float32(max32 - ulp32/2 + ulp32/two64), "max32 - ulp32/2 + ulp32/two64"}, + {0x7f7fffff, float32(max32), float32(max32), "max32"}, + {0x7f7fffff, float32(max32), float32(max32 + ulp32/2 - ulp32/two64), "max32 + ulp32/2 - ulp32/two64"}, + + {0xff7ffffe, float32(-(max32 - ulp32)), float32(-(max32 - ulp32 - ulp32/2)), "-(max32 - ulp32 - ulp32/2)"}, + {0xff7ffffe, float32(-(max32 - ulp32)), float32(-(max32 - ulp32)), "-(max32 - ulp32)"}, + {0xff7ffffe, float32(-(max32 - ulp32)), float32(-(max32 - ulp32/2)), "-(max32 - ulp32/2)"}, + {0xff7ffffe, float32(-(max32 - ulp32)), float32(-(max32 - ulp32 + ulp32/2)), "-(max32 - ulp32 + ulp32/2)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 - ulp32 + ulp32/2 + ulp32/two64)), "-(max32 - ulp32 + ulp32/2 + ulp32/two64)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 - ulp32/2 + ulp32/two64)), "-(max32 - ulp32/2 + ulp32/two64)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32)), "-(max32)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 + ulp32/2 - ulp32/two64)), "-(max32 + ulp32/2 - ulp32/two64)"}, + + // These are required to work: according to the Go spec, the internal float mantissa must be at least 256 bits, + // and these expressions can be represented exactly with a 256-bit mantissa. + {0x7f7fffff, float32(max32), float32(max32 - ulp32 + ulp32/2 + 1), "max32 - ulp32 + ulp32/2 + 1"}, + {0x7f7fffff, float32(max32), float32(max32 - ulp32/2 + 1), "max32 - ulp32/2 + 1"}, + {0x7f7fffff, float32(max32), float32(max32 + ulp32/2 - 1), "max32 + ulp32/2 - 1"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 - ulp32 + ulp32/2 + 1)), "-(max32 - ulp32 + ulp32/2 + 1)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 - ulp32/2 + 1)), "-(max32 - ulp32/2 + 1)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 + ulp32/2 - 1)), "-(max32 + ulp32/2 - 1)"}, + + {0x7f7fffff, float32(max32), float32(max32 - ulp32 + ulp32/2 + 1/two128), "max32 - ulp32 + ulp32/2 + 1/two128"}, + {0x7f7fffff, float32(max32), float32(max32 - ulp32/2 + 1/two128), "max32 - ulp32/2 + 1/two128"}, + {0x7f7fffff, float32(max32), float32(max32 + ulp32/2 - 1/two128), "max32 + ulp32/2 - 1/two128"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 - ulp32 + ulp32/2 + 1/two128)), "-(max32 - ulp32 + ulp32/2 + 1/two128)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 - ulp32/2 + 1/two128)), "-(max32 - ulp32/2 + 1/two128)"}, + {0xff7fffff, float32(-(max32)), float32(-(max32 + ulp32/2 - 1/two128)), "-(max32 + ulp32/2 - 1/two128)"}, + + {0x7feffffffffffffe, float64(max64 - ulp64), float64(max64 - ulp64 - ulp64/2), "max64 - ulp64 - ulp64/2"}, + {0x7feffffffffffffe, float64(max64 - ulp64), float64(max64 - ulp64), "max64 - ulp64"}, + {0x7feffffffffffffe, float64(max64 - ulp64), float64(max64 - ulp64/2), "max64 - ulp64/2"}, + {0x7feffffffffffffe, float64(max64 - ulp64), float64(max64 - ulp64 + ulp64/2), "max64 - ulp64 + ulp64/2"}, + {0x7fefffffffffffff, float64(max64), float64(max64 - ulp64 + ulp64/2 + ulp64/two64), "max64 - ulp64 + ulp64/2 + ulp64/two64"}, + {0x7fefffffffffffff, float64(max64), float64(max64 - ulp64/2 + ulp64/two64), "max64 - ulp64/2 + ulp64/two64"}, + {0x7fefffffffffffff, float64(max64), float64(max64), "max64"}, + {0x7fefffffffffffff, float64(max64), float64(max64 + ulp64/2 - ulp64/two64), "max64 + ulp64/2 - ulp64/two64"}, + + {0xffeffffffffffffe, float64(-(max64 - ulp64)), float64(-(max64 - ulp64 - ulp64/2)), "-(max64 - ulp64 - ulp64/2)"}, + {0xffeffffffffffffe, float64(-(max64 - ulp64)), float64(-(max64 - ulp64)), "-(max64 - ulp64)"}, + {0xffeffffffffffffe, float64(-(max64 - ulp64)), float64(-(max64 - ulp64/2)), "-(max64 - ulp64/2)"}, + {0xffeffffffffffffe, float64(-(max64 - ulp64)), float64(-(max64 - ulp64 + ulp64/2)), "-(max64 - ulp64 + ulp64/2)"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64 - ulp64 + ulp64/2 + ulp64/two64)), "-(max64 - ulp64 + ulp64/2 + ulp64/two64)"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64 - ulp64/2 + ulp64/two64)), "-(max64 - ulp64/2 + ulp64/two64)"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64)), "-(max64)"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64 + ulp64/2 - ulp64/two64)), "-(max64 + ulp64/2 - ulp64/two64)"}, + + // These are required to work. + // The mantissas are exactly 256 bits. + // max64 is just below 2¹⁰²⁴ so the bottom bit we can use is 2⁷⁶⁸. + {0x7fefffffffffffff, float64(max64), float64(max64 - ulp64 + ulp64/2 + two768), "max64 - ulp64 + ulp64/2 + two768"}, + {0x7fefffffffffffff, float64(max64), float64(max64 - ulp64/2 + two768), "max64 - ulp64/2 + two768"}, + {0x7fefffffffffffff, float64(max64), float64(max64 + ulp64/2 - two768), "max64 + ulp64/2 - two768"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64 - ulp64 + ulp64/2 + two768)), "-(max64 - ulp64 + ulp64/2 + two768)"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64 - ulp64/2 + two768)), "-(max64 - ulp64/2 + two768)"}, + {0xffefffffffffffff, float64(-(max64)), float64(-(max64 + ulp64/2 - two768)), "-(max64 + ulp64/2 - two768)"}, +} + +var bugged = false + +func bug() { + if !bugged { + bugged = true + fmt.Println("BUG") + } +} + +func main() { + u64 := math.Float64frombits(0x7fefffffffffffff) - math.Float64frombits(0x7feffffffffffffe) + if ulp64 != u64 { + bug() + fmt.Printf("ulp64=%g, want %g", ulp64, u64) + } + + u32 := math.Float32frombits(0x7f7fffff) - math.Float32frombits(0x7f7ffffe) + if ulp32 != u32 { + bug() + fmt.Printf("ulp32=%g, want %g", ulp32, u32) + } + + for _, c := range cvt { + if bits(c.exact) != c.bits { + bug() + fmt.Printf("%s: inconsistent table: bits=%#x (%g) but exact=%g (%#x)\n", c.text, c.bits, fromBits(c.bits, c.exact), c.exact, bits(c.exact)) + } + if c.approx != c.exact || bits(c.approx) != c.bits { + bug() + fmt.Printf("%s: have %g (%#x) want %g (%#x)\n", c.text, c.approx, bits(c.approx), c.exact, c.bits) + } + } +} + +func bits(x interface{}) interface{} { + switch x := x.(type) { + case float32: + return uint64(math.Float32bits(x)) + case float64: + return math.Float64bits(x) + } + return 0 +} + +func fromBits(b uint64, x interface{}) interface{} { + switch x.(type) { + case float32: + return math.Float32frombits(uint32(b)) + case float64: + return math.Float64frombits(b) + } + return "?" +} |