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-rw-r--r--test/float_lit2.go164
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diff --git a/test/float_lit2.go b/test/float_lit2.go
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+// 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 "?"
+}