Adding upstream version 1.16.10.upstream/1.16.10upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

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 "?"
+}