go/test/float_lit2.go

// 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+(1-2²³))×2¹²⁷ = (1-2²⁴)×2¹²⁸ = 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 - 2¹⁰⁵.
//
// 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 "?"
}
-												cmd/gc: fix float32 const conversion and printing of big float consts

The float32 const conversion used to round to float64
and then use the hardware to round to float32.
Even though there was a range check before this
conversion, the double rounding introduced inaccuracy:
the round to float64 might round the value further away
from the float32 range, reaching a float64 value that
could not actually be rounded to float32. The hardware
appears to give us 0 in that case, but it is probably undefined.
Double rounding also meant that the wrong value might
be used for certain border cases.

Do the rounding the float32 ourselves, just as we already
did the rounding to float64. This makes the conversion
precise and also makes the conversion match the range check.

Finally, add some code to print very large (bigger than float64)
floating point constants in decimal floating point notation instead
of falling back to the precise but human-unreadable binary floating
point notation.

Fixes #8015.

LGTM=iant
R=golang-codereviews, iant
CC=golang-codereviews, r
https://golang.org/cl/100580044

											
										
										
											2014-05-19 20:57:59 -06:00
+								// 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"
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+									"math"
-												cmd/gc: fix float32 const conversion and printing of big float consts

The float32 const conversion used to round to float64
and then use the hardware to round to float32.
Even though there was a range check before this
conversion, the double rounding introduced inaccuracy:
the round to float64 might round the value further away
from the float32 range, reaching a float64 value that
could not actually be rounded to float32. The hardware
appears to give us 0 in that case, but it is probably undefined.
Double rounding also meant that the wrong value might
be used for certain border cases.

Do the rounding the float32 ourselves, just as we already
did the rounding to float64. This makes the conversion
precise and also makes the conversion match the range check.

Finally, add some code to print very large (bigger than float64)
floating point constants in decimal floating point notation instead
of falling back to the precise but human-unreadable binary floating
point notation.

Fixes #8015.

LGTM=iant
R=golang-codereviews, iant
CC=golang-codereviews, r
https://golang.org/cl/100580044

											
										
										
											2014-05-19 20:57:59 -06:00
+								)
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								// The largest exact float32 is f₁ = (1+(1-2²³))×2¹²⁷ = (1-2²⁴)×2¹²⁸ = 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:
-												test: fix two typos in float_lit2.go

Noted by gri in CL 100660044 review but I missed them.

TBR=gri
CC=golang-codereviews
https://golang.org/cl/97570049

											
										
										
											2014-05-21 15:19:12 -06:00
+								// between f₁ and f₂, values closer to f₁ round to f₁ and values closer to f₂ are rejected as out of range.
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								// f₁ is an odd mantissa, so the halfway point (f₁+f₂)/2 rounds to f₂ and is rejected.
-												test: fix two typos in float_lit2.go

Noted by gri in CL 100660044 review but I missed them.

TBR=gri
CC=golang-codereviews
https://golang.org/cl/97570049

											
										
										
											2014-05-21 15:19:12 -06:00
+								// The halfway point is (f₁+f₂)/2 = 2¹²⁸ - 2¹⁰⁵.
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								//
 								// The same is true of float64, with different constants: s/24/53/ and s/128/1024/.
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
+								const (
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+									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
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
+								)
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								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)"},
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
+								}
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								var bugged = false
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								func bug() {
 									if !bugged {
 										bugged = true
 										fmt.Println("BUG")
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
+									}
 								}
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								func main() {
 									u64 := math.Float64frombits(0x7fefffffffffffff) - math.Float64frombits(0x7feffffffffffffe)
 									if ulp64 != u64 {
 										bug()
 										fmt.Printf("ulp64=%g, want %g", ulp64, u64)
 									}
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+									u32 := math.Float32frombits(0x7f7fffff) - math.Float32frombits(0x7f7ffffe)
 									if ulp32 != u32 {
 										bug()
 										fmt.Printf("ulp32=%g, want %g", ulp32, u32)
 									}
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+									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)
 										}
 									}
 								}
-												test/float_lit2.go: compute test values from first principles

These constants pass go/types constant conversions as well.

LGTM=r
R=r
CC=golang-codereviews
https://golang.org/cl/91590047

											
										
										
											2014-05-21 09:53:47 -06:00
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								func bits(x interface{}) interface{} {
 									switch x := x.(type) {
 									case float32:
 										return uint64(math.Float32bits(x))
 									case float64:
 										return math.Float64bits(x)
 									}
 									return 0
-												cmd/gc: fix float32 const conversion and printing of big float consts

The float32 const conversion used to round to float64
and then use the hardware to round to float32.
Even though there was a range check before this
conversion, the double rounding introduced inaccuracy:
the round to float64 might round the value further away
from the float32 range, reaching a float64 value that
could not actually be rounded to float32. The hardware
appears to give us 0 in that case, but it is probably undefined.
Double rounding also meant that the wrong value might
be used for certain border cases.

Do the rounding the float32 ourselves, just as we already
did the rounding to float64. This makes the conversion
precise and also makes the conversion match the range check.

Finally, add some code to print very large (bigger than float64)
floating point constants in decimal floating point notation instead
of falling back to the precise but human-unreadable binary floating
point notation.

Fixes #8015.

LGTM=iant
R=golang-codereviews, iant
CC=golang-codereviews, r
https://golang.org/cl/100580044

											
										
										
											2014-05-19 20:57:59 -06:00
+								}
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+								func fromBits(b uint64, x interface{}) interface{} {
 									switch x.(type) {
 									case float32:
 										return math.Float32frombits(uint32(b))
 									case float64:
 										return math.Float64frombits(b)
-												cmd/gc: fix float32 const conversion and printing of big float consts

The float32 const conversion used to round to float64
and then use the hardware to round to float32.
Even though there was a range check before this
conversion, the double rounding introduced inaccuracy:
the round to float64 might round the value further away
from the float32 range, reaching a float64 value that
could not actually be rounded to float32. The hardware
appears to give us 0 in that case, but it is probably undefined.
Double rounding also meant that the wrong value might
be used for certain border cases.

Do the rounding the float32 ourselves, just as we already
did the rounding to float64. This makes the conversion
precise and also makes the conversion match the range check.

Finally, add some code to print very large (bigger than float64)
floating point constants in decimal floating point notation instead
of falling back to the precise but human-unreadable binary floating
point notation.

Fixes #8015.

LGTM=iant
R=golang-codereviews, iant
CC=golang-codereviews, r
https://golang.org/cl/100580044

											
										
										
											2014-05-19 20:57:59 -06:00
+									}
-												test/float_lit2.go: rewrite to test values near boundaries

Add larger comment explaining testing methodology,
and derive tests arithmetically.

(These tests are checking rounding again; the derived
tests they replace were checking exact values.)

LGTM=r, gri
R=gri, r
CC=golang-codereviews
https://golang.org/cl/100660044

											
										
										
											2014-05-21 15:12:06 -06:00
+									return "?"
-												cmd/gc: fix float32 const conversion and printing of big float consts

The float32 const conversion used to round to float64
and then use the hardware to round to float32.
Even though there was a range check before this
conversion, the double rounding introduced inaccuracy:
the round to float64 might round the value further away
from the float32 range, reaching a float64 value that
could not actually be rounded to float32. The hardware
appears to give us 0 in that case, but it is probably undefined.
Double rounding also meant that the wrong value might
be used for certain border cases.

Do the rounding the float32 ourselves, just as we already
did the rounding to float64. This makes the conversion
precise and also makes the conversion match the range check.

Finally, add some code to print very large (bigger than float64)
floating point constants in decimal floating point notation instead
of falling back to the precise but human-unreadable binary floating
point notation.

Fixes #8015.

LGTM=iant
R=golang-codereviews, iant
CC=golang-codereviews, r
https://golang.org/cl/100580044

											
										
										
											2014-05-19 20:57:59 -06:00
+								}