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Commit c12e1b0b authored by Robert Griesemer's avatar Robert Griesemer
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cmd/compile: update vendored math/big to latest version 

This makes the rounding bug fix in math/big for issue 14651 available
to the compiler.

- changes to cmd/compile/internal/big fully automatic via script
- added test case for issue
- updated old test case with correct test data

Fixes #14651.

Change-Id: Iea37a2cd8d3a75f8c96193748b66156a987bbe40
Reviewed-on: https://go-review.googlesource.com/20818Reviewed-by: default avatarBrad Fitzpatrick <bradfitz@golang.org>
parent 7c86263b
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Showing with 260 additions and 193 deletions
src/cmd/compile/internal/big/arith_test.go
View file @ c12e1b0b
......@@ -158,21 +158,6 @@ var sumVW = []argVW{
{nat{585}, nat{314}, 271, 0},
}
var prodVW = []argVW{
{},
{nat{0}, nat{0}, 0, 0},
{nat{0}, nat{_M}, 0, 0},
{nat{0}, nat{0}, _M, 0},
{nat{1}, nat{1}, 1, 0},
{nat{22793}, nat{991}, 23, 0},
{nat{0, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 0},
{nat{0, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 0},
{nat{0, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 0},
{nat{_M << 1 & _M}, nat{_M}, 1 << 1, _M >> (_W - 1)},
{nat{_M << 7 & _M}, nat{_M}, 1 << 7, _M >> (_W - 7)},
{nat{_M << 7 & _M, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, _M >> (_W - 7)},
}
var lshVW = []argVW{
{},
{nat{0}, nat{0}, 0, 0},
......
src/cmd/compile/internal/big/float.go
View file @ c12e1b0b
......@@ -392,15 +392,13 @@ func (z *Float) round(sbit uint) {
// m > 0 implies z.prec > 0 (checked by validate)
m := uint32(len(z.mant)) // present mantissa length in words
bits := m * _W // present mantissa bits
bits := m * _W // present mantissa bits; bits > 0
if bits <= z.prec {
// mantissa fits => nothing to do
return
}
// bits > z.prec
n := (z.prec + (_W - 1)) / _W // mantissa length in words for desired precision
// Rounding is based on two bits: the rounding bit (rbit) and the
// sticky bit (sbit). The rbit is the bit immediately before the
// z.prec leading mantissa bits (the "0.5"). The sbit is set if any
......@@ -415,111 +413,77 @@ func (z *Float) round(sbit uint) {
// bits > z.prec: mantissa too large => round
r := uint(bits - z.prec - 1) // rounding bit position; r >= 0
rbit := z.mant.bit(r) // rounding bit
rbit := z.mant.bit(r) & 1 // rounding bit; be safe and ensure it's a single bit
if sbit == 0 {
// TODO(gri) if rbit != 0 we don't need to compute sbit for some rounding modes (optimization)
sbit = z.mant.sticky(r)
}
if debugFloat && sbit&^1 != 0 {
panic(fmt.Sprintf("invalid sbit %#x", sbit))
}
// convert ToXInf rounding modes
mode := z.mode
switch mode {
case ToNegativeInf:
mode = ToZero
if z.neg {
mode = AwayFromZero
}
case ToPositiveInf:
mode = AwayFromZero
if z.neg {
mode = ToZero
}
}
sbit &= 1 // be safe and ensure it's a single bit
// cut off extra words
n := (z.prec + (_W - 1)) / _W // mantissa length in words for desired precision
if m > n {
copy(z.mant, z.mant[m-n:]) // move n last words to front
z.mant = z.mant[:n]
}
// determine number of trailing zero bits t
t := n*_W - z.prec // 0 <= t < _W
lsb := Word(1) << t
// make rounding decision
// TODO(gri) This can be simplified (see Bits.round in bits_test.go).
switch mode {
case ToZero:
// nothing to do
case ToNearestEven, ToNearestAway:
if rbit == 0 {
// rounding bits == 0b0x
mode = ToZero
} else if sbit == 1 {
// rounding bits == 0b11
mode = AwayFromZero
}
case AwayFromZero:
if rbit|sbit == 0 {
mode = ToZero
}
default:
// ToXInf modes have been converted to ToZero or AwayFromZero
panic("unreachable")
}
// round and determine accuracy
switch mode {
case ToZero:
if rbit|sbit != 0 {
z.acc = Below
// determine number of trailing zero bits (ntz) and compute lsb mask of mantissa's least-significant word
ntz := n*_W - z.prec // 0 <= ntz < _W
lsb := Word(1) << ntz
// round if result is inexact
if rbit|sbit != 0 {
// Make rounding decision: The result mantissa is truncated ("rounded down")
// by default. Decide if we need to increment, or "round up", the (unsigned)
// mantissa.
inc := false
switch z.mode {
case ToNegativeInf:
inc = z.neg
case ToZero:
// nothing to do
case ToNearestEven:
inc = rbit != 0 && (sbit != 0 || z.mant[0]&lsb != 0)
case ToNearestAway:
inc = rbit != 0
case AwayFromZero:
inc = true
case ToPositiveInf:
inc = !z.neg
default:
panic("unreachable")
}
case ToNearestEven, ToNearestAway:
if debugFloat && rbit != 1 {
panic("internal error in rounding")
}
if mode == ToNearestEven && sbit == 0 && z.mant[0]&lsb == 0 {
z.acc = Below
break
}
// mode == ToNearestAway || sbit == 1 || z.mant[0]&lsb != 0
fallthrough
case AwayFromZero:
// add 1 to mantissa
if addVW(z.mant, z.mant, lsb) != 0 {
// overflow => shift mantissa right by 1 and add msb
shrVU(z.mant, z.mant, 1)
z.mant[n-1] |= 1 << (_W - 1)
// adjust exponent
if z.exp < MaxExp {
// A positive result (!z.neg) is Above the exact result if we increment,
// and it's Below if we truncate (Exact results require no rounding).
// For a negative result (z.neg) it is exactly the opposite.
z.acc = makeAcc(inc != z.neg)
if inc {
// add 1 to mantissa
if addVW(z.mant, z.mant, lsb) != 0 {
// mantissa overflow => adjust exponent
if z.exp >= MaxExp {
// exponent overflow
z.form = inf
return
}
z.exp++
} else {
// exponent overflow
z.acc = makeAcc(!z.neg)
z.form = inf
return
// adjust mantissa: divide by 2 to compensate for exponent adjustment
shrVU(z.mant, z.mant, 1)
// set msb == carry == 1 from the mantissa overflow above
const msb = 1 << (_W - 1)
z.mant[n-1] |= msb
}
}
z.acc = Above
}
// zero out trailing bits in least-significant word
z.mant[0] &^= lsb - 1
// update accuracy
if z.acc != Exact && z.neg {
z.acc = -z.acc
}
if debugFloat {
z.validate()
}
return
}
func (z *Float) setBits64(neg bool, x uint64) *Float {
......@@ -874,21 +838,43 @@ func (x *Float) Float32() (float32, Accuracy) {
emax = bias // 127 largest unbiased exponent (normal)
)
// Float mantissa m is 0.5 <= m < 1.0; compute exponent for float32 mantissa.
e := x.exp - 1 // exponent for mantissa m with 1.0 <= m < 2.0
p := mbits + 1 // precision of normal float
// Float mantissa m is 0.5 <= m < 1.0; compute exponent e for float32 mantissa.
e := x.exp - 1 // exponent for normal mantissa m with 1.0 <= m < 2.0
// If the exponent is too small, we may have a denormal number
// in which case we have fewer mantissa bits available: recompute
// precision.
// Compute precision p for float32 mantissa.
// If the exponent is too small, we have a denormal number before
// rounding and fewer than p mantissa bits of precision available
// (the exponent remains fixed but the mantissa gets shifted right).
p := mbits + 1 // precision of normal float
if e < emin {
// recompute precision
p = mbits + 1 - emin + int(e)
// Make sure we have at least 1 bit so that we don't
// lose numbers rounded up to the smallest denormal.
if p < 1 {
p = 1
// If p == 0, the mantissa of x is shifted so much to the right
// that its msb falls immediately to the right of the float32
// mantissa space. In other words, if the smallest denormal is
// considered "1.0", for p == 0, the mantissa value m is >= 0.5.
// If m > 0.5, it is rounded up to 1.0; i.e., the smallest denormal.
// If m == 0.5, it is rounded down to even, i.e., 0.0.
// If p < 0, the mantissa value m is <= "0.25" which is never rounded up.
if p < 0 /* m <= 0.25 */ || p == 0 && x.mant.sticky(uint(len(x.mant))*_W-1) == 0 /* m == 0.5 */ {
// underflow to ±0
if x.neg {
var z float32
return -z, Above
}
return 0.0, Below
}
// otherwise, round up
// We handle p == 0 explicitly because it's easy and because
// Float.round doesn't support rounding to 0 bits of precision.
if p == 0 {
if x.neg {
return -math.SmallestNonzeroFloat32, Below
}
return math.SmallestNonzeroFloat32, Above
}
}
// p > 0
// round
var r Float
......@@ -898,12 +884,8 @@ func (x *Float) Float32() (float32, Accuracy) {
// Rounding may have caused r to overflow to ±Inf
// (rounding never causes underflows to 0).
if r.form == inf {
e = emax + 1 // cause overflow below
}
// If the exponent is too large, overflow to ±Inf.
if e > emax {
// If the exponent is too large, also overflow to ±Inf.
if r.form == inf || e > emax {
// overflow
if x.neg {
return float32(math.Inf(-1)), Below
......@@ -921,17 +903,10 @@ func (x *Float) Float32() (float32, Accuracy) {
// Rounding may have caused a denormal number to
// become normal. Check again.
if e < emin {
// denormal number
if e < dmin {
// underflow to ±0
if x.neg {
var z float32
return -z, Above
}
return 0.0, Below
}
// bexp = 0
// recompute precision
// denormal number: recompute precision
// Since rounding may have at best increased precision
// and we have eliminated p <= 0 early, we know p > 0.
// bexp == 0 for denormals
p = mbits + 1 - emin + int(e)
mant = msb32(r.mant) >> uint(fbits-p)
} else {
......@@ -983,21 +958,43 @@ func (x *Float) Float64() (float64, Accuracy) {
emax = bias // 1023 largest unbiased exponent (normal)
)
// Float mantissa m is 0.5 <= m < 1.0; compute exponent for float64 mantissa.
e := x.exp - 1 // exponent for mantissa m with 1.0 <= m < 2.0
p := mbits + 1 // precision of normal float
// Float mantissa m is 0.5 <= m < 1.0; compute exponent e for float64 mantissa.
e := x.exp - 1 // exponent for normal mantissa m with 1.0 <= m < 2.0
// If the exponent is too small, we may have a denormal number
// in which case we have fewer mantissa bits available: recompute
// precision.
// Compute precision p for float64 mantissa.
// If the exponent is too small, we have a denormal number before
// rounding and fewer than p mantissa bits of precision available
// (the exponent remains fixed but the mantissa gets shifted right).
p := mbits + 1 // precision of normal float
if e < emin {
// recompute precision
p = mbits + 1 - emin + int(e)
// Make sure we have at least 1 bit so that we don't
// lose numbers rounded up to the smallest denormal.
if p < 1 {
p = 1
// If p == 0, the mantissa of x is shifted so much to the right
// that its msb falls immediately to the right of the float64
// mantissa space. In other words, if the smallest denormal is
// considered "1.0", for p == 0, the mantissa value m is >= 0.5.
// If m > 0.5, it is rounded up to 1.0; i.e., the smallest denormal.
// If m == 0.5, it is rounded down to even, i.e., 0.0.
// If p < 0, the mantissa value m is <= "0.25" which is never rounded up.
if p < 0 /* m <= 0.25 */ || p == 0 && x.mant.sticky(uint(len(x.mant))*_W-1) == 0 /* m == 0.5 */ {
// underflow to ±0
if x.neg {
var z float64
return -z, Above
}
return 0.0, Below
}
// otherwise, round up
// We handle p == 0 explicitly because it's easy and because
// Float.round doesn't support rounding to 0 bits of precision.
if p == 0 {
if x.neg {
return -math.SmallestNonzeroFloat64, Below
}
return math.SmallestNonzeroFloat64, Above
}
}
// p > 0
// round
var r Float
......@@ -1007,17 +1004,13 @@ func (x *Float) Float64() (float64, Accuracy) {
// Rounding may have caused r to overflow to ±Inf
// (rounding never causes underflows to 0).
if r.form == inf {
e = emax + 1 // cause overflow below
}
// If the exponent is too large, overflow to ±Inf.
if e > emax {
// If the exponent is too large, also overflow to ±Inf.
if r.form == inf || e > emax {
// overflow
if x.neg {
return math.Inf(-1), Below
return float64(math.Inf(-1)), Below
}
return math.Inf(+1), Above
return float64(math.Inf(+1)), Above
}
// e <= emax
......@@ -1030,17 +1023,10 @@ func (x *Float) Float64() (float64, Accuracy) {
// Rounding may have caused a denormal number to
// become normal. Check again.
if e < emin {
// denormal number
if e < dmin {
// underflow to ±0
if x.neg {
var z float64
return -z, Above
}
return 0.0, Below
}
// bexp = 0
// recompute precision
// denormal number: recompute precision
// Since rounding may have at best increased precision
// and we have eliminated p <= 0 early, we know p > 0.
// bexp == 0 for denormals
p = mbits + 1 - emin + int(e)
mant = msb64(r.mant) >> uint(fbits-p)
} else {
......
src/cmd/compile/internal/big/float_test.go
View file @ c12e1b0b
......@@ -829,7 +829,7 @@ func TestFloatFloat32(t *testing.T) {
}{
{"0", 0, Exact},
// underflow
// underflow to zero
{"1e-1000", 0, Below},
{"0x0.000002p-127", 0, Below},
{"0x.0000010p-126", 0, Below},
......@@ -843,25 +843,39 @@ func TestFloatFloat32(t *testing.T) {
{"1p-149", math.SmallestNonzeroFloat32, Exact},
{"0x.fffffep-126", math.Float32frombits(0x7fffff), Exact}, // largest denormal
// special cases (see issue 14553)
{"0x0.bp-149", math.Float32frombits(0x000000000), Below}, // ToNearestEven rounds down (to even)
{"0x0.cp-149", math.Float32frombits(0x000000001), Above},
{"0x1.0p-149", math.Float32frombits(0x000000001), Exact},
// special denormal cases (see issues 14553, 14651)
{"0x0.0000001p-126", math.Float32frombits(0x00000000), Below}, // underflow to zero
{"0x0.0000008p-126", math.Float32frombits(0x00000000), Below}, // underflow to zero
{"0x0.0000010p-126", math.Float32frombits(0x00000000), Below}, // rounded down to even
{"0x0.0000011p-126", math.Float32frombits(0x00000001), Above}, // rounded up to smallest denormal
{"0x0.0000018p-126", math.Float32frombits(0x00000001), Above}, // rounded up to smallest denormal
{"0x1.0000000p-149", math.Float32frombits(0x00000001), Exact}, // smallest denormal
{"0x0.0000020p-126", math.Float32frombits(0x00000001), Exact}, // smallest denormal
{"0x0.fffffe0p-126", math.Float32frombits(0x007fffff), Exact}, // largest denormal
{"0x1.0000000p-126", math.Float32frombits(0x00800000), Exact}, // smallest normal
{"0x0.8p-149", math.Float32frombits(0x000000000), Below}, // rounded down to even
{"0x0.9p-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
{"0x0.ap-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
{"0x0.bp-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
{"0x0.cp-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
{"0x1.0p-149", math.Float32frombits(0x000000001), Exact}, // smallest denormal
{"0x1.7p-149", math.Float32frombits(0x000000001), Below},
{"0x1.8p-149", math.Float32frombits(0x000000002), Above},
{"0x1.9p-149", math.Float32frombits(0x000000002), Above},
{"0x2.0p-149", math.Float32frombits(0x000000002), Exact},
{"0x2.8p-149", math.Float32frombits(0x000000002), Below}, // ToNearestEven rounds down (to even)
{"0x2.8p-149", math.Float32frombits(0x000000002), Below}, // rounded down to even
{"0x2.9p-149", math.Float32frombits(0x000000003), Above},
{"0x3.0p-149", math.Float32frombits(0x000000003), Exact},
{"0x3.7p-149", math.Float32frombits(0x000000003), Below},
{"0x3.8p-149", math.Float32frombits(0x000000004), Above}, // ToNearestEven rounds up (to even)
{"0x3.8p-149", math.Float32frombits(0x000000004), Above}, // rounded up to even
{"0x4.0p-149", math.Float32frombits(0x000000004), Exact},
{"0x4.8p-149", math.Float32frombits(0x000000004), Below}, // ToNearestEven rounds down (to even)
{"0x4.8p-149", math.Float32frombits(0x000000004), Below}, // rounded down to even
{"0x4.9p-149", math.Float32frombits(0x000000005), Above},
// specific case from issue 14553
......@@ -907,7 +921,7 @@ func TestFloatFloat32(t *testing.T) {
x := makeFloat(tx)
out, acc := x.Float32()
if !alike32(out, tout) || acc != tacc {
t.Errorf("%s: got %g (%#x, %s); want %g (%#x, %s)", tx, out, math.Float32bits(out), acc, test.out, math.Float32bits(test.out), tacc)
t.Errorf("%s: got %g (%#08x, %s); want %g (%#08x, %s)", tx, out, math.Float32bits(out), acc, test.out, math.Float32bits(test.out), tacc)
}
// test that x.SetFloat64(float64(f)).Float32() == f
......@@ -929,21 +943,30 @@ func TestFloatFloat64(t *testing.T) {
}{
{"0", 0, Exact},
// underflow
// underflow to zero
{"1e-1000", 0, Below},
{"0x0.0000000000001p-1023", 0, Below},
{"0x0.00000000000008p-1022", 0, Below},
// denormals
{"0x0.0000000000000cp-1022", math.SmallestNonzeroFloat64, Above}, // rounded up to smallest denormal
{"0x0.0000000000001p-1022", math.SmallestNonzeroFloat64, Exact}, // smallest denormal
{"0x0.00000000000010p-1022", math.SmallestNonzeroFloat64, Exact}, // smallest denormal
{"0x.8p-1073", math.SmallestNonzeroFloat64, Exact},
{"1p-1074", math.SmallestNonzeroFloat64, Exact},
{"0x.fffffffffffffp-1022", math.Float64frombits(0x000fffffffffffff), Exact}, // largest denormal
// special cases (see issue 14553)
{"0x0.bp-1074", math.Float64frombits(0x00000000000000000), Below}, // ToNearestEven rounds down (to even)
{"0x0.cp-1074", math.Float64frombits(0x00000000000000001), Above},
// special denormal cases (see issues 14553, 14651)
{"0x0.00000000000001p-1022", math.Float64frombits(0x00000000000000000), Below}, // underflow to zero
{"0x0.00000000000004p-1022", math.Float64frombits(0x00000000000000000), Below}, // underflow to zero
{"0x0.00000000000008p-1022", math.Float64frombits(0x00000000000000000), Below}, // rounded down to even
{"0x0.00000000000009p-1022", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
{"0x0.0000000000000ap-1022", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
{"0x0.8p-1074", math.Float64frombits(0x00000000000000000), Below}, // rounded down to even
{"0x0.9p-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
{"0x0.ap-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
{"0x0.bp-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
{"0x0.cp-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
{"0x1.0p-1074", math.Float64frombits(0x00000000000000001), Exact},
{"0x1.7p-1074", math.Float64frombits(0x00000000000000001), Below},
......@@ -951,15 +974,15 @@ func TestFloatFloat64(t *testing.T) {
{"0x1.9p-1074", math.Float64frombits(0x00000000000000002), Above},
{"0x2.0p-1074", math.Float64frombits(0x00000000000000002), Exact},
{"0x2.8p-1074", math.Float64frombits(0x00000000000000002), Below}, // ToNearestEven rounds down (to even)
{"0x2.8p-1074", math.Float64frombits(0x00000000000000002), Below}, // rounded down to even
{"0x2.9p-1074", math.Float64frombits(0x00000000000000003), Above},
{"0x3.0p-1074", math.Float64frombits(0x00000000000000003), Exact},
{"0x3.7p-1074", math.Float64frombits(0x00000000000000003), Below},
{"0x3.8p-1074", math.Float64frombits(0x00000000000000004), Above}, // ToNearestEven rounds up (to even)
{"0x3.8p-1074", math.Float64frombits(0x00000000000000004), Above}, // rounded up to even
{"0x4.0p-1074", math.Float64frombits(0x00000000000000004), Exact},
{"0x4.8p-1074", math.Float64frombits(0x00000000000000004), Below}, // ToNearestEven rounds down (to even)
{"0x4.8p-1074", math.Float64frombits(0x00000000000000004), Below}, // rounded down to even
{"0x4.9p-1074", math.Float64frombits(0x00000000000000005), Above},
// normals
......@@ -1005,7 +1028,7 @@ func TestFloatFloat64(t *testing.T) {
x := makeFloat(tx)
out, acc := x.Float64()
if !alike64(out, tout) || acc != tacc {
t.Errorf("%s: got %g (%#x, %s); want %g (%#x, %s)", tx, out, math.Float64bits(out), acc, test.out, math.Float64bits(test.out), tacc)
t.Errorf("%s: got %g (%#016x, %s); want %g (%#016x, %s)", tx, out, math.Float64bits(out), acc, test.out, math.Float64bits(test.out), tacc)
}
// test that x.SetFloat64(f).Float64() == f
......
src/cmd/compile/internal/big/ftoa.go
View file @ c12e1b0b
......@@ -333,9 +333,9 @@ func (x *Float) fmtB(buf []byte) []byte {
return strconv.AppendInt(buf, e, 10)
}
// fmtP appends the string of x in the format 0x." mantissa "p" exponent
// with a hexadecimal mantissa and a binary exponent, or 0" if x is zero,
// ad returns the extended buffer.
// fmtP appends the string of x in the format "0x." mantissa "p" exponent
// with a hexadecimal mantissa and a binary exponent, or "0" if x is zero,
// and returns the extended buffer.
// The mantissa is normalized such that 0.5 <= 0.mantissa < 1.0.
// The sign of x is ignored, and x must not be an Inf.
func (x *Float) fmtP(buf []byte) []byte {
......@@ -374,12 +374,11 @@ func min(x, y int) int {
}
// Format implements fmt.Formatter. It accepts all the regular
// formats for floating-point numbers ('e', 'E', 'f', 'F', 'g',
// 'G') as well as 'b', 'p', and 'v'. See (*Float).Text for the
// interpretation of 'b' and 'p'. The 'v' format is handled like
// 'g'.
// formats for floating-point numbers ('b', 'e', 'E', 'f', 'F',
// 'g', 'G') as well as 'p' and 'v'. See (*Float).Text for the
// interpretation of 'p'. The 'v' format is handled like 'g'.
// Format also supports specification of the minimum precision
// in digits, the output field width, as well as the format verbs
// in digits, the output field width, as well as the format flags
// '+' and ' ' for sign control, '0' for space or zero padding,
// and '-' for left or right justification. See the fmt package
// for details.
......
src/cmd/compile/internal/big/intconv.go
View file @ c12e1b0b
......@@ -52,16 +52,16 @@ func writeMultiple(s fmt.State, text string, count int) {
}
}
// Format is a support routine for fmt.Formatter. It accepts
// the formats 'b' (binary), 'o' (octal), 'd' (decimal), 'x'
// (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
// Format implements fmt.Formatter. It accepts the formats
// 'b' (binary), 'o' (octal), 'd' (decimal), 'x' (lowercase
// hexadecimal), and 'X' (uppercase hexadecimal).
// Also supported are the full suite of package fmt's format
// verbs for integral types, including '+', '-', and ' '
// for sign control, '#' for leading zero in octal and for
// hexadecimal, a leading "0x" or "0X" for "%#x" and "%#X"
// respectively, specification of minimum digits precision,
// output field width, space or zero padding, and left or
// right justification.
// flags for integral types, including '+' and ' ' for sign
// control, '#' for leading zero in octal and for hexadecimal,
// a leading "0x" or "0X" for "%#x" and "%#X" respectively,
// specification of minimum digits precision, output field
// width, space or zero padding, and '-' for left or right
// justification.
//
func (x *Int) Format(s fmt.State, ch rune) {
// determine base
......
test/fixedbugs/issue14553.go
View file @ c12e1b0b
......@@ -20,7 +20,10 @@ func main() {
bits uint32
}{
{0e+00, 0x00000000},
{1e-45, 0x00000000},
{1e-46, 0x00000000},
{0.5e-45, 0x00000000},
{0.8e-45, 0x00000001},
{1e-45, 0x00000001},
{2e-45, 0x00000001},
{3e-45, 0x00000002},
{4e-45, 0x00000003},
......
test/fixedbugs/issue14651.go 0 → 100644
View file @ c12e1b0b
// run
// Copyright 2016 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.
// This test checks if the compiler's internal constant
// arithmetic correctly rounds up floating-point values
// that become the smallest denormal value.
//
// See also related issue 14553 and test issue14553.go.
package main
import (
"fmt"
"math"
)
const (
p149 = 1.0 / (1 << 149) // 1p-149
p500 = 1.0 / (1 << 500) // 1p-500
p1074 = p500 * p500 / (1<<74) // 1p-1074
)
const (
m0000p149 = 0x0 / 16.0 * p149 // = 0.0000p-149
m1000p149 = 0x8 / 16.0 * p149 // = 0.1000p-149
m1001p149 = 0x9 / 16.0 * p149 // = 0.1001p-149
m1011p149 = 0xb / 16.0 * p149 // = 0.1011p-149
m1100p149 = 0xc / 16.0 * p149 // = 0.1100p-149
m0000p1074 = 0x0 / 16.0 * p1074 // = 0.0000p-1074
m1000p1074 = 0x8 / 16.0 * p1074 // = 0.1000p-1074
m1001p1074 = 0x9 / 16.0 * p1074 // = 0.1001p-1074
m1011p1074 = 0xb / 16.0 * p1074 // = 0.1011p-1074
m1100p1074 = 0xc / 16.0 * p1074 // = 0.1100p-1074
)
func main() {
test32(float32(m0000p149), f32(m0000p149))
test32(float32(m1000p149), f32(m1000p149))
test32(float32(m1001p149), f32(m1001p149))
test32(float32(m1011p149), f32(m1011p149))
test32(float32(m1100p149), f32(m1100p149))
test64(float64(m0000p1074), f64(m0000p1074))
test64(float64(m1000p1074), f64(m1000p1074))
test64(float64(m1001p1074), f64(m1001p1074))
test64(float64(m1011p1074), f64(m1011p1074))
test64(float64(m1100p1074), f64(m1100p1074))
}
func f32(x float64) float32 { return float32(x) }
func f64(x float64) float64 { return float64(x) }
func test32(a, b float32) {
abits := math.Float32bits(a)
bbits := math.Float32bits(b)
if abits != bbits {
panic(fmt.Sprintf("%08x != %08x\n", abits, bbits))
}
}
func test64(a, b float64) {
abits := math.Float64bits(a)
bbits := math.Float64bits(b)
if abits != bbits {
panic(fmt.Sprintf("%016x != %016x\n", abits, bbits))
}
}
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