{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},
// 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
// 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 {
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
// 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
// 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 {
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
// 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
// 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 {
}{
{"0", 0, Exact},
- // underflow
+ // underflow to zero
{"1e-1000", 0, Below},
{"0x0.000002p-127", 0, Below},
{"0x.0000010p-126", 0, Below},
{"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
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
}{
{"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},
{"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
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
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 {
}
// 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.
}
}
-// 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
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},
--- /dev/null
+// 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))
+ }
+}