Adding upstream version 1.17.13.upstream/1.17.13upstream

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

1 files changed, 567 insertions, 0 deletions

diff --git a/src/strconv/ftoaryu.go b/src/strconv/ftoaryu.go
new file mode 100644
index 0000000..1c61288
--- /dev/null
+++ b/src/strconv/ftoaryu.go
@@ -0,0 +1,567 @@
+// Copyright 2021 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 strconv
+
+import (
+	"math/bits"
+)
+
+// binary to decimal conversion using the Ryū algorithm.
+//
+// See Ulf Adams, "Ryū: Fast Float-to-String Conversion" (doi:10.1145/3192366.3192369)
+//
+// Fixed precision formatting is a variant of the original paper's
+// algorithm, where a single multiplication by 10^k is required,
+// sharing the same rounding guarantees.
+
+// ryuFtoaFixed32 formats mant*(2^exp) with prec decimal digits.
+func ryuFtoaFixed32(d *decimalSlice, mant uint32, exp int, prec int) {
+	if prec < 0 {
+		panic("ryuFtoaFixed32 called with negative prec")
+	}
+	if prec > 9 {
+		panic("ryuFtoaFixed32 called with prec > 9")
+	}
+	// Zero input.
+	if mant == 0 {
+		d.nd, d.dp = 0, 0
+		return
+	}
+	// Renormalize to a 25-bit mantissa.
+	e2 := exp
+	if b := bits.Len32(mant); b < 25 {
+		mant <<= uint(25 - b)
+		e2 += int(b) - 25
+	}
+	// Choose an exponent such that rounded mant*(2^e2)*(10^q) has
+	// at least prec decimal digits, i.e
+	//     mant*(2^e2)*(10^q) >= 10^(prec-1)
+	// Because mant >= 2^24, it is enough to choose:
+	//     2^(e2+24) >= 10^(-q+prec-1)
+	// or q = -mulByLog2Log10(e2+24) + prec - 1
+	q := -mulByLog2Log10(e2+24) + prec - 1
+
+	// Now compute mant*(2^e2)*(10^q).
+	// Is it an exact computation?
+	// Only small positive powers of 10 are exact (5^28 has 66 bits).
+	exact := q <= 27 && q >= 0
+
+	di, dexp2, d0 := mult64bitPow10(mant, e2, q)
+	if dexp2 >= 0 {
+		panic("not enough significant bits after mult64bitPow10")
+	}
+	// As a special case, computation might still be exact, if exponent
+	// was negative and if it amounts to computing an exact division.
+	// In that case, we ignore all lower bits.
+	// Note that division by 10^11 cannot be exact as 5^11 has 26 bits.
+	if q < 0 && q >= -10 && divisibleByPower5(uint64(mant), -q) {
+		exact = true
+		d0 = true
+	}
+	// Remove extra lower bits and keep rounding info.
+	extra := uint(-dexp2)
+	extraMask := uint32(1<<extra - 1)
+
+	di, dfrac := di>>extra, di&extraMask
+	roundUp := false
+	if exact {
+		// If we computed an exact product, d + 1/2
+		// should round to d+1 if 'd' is odd.
+		roundUp = dfrac > 1<<(extra-1) ||
+			(dfrac == 1<<(extra-1) && !d0) ||
+			(dfrac == 1<<(extra-1) && d0 && di&1 == 1)
+	} else {
+		// otherwise, d+1/2 always rounds up because
+		// we truncated below.
+		roundUp = dfrac>>(extra-1) == 1
+	}
+	if dfrac != 0 {
+		d0 = false
+	}
+	// Proceed to the requested number of digits
+	formatDecimal(d, uint64(di), !d0, roundUp, prec)
+	// Adjust exponent
+	d.dp -= q
+}
+
+// ryuFtoaFixed64 formats mant*(2^exp) with prec decimal digits.
+func ryuFtoaFixed64(d *decimalSlice, mant uint64, exp int, prec int) {
+	if prec > 18 {
+		panic("ryuFtoaFixed64 called with prec > 18")
+	}
+	// Zero input.
+	if mant == 0 {
+		d.nd, d.dp = 0, 0
+		return
+	}
+	// Renormalize to a 55-bit mantissa.
+	e2 := exp
+	if b := bits.Len64(mant); b < 55 {
+		mant = mant << uint(55-b)
+		e2 += int(b) - 55
+	}
+	// Choose an exponent such that rounded mant*(2^e2)*(10^q) has
+	// at least prec decimal digits, i.e
+	//     mant*(2^e2)*(10^q) >= 10^(prec-1)
+	// Because mant >= 2^54, it is enough to choose:
+	//     2^(e2+54) >= 10^(-q+prec-1)
+	// or q = -mulByLog2Log10(e2+54) + prec - 1
+	//
+	// The minimal required exponent is -mulByLog2Log10(1025)+18 = -291
+	// The maximal required exponent is mulByLog2Log10(1074)+18 = 342
+	q := -mulByLog2Log10(e2+54) + prec - 1
+
+	// Now compute mant*(2^e2)*(10^q).
+	// Is it an exact computation?
+	// Only small positive powers of 10 are exact (5^55 has 128 bits).
+	exact := q <= 55 && q >= 0
+
+	di, dexp2, d0 := mult128bitPow10(mant, e2, q)
+	if dexp2 >= 0 {
+		panic("not enough significant bits after mult128bitPow10")
+	}
+	// As a special case, computation might still be exact, if exponent
+	// was negative and if it amounts to computing an exact division.
+	// In that case, we ignore all lower bits.
+	// Note that division by 10^23 cannot be exact as 5^23 has 54 bits.
+	if q < 0 && q >= -22 && divisibleByPower5(mant, -q) {
+		exact = true
+		d0 = true
+	}
+	// Remove extra lower bits and keep rounding info.
+	extra := uint(-dexp2)
+	extraMask := uint64(1<<extra - 1)
+
+	di, dfrac := di>>extra, di&extraMask
+	roundUp := false
+	if exact {
+		// If we computed an exact product, d + 1/2
+		// should round to d+1 if 'd' is odd.
+		roundUp = dfrac > 1<<(extra-1) ||
+			(dfrac == 1<<(extra-1) && !d0) ||
+			(dfrac == 1<<(extra-1) && d0 && di&1 == 1)
+	} else {
+		// otherwise, d+1/2 always rounds up because
+		// we truncated below.
+		roundUp = dfrac>>(extra-1) == 1
+	}
+	if dfrac != 0 {
+		d0 = false
+	}
+	// Proceed to the requested number of digits
+	formatDecimal(d, di, !d0, roundUp, prec)
+	// Adjust exponent
+	d.dp -= q
+}
+
+var uint64pow10 = [...]uint64{
+	1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+}
+
+// formatDecimal fills d with at most prec decimal digits
+// of mantissa m. The boolean trunc indicates whether m
+// is truncated compared to the original number being formatted.
+func formatDecimal(d *decimalSlice, m uint64, trunc bool, roundUp bool, prec int) {
+	max := uint64pow10[prec]
+	trimmed := 0
+	for m >= max {
+		a, b := m/10, m%10
+		m = a
+		trimmed++
+		if b > 5 {
+			roundUp = true
+		} else if b < 5 {
+			roundUp = false
+		} else { // b == 5
+			// round up if there are trailing digits,
+			// or if the new value of m is odd (round-to-even convention)
+			roundUp = trunc || m&1 == 1
+		}
+		if b != 0 {
+			trunc = true
+		}
+	}
+	if roundUp {
+		m++
+	}
+	if m >= max {
+		// Happens if di was originally 99999....xx
+		m /= 10
+		trimmed++
+	}
+	// render digits (similar to formatBits)
+	n := uint(prec)
+	d.nd = int(prec)
+	v := m
+	for v >= 100 {
+		var v1, v2 uint64
+		if v>>32 == 0 {
+			v1, v2 = uint64(uint32(v)/100), uint64(uint32(v)%100)
+		} else {
+			v1, v2 = v/100, v%100
+		}
+		n -= 2
+		d.d[n+1] = smallsString[2*v2+1]
+		d.d[n+0] = smallsString[2*v2+0]
+		v = v1
+	}
+	if v > 0 {
+		n--
+		d.d[n] = smallsString[2*v+1]
+	}
+	if v >= 10 {
+		n--
+		d.d[n] = smallsString[2*v]
+	}
+	for d.d[d.nd-1] == '0' {
+		d.nd--
+		trimmed++
+	}
+	d.dp = d.nd + trimmed
+}
+
+// ryuFtoaShortest formats mant*2^exp with prec decimal digits.
+func ryuFtoaShortest(d *decimalSlice, mant uint64, exp int, flt *floatInfo) {
+	if mant == 0 {
+		d.nd, d.dp = 0, 0
+		return
+	}
+	// If input is an exact integer with fewer bits than the mantissa,
+	// the previous and next integer are not admissible representations.
+	if exp <= 0 && bits.TrailingZeros64(mant) >= -exp {
+		mant >>= uint(-exp)
+		ryuDigits(d, mant, mant, mant, true, false)
+		return
+	}
+	ml, mc, mu, e2 := computeBounds(mant, exp, flt)
+	if e2 == 0 {
+		ryuDigits(d, ml, mc, mu, true, false)
+		return
+	}
+	// Find 10^q *larger* than 2^-e2
+	q := mulByLog2Log10(-e2) + 1
+
+	// We are going to multiply by 10^q using 128-bit arithmetic.
+	// The exponent is the same for all 3 numbers.
+	var dl, dc, du uint64
+	var dl0, dc0, du0 bool
+	if flt == &float32info {
+		var dl32, dc32, du32 uint32
+		dl32, _, dl0 = mult64bitPow10(uint32(ml), e2, q)
+		dc32, _, dc0 = mult64bitPow10(uint32(mc), e2, q)
+		du32, e2, du0 = mult64bitPow10(uint32(mu), e2, q)
+		dl, dc, du = uint64(dl32), uint64(dc32), uint64(du32)
+	} else {
+		dl, _, dl0 = mult128bitPow10(ml, e2, q)
+		dc, _, dc0 = mult128bitPow10(mc, e2, q)
+		du, e2, du0 = mult128bitPow10(mu, e2, q)
+	}
+	if e2 >= 0 {
+		panic("not enough significant bits after mult128bitPow10")
+	}
+	// Is it an exact computation?
+	if q > 55 {
+		// Large positive powers of ten are not exact
+		dl0, dc0, du0 = false, false, false
+	}
+	if q < 0 && q >= -24 {
+		// Division by a power of ten may be exact.
+		// (note that 5^25 is a 59-bit number so division by 5^25 is never exact).
+		if divisibleByPower5(ml, -q) {
+			dl0 = true
+		}
+		if divisibleByPower5(mc, -q) {
+			dc0 = true
+		}
+		if divisibleByPower5(mu, -q) {
+			du0 = true
+		}
+	}
+	// Express the results (dl, dc, du)*2^e2 as integers.
+	// Extra bits must be removed and rounding hints computed.
+	extra := uint(-e2)
+	extraMask := uint64(1<<extra - 1)
+	// Now compute the floored, integral base 10 mantissas.
+	dl, fracl := dl>>extra, dl&extraMask
+	dc, fracc := dc>>extra, dc&extraMask
+	du, fracu := du>>extra, du&extraMask
+	// Is it allowed to use 'du' as a result?
+	// It is always allowed when it is truncated, but also
+	// if it is exact and the original binary mantissa is even
+	// When disallowed, we can substract 1.
+	uok := !du0 || fracu > 0
+	if du0 && fracu == 0 {
+		uok = mant&1 == 0
+	}
+	if !uok {
+		du--
+	}
+	// Is 'dc' the correctly rounded base 10 mantissa?
+	// The correct rounding might be dc+1
+	cup := false // don't round up.
+	if dc0 {
+		// If we computed an exact product, the half integer
+		// should round to next (even) integer if 'dc' is odd.
+		cup = fracc > 1<<(extra-1) ||
+			(fracc == 1<<(extra-1) && dc&1 == 1)
+	} else {
+		// otherwise, the result is a lower truncation of the ideal
+		// result.
+		cup = fracc>>(extra-1) == 1
+	}
+	// Is 'dl' an allowed representation?
+	// Only if it is an exact value, and if the original binary mantissa
+	// was even.
+	lok := dl0 && fracl == 0 && (mant&1 == 0)
+	if !lok {
+		dl++
+	}
+	// We need to remember whether the trimmed digits of 'dc' are zero.
+	c0 := dc0 && fracc == 0
+	// render digits
+	ryuDigits(d, dl, dc, du, c0, cup)
+	d.dp -= q
+}
+
+// mulByLog2Log10 returns math.Floor(x * log(2)/log(10)) for an integer x in
+// the range -1600 <= x && x <= +1600.
+//
+// The range restriction lets us work in faster integer arithmetic instead of
+// slower floating point arithmetic. Correctness is verified by unit tests.
+func mulByLog2Log10(x int) int {
+	// log(2)/log(10) ≈ 0.30102999566 ≈ 78913 / 2^18
+	return (x * 78913) >> 18
+}
+
+// mulByLog10Log2 returns math.Floor(x * log(10)/log(2)) for an integer x in
+// the range -500 <= x && x <= +500.
+//
+// The range restriction lets us work in faster integer arithmetic instead of
+// slower floating point arithmetic. Correctness is verified by unit tests.
+func mulByLog10Log2(x int) int {
+	// log(10)/log(2) ≈ 3.32192809489 ≈ 108853 / 2^15
+	return (x * 108853) >> 15
+}
+
+// computeBounds returns a floating-point vector (l, c, u)×2^e2
+// where the mantissas are 55-bit (or 26-bit) integers, describing the interval
+// represented by the input float64 or float32.
+func computeBounds(mant uint64, exp int, flt *floatInfo) (lower, central, upper uint64, e2 int) {
+	if mant != 1<<flt.mantbits || exp == flt.bias+1-int(flt.mantbits) {
+		// regular case (or denormals)
+		lower, central, upper = 2*mant-1, 2*mant, 2*mant+1
+		e2 = exp - 1
+		return
+	} else {
+		// border of an exponent
+		lower, central, upper = 4*mant-1, 4*mant, 4*mant+2
+		e2 = exp - 2
+		return
+	}
+}
+
+func ryuDigits(d *decimalSlice, lower, central, upper uint64,
+	c0, cup bool) {
+	lhi, llo := divmod1e9(lower)
+	chi, clo := divmod1e9(central)
+	uhi, ulo := divmod1e9(upper)
+	if uhi == 0 {
+		// only low digits (for denormals)
+		ryuDigits32(d, llo, clo, ulo, c0, cup, 8)
+	} else if lhi < uhi {
+		// truncate 9 digits at once.
+		if llo != 0 {
+			lhi++
+		}
+		c0 = c0 && clo == 0
+		cup = (clo > 5e8) || (clo == 5e8 && cup)
+		ryuDigits32(d, lhi, chi, uhi, c0, cup, 8)
+		d.dp += 9
+	} else {
+		d.nd = 0
+		// emit high part
+		n := uint(9)
+		for v := chi; v > 0; {
+			v1, v2 := v/10, v%10
+			v = v1
+			n--
+			d.d[n] = byte(v2 + '0')
+		}
+		d.d = d.d[n:]
+		d.nd = int(9 - n)
+		// emit low part
+		ryuDigits32(d, llo, clo, ulo,
+			c0, cup, d.nd+8)
+	}
+	// trim trailing zeros
+	for d.nd > 0 && d.d[d.nd-1] == '0' {
+		d.nd--
+	}
+	// trim initial zeros
+	for d.nd > 0 && d.d[0] == '0' {
+		d.nd--
+		d.dp--
+		d.d = d.d[1:]
+	}
+}
+
+// ryuDigits32 emits decimal digits for a number less than 1e9.
+func ryuDigits32(d *decimalSlice, lower, central, upper uint32,
+	c0, cup bool, endindex int) {
+	if upper == 0 {
+		d.dp = endindex + 1
+		return
+	}
+	trimmed := 0
+	// Remember last trimmed digit to check for round-up.
+	// c0 will be used to remember zeroness of following digits.
+	cNextDigit := 0
+	for upper > 0 {
+		// Repeatedly compute:
+		// l = Ceil(lower / 10^k)
+		// c = Round(central / 10^k)
+		// u = Floor(upper / 10^k)
+		// and stop when c goes out of the (l, u) interval.
+		l := (lower + 9) / 10
+		c, cdigit := central/10, central%10
+		u := upper / 10
+		if l > u {
+			// don't trim the last digit as it is forbidden to go below l
+			// other, trim and exit now.
+			break
+		}
+		// Check that we didn't cross the lower boundary.
+		// The case where l < u but c == l-1 is essentially impossible,
+		// but may happen if:
+		//    lower   = ..11
+		//    central = ..19
+		//    upper   = ..31
+		// and means that 'central' is very close but less than
+		// an integer ending with many zeros, and usually
+		// the "round-up" logic hides the problem.
+		if l == c+1 && c < u {
+			c++
+			cdigit = 0
+			cup = false
+		}
+		trimmed++
+		// Remember trimmed digits of c
+		c0 = c0 && cNextDigit == 0
+		cNextDigit = int(cdigit)
+		lower, central, upper = l, c, u
+	}
+	// should we round up?
+	if trimmed > 0 {
+		cup = cNextDigit > 5 ||
+			(cNextDigit == 5 && !c0) ||
+			(cNextDigit == 5 && c0 && central&1 == 1)
+	}
+	if central < upper && cup {
+		central++
+	}
+	// We know where the number ends, fill directly
+	endindex -= trimmed
+	v := central
+	n := endindex
+	for n > d.nd {
+		v1, v2 := v/100, v%100
+		d.d[n] = smallsString[2*v2+1]
+		d.d[n-1] = smallsString[2*v2+0]
+		n -= 2
+		v = v1
+	}
+	if n == d.nd {
+		d.d[n] = byte(v + '0')
+	}
+	d.nd = endindex + 1
+	d.dp = d.nd + trimmed
+}
+
+// mult64bitPow10 takes a floating-point input with a 25-bit
+// mantissa and multiplies it with 10^q. The resulting mantissa
+// is m*P >> 57 where P is a 64-bit element of the detailedPowersOfTen tables.
+// It is typically 31 or 32-bit wide.
+// The returned boolean is true if all trimmed bits were zero.
+//
+// That is:
+//     m*2^e2 * round(10^q) = resM * 2^resE + ε
+//     exact = ε == 0
+func mult64bitPow10(m uint32, e2, q int) (resM uint32, resE int, exact bool) {
+	if q == 0 {
+		// P == 1<<63
+		return m << 6, e2 - 6, true
+	}
+	if q < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < q {
+		// This never happens due to the range of float32/float64 exponent
+		panic("mult64bitPow10: power of 10 is out of range")
+	}
+	pow := detailedPowersOfTen[q-detailedPowersOfTenMinExp10][1]
+	if q < 0 {
+		// Inverse powers of ten must be rounded up.
+		pow += 1
+	}
+	hi, lo := bits.Mul64(uint64(m), pow)
+	e2 += mulByLog10Log2(q) - 63 + 57
+	return uint32(hi<<7 | lo>>57), e2, lo<<7 == 0
+}
+
+// mult128bitPow10 takes a floating-point input with a 55-bit
+// mantissa and multiplies it with 10^q. The resulting mantissa
+// is m*P >> 119 where P is a 128-bit element of the detailedPowersOfTen tables.
+// It is typically 63 or 64-bit wide.
+// The returned boolean is true is all trimmed bits were zero.
+//
+// That is:
+//     m*2^e2 * round(10^q) = resM * 2^resE + ε
+//     exact = ε == 0
+func mult128bitPow10(m uint64, e2, q int) (resM uint64, resE int, exact bool) {
+	if q == 0 {
+		// P == 1<<127
+		return m << 8, e2 - 8, true
+	}
+	if q < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < q {
+		// This never happens due to the range of float32/float64 exponent
+		panic("mult128bitPow10: power of 10 is out of range")
+	}
+	pow := detailedPowersOfTen[q-detailedPowersOfTenMinExp10]
+	if q < 0 {
+		// Inverse powers of ten must be rounded up.
+		pow[0] += 1
+	}
+	e2 += mulByLog10Log2(q) - 127 + 119
+
+	// long multiplication
+	l1, l0 := bits.Mul64(m, pow[0])
+	h1, h0 := bits.Mul64(m, pow[1])
+	mid, carry := bits.Add64(l1, h0, 0)
+	h1 += carry
+	return h1<<9 | mid>>55, e2, mid<<9 == 0 && l0 == 0
+}
+
+func divisibleByPower5(m uint64, k int) bool {
+	if m == 0 {
+		return true
+	}
+	for i := 0; i < k; i++ {
+		if m%5 != 0 {
+			return false
+		}
+		m /= 5
+	}
+	return true
+}
+
+// divmod1e9 computes quotient and remainder of division by 1e9,
+// avoiding runtime uint64 division on 32-bit platforms.
+func divmod1e9(x uint64) (uint32, uint32) {
+	if !host32bit {
+		return uint32(x / 1e9), uint32(x % 1e9)
+	}
+	// Use the same sequence of operations as the amd64 compiler.
+	hi, _ := bits.Mul64(x>>1, 0x89705f4136b4a598) // binary digits of 1e-9
+	q := hi >> 28
+	return uint32(q), uint32(x - q*1e9)
+}