Adding upstream version 1.16.10.upstream/1.16.10upstream

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

1 files changed, 517 insertions, 0 deletions

diff --git a/src/strconv/extfloat.go b/src/strconv/extfloat.go
new file mode 100644
index 0000000..e7bfe51
--- /dev/null
+++ b/src/strconv/extfloat.go
@@ -0,0 +1,517 @@
+// Copyright 2011 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"
+)
+
+// An extFloat represents an extended floating-point number, with more
+// precision than a float64. It does not try to save bits: the
+// number represented by the structure is mant*(2^exp), with a negative
+// sign if neg is true.
+type extFloat struct {
+	mant uint64
+	exp  int
+	neg  bool
+}
+
+// Powers of ten taken from double-conversion library.
+// https://code.google.com/p/double-conversion/
+const (
+	firstPowerOfTen = -348
+	stepPowerOfTen  = 8
+)
+
+var smallPowersOfTen = [...]extFloat{
+	{1 << 63, -63, false},        // 1
+	{0xa << 60, -60, false},      // 1e1
+	{0x64 << 57, -57, false},     // 1e2
+	{0x3e8 << 54, -54, false},    // 1e3
+	{0x2710 << 50, -50, false},   // 1e4
+	{0x186a0 << 47, -47, false},  // 1e5
+	{0xf4240 << 44, -44, false},  // 1e6
+	{0x989680 << 40, -40, false}, // 1e7
+}
+
+var powersOfTen = [...]extFloat{
+	{0xfa8fd5a0081c0288, -1220, false}, // 10^-348
+	{0xbaaee17fa23ebf76, -1193, false}, // 10^-340
+	{0x8b16fb203055ac76, -1166, false}, // 10^-332
+	{0xcf42894a5dce35ea, -1140, false}, // 10^-324
+	{0x9a6bb0aa55653b2d, -1113, false}, // 10^-316
+	{0xe61acf033d1a45df, -1087, false}, // 10^-308
+	{0xab70fe17c79ac6ca, -1060, false}, // 10^-300
+	{0xff77b1fcbebcdc4f, -1034, false}, // 10^-292
+	{0xbe5691ef416bd60c, -1007, false}, // 10^-284
+	{0x8dd01fad907ffc3c, -980, false},  // 10^-276
+	{0xd3515c2831559a83, -954, false},  // 10^-268
+	{0x9d71ac8fada6c9b5, -927, false},  // 10^-260
+	{0xea9c227723ee8bcb, -901, false},  // 10^-252
+	{0xaecc49914078536d, -874, false},  // 10^-244
+	{0x823c12795db6ce57, -847, false},  // 10^-236
+	{0xc21094364dfb5637, -821, false},  // 10^-228
+	{0x9096ea6f3848984f, -794, false},  // 10^-220
+	{0xd77485cb25823ac7, -768, false},  // 10^-212
+	{0xa086cfcd97bf97f4, -741, false},  // 10^-204
+	{0xef340a98172aace5, -715, false},  // 10^-196
+	{0xb23867fb2a35b28e, -688, false},  // 10^-188
+	{0x84c8d4dfd2c63f3b, -661, false},  // 10^-180
+	{0xc5dd44271ad3cdba, -635, false},  // 10^-172
+	{0x936b9fcebb25c996, -608, false},  // 10^-164
+	{0xdbac6c247d62a584, -582, false},  // 10^-156
+	{0xa3ab66580d5fdaf6, -555, false},  // 10^-148
+	{0xf3e2f893dec3f126, -529, false},  // 10^-140
+	{0xb5b5ada8aaff80b8, -502, false},  // 10^-132
+	{0x87625f056c7c4a8b, -475, false},  // 10^-124
+	{0xc9bcff6034c13053, -449, false},  // 10^-116
+	{0x964e858c91ba2655, -422, false},  // 10^-108
+	{0xdff9772470297ebd, -396, false},  // 10^-100
+	{0xa6dfbd9fb8e5b88f, -369, false},  // 10^-92
+	{0xf8a95fcf88747d94, -343, false},  // 10^-84
+	{0xb94470938fa89bcf, -316, false},  // 10^-76
+	{0x8a08f0f8bf0f156b, -289, false},  // 10^-68
+	{0xcdb02555653131b6, -263, false},  // 10^-60
+	{0x993fe2c6d07b7fac, -236, false},  // 10^-52
+	{0xe45c10c42a2b3b06, -210, false},  // 10^-44
+	{0xaa242499697392d3, -183, false},  // 10^-36
+	{0xfd87b5f28300ca0e, -157, false},  // 10^-28
+	{0xbce5086492111aeb, -130, false},  // 10^-20
+	{0x8cbccc096f5088cc, -103, false},  // 10^-12
+	{0xd1b71758e219652c, -77, false},   // 10^-4
+	{0x9c40000000000000, -50, false},   // 10^4
+	{0xe8d4a51000000000, -24, false},   // 10^12
+	{0xad78ebc5ac620000, 3, false},     // 10^20
+	{0x813f3978f8940984, 30, false},    // 10^28
+	{0xc097ce7bc90715b3, 56, false},    // 10^36
+	{0x8f7e32ce7bea5c70, 83, false},    // 10^44
+	{0xd5d238a4abe98068, 109, false},   // 10^52
+	{0x9f4f2726179a2245, 136, false},   // 10^60
+	{0xed63a231d4c4fb27, 162, false},   // 10^68
+	{0xb0de65388cc8ada8, 189, false},   // 10^76
+	{0x83c7088e1aab65db, 216, false},   // 10^84
+	{0xc45d1df942711d9a, 242, false},   // 10^92
+	{0x924d692ca61be758, 269, false},   // 10^100
+	{0xda01ee641a708dea, 295, false},   // 10^108
+	{0xa26da3999aef774a, 322, false},   // 10^116
+	{0xf209787bb47d6b85, 348, false},   // 10^124
+	{0xb454e4a179dd1877, 375, false},   // 10^132
+	{0x865b86925b9bc5c2, 402, false},   // 10^140
+	{0xc83553c5c8965d3d, 428, false},   // 10^148
+	{0x952ab45cfa97a0b3, 455, false},   // 10^156
+	{0xde469fbd99a05fe3, 481, false},   // 10^164
+	{0xa59bc234db398c25, 508, false},   // 10^172
+	{0xf6c69a72a3989f5c, 534, false},   // 10^180
+	{0xb7dcbf5354e9bece, 561, false},   // 10^188
+	{0x88fcf317f22241e2, 588, false},   // 10^196
+	{0xcc20ce9bd35c78a5, 614, false},   // 10^204
+	{0x98165af37b2153df, 641, false},   // 10^212
+	{0xe2a0b5dc971f303a, 667, false},   // 10^220
+	{0xa8d9d1535ce3b396, 694, false},   // 10^228
+	{0xfb9b7cd9a4a7443c, 720, false},   // 10^236
+	{0xbb764c4ca7a44410, 747, false},   // 10^244
+	{0x8bab8eefb6409c1a, 774, false},   // 10^252
+	{0xd01fef10a657842c, 800, false},   // 10^260
+	{0x9b10a4e5e9913129, 827, false},   // 10^268
+	{0xe7109bfba19c0c9d, 853, false},   // 10^276
+	{0xac2820d9623bf429, 880, false},   // 10^284
+	{0x80444b5e7aa7cf85, 907, false},   // 10^292
+	{0xbf21e44003acdd2d, 933, false},   // 10^300
+	{0x8e679c2f5e44ff8f, 960, false},   // 10^308
+	{0xd433179d9c8cb841, 986, false},   // 10^316
+	{0x9e19db92b4e31ba9, 1013, false},  // 10^324
+	{0xeb96bf6ebadf77d9, 1039, false},  // 10^332
+	{0xaf87023b9bf0ee6b, 1066, false},  // 10^340
+}
+
+// AssignComputeBounds sets f to the floating point value
+// defined by mant, exp and precision given by flt. It returns
+// lower, upper such that any number in the closed interval
+// [lower, upper] is converted back to the same floating point number.
+func (f *extFloat) AssignComputeBounds(mant uint64, exp int, neg bool, flt *floatInfo) (lower, upper extFloat) {
+	f.mant = mant
+	f.exp = exp - int(flt.mantbits)
+	f.neg = neg
+	if f.exp <= 0 && mant == (mant>>uint(-f.exp))<<uint(-f.exp) {
+		// An exact integer
+		f.mant >>= uint(-f.exp)
+		f.exp = 0
+		return *f, *f
+	}
+	expBiased := exp - flt.bias
+
+	upper = extFloat{mant: 2*f.mant + 1, exp: f.exp - 1, neg: f.neg}
+	if mant != 1<<flt.mantbits || expBiased == 1 {
+		lower = extFloat{mant: 2*f.mant - 1, exp: f.exp - 1, neg: f.neg}
+	} else {
+		lower = extFloat{mant: 4*f.mant - 1, exp: f.exp - 2, neg: f.neg}
+	}
+	return
+}
+
+// Normalize normalizes f so that the highest bit of the mantissa is
+// set, and returns the number by which the mantissa was left-shifted.
+func (f *extFloat) Normalize() uint {
+	// bits.LeadingZeros64 would return 64
+	if f.mant == 0 {
+		return 0
+	}
+	shift := bits.LeadingZeros64(f.mant)
+	f.mant <<= uint(shift)
+	f.exp -= shift
+	return uint(shift)
+}
+
+// Multiply sets f to the product f*g: the result is correctly rounded,
+// but not normalized.
+func (f *extFloat) Multiply(g extFloat) {
+	hi, lo := bits.Mul64(f.mant, g.mant)
+	// Round up.
+	f.mant = hi + (lo >> 63)
+	f.exp = f.exp + g.exp + 64
+}
+
+var uint64pow10 = [...]uint64{
+	1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+}
+
+// Frexp10 is an analogue of math.Frexp for decimal powers. It scales
+// f by an approximate power of ten 10^-exp, and returns exp10, so
+// that f*10^exp10 has the same value as the old f, up to an ulp,
+// as well as the index of 10^-exp in the powersOfTen table.
+func (f *extFloat) frexp10() (exp10, index int) {
+	// The constants expMin and expMax constrain the final value of the
+	// binary exponent of f. We want a small integral part in the result
+	// because finding digits of an integer requires divisions, whereas
+	// digits of the fractional part can be found by repeatedly multiplying
+	// by 10.
+	const expMin = -60
+	const expMax = -32
+	// Find power of ten such that x * 10^n has a binary exponent
+	// between expMin and expMax.
+	approxExp10 := ((expMin+expMax)/2 - f.exp) * 28 / 93 // log(10)/log(2) is close to 93/28.
+	i := (approxExp10 - firstPowerOfTen) / stepPowerOfTen
+Loop:
+	for {
+		exp := f.exp + powersOfTen[i].exp + 64
+		switch {
+		case exp < expMin:
+			i++
+		case exp > expMax:
+			i--
+		default:
+			break Loop
+		}
+	}
+	// Apply the desired decimal shift on f. It will have exponent
+	// in the desired range. This is multiplication by 10^-exp10.
+	f.Multiply(powersOfTen[i])
+
+	return -(firstPowerOfTen + i*stepPowerOfTen), i
+}
+
+// frexp10Many applies a common shift by a power of ten to a, b, c.
+func frexp10Many(a, b, c *extFloat) (exp10 int) {
+	exp10, i := c.frexp10()
+	a.Multiply(powersOfTen[i])
+	b.Multiply(powersOfTen[i])
+	return
+}
+
+// FixedDecimal stores in d the first n significant digits
+// of the decimal representation of f. It returns false
+// if it cannot be sure of the answer.
+func (f *extFloat) FixedDecimal(d *decimalSlice, n int) bool {
+	if f.mant == 0 {
+		d.nd = 0
+		d.dp = 0
+		d.neg = f.neg
+		return true
+	}
+	if n == 0 {
+		panic("strconv: internal error: extFloat.FixedDecimal called with n == 0")
+	}
+	// Multiply by an appropriate power of ten to have a reasonable
+	// number to process.
+	f.Normalize()
+	exp10, _ := f.frexp10()
+
+	shift := uint(-f.exp)
+	integer := uint32(f.mant >> shift)
+	fraction := f.mant - (uint64(integer) << shift)
+	ε := uint64(1) // ε is the uncertainty we have on the mantissa of f.
+
+	// Write exactly n digits to d.
+	needed := n        // how many digits are left to write.
+	integerDigits := 0 // the number of decimal digits of integer.
+	pow10 := uint64(1) // the power of ten by which f was scaled.
+	for i, pow := 0, uint64(1); i < 20; i++ {
+		if pow > uint64(integer) {
+			integerDigits = i
+			break
+		}
+		pow *= 10
+	}
+	rest := integer
+	if integerDigits > needed {
+		// the integral part is already large, trim the last digits.
+		pow10 = uint64pow10[integerDigits-needed]
+		integer /= uint32(pow10)
+		rest -= integer * uint32(pow10)
+	} else {
+		rest = 0
+	}
+
+	// Write the digits of integer: the digits of rest are omitted.
+	var buf [32]byte
+	pos := len(buf)
+	for v := integer; v > 0; {
+		v1 := v / 10
+		v -= 10 * v1
+		pos--
+		buf[pos] = byte(v + '0')
+		v = v1
+	}
+	for i := pos; i < len(buf); i++ {
+		d.d[i-pos] = buf[i]
+	}
+	nd := len(buf) - pos
+	d.nd = nd
+	d.dp = integerDigits + exp10
+	needed -= nd
+
+	if needed > 0 {
+		if rest != 0 || pow10 != 1 {
+			panic("strconv: internal error, rest != 0 but needed > 0")
+		}
+		// Emit digits for the fractional part. Each time, 10*fraction
+		// fits in a uint64 without overflow.
+		for needed > 0 {
+			fraction *= 10
+			ε *= 10 // the uncertainty scales as we multiply by ten.
+			if 2*ε > 1<<shift {
+				// the error is so large it could modify which digit to write, abort.
+				return false
+			}
+			digit := fraction >> shift
+			d.d[nd] = byte(digit + '0')
+			fraction -= digit << shift
+			nd++
+			needed--
+		}
+		d.nd = nd
+	}
+
+	// We have written a truncation of f (a numerator / 10^d.dp). The remaining part
+	// can be interpreted as a small number (< 1) to be added to the last digit of the
+	// numerator.
+	//
+	// If rest > 0, the amount is:
+	//    (rest<<shift | fraction) / (pow10 << shift)
+	//    fraction being known with a ±ε uncertainty.
+	//    The fact that n > 0 guarantees that pow10 << shift does not overflow a uint64.
+	//
+	// If rest = 0, pow10 == 1 and the amount is
+	//    fraction / (1 << shift)
+	//    fraction being known with a ±ε uncertainty.
+	//
+	// We pass this information to the rounding routine for adjustment.
+
+	ok := adjustLastDigitFixed(d, uint64(rest)<<shift|fraction, pow10, shift, ε)
+	if !ok {
+		return false
+	}
+	// Trim trailing zeros.
+	for i := d.nd - 1; i >= 0; i-- {
+		if d.d[i] != '0' {
+			d.nd = i + 1
+			break
+		}
+	}
+	return true
+}
+
+// adjustLastDigitFixed assumes d contains the representation of the integral part
+// of some number, whose fractional part is num / (den << shift). The numerator
+// num is only known up to an uncertainty of size ε, assumed to be less than
+// (den << shift)/2.
+//
+// It will increase the last digit by one to account for correct rounding, typically
+// when the fractional part is greater than 1/2, and will return false if ε is such
+// that no correct answer can be given.
+func adjustLastDigitFixed(d *decimalSlice, num, den uint64, shift uint, ε uint64) bool {
+	if num > den<<shift {
+		panic("strconv: num > den<<shift in adjustLastDigitFixed")
+	}
+	if 2*ε > den<<shift {
+		panic("strconv: ε > (den<<shift)/2")
+	}
+	if 2*(num+ε) < den<<shift {
+		return true
+	}
+	if 2*(num-ε) > den<<shift {
+		// increment d by 1.
+		i := d.nd - 1
+		for ; i >= 0; i-- {
+			if d.d[i] == '9' {
+				d.nd--
+			} else {
+				break
+			}
+		}
+		if i < 0 {
+			d.d[0] = '1'
+			d.nd = 1
+			d.dp++
+		} else {
+			d.d[i]++
+		}
+		return true
+	}
+	return false
+}
+
+// ShortestDecimal stores in d the shortest decimal representation of f
+// which belongs to the open interval (lower, upper), where f is supposed
+// to lie. It returns false whenever the result is unsure. The implementation
+// uses the Grisu3 algorithm.
+func (f *extFloat) ShortestDecimal(d *decimalSlice, lower, upper *extFloat) bool {
+	if f.mant == 0 {
+		d.nd = 0
+		d.dp = 0
+		d.neg = f.neg
+		return true
+	}
+	if f.exp == 0 && *lower == *f && *lower == *upper {
+		// an exact integer.
+		var buf [24]byte
+		n := len(buf) - 1
+		for v := f.mant; v > 0; {
+			v1 := v / 10
+			v -= 10 * v1
+			buf[n] = byte(v + '0')
+			n--
+			v = v1
+		}
+		nd := len(buf) - n - 1
+		for i := 0; i < nd; i++ {
+			d.d[i] = buf[n+1+i]
+		}
+		d.nd, d.dp = nd, nd
+		for d.nd > 0 && d.d[d.nd-1] == '0' {
+			d.nd--
+		}
+		if d.nd == 0 {
+			d.dp = 0
+		}
+		d.neg = f.neg
+		return true
+	}
+	upper.Normalize()
+	// Uniformize exponents.
+	if f.exp > upper.exp {
+		f.mant <<= uint(f.exp - upper.exp)
+		f.exp = upper.exp
+	}
+	if lower.exp > upper.exp {
+		lower.mant <<= uint(lower.exp - upper.exp)
+		lower.exp = upper.exp
+	}
+
+	exp10 := frexp10Many(lower, f, upper)
+	// Take a safety margin due to rounding in frexp10Many, but we lose precision.
+	upper.mant++
+	lower.mant--
+
+	// The shortest representation of f is either rounded up or down, but
+	// in any case, it is a truncation of upper.
+	shift := uint(-upper.exp)
+	integer := uint32(upper.mant >> shift)
+	fraction := upper.mant - (uint64(integer) << shift)
+
+	// How far we can go down from upper until the result is wrong.
+	allowance := upper.mant - lower.mant
+	// How far we should go to get a very precise result.
+	targetDiff := upper.mant - f.mant
+
+	// Count integral digits: there are at most 10.
+	var integerDigits int
+	for i, pow := 0, uint64(1); i < 20; i++ {
+		if pow > uint64(integer) {
+			integerDigits = i
+			break
+		}
+		pow *= 10
+	}
+	for i := 0; i < integerDigits; i++ {
+		pow := uint64pow10[integerDigits-i-1]
+		digit := integer / uint32(pow)
+		d.d[i] = byte(digit + '0')
+		integer -= digit * uint32(pow)
+		// evaluate whether we should stop.
+		if currentDiff := uint64(integer)<<shift + fraction; currentDiff < allowance {
+			d.nd = i + 1
+			d.dp = integerDigits + exp10
+			d.neg = f.neg
+			// Sometimes allowance is so large the last digit might need to be
+			// decremented to get closer to f.
+			return adjustLastDigit(d, currentDiff, targetDiff, allowance, pow<<shift, 2)
+		}
+	}
+	d.nd = integerDigits
+	d.dp = d.nd + exp10
+	d.neg = f.neg
+
+	// Compute digits of the fractional part. At each step fraction does not
+	// overflow. The choice of minExp implies that fraction is less than 2^60.
+	var digit int
+	multiplier := uint64(1)
+	for {
+		fraction *= 10
+		multiplier *= 10
+		digit = int(fraction >> shift)
+		d.d[d.nd] = byte(digit + '0')
+		d.nd++
+		fraction -= uint64(digit) << shift
+		if fraction < allowance*multiplier {
+			// We are in the admissible range. Note that if allowance is about to
+			// overflow, that is, allowance > 2^64/10, the condition is automatically
+			// true due to the limited range of fraction.
+			return adjustLastDigit(d,
+				fraction, targetDiff*multiplier, allowance*multiplier,
+				1<<shift, multiplier*2)
+		}
+	}
+}
+
+// adjustLastDigit modifies d = x-currentDiff*ε, to get closest to
+// d = x-targetDiff*ε, without becoming smaller than x-maxDiff*ε.
+// It assumes that a decimal digit is worth ulpDecimal*ε, and that
+// all data is known with an error estimate of ulpBinary*ε.
+func adjustLastDigit(d *decimalSlice, currentDiff, targetDiff, maxDiff, ulpDecimal, ulpBinary uint64) bool {
+	if ulpDecimal < 2*ulpBinary {
+		// Approximation is too wide.
+		return false
+	}
+	for currentDiff+ulpDecimal/2+ulpBinary < targetDiff {
+		d.d[d.nd-1]--
+		currentDiff += ulpDecimal
+	}
+	if currentDiff+ulpDecimal <= targetDiff+ulpDecimal/2+ulpBinary {
+		// we have two choices, and don't know what to do.
+		return false
+	}
+	if currentDiff < ulpBinary || currentDiff > maxDiff-ulpBinary {
+		// we went too far
+		return false
+	}
+	if d.nd == 1 && d.d[0] == '0' {
+		// the number has actually reached zero.
+		d.nd = 0
+		d.dp = 0
+	}
+	return true
+}