--- /dev/null
+// 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"
+
+// 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.
+// http://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
+}
+
+// floatBits returns the bits of the float64 that best approximates
+// the extFloat passed as receiver. Overflow is set to true if
+// the resulting float64 is ±Inf.
+func (f *extFloat) floatBits() (bits uint64, overflow bool) {
+ flt := &float64info
+ f.Normalize()
+
+ exp := f.exp + 63
+
+ // Exponent too small.
+ if exp < flt.bias+1 {
+ n := flt.bias + 1 - exp
+ f.mant >>= uint(n)
+ exp += n
+ }
+
+ // Extract 1+flt.mantbits bits.
+ mant := f.mant >> (63 - flt.mantbits)
+ if f.mant&(1<<(62-flt.mantbits)) != 0 {
+ // Round up.
+ mant += 1
+ }
+
+ // Rounding might have added a bit; shift down.
+ if mant == 2<<flt.mantbits {
+ mant >>= 1
+ exp++
+ }
+
+ // Infinities.
+ if exp-flt.bias >= 1<<flt.expbits-1 {
+ goto overflow
+ }
+
+ // Denormalized?
+ if mant&(1<<flt.mantbits) == 0 {
+ exp = flt.bias
+ }
+ goto out
+
+overflow:
+ // ±Inf
+ mant = 0
+ exp = 1<<flt.expbits - 1 + flt.bias
+ overflow = true
+
+out:
+ // Assemble bits.
+ bits = mant & (uint64(1)<<flt.mantbits - 1)
+ bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
+ if f.neg {
+ bits |= 1 << (flt.mantbits + flt.expbits)
+ }
+ return
+}
+
+// Assign sets f to the value of x.
+func (f *extFloat) Assign(x float64) {
+ if x < 0 {
+ x = -x
+ f.neg = true
+ }
+ x, f.exp = math.Frexp(x)
+ f.mant = uint64(x * float64(1<<64))
+ f.exp -= 64
+}
+
+// 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 {
+ if f.mant == 0 {
+ return 0
+ }
+ exp_before := f.exp
+ for f.mant < (1 << 55) {
+ f.mant <<= 8
+ f.exp -= 8
+ }
+ for f.mant < (1 << 63) {
+ f.mant <<= 1
+ f.exp -= 1
+ }
+ return uint(exp_before - f.exp)
+}
+
+// Multiply sets f to the product f*g: the result is correctly rounded,
+// but not normalized.
+func (f *extFloat) Multiply(g extFloat) {
+ fhi, flo := f.mant>>32, uint64(uint32(f.mant))
+ ghi, glo := g.mant>>32, uint64(uint32(g.mant))
+
+ // Cross products.
+ cross1 := fhi * glo
+ cross2 := flo * ghi
+
+ // f.mant*g.mant is fhi*ghi << 64 + (cross1+cross2) << 32 + flo*glo
+ f.mant = fhi*ghi + (cross1 >> 32) + (cross2 >> 32)
+ rem := uint64(uint32(cross1)) + uint64(uint32(cross2)) + ((flo * glo) >> 32)
+ // Round up.
+ rem += (1 << 31)
+
+ f.mant += (rem >> 32)
+ 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,
+}
+
+// AssignDecimal sets f to an approximate value of the decimal d. It
+// returns true if the value represented by f is guaranteed to be the
+// best approximation of d after being rounded to a float64.
+func (f *extFloat) AssignDecimal(d *decimal) (ok bool) {
+ const uint64digits = 19
+ const errorscale = 8
+ mant10, digits := d.atou64()
+ exp10 := d.dp - digits
+ errors := 0 // An upper bound for error, computed in errorscale*ulp.
+
+ if digits < d.nd {
+ // the decimal number was truncated.
+ errors += errorscale / 2
+ }
+
+ f.mant = mant10
+ f.exp = 0
+ f.neg = d.neg
+
+ // Multiply by powers of ten.
+ i := (exp10 - firstPowerOfTen) / stepPowerOfTen
+ if exp10 < firstPowerOfTen || i >= len(powersOfTen) {
+ return false
+ }
+ adjExp := (exp10 - firstPowerOfTen) % stepPowerOfTen
+
+ // We multiply by exp%step
+ if digits+adjExp <= uint64digits {
+ // We can multiply the mantissa
+ f.mant *= uint64(float64pow10[adjExp])
+ f.Normalize()
+ } else {
+ f.Normalize()
+ f.Multiply(smallPowersOfTen[adjExp])
+ errors += errorscale / 2
+ }
+
+ // We multiply by 10 to the exp - exp%step.
+ f.Multiply(powersOfTen[i])
+ if errors > 0 {
+ errors += 1
+ }
+ errors += errorscale / 2
+
+ // Normalize
+ shift := f.Normalize()
+ errors <<= shift
+
+ // Now f is a good approximation of the decimal.
+ // Check whether the error is too large: that is, if the mantissa
+ // is perturbated by the error, the resulting float64 will change.
+ // The 64 bits mantissa is 1 + 52 bits for float64 + 11 extra bits.
+ //
+ // In many cases the approximation will be good enough.
+ const denormalExp = -1023 - 63
+ flt := &float64info
+ var extrabits uint
+ if f.exp <= denormalExp || f.exp >= 1023-64 {
+ extrabits = uint(63 - flt.mantbits + 1 + uint(denormalExp-f.exp))
+ } else {
+ extrabits = uint(63 - flt.mantbits)
+ }
+
+ halfway := uint64(1) << (extrabits - 1)
+ mant_extra := f.mant & (1<<extrabits - 1)
+
+ // Do a signed comparison here! If the error estimate could make
+ // the mantissa round differently for the conversion to double,
+ // then we can't give a definite answer.
+ if int64(halfway)-int64(errors) < int64(mant_extra) &&
+ int64(mant_extra) < int64(halfway)+int64(errors) {
+ return false
+ }
+ return true
+}