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Editing: softfloat64.go
// Copyright 2010 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. // Software IEEE754 64-bit floating point. // Only referred to (and thus linked in) by softfloat targets // and by tests in this directory. package runtime const ( mantbits64 uint = 52 expbits64 uint = 11 bias64 = -1<<(expbits64-1) + 1 nan64 uint64 = (1<<expbits64-1)<<mantbits64 + 1<<(mantbits64-1) // quiet NaN, 0 payload inf64 uint64 = (1<<expbits64 - 1) << mantbits64 neg64 uint64 = 1 << (expbits64 + mantbits64) mantbits32 uint = 23 expbits32 uint = 8 bias32 = -1<<(expbits32-1) + 1 nan32 uint32 = (1<<expbits32-1)<<mantbits32 + 1<<(mantbits32-1) // quiet NaN, 0 payload inf32 uint32 = (1<<expbits32 - 1) << mantbits32 neg32 uint32 = 1 << (expbits32 + mantbits32) ) func funpack64(f uint64) (sign, mant uint64, exp int, inf, nan bool) { sign = f & (1 << (mantbits64 + expbits64)) mant = f & (1<<mantbits64 - 1) exp = int(f>>mantbits64) & (1<<expbits64 - 1) switch exp { case 1<<expbits64 - 1: if mant != 0 { nan = true return } inf = true return case 0: // denormalized if mant != 0 { exp += bias64 + 1 for mant < 1<<mantbits64 { mant <<= 1 exp-- } } default: // add implicit top bit mant |= 1 << mantbits64 exp += bias64 } return } func funpack32(f uint32) (sign, mant uint32, exp int, inf, nan bool) { sign = f & (1 << (mantbits32 + expbits32)) mant = f & (1<<mantbits32 - 1) exp = int(f>>mantbits32) & (1<<expbits32 - 1) switch exp { case 1<<expbits32 - 1: if mant != 0 { nan = true return } inf = true return case 0: // denormalized if mant != 0 { exp += bias32 + 1 for mant < 1<<mantbits32 { mant <<= 1 exp-- } } default: // add implicit top bit mant |= 1 << mantbits32 exp += bias32 } return } func fpack64(sign, mant uint64, exp int, trunc uint64) uint64 { mant0, exp0, trunc0 := mant, exp, trunc if mant == 0 { return sign } for mant < 1<<mantbits64 { mant <<= 1 exp-- } for mant >= 4<<mantbits64 { trunc |= mant & 1 mant >>= 1 exp++ } if mant >= 2<<mantbits64 { if mant&1 != 0 && (trunc != 0 || mant&2 != 0) { mant++ if mant >= 4<<mantbits64 { mant >>= 1 exp++ } } mant >>= 1 exp++ } if exp >= 1<<expbits64-1+bias64 { return sign ^ inf64 } if exp < bias64+1 { if exp < bias64-int(mantbits64) { return sign | 0 } // repeat expecting denormal mant, exp, trunc = mant0, exp0, trunc0 for exp < bias64 { trunc |= mant & 1 mant >>= 1 exp++ } if mant&1 != 0 && (trunc != 0 || mant&2 != 0) { mant++ } mant >>= 1 exp++ if mant < 1<<mantbits64 { return sign | mant } } return sign | uint64(exp-bias64)<<mantbits64 | mant&(1<<mantbits64-1) } func fpack32(sign, mant uint32, exp int, trunc uint32) uint32 { mant0, exp0, trunc0 := mant, exp, trunc if mant == 0 { return sign } for mant < 1<<mantbits32 { mant <<= 1 exp-- } for mant >= 4<<mantbits32 { trunc |= mant & 1 mant >>= 1 exp++ } if mant >= 2<<mantbits32 { if mant&1 != 0 && (trunc != 0 || mant&2 != 0) { mant++ if mant >= 4<<mantbits32 { mant >>= 1 exp++ } } mant >>= 1 exp++ } if exp >= 1<<expbits32-1+bias32 { return sign ^ inf32 } if exp < bias32+1 { if exp < bias32-int(mantbits32) { return sign | 0 } // repeat expecting denormal mant, exp, trunc = mant0, exp0, trunc0 for exp < bias32 { trunc |= mant & 1 mant >>= 1 exp++ } if mant&1 != 0 && (trunc != 0 || mant&2 != 0) { mant++ } mant >>= 1 exp++ if mant < 1<<mantbits32 { return sign | mant } } return sign | uint32(exp-bias32)<<mantbits32 | mant&(1<<mantbits32-1) } func fadd64(f, g uint64) uint64 { fs, fm, fe, fi, fn := funpack64(f) gs, gm, ge, gi, gn := funpack64(g) // Special cases. switch { case fn || gn: // NaN + x or x + NaN = NaN return nan64 case fi && gi && fs != gs: // +Inf + -Inf or -Inf + +Inf = NaN return nan64 case fi: // ±Inf + g = ±Inf return f case gi: // f + ±Inf = ±Inf return g case fm == 0 && gm == 0 && fs != 0 && gs != 0: // -0 + -0 = -0 return f case fm == 0: // 0 + g = g but 0 + -0 = +0 if gm == 0 { g ^= gs } return g case gm == 0: // f + 0 = f return f } if fe < ge || fe == ge && fm < gm { f, g, fs, fm, fe, gs, gm, ge = g, f, gs, gm, ge, fs, fm, fe } shift := uint(fe - ge) fm <<= 2 gm <<= 2 trunc := gm & (1<<shift - 1) gm >>= shift if fs == gs { fm += gm } else { fm -= gm if trunc != 0 { fm-- } } if fm == 0 { fs = 0 } return fpack64(fs, fm, fe-2, trunc) } func fsub64(f, g uint64) uint64 { return fadd64(f, fneg64(g)) } func fneg64(f uint64) uint64 { return f ^ (1 << (mantbits64 + expbits64)) } func fmul64(f, g uint64) uint64 { fs, fm, fe, fi, fn := funpack64(f) gs, gm, ge, gi, gn := funpack64(g) // Special cases. switch { case fn || gn: // NaN * g or f * NaN = NaN return nan64 case fi && gi: // Inf * Inf = Inf (with sign adjusted) return f ^ gs case fi && gm == 0, fm == 0 && gi: // 0 * Inf = Inf * 0 = NaN return nan64 case fm == 0: // 0 * x = 0 (with sign adjusted) return f ^ gs case gm == 0: // x * 0 = 0 (with sign adjusted) return g ^ fs } // 53-bit * 53-bit = 107- or 108-bit lo, hi := mullu(fm, gm) shift := mantbits64 - 1 trunc := lo & (1<<shift - 1) mant := hi<<(64-shift) | lo>>shift return fpack64(fs^gs, mant, fe+ge-1, trunc) } func fdiv64(f, g uint64) uint64 { fs, fm, fe, fi, fn := funpack64(f) gs, gm, ge, gi, gn := funpack64(g) // Special cases. switch { case fn || gn: // NaN / g = f / NaN = NaN return nan64 case fi && gi: // ±Inf / ±Inf = NaN return nan64 case !fi && !gi && fm == 0 && gm == 0: // 0 / 0 = NaN return nan64 case fi, !gi && gm == 0: // Inf / g = f / 0 = Inf return fs ^ gs ^ inf64 case gi, fm == 0: // f / Inf = 0 / g = Inf return fs ^ gs ^ 0 } _, _, _, _ = fi, fn, gi, gn // 53-bit<<54 / 53-bit = 53- or 54-bit. shift := mantbits64 + 2 q, r := divlu(fm>>(64-shift), fm<<shift, gm) return fpack64(fs^gs, q, fe-ge-2, r) } func f64to32(f uint64) uint32 { fs, fm, fe, fi, fn := funpack64(f) if fn { return nan32 } fs32 := uint32(fs >> 32) if fi { return fs32 ^ inf32 } const d = mantbits64 - mantbits32 - 1 return fpack32(fs32, uint32(fm>>d), fe-1, uint32(fm&(1<<d-1))) } func f32to64(f uint32) uint64 { const d = mantbits64 - mantbits32 fs, fm, fe, fi, fn := funpack32(f) if fn { return nan64 } fs64 := uint64(fs) << 32 if fi { return fs64 ^ inf64 } return fpack64(fs64, uint64(fm)<<d, fe, 0) } func fcmp64(f, g uint64) (cmp int32, isnan bool) { fs, fm, _, fi, fn := funpack64(f) gs, gm, _, gi, gn := funpack64(g) switch { case fn, gn: // flag NaN return 0, true case !fi && !gi && fm == 0 && gm == 0: // ±0 == ±0 return 0, false case fs > gs: // f < 0, g > 0 return -1, false case fs < gs: // f > 0, g < 0 return +1, false // Same sign, not NaN. // Can compare encodings directly now. // Reverse for sign. case fs == 0 && f < g, fs != 0 && f > g: return -1, false case fs == 0 && f > g, fs != 0 && f < g: return +1, false } // f == g return 0, false } func f64toint(f uint64) (val int64, ok bool) { fs, fm, fe, fi, fn := funpack64(f) switch { case fi, fn: // NaN return 0, false case fe < -1: // f < 0.5 return 0, false case fe > 63: // f >= 2^63 if fs != 0 && fm == 0 { // f == -2^63 return -1 << 63, true } if fs != 0 { return 0, false } return 0, false } for fe > int(mantbits64) { fe-- fm <<= 1 } for fe < int(mantbits64) { fe++ fm >>= 1 } val = int64(fm) if fs != 0 { val = -val } return val, true } func fintto64(val int64) (f uint64) { fs := uint64(val) & (1 << 63) mant := uint64(val) if fs != 0 { mant = -mant } return fpack64(fs, mant, int(mantbits64), 0) } func fintto32(val int64) (f uint32) { fs := uint64(val) & (1 << 63) mant := uint64(val) if fs != 0 { mant = -mant } // Reduce mantissa size until it fits into a uint32. // Keep track of the bits we throw away, and if any are // nonzero or them into the lowest bit. exp := int(mantbits32) var trunc uint32 for mant >= 1<<32 { trunc |= uint32(mant) & 1 mant >>= 1 exp++ } return fpack32(uint32(fs>>32), uint32(mant), exp, trunc) } // 64x64 -> 128 multiply. // adapted from hacker's delight. func mullu(u, v uint64) (lo, hi uint64) { const ( s = 32 mask = 1<<s - 1 ) u0 := u & mask u1 := u >> s v0 := v & mask v1 := v >> s w0 := u0 * v0 t := u1*v0 + w0>>s w1 := t & mask w2 := t >> s w1 += u0 * v1 return u * v, u1*v1 + w2 + w1>>s } // 128/64 -> 64 quotient, 64 remainder. // adapted from hacker's delight func divlu(u1, u0, v uint64) (q, r uint64) { const b = 1 << 32 if u1 >= v { return 1<<64 - 1, 1<<64 - 1 } // s = nlz(v); v <<= s s := uint(0) for v&(1<<63) == 0 { s++ v <<= 1 } vn1 := v >> 32 vn0 := v & (1<<32 - 1) un32 := u1<<s | u0>>(64-s) un10 := u0 << s un1 := un10 >> 32 un0 := un10 & (1<<32 - 1) q1 := un32 / vn1 rhat := un32 - q1*vn1 again1: if q1 >= b || q1*vn0 > b*rhat+un1 { q1-- rhat += vn1 if rhat < b { goto again1 } } un21 := un32*b + un1 - q1*v q0 := un21 / vn1 rhat = un21 - q0*vn1 again2: if q0 >= b || q0*vn0 > b*rhat+un0 { q0-- rhat += vn1 if rhat < b { goto again2 } } return q1*b + q0, (un21*b + un0 - q0*v) >> s } func fadd32(x, y uint32) uint32 { return f64to32(fadd64(f32to64(x), f32to64(y))) } func fmul32(x, y uint32) uint32 { return f64to32(fmul64(f32to64(x), f32to64(y))) } func fdiv32(x, y uint32) uint32 { // TODO: are there double-rounding problems here? See issue 48807. return f64to32(fdiv64(f32to64(x), f32to64(y))) } func feq32(x, y uint32) bool { cmp, nan := fcmp64(f32to64(x), f32to64(y)) return cmp == 0 && !nan } func fgt32(x, y uint32) bool { cmp, nan := fcmp64(f32to64(x), f32to64(y)) return cmp >= 1 && !nan } func fge32(x, y uint32) bool { cmp, nan := fcmp64(f32to64(x), f32to64(y)) return cmp >= 0 && !nan } func feq64(x, y uint64) bool { cmp, nan := fcmp64(x, y) return cmp == 0 && !nan } func fgt64(x, y uint64) bool { cmp, nan := fcmp64(x, y) return cmp >= 1 && !nan } func fge64(x, y uint64) bool { cmp, nan := fcmp64(x, y) return cmp >= 0 && !nan } func fint32to32(x int32) uint32 { return fintto32(int64(x)) } func fint32to64(x int32) uint64 { return fintto64(int64(x)) } func fint64to32(x int64) uint32 { return fintto32(x) } func fint64to64(x int64) uint64 { return fintto64(x) } func f32toint32(x uint32) int32 { val, _ := f64toint(f32to64(x)) return int32(val) } func f32toint64(x uint32) int64 { val, _ := f64toint(f32to64(x)) return val } func f64toint32(x uint64) int32 { val, _ := f64toint(x) return int32(val) } func f64toint64(x uint64) int64 { val, _ := f64toint(x) return val } func f64touint64(x uint64) uint64 { var m uint64 = 0x43e0000000000000 // float64 1<<63 if fgt64(m, x) { return uint64(f64toint64(x)) } y := fadd64(x, -m) z := uint64(f64toint64(y)) return z | (1 << 63) } func f32touint64(x uint32) uint64 { var m uint32 = 0x5f000000 // float32 1<<63 if fgt32(m, x) { return uint64(f32toint64(x)) } y := fadd32(x, -m) z := uint64(f32toint64(y)) return z | (1 << 63) } func fuint64to64(x uint64) uint64 { if int64(x) >= 0 { return fint64to64(int64(x)) } // See ../cmd/compile/internal/ssagen/ssa.go:uint64Tofloat y := x & 1 z := x >> 1 z = z | y r := fint64to64(int64(z)) return fadd64(r, r) } func fuint64to32(x uint64) uint32 { if int64(x) >= 0 { return fint64to32(int64(x)) } // See ../cmd/compile/internal/ssagen/ssa.go:uint64Tofloat y := x & 1 z := x >> 1 z = z | y r := fint64to32(int64(z)) return fadd32(r, r) }
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