| // 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 arm port |
| // 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 |
| 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 |
| 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) |
| } |
| |
| // 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 |
| } |
