499 lines
9.5 KiB
Go
499 lines
9.5 KiB
Go
// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Software IEEE754 64-bit floating point.
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// Only referred to (and thus linked in) by arm port
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// and by gotest in this directory.
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package runtime
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const (
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mantbits64 uint = 52
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expbits64 uint = 11
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bias64 = -1<<(expbits64-1) + 1
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nan64 uint64 = (1<<expbits64-1)<<mantbits64 + 1
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inf64 uint64 = (1<<expbits64 - 1) << mantbits64
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neg64 uint64 = 1 << (expbits64 + mantbits64)
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mantbits32 uint = 23
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expbits32 uint = 8
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bias32 = -1<<(expbits32-1) + 1
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nan32 uint32 = (1<<expbits32-1)<<mantbits32 + 1
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inf32 uint32 = (1<<expbits32 - 1) << mantbits32
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neg32 uint32 = 1 << (expbits32 + mantbits32)
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)
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func funpack64(f uint64) (sign, mant uint64, exp int, inf, nan bool) {
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sign = f & (1 << (mantbits64 + expbits64))
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mant = f & (1<<mantbits64 - 1)
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exp = int(f>>mantbits64) & (1<<expbits64 - 1)
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switch exp {
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case 1<<expbits64 - 1:
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if mant != 0 {
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nan = true
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return
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}
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inf = true
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return
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case 0:
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// denormalized
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if mant != 0 {
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exp += bias64 + 1
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for mant < 1<<mantbits64 {
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mant <<= 1
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exp--
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}
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}
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default:
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// add implicit top bit
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mant |= 1 << mantbits64
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exp += bias64
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}
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return
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}
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func funpack32(f uint32) (sign, mant uint32, exp int, inf, nan bool) {
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sign = f & (1 << (mantbits32 + expbits32))
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mant = f & (1<<mantbits32 - 1)
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exp = int(f>>mantbits32) & (1<<expbits32 - 1)
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switch exp {
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case 1<<expbits32 - 1:
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if mant != 0 {
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nan = true
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return
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}
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inf = true
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return
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case 0:
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// denormalized
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if mant != 0 {
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exp += bias32 + 1
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for mant < 1<<mantbits32 {
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mant <<= 1
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exp--
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}
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}
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default:
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// add implicit top bit
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mant |= 1 << mantbits32
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exp += bias32
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}
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return
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}
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func fpack64(sign, mant uint64, exp int, trunc uint64) uint64 {
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mant0, exp0, trunc0 := mant, exp, trunc
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if mant == 0 {
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return sign
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}
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for mant < 1<<mantbits64 {
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mant <<= 1
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exp--
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}
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for mant >= 4<<mantbits64 {
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trunc |= mant & 1
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mant >>= 1
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exp++
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}
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if mant >= 2<<mantbits64 {
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if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
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mant++
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if mant >= 4<<mantbits64 {
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mant >>= 1
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exp++
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}
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}
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mant >>= 1
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exp++
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}
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if exp >= 1<<expbits64-1+bias64 {
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return sign ^ inf64
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}
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if exp < bias64+1 {
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if exp < bias64-int(mantbits64) {
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return sign | 0
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}
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// repeat expecting denormal
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mant, exp, trunc = mant0, exp0, trunc0
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for exp < bias64 {
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trunc |= mant & 1
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mant >>= 1
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exp++
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}
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if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
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mant++
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}
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mant >>= 1
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exp++
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if mant < 1<<mantbits64 {
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return sign | mant
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}
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}
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return sign | uint64(exp-bias64)<<mantbits64 | mant&(1<<mantbits64-1)
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}
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func fpack32(sign, mant uint32, exp int, trunc uint32) uint32 {
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mant0, exp0, trunc0 := mant, exp, trunc
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if mant == 0 {
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return sign
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}
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for mant < 1<<mantbits32 {
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mant <<= 1
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exp--
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}
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for mant >= 4<<mantbits32 {
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trunc |= mant & 1
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mant >>= 1
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exp++
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}
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if mant >= 2<<mantbits32 {
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if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
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mant++
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if mant >= 4<<mantbits32 {
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mant >>= 1
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exp++
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}
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}
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mant >>= 1
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exp++
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}
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if exp >= 1<<expbits32-1+bias32 {
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return sign ^ inf32
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}
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if exp < bias32+1 {
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if exp < bias32-int(mantbits32) {
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return sign | 0
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}
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// repeat expecting denormal
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mant, exp, trunc = mant0, exp0, trunc0
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for exp < bias32 {
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trunc |= mant & 1
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mant >>= 1
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exp++
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}
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if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
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mant++
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}
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mant >>= 1
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exp++
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if mant < 1<<mantbits32 {
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return sign | mant
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}
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}
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return sign | uint32(exp-bias32)<<mantbits32 | mant&(1<<mantbits32-1)
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}
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func fadd64(f, g uint64) uint64 {
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fs, fm, fe, fi, fn := funpack64(f)
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gs, gm, ge, gi, gn := funpack64(g)
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// Special cases.
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switch {
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case fn || gn: // NaN + x or x + NaN = NaN
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return nan64
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case fi && gi && fs != gs: // +Inf + -Inf or -Inf + +Inf = NaN
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return nan64
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case fi: // ±Inf + g = ±Inf
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return f
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case gi: // f + ±Inf = ±Inf
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return g
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case fm == 0 && gm == 0 && fs != 0 && gs != 0: // -0 + -0 = -0
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return f
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case fm == 0: // 0 + g = g but 0 + -0 = +0
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if gm == 0 {
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g ^= gs
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}
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return g
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case gm == 0: // f + 0 = f
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return f
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}
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if fe < ge || fe == ge && fm < gm {
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f, g, fs, fm, fe, gs, gm, ge = g, f, gs, gm, ge, fs, fm, fe
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}
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shift := uint(fe - ge)
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fm <<= 2
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gm <<= 2
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trunc := gm & (1<<shift - 1)
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gm >>= shift
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if fs == gs {
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fm += gm
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} else {
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fm -= gm
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if trunc != 0 {
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fm--
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}
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}
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if fm == 0 {
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fs = 0
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}
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return fpack64(fs, fm, fe-2, trunc)
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}
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func fsub64(f, g uint64) uint64 {
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return fadd64(f, fneg64(g))
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}
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func fneg64(f uint64) uint64 {
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return f ^ (1 << (mantbits64 + expbits64))
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}
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func fmul64(f, g uint64) uint64 {
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fs, fm, fe, fi, fn := funpack64(f)
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gs, gm, ge, gi, gn := funpack64(g)
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// Special cases.
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switch {
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case fn || gn: // NaN * g or f * NaN = NaN
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return nan64
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case fi && gi: // Inf * Inf = Inf (with sign adjusted)
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return f ^ gs
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case fi && gm == 0, fm == 0 && gi: // 0 * Inf = Inf * 0 = NaN
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return nan64
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case fm == 0: // 0 * x = 0 (with sign adjusted)
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return f ^ gs
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case gm == 0: // x * 0 = 0 (with sign adjusted)
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return g ^ fs
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}
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// 53-bit * 53-bit = 107- or 108-bit
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lo, hi := mullu(fm, gm)
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shift := mantbits64 - 1
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trunc := lo & (1<<shift - 1)
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mant := hi<<(64-shift) | lo>>shift
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return fpack64(fs^gs, mant, fe+ge-1, trunc)
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}
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func fdiv64(f, g uint64) uint64 {
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fs, fm, fe, fi, fn := funpack64(f)
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gs, gm, ge, gi, gn := funpack64(g)
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// Special cases.
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switch {
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case fn || gn: // NaN / g = f / NaN = NaN
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return nan64
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case fi && gi: // ±Inf / ±Inf = NaN
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return nan64
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case !fi && !gi && fm == 0 && gm == 0: // 0 / 0 = NaN
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return nan64
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case fi, !gi && gm == 0: // Inf / g = f / 0 = Inf
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return fs ^ gs ^ inf64
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case gi, fm == 0: // f / Inf = 0 / g = Inf
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return fs ^ gs ^ 0
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}
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_, _, _, _ = fi, fn, gi, gn
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// 53-bit<<54 / 53-bit = 53- or 54-bit.
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shift := mantbits64 + 2
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q, r := divlu(fm>>(64-shift), fm<<shift, gm)
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return fpack64(fs^gs, q, fe-ge-2, r)
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}
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func f64to32(f uint64) uint32 {
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fs, fm, fe, fi, fn := funpack64(f)
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if fn {
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return nan32
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}
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fs32 := uint32(fs >> 32)
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if fi {
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return fs32 ^ inf32
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}
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const d = mantbits64 - mantbits32 - 1
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return fpack32(fs32, uint32(fm>>d), fe-1, uint32(fm&(1<<d-1)))
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}
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func f32to64(f uint32) uint64 {
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const d = mantbits64 - mantbits32
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fs, fm, fe, fi, fn := funpack32(f)
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if fn {
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return nan64
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}
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fs64 := uint64(fs) << 32
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if fi {
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return fs64 ^ inf64
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}
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return fpack64(fs64, uint64(fm)<<d, fe, 0)
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}
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func fcmp64(f, g uint64) (cmp int, isnan bool) {
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fs, fm, _, fi, fn := funpack64(f)
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gs, gm, _, gi, gn := funpack64(g)
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switch {
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case fn, gn: // flag NaN
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return 0, true
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case !fi && !gi && fm == 0 && gm == 0: // ±0 == ±0
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return 0, false
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case fs > gs: // f < 0, g > 0
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return -1, false
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case fs < gs: // f > 0, g < 0
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return +1, false
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// Same sign, not NaN.
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// Can compare encodings directly now.
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// Reverse for sign.
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case fs == 0 && f < g, fs != 0 && f > g:
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return -1, false
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case fs == 0 && f > g, fs != 0 && f < g:
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return +1, false
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}
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// f == g
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return 0, false
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}
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func f64toint(f uint64) (val int64, ok bool) {
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fs, fm, fe, fi, fn := funpack64(f)
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switch {
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case fi, fn: // NaN
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return 0, false
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case fe < -1: // f < 0.5
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return 0, false
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case fe > 63: // f >= 2^63
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if fs != 0 && fm == 0 { // f == -2^63
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return -1 << 63, true
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}
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if fs != 0 {
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return 0, false
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}
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return 0, false
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}
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for fe > int(mantbits64) {
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fe--
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fm <<= 1
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}
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for fe < int(mantbits64) {
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fe++
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fm >>= 1
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}
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val = int64(fm)
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if fs != 0 {
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val = -val
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}
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return val, true
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}
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func fintto64(val int64) (f uint64) {
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fs := uint64(val) & (1 << 63)
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mant := uint64(val)
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if fs != 0 {
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mant = -mant
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}
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return fpack64(fs, mant, int(mantbits64), 0)
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}
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// 64x64 -> 128 multiply.
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// adapted from hacker's delight.
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func mullu(u, v uint64) (lo, hi uint64) {
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const (
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s = 32
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mask = 1<<s - 1
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)
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u0 := u & mask
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u1 := u >> s
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v0 := v & mask
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v1 := v >> s
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w0 := u0 * v0
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t := u1*v0 + w0>>s
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w1 := t & mask
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w2 := t >> s
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w1 += u0 * v1
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return u * v, u1*v1 + w2 + w1>>s
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}
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// 128/64 -> 64 quotient, 64 remainder.
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// adapted from hacker's delight
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func divlu(u1, u0, v uint64) (q, r uint64) {
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const b = 1 << 32
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if u1 >= v {
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return 1<<64 - 1, 1<<64 - 1
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}
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// s = nlz(v); v <<= s
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s := uint(0)
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for v&(1<<63) == 0 {
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s++
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v <<= 1
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}
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vn1 := v >> 32
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vn0 := v & (1<<32 - 1)
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un32 := u1<<s | u0>>(64-s)
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un10 := u0 << s
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un1 := un10 >> 32
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un0 := un10 & (1<<32 - 1)
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q1 := un32 / vn1
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rhat := un32 - q1*vn1
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again1:
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if q1 >= b || q1*vn0 > b*rhat+un1 {
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q1--
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rhat += vn1
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if rhat < b {
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goto again1
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}
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}
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un21 := un32*b + un1 - q1*v
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q0 := un21 / vn1
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rhat = un21 - q0*vn1
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again2:
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if q0 >= b || q0*vn0 > b*rhat+un0 {
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q0--
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rhat += vn1
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if rhat < b {
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goto again2
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}
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}
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return q1*b + q0, (un21*b + un0 - q0*v) >> s
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}
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// callable from C
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func fadd64c(f, g uint64, ret *uint64) { *ret = fadd64(f, g) }
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func fsub64c(f, g uint64, ret *uint64) { *ret = fsub64(f, g) }
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func fmul64c(f, g uint64, ret *uint64) { *ret = fmul64(f, g) }
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func fdiv64c(f, g uint64, ret *uint64) { *ret = fdiv64(f, g) }
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func fneg64c(f uint64, ret *uint64) { *ret = fneg64(f) }
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func f32to64c(f uint32, ret *uint64) { *ret = f32to64(f) }
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func f64to32c(f uint64, ret *uint32) { *ret = f64to32(f) }
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func fcmp64c(f, g uint64, ret *int, retnan *bool) { *ret, *retnan = fcmp64(f, g) }
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func fintto64c(val int64, ret *uint64) { *ret = fintto64(val) }
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func f64tointc(f uint64, ret *int64, retok *bool) { *ret, *retok = f64toint(f) }
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