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// Copyright 2009 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 gc
// Transmogrify slow integer division into fast multiplication using magic.
// argument passing to/from
// smagic and umagic
type Magic struct {
W int // input for both - width
S int // output for both - shift
Bad int // output for both - unexpected failure
// magic multiplier for signed literal divisors
Sd int64 // input - literal divisor
Sm int64 // output - multiplier
// magic multiplier for unsigned literal divisors
Ud uint64 // input - literal divisor
Um uint64 // output - multiplier
Ua int // output - adder
}
// magic number for signed division
// see hacker's delight chapter 10
func smagic(m *Magic) {
var mask uint64
m.Bad = 0
switch m.W {
default:
m.Bad = 1
return
case 8:
mask = 0xff
case 16:
mask = 0xffff
case 32:
mask = 0xffffffff
case 64:
mask = 0xffffffffffffffff
}
two31 := mask ^ (mask >> 1)
p := m.W - 1
ad := uint64(m.Sd)
if m.Sd < 0 {
ad = -uint64(m.Sd)
}
// bad denominators
if ad == 0 || ad == 1 || ad == two31 {
m.Bad = 1
return
}
t := two31
ad &= mask
anc := t - 1 - t%ad
anc &= mask
q1 := two31 / anc
r1 := two31 - q1*anc
q1 &= mask
r1 &= mask
q2 := two31 / ad
r2 := two31 - q2*ad
q2 &= mask
r2 &= mask
var delta uint64
for {
p++
q1 <<= 1
r1 <<= 1
q1 &= mask
r1 &= mask
if r1 >= anc {
q1++
r1 -= anc
q1 &= mask
r1 &= mask
}
q2 <<= 1
r2 <<= 1
q2 &= mask
r2 &= mask
if r2 >= ad {
q2++
r2 -= ad
q2 &= mask
r2 &= mask
}
delta = ad - r2
delta &= mask
if q1 < delta || (q1 == delta && r1 == 0) {
continue
}
break
}
m.Sm = int64(q2 + 1)
if uint64(m.Sm)&two31 != 0 {
m.Sm |= ^int64(mask)
}
m.S = p - m.W
}
// magic number for unsigned division
// see hacker's delight chapter 10
func umagic(m *Magic) {
var mask uint64
m.Bad = 0
m.Ua = 0
switch m.W {
default:
m.Bad = 1
return
case 8:
mask = 0xff
case 16:
mask = 0xffff
case 32:
mask = 0xffffffff
case 64:
mask = 0xffffffffffffffff
}
two31 := mask ^ (mask >> 1)
m.Ud &= mask
if m.Ud == 0 || m.Ud == two31 {
m.Bad = 1
return
}
nc := mask - (-m.Ud&mask)%m.Ud
p := m.W - 1
q1 := two31 / nc
r1 := two31 - q1*nc
q1 &= mask
r1 &= mask
q2 := (two31 - 1) / m.Ud
r2 := (two31 - 1) - q2*m.Ud
q2 &= mask
r2 &= mask
var delta uint64
for {
p++
if r1 >= nc-r1 {
q1 <<= 1
q1++
r1 <<= 1
r1 -= nc
} else {
q1 <<= 1
r1 <<= 1
}
q1 &= mask
r1 &= mask
if r2+1 >= m.Ud-r2 {
if q2 >= two31-1 {
m.Ua = 1
}
q2 <<= 1
q2++
r2 <<= 1
r2++
r2 -= m.Ud
} else {
if q2 >= two31 {
m.Ua = 1
}
q2 <<= 1
r2 <<= 1
r2++
}
q2 &= mask
r2 &= mask
delta = m.Ud - 1 - r2
delta &= mask
if p < m.W+m.W {
if q1 < delta || (q1 == delta && r1 == 0) {
continue
}
}
break
}
m.Um = q2 + 1
m.S = p - m.W
}
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