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Commit 8db86824 authored by Robert Griesemer's avatar Robert Griesemer
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- factored out 128-bit muladd and div into arith.go 

- wrote corresponding fast versions in fast.arith.s
- implemented in-place operations for some routines
- updated existing code to be compatible with in-place
  routines

These changes allow the pidigits benchmark to run
approx. 30% faster. Enabling the assembly routines
in fast.arith.s will give another approx. 3%.

R=r
DELTA=486  (252 added, 68 deleted, 166 changed)
OCL=32980
CL=33003
parent ea8197cb
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Showing with 242 additions and 48 deletions
src/pkg/bignum/Makefile
View file @ 8db86824
......@@ -4,7 +4,7 @@
# DO NOT EDIT. Automatically generated by gobuild.
# gobuild -m bignum.go integer.go rational.go >Makefile
# gobuild -m arith.go bignum.go integer.go rational.go >Makefile
D=
......@@ -33,30 +33,37 @@ coverage: packages
$(AS) $*.s
O1=\
bignum.$O\
arith.$O\
O2=\
integer.$O\
bignum.$O\
O3=\
integer.$O\
O4=\
rational.$O\
phases: a1 a2 a3
phases: a1 a2 a3 a4
_obj$D/bignum.a: phases
a1: $(O1)
$(AR) grc _obj$D/bignum.a bignum.$O
$(AR) grc _obj$D/bignum.a arith.$O
rm -f $(O1)
a2: $(O2)
$(AR) grc _obj$D/bignum.a integer.$O
$(AR) grc _obj$D/bignum.a bignum.$O
rm -f $(O2)
a3: $(O3)
$(AR) grc _obj$D/bignum.a rational.$O
$(AR) grc _obj$D/bignum.a integer.$O
rm -f $(O3)
a4: $(O4)
$(AR) grc _obj$D/bignum.a rational.$O
rm -f $(O4)
newpkg: clean
mkdir -p _obj$D
......@@ -66,6 +73,7 @@ $(O1): newpkg
$(O2): a1
$(O3): a2
$(O4): a3
$(O5): a4
nuke: clean
rm -f $(GOROOT)/pkg/$(GOOS)_$(GOARCH)$D/bignum.a
......
src/pkg/bignum/arith.go 0 → 100644
View file @ 8db86824
// 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.
// Fast versions of the routines in this file are in fast.arith.s.
// Simply replace this file with arith.s (renamed from fast.arith.s)
// and the bignum package will build and run on a platform that
// supports the assembly routines.
package bignum
import "unsafe"
// z1<<64 + z0 = x*y
func Mul128(x, y uint64) (z1, z0 uint64) {
// Split x and y into 2 halfwords each, multiply
// the halfwords separately while avoiding overflow,
// and return the product as 2 words.
const (
W = uint(unsafe.Sizeof(x))*8;
W2 = W/2;
B2 = 1<<W2;
M2 = B2-1;
)
if x < y {
x, y = y, x
}
if x < B2 {
// y < B2 because y <= x
// sub-digits of x and y are (0, x) and (0, y)
// z = z[0] = x*y
z0 = x*y;
return;
}
if y < B2 {
// sub-digits of x and y are (x1, x0) and (0, y)
// x = (x1*B2 + x0)
// y = (y1*B2 + y0)
x1, x0 := x>>W2, x&M2;
// x*y = t2*B2*B2 + t1*B2 + t0
t0 := x0*y;
t1 := x1*y;
// compute result digits but avoid overflow
// z = z[1]*B + z[0] = x*y
z0 = t1<<W2 + t0;
z1 = (t1 + t0>>W2) >> W2;
return;
}
// general case
// sub-digits of x and y are (x1, x0) and (y1, y0)
// x = (x1*B2 + x0)
// y = (y1*B2 + y0)
x1, x0 := x>>W2, x&M2;
y1, y0 := y>>W2, y&M2;
// x*y = t2*B2*B2 + t1*B2 + t0
t0 := x0*y0;
t1 := x1*y0 + x0*y1;
t2 := x1*y1;
// compute result digits but avoid overflow
// z = z[1]*B + z[0] = x*y
z0 = t1<<W2 + t0;
z1 = t2 + (t1 + t0>>W2) >> W2;
return;
}
// z1<<64 + z0 = x*y + c
func MulAdd128(x, y, c uint64) (z1, z0 uint64) {
// Split x and y into 2 halfwords each, multiply
// the halfwords separately while avoiding overflow,
// and return the product as 2 words.
const (
W = uint(unsafe.Sizeof(x))*8;
W2 = W/2;
B2 = 1<<W2;
M2 = B2-1;
)
// TODO(gri) Should implement special cases for faster execution.
// general case
// sub-digits of x, y, and c are (x1, x0), (y1, y0), (c1, c0)
// x = (x1*B2 + x0)
// y = (y1*B2 + y0)
x1, x0 := x>>W2, x&M2;
y1, y0 := y>>W2, y&M2;
c1, c0 := c>>W2, c&M2;
// x*y + c = t2*B2*B2 + t1*B2 + t0
t0 := x0*y0 + c0;
t1 := x1*y0 + x0*y1 + c1;
t2 := x1*y1;
// compute result digits but avoid overflow
// z = z[1]*B + z[0] = x*y
z0 = t1<<W2 + t0;
z1 = t2 + (t1 + t0>>W2) >> W2;
return;
}
// q = (x1<<64 + x0)/y + r
func Div128(x1, x0, y uint64) (q, r uint64) {
if x1 == 0 {
q, r = x0/y, x0%y;
return;
}
// TODO(gri) Implement general case.
panic("Div128 not implemented for x > 1<<64-1");
}
src/pkg/bignum/bignum.go
View file @ 8db86824
This diff is collapsed.
src/pkg/bignum/fast.arith.s 0 → 100644
View file @ 8db86824
// 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.
// This file provides fast assembly versions
// of the routines in arith.go.
// func Mul128(x, y uint64) (z1, z0 uint64)
// z1<<64 + z0 = x*y
//
TEXT bignum·Mul128(SB),7,$0
MOVQ a+0(FP), AX
MULQ a+8(FP)
MOVQ DX, a+16(FP)
MOVQ AX, a+24(FP)
RET
// func MulAdd128(x, y, c uint64) (z1, z0 uint64)
// z1<<64 + z0 = x*y + c
//
TEXT bignum·MulAdd128(SB),7,$0
MOVQ a+0(FP), AX
MULQ a+8(FP)
ADDQ a+16(FP), AX
ADCQ $0, DX
MOVQ DX, a+24(FP)
MOVQ AX, a+32(FP)
RET
// func Div128(x1, x0, y uint64) (q, r uint64)
// q = (x1<<64 + x0)/y + r
//
TEXT bignum·Div128(SB),7,$0
MOVQ a+0(FP), DX
MOVQ a+8(FP), AX
DIVQ a+16(FP)
MOVQ AX, a+24(FP)
MOVQ DX, a+32(FP)
RET
src/pkg/bignum/integer.go
View file @ 8db86824
......@@ -9,9 +9,12 @@
package bignum
import "bignum"
import "fmt"
import (
"bignum";
"fmt";
)
// TODO(gri) Complete the set of in-place operations.
// Integer represents a signed integer value of arbitrary precision.
//
......@@ -113,61 +116,82 @@ func (x *Integer) Neg() *Integer {
}
// Add returns the sum x + y.
// Iadd sets z to the sum x + y.
// z must exist and may be x or y.
//
func (x *Integer) Add(y *Integer) *Integer {
var z *Integer;
func Iadd(z, x, y *Integer) {
if x.sign == y.sign {
// x + y == x + y
// (-x) + (-y) == -(x + y)
z = MakeInt(x.sign, x.mant.Add(y.mant));
z.sign = x.sign;
Nadd(&z.mant, x.mant, y.mant);
} else {
// x + (-y) == x - y == -(y - x)
// (-x) + y == y - x == -(x - y)
if x.mant.Cmp(y.mant) >= 0 {
z = MakeInt(false, x.mant.Sub(y.mant));
z.sign = x.sign;
Nsub(&z.mant, x.mant, y.mant);
} else {
z = MakeInt(true, y.mant.Sub(x.mant));
z.sign = !x.sign;
Nsub(&z.mant, y.mant, x.mant);
}
}
if x.sign {
z.sign = !z.sign;
}
return z;
}
// Sub returns the difference x - y.
// Add returns the sum x + y.
//
func (x *Integer) Sub(y *Integer) *Integer {
var z *Integer;
func (x *Integer) Add(y *Integer) *Integer {
var z Integer;
Iadd(&z, x, y);
return &z;
}
func Isub(z, x, y *Integer) {
if x.sign != y.sign {
// x - (-y) == x + y
// (-x) - y == -(x + y)
z = MakeInt(false, x.mant.Add(y.mant));
z.sign = x.sign;
Nadd(&z.mant, x.mant, y.mant);
} else {
// x - y == x - y == -(y - x)
// (-x) - (-y) == y - x == -(x - y)
if x.mant.Cmp(y.mant) >= 0 {
z = MakeInt(false, x.mant.Sub(y.mant));
z.sign = x.sign;
Nsub(&z.mant, x.mant, y.mant);
} else {
z = MakeInt(true, y.mant.Sub(x.mant));
z.sign = !x.sign;
Nsub(&z.mant, y.mant, x.mant);
}
}
if x.sign {
z.sign = !z.sign;
}
// Sub returns the difference x - y.
//
func (x *Integer) Sub(y *Integer) *Integer {
var z Integer;
Isub(&z, x, y);
return &z;
}
// Nscale sets *z to the scaled value (*z) * d.
//
func Iscale(z *Integer, d int64) {
f := uint64(d);
if d < 0 {
f = uint64(-d);
}
return z;
z.sign = z.sign != (d < 0);
Nscale(&z.mant, f);
}
// Mul1 returns the product x * d.
//
func (x *Integer) Mul1(d int64) *Integer {
// x * y == x * y
// x * (-y) == -(x * y)
// (-x) * y == -(x * y)
// (-x) * (-y) == x * y
f := uint64(d);
if d < 0 {
f = uint64(-d);
......@@ -326,7 +350,7 @@ func (x *Integer) Shl(s uint) *Integer {
func (x *Integer) Shr(s uint) *Integer {
if x.sign {
// (-x) >> s == ^(x-1) >> s == ^((x-1) >> s) == -(((x-1) >> s) + 1)
return MakeInt(true, x.mant.Sub(nat[1]).Shr(s).Add(nat[1]));
return MakeInt(true, x.mant.Sub(Nat(1)).Shr(s).Add(Nat(1)));
}
return MakeInt(false, x.mant.Shr(s));
......@@ -337,11 +361,11 @@ func (x *Integer) Shr(s uint) *Integer {
func (x *Integer) Not() *Integer {
if x.sign {
// ^(-x) == ^(^(x-1)) == x-1
return MakeInt(false, x.mant.Sub(nat[1]));
return MakeInt(false, x.mant.Sub(Nat(1)));
}
// ^x == -x-1 == -(x+1)
return MakeInt(true, x.mant.Add(nat[1]));
return MakeInt(true, x.mant.Add(Nat(1)));
}
......@@ -351,7 +375,7 @@ func (x *Integer) And(y *Integer) *Integer {
if x.sign == y.sign {
if x.sign {
// (-x) & (-y) == ^(x-1) & ^(y-1) == ^((x-1) | (y-1)) == -(((x-1) | (y-1)) + 1)
return MakeInt(true, x.mant.Sub(nat[1]).Or(y.mant.Sub(nat[1])).Add(nat[1]));
return MakeInt(true, x.mant.Sub(Nat(1)).Or(y.mant.Sub(Nat(1))).Add(Nat(1)));
}
// x & y == x & y
......@@ -364,7 +388,7 @@ func (x *Integer) And(y *Integer) *Integer {
}
// x & (-y) == x & ^(y-1) == x &^ (y-1)
return MakeInt(false, x.mant.AndNot(y.mant.Sub(nat[1])));
return MakeInt(false, x.mant.AndNot(y.mant.Sub(Nat(1))));
}
......@@ -374,7 +398,7 @@ func (x *Integer) AndNot(y *Integer) *Integer {
if x.sign == y.sign {
if x.sign {
// (-x) &^ (-y) == ^(x-1) &^ ^(y-1) == ^(x-1) & (y-1) == (y-1) &^ (x-1)
return MakeInt(false, y.mant.Sub(nat[1]).AndNot(x.mant.Sub(nat[1])));
return MakeInt(false, y.mant.Sub(Nat(1)).AndNot(x.mant.Sub(Nat(1))));
}
// x &^ y == x &^ y
......@@ -383,11 +407,11 @@ func (x *Integer) AndNot(y *Integer) *Integer {
if x.sign {
// (-x) &^ y == ^(x-1) &^ y == ^(x-1) & ^y == ^((x-1) | y) == -(((x-1) | y) + 1)
return MakeInt(true, x.mant.Sub(nat[1]).Or(y.mant).Add(nat[1]));
return MakeInt(true, x.mant.Sub(Nat(1)).Or(y.mant).Add(Nat(1)));
}
// x &^ (-y) == x &^ ^(y-1) == x & (y-1)
return MakeInt(false, x.mant.And(y.mant.Sub(nat[1])));
return MakeInt(false, x.mant.And(y.mant.Sub(Nat(1))));
}
......@@ -397,7 +421,7 @@ func (x *Integer) Or(y *Integer) *Integer {
if x.sign == y.sign {
if x.sign {
// (-x) | (-y) == ^(x-1) | ^(y-1) == ^((x-1) & (y-1)) == -(((x-1) & (y-1)) + 1)
return MakeInt(true, x.mant.Sub(nat[1]).And(y.mant.Sub(nat[1])).Add(nat[1]));
return MakeInt(true, x.mant.Sub(Nat(1)).And(y.mant.Sub(Nat(1))).Add(Nat(1)));
}
// x | y == x | y
......@@ -410,7 +434,7 @@ func (x *Integer) Or(y *Integer) *Integer {
}
// x | (-y) == x | ^(y-1) == ^((y-1) &^ x) == -(^((y-1) &^ x) + 1)
return MakeInt(true, y.mant.Sub(nat[1]).AndNot(x.mant).Add(nat[1]));
return MakeInt(true, y.mant.Sub(Nat(1)).AndNot(x.mant).Add(Nat(1)));
}
......@@ -420,7 +444,7 @@ func (x *Integer) Xor(y *Integer) *Integer {
if x.sign == y.sign {
if x.sign {
// (-x) ^ (-y) == ^(x-1) ^ ^(y-1) == (x-1) ^ (y-1)
return MakeInt(false, x.mant.Sub(nat[1]).Xor(y.mant.Sub(nat[1])));
return MakeInt(false, x.mant.Sub(Nat(1)).Xor(y.mant.Sub(Nat(1))));
}
// x ^ y == x ^ y
......@@ -433,7 +457,7 @@ func (x *Integer) Xor(y *Integer) *Integer {
}
// x ^ (-y) == x ^ ^(y-1) == ^(x ^ (y-1)) == -((x ^ (y-1)) + 1)
return MakeInt(true, x.mant.Xor(y.mant.Sub(nat[1])).Add(nat[1]));
return MakeInt(true, x.mant.Xor(y.mant.Sub(Nat(1))).Add(Nat(1)));
}
......
src/pkg/bignum/rational.go
View file @ 8db86824
......@@ -22,7 +22,7 @@ type Rational struct {
//
func MakeRat(a *Integer, b Natural) *Rational {
f := a.mant.Gcd(b); // f > 0
if f.Cmp(nat[1]) != 0 {
if f.Cmp(Nat(1)) != 0 {
a = MakeInt(a.sign, a.mant.Div(f));
b = b.Div(f);
}
......@@ -75,7 +75,7 @@ func (x *Rational) IsPos() bool {
// in the form x == x'/1; i.e., if x is an integer value.
//
func (x *Rational) IsInt() bool {
return x.b.Cmp(nat[1]) == 0;
return x.b.Cmp(Nat(1)) == 0;
}
......@@ -184,7 +184,7 @@ func (x *Rational) Format(h fmt.State, c int) {
func RatFromString(s string, base uint) (*Rational, uint, int) {
// read numerator
a, abase, alen := IntFromString(s, base);
b := nat[1];
b := Nat(1);
// read denominator or fraction, if any
var blen int;
......@@ -211,7 +211,7 @@ func RatFromString(s string, base uint) (*Rational, uint, int) {
rlen++;
e, _, elen := IntFromString(s[rlen : len(s)], 10);
rlen += elen;
m := nat[10].Pow(uint(e.mant.Value()));
m := Nat(10).Pow(uint(e.mant.Value()));
if e.sign {
b = b.Mul(m);
} else {
......
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