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go/src/pkg/bignum/arith.go
Robert Griesemer 5a1d3323fe 1) Change default gofmt default settings for
parsing and printing to new syntax.

                  Use -oldparser to parse the old syntax,
                  use -oldprinter to print the old syntax.

               2) Change default gofmt formatting settings
                  to use tabs for indentation only and to use
                  spaces for alignment. This will make the code
                  alignment insensitive to an editor's tabwidth.

                  Use -spaces=false to use tabs for alignment.

               3) Manually changed src/exp/parser/parser_test.go
                  so that it doesn't try to parse the parser's
                  source files using the old syntax (they have
                  new syntax now).

               4) gofmt -w src misc test/bench

	       1st set of files.

R=rsc
CC=agl, golang-dev, iant, ken2, r
https://golang.org/cl/180047
2009-12-15 15:33:31 -08:00

122 lines
2.5 KiB
Go

// 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")
}