Merge asm primitives from math/big

arith.go

@@ -0,0 +1,216 @@
+// 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 Go implementations of elementary multi-precision
+// arithmetic operations on word vectors. These have the suffix _g.
+// These are needed for platforms without assembly implementations of these routines.
+// This file also contains elementary operations that can be implemented
+// sufficiently efficiently in Go.
+
+package decimal
+
+import "math/bits"
+
+// A Word represents a single digit of a multi-precision unsigned integer.
+type Word uint
+
+const (
+	_S = _W / 8 // word size in bytes
+
+	_W = bits.UintSize // word size in bits
+	_B = 1 << _W       // digit base
+	_M = _B - 1        // digit mask
+)
+
+// Many of the loops in this file are of the form
+//   for i := 0; i < len(z) && i < len(x) && i < len(y); i++
+// i < len(z) is the real condition.
+// However, checking i < len(x) && i < len(y) as well is faster than
+// having the compiler do a bounds check in the body of the loop;
+// remarkably it is even faster than hoisting the bounds check
+// out of the loop, by doing something like
+//   _, _ = x[len(z)-1], y[len(z)-1]
+// There are other ways to hoist the bounds check out of the loop,
+// but the compiler's BCE isn't powerful enough for them (yet?).
+// See the discussion in CL 164966.
+
+// ----------------------------------------------------------------------------
+// Elementary operations on words
+//
+// These operations are used by the vector operations below.
+
+// z1<<_W + z0 = x*y
+func mulWW_g(x, y Word) (z1, z0 Word) {
+	hi, lo := bits.Mul(uint(x), uint(y))
+	return Word(hi), Word(lo)
+}
+
+// z1<<_W + z0 = x*y + c
+func mulAddWWW_g(x, y, c Word) (z1, z0 Word) {
+	hi, lo := bits.Mul(uint(x), uint(y))
+	var cc uint
+	lo, cc = bits.Add(lo, uint(c), 0)
+	return Word(hi + cc), Word(lo)
+}
+
+// nlz returns the number of leading zeros in x.
+// Wraps bits.LeadingZeros call for convenience.
+func nlz(x Word) uint {
+	return uint(bits.LeadingZeros(uint(x)))
+}
+
+// q = (u1<<_W + u0 - r)/v
+func divWW_g(u1, u0, v Word) (q, r Word) {
+	qq, rr := bits.Div(uint(u1), uint(u0), uint(v))
+	return Word(qq), Word(rr)
+}
+
+// The resulting carry c is either 0 or 1.
+func addVV_g(z, x, y []Word) (c Word) {
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x) && i < len(y); i++ {
+		zi, cc := bits.Add(uint(x[i]), uint(y[i]), uint(c))
+		z[i] = Word(zi)
+		c = Word(cc)
+	}
+	return
+}
+
+// The resulting carry c is either 0 or 1.
+func subVV_g(z, x, y []Word) (c Word) {
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x) && i < len(y); i++ {
+		zi, cc := bits.Sub(uint(x[i]), uint(y[i]), uint(c))
+		z[i] = Word(zi)
+		c = Word(cc)
+	}
+	return
+}
+
+// The resulting carry c is either 0 or 1.
+func addVW_g(z, x []Word, y Word) (c Word) {
+	c = y
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x); i++ {
+		zi, cc := bits.Add(uint(x[i]), uint(c), 0)
+		z[i] = Word(zi)
+		c = Word(cc)
+	}
+	return
+}
+
+// addVWlarge is addVW, but intended for large z.
+// The only difference is that we check on every iteration
+// whether we are done with carries,
+// and if so, switch to a much faster copy instead.
+// This is only a good idea for large z,
+// because the overhead of the check and the function call
+// outweigh the benefits when z is small.
+func addVWlarge(z, x []Word, y Word) (c Word) {
+	c = y
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x); i++ {
+		if c == 0 {
+			copy(z[i:], x[i:])
+			return
+		}
+		zi, cc := bits.Add(uint(x[i]), uint(c), 0)
+		z[i] = Word(zi)
+		c = Word(cc)
+	}
+	return
+}
+
+func subVW_g(z, x []Word, y Word) (c Word) {
+	c = y
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x); i++ {
+		zi, cc := bits.Sub(uint(x[i]), uint(c), 0)
+		z[i] = Word(zi)
+		c = Word(cc)
+	}
+	return
+}
+
+// subVWlarge is to subVW as addVWlarge is to addVW.
+func subVWlarge(z, x []Word, y Word) (c Word) {
+	c = y
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x); i++ {
+		if c == 0 {
+			copy(z[i:], x[i:])
+			return
+		}
+		zi, cc := bits.Sub(uint(x[i]), uint(c), 0)
+		z[i] = Word(zi)
+		c = Word(cc)
+	}
+	return
+}
+
+func shlVU_g(z, x []Word, s uint) (c Word) {
+	if s == 0 {
+		copy(z, x)
+		return
+	}
+	if len(z) == 0 {
+		return
+	}
+	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
+	ŝ := _W - s
+	ŝ &= _W - 1 // ditto
+	c = x[len(z)-1] >> ŝ
+	for i := len(z) - 1; i > 0; i-- {
+		z[i] = x[i]<<s | x[i-1]>>ŝ
+	}
+	z[0] = x[0] << s
+	return
+}
+
+func shrVU_g(z, x []Word, s uint) (c Word) {
+	if s == 0 {
+		copy(z, x)
+		return
+	}
+	if len(z) == 0 {
+		return
+	}
+	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
+	ŝ := _W - s
+	ŝ &= _W - 1 // ditto
+	c = x[0] << ŝ
+	for i := 0; i < len(z)-1; i++ {
+		z[i] = x[i]>>s | x[i+1]<<ŝ
+	}
+	z[len(z)-1] = x[len(z)-1] >> s
+	return
+}
+
+func mulAddVWW_g(z, x []Word, y, r Word) (c Word) {
+	c = r
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x); i++ {
+		c, z[i] = mulAddWWW_g(x[i], y, c)
+	}
+	return
+}
+
+func addMulVVW_g(z, x []Word, y Word) (c Word) {
+	// The comment near the top of this file discusses this for loop condition.
+	for i := 0; i < len(z) && i < len(x); i++ {
+		z1, z0 := mulAddWWW_g(x[i], y, z[i])
+		lo, cc := bits.Add(uint(z0), uint(c), 0)
+		c, z[i] = Word(cc), Word(lo)
+		c += z1
+	}
+	return
+}
+
+func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
+	r = xn
+	for i := len(z) - 1; i >= 0; i-- {
+		z[i], r = divWW_g(r, x[i], y)
+	}
+	return
+}