- initial version of pidigits.go benchmark

- extra bignum.go functionality for pidigits.go
- tuned bignum multiplication

R=r
DELTA=193  (186 added, 0 deleted, 7 changed)
OCL=32852
CL=32856

src/pkg/bignum/bignum.go

@@ -283,7 +283,7 @@ func (x Natural) Sub(y Natural) Natural {
 
 // Returns c = x*y div B, z = x*y mod B.
 //
-func mul11(x, y digit) (digit, digit) {
+func mul11(x, y digit) (z1, z0 digit) {
 	// Split x and y into 2 sub-digits each,
 	// multiply the digits separately while avoiding overflow,
 	// and return the product as two separate digits.
@@ -296,7 +296,44 @@ func mul11(x, y digit) (digit, digit) {
 	const B2  = 1<<W2;
 	const M2  = _B2 - 1;
 
-	// split x and y into sub-digits
+	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)
+		// x = x
+		// y = y
+		t0 := x*y;
+
+		// compute result digits but avoid overflow
+		// z = z1*B + z0 = x*y
+		z0 = t0 & _M;
+		z1 = (t0>>W2) >> (_W-W2);
+		return;
+	}
+
+	if y < _B2 {
+		// split x and y into sub-digits
+		// sub-digits of y are (x1, x0) and (0, y)
+		// x = (x1*B2 + x0)
+		// y = y
+		x1, x0 := x>>W2, x&M2;
+
+		// x*y = t1*B2 + t0
+		t0 := x0*y;
+		t1 := x1*y;
+
+		// compute result digits but avoid overflow
+		// z = z1*B + z0 = x*y
+		z0 = (t1<<W2 + t0)&_M;
+		z1 = (t1 + t0>>W2) >> (_W-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;
@@ -307,12 +344,40 @@ func mul11(x, y digit) (digit, digit) {
 	t1 := x1*y0 + x0*y1;
 	t2 := x1*y1;
 
-	// compute the result digits but avoid overflow
+	// compute result digits but avoid overflow
 	// z = z1*B + z0 = x*y
-	z0 := (t1<<W2 + t0)&_M;
-	z1 := t2<<DW + (t1 + t0>>W2)>>(_W-W2);
+	z0 = (t1<<W2 + t0)&_M;
+	z1 = t2<<DW + (t1 + t0>>W2) >> (_W-W2);
+	return;
+}
 
-	return z1, z0;
+
+func (x Natural) Mul(y Natural) Natural
+
+// Mul1 returns the product x * d.
+//
+func (x Natural) Mul1(d uint64) Natural {
+	switch {
+	case d == 0: return nat[0];
+	case d == 1: return x;
+	case d >= _B: return x.Mul(Nat(d));
+	}
+
+	n := len(x);
+	z := make(Natural, n + 1);
+	if d != 0 {
+		c := digit(0);
+		for i := 0; i < n; i++ {
+			// z[i] += c + x[i]*d;
+			z1, z0 := mul11(x[i], digit(d));
+			t := c + z[i] + z0;
+			c, z[i] = t>>_W, t&_M;
+			c += z1;
+		}
+		z[n] = c;
+	}
+
+	return normalize(z);
 }
 
 
@@ -321,6 +386,13 @@ func mul11(x, y digit) (digit, digit) {
 func (x Natural) Mul(y Natural) Natural {
 	n := len(x);
 	m := len(y);
+	if n < m {
+		return y.Mul(x);
+	}
+
+	if m == 1 && y[0] < _B {
+		return x.Mul1(uint64(y[0]));
+	}
 
 	z := make(Natural, n + m);
 	for j := 0; j < m; j++ {

src/pkg/bignum/integer.go

@@ -161,6 +161,21 @@ func (x *Integer) Sub(y *Integer) *Integer {
 }
 
 
+// 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);
+	}
+	return MakeInt(x.sign != (d < 0), x.mant.Mul1(f));
+}
+
+
 // Mul returns the product x * y.
 //
 func (x *Integer) Mul(y *Integer) *Integer {

test/bench/pidigits.go

@@ -0,0 +1,128 @@
+/*
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+    notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above copyright
+    notice, this list of conditions and the following disclaimer in the
+    documentation and/or other materials provided with the distribution.
+
+    * Neither the name of "The Computer Language Benchmarks Game" nor the
+    name of "The Computer Language Shootout Benchmarks" nor the names of
+    its contributors may be used to endorse or promote products derived
+    from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.
+*/
+
+/* The Computer Language Benchmarks Game
+ * http://shootout.alioth.debian.org/
+ *
+ * contributed by The Go Authors.
+ * based on pidigits.c (by Paolo Bonzini & Sean Bartlett,
+ *                      modified by Michael Mellor)
+ */
+
+package main
+
+import (
+	"bignum";
+	"flag";
+	"fmt";
+)
+
+var n = flag.Int("n", 27, "number of digits");
+
+// TODO for easier profiling, remove eventually
+var silent = flag.Bool("s", false, "don't print result");
+
+var (
+	tmp1 *bignum.Integer;
+	tmp2 *bignum.Integer;
+	numer = bignum.Int(1);
+	accum = bignum.Int(0);
+	denom = bignum.Int(1);
+)
+
+func extract_digit() int64 {
+	if numer.Cmp(accum) > 0 {
+		return -1;
+	}
+
+	/* Compute (numer * 3 + accum) / denom */
+	tmp1, tmp2 = numer.MulNat(bignum.Nat(3)).Add(accum).QuoRem(denom);
+
+	/* Now, if (numer * 4 + accum) % denom... */
+	tmp2 = tmp2.Add(numer);
+
+	/* ... is normalized, then the two divisions have the same result.  */
+	if tmp2.Cmp(denom) >= 0 {
+		return -1;
+	}
+
+	return tmp1.Value();
+}
+
+func next_term(k int64) {
+	y2 := k*2 + 1;
+
+	tmp1 = numer.Shl(1);
+	accum = accum.Add(tmp1);
+	accum = accum.Mul1(y2);
+	numer = numer.Mul1(k);
+	denom = denom.Mul1(y2);
+}
+
+func eliminate_digit(d int64) {
+	accum = accum.Sub(denom.Mul1(d));
+	accum = accum.Mul1(10);
+	numer = numer.Mul1(10);
+}
+
+func printf(s string, arg ...) {
+	if !*silent {
+		fmt.Printf(s, arg);
+	}
+}
+
+func main() {
+	flag.Parse();
+
+	var m int;	// 0 <= m < 10
+	for i, k := 0, int64(0); ; {
+		d := int64(-1);
+		for d < 0 {
+			k++;
+			next_term(k);
+			d = extract_digit();
+		}
+
+		printf("%c", d + '0');
+
+		i++;
+		m = i%10;
+		if m == 0 {
+			printf("\t:%d\n", i);
+		}
+		if i >= *n {
+			break;
+		}
+		eliminate_digit(d);
+	}
+
+	if m > 0 {
+		printf("%s\t:%d\n", "          "[m : 10], *n);
+	}
+}