math/big: factored out an internal accessor method (cleanup), added benchmark

Current result of DecimalConversion benchmark (for future reference):

BenchmarkDecimalConversion-8	   10000	    204770 ns/op

Measured on Mac Mini (late 2012) running OS X 10.10.5,
2.3 GHz Intel Core i7, 8 GB 1333 MHz DDR3.

Also: Removed comment suggesting to implement decimal by representing
digits as numbers 0..9 rather than ASCII chars '0'..'9' to avoid
repeated +/-'0' operations. Tried and it appears (per above benchmark)
that the +/-'0' operations are neglibile but the addition conversion
passes around it are not and that it makes things significantly slower.

Change-Id: I6ee033b1172043248093cc5d02abff5fc54c2e7a
Reviewed-on: https://go-review.googlesource.com/14857
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Alan Donovan <adonovan@google.com>

src/math/big/decimal.go

@@ -29,6 +29,14 @@ type decimal struct {
 	exp  int    // exponent
 }
 
+// at returns the i'th mantissa digit, starting with the most significant digit at 0.
+func (d *decimal) at(i int) byte {
+	if 0 <= i && i < len(d.mant) {
+		return d.mant[i]
+	}
+	return '0'
+}
+
 // Maximum shift amount that can be done in one pass without overflow.
 // A Word has _W bits and (1<<maxShift - 1)*10 + 9 must fit into Word.
 const maxShift = _W - 4
@@ -92,12 +100,6 @@ func (x *decimal) init(m nat, shift int) {
 	}
 }
 
-// Possibly optimization: The current implementation of nat.string takes
-// a charset argument. When a right shift is needed, we could provide
-// "\x00\x01...\x09" instead of "012..9" (as in nat.decimalString) and
-// avoid the repeated +'0' and -'0' operations in decimal.shr (and do a
-// single +'0' pass at the end).
-
 // shr implements x >> s, for s <= maxShift.
 func shr(x *decimal, s uint) {
 	// Division by 1<<s using shift-and-subtract algorithm.

src/math/big/decimal_test.go

@@ -104,3 +104,13 @@ func TestDecimalRounding(t *testing.T) {
 		}
 	}
 }
+
+func BenchmarkDecimalConversion(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		for shift := -100; shift <= +100; shift++ {
+			var d decimal
+			d.init(natOne, shift)
+			d.String()
+		}
+	}
+}

src/math/big/ftoa.go

@@ -201,14 +201,8 @@ func roundShortest(d *decimal, x *Float) {
 	// Now we can figure out the minimum number of digits required.
 	// Walk along until d has distinguished itself from upper and lower.
 	for i, m := range d.mant {
-		l := byte('0') // lower digit
-		if i < len(lower.mant) {
-			l = lower.mant[i]
-		}
-		u := byte('0') // upper digit
-		if i < len(upper.mant) {
-			u = upper.mant[i]
-		}
+		l := lower.at(i)
+		u := upper.at(i)
 
 		// Okay to round down (truncate) if lower has a different digit
 		// or if lower is inclusive and is exactly the result of rounding
@@ -296,11 +290,7 @@ func fmtF(buf []byte, prec int, d decimal) []byte {
 	if prec > 0 {
 		buf = append(buf, '.')
 		for i := 0; i < prec; i++ {
-			ch := byte('0')
-			if j := d.exp + i; 0 <= j && j < len(d.mant) {
-				ch = d.mant[j]
-			}
-			buf = append(buf, ch)
+			buf = append(buf, d.at(d.exp+i))
 		}
 	}