math/big: fix formatting for 'b' format

Fixes #9939.

Change-Id: I9d60722b648fbc00650115da539a7466c6c86552
Reviewed-on: https://go-review.googlesource.com/5640Reviewed-by: Alan Donovan <adonovan@google.com>

src/math/big/floatconv.go

@@ -171,7 +171,7 @@ func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b i
 //
 // For the binary exponent formats, the mantissa is printed in normalized form:
 //
-//	'b'	decimal integer mantissa using x.Precision() bits, or -0
+//	'b'	decimal integer mantissa using x.Prec() bits, or -0
 //	'p'	hexadecimal fraction with 0.5 <= 0.mantissa < 1.0, or -0
 //
 // The precision prec controls the number of digits (excluding the exponent)
@@ -221,7 +221,7 @@ func (x *Float) String() string {
 // bstring appends the string of x in the format ["-"] mantissa "p" exponent
 // with a decimal mantissa and a binary exponent, or ["-"] "0" if x is zero,
 // and returns the extended buffer.
-// The mantissa is normalized such that is uses x.Precision() bits in binary
+// The mantissa is normalized such that is uses x.Prec() bits in binary
 // representation.
 func (x *Float) bstring(buf []byte) []byte {
 	if x.neg {
@@ -231,12 +231,16 @@ func (x *Float) bstring(buf []byte) []byte {
 		return append(buf, '0')
 	}
 	// x != 0
-	// normalize mantissa
+
+	// adjust mantissa to use exactly x.prec bits
 	m := x.mant
-	t := uint(len(x.mant)*_W) - x.prec // 0 <= t < _W
-	if t > 0 {
-		m = nat(nil).shr(m, t)
+	switch w := uint(len(x.mant)) * _W; {
+	case w < x.prec:
+		m = nat(nil).shl(m, x.prec-w)
+	case w > x.prec:
+		m = nat(nil).shr(m, w-x.prec)
 	}
+
 	buf = append(buf, m.decimalString()...)
 	buf = append(buf, 'p')
 	e := int64(x.exp) - int64(x.prec)
@@ -258,7 +262,16 @@ func (x *Float) pstring(buf []byte) []byte {
 		return append(buf, '0')
 	}
 	// x != 0
-	// mantissa is stored in normalized form
+
+	// remove trailing 0 words early
+	// (no need to convert to hex 0's and trim later)
+	m := x.mant
+	i := 0
+	for i < len(m) && m[i] == 0 {
+		i++
+	}
+	m = m[i:]
+
 	buf = append(buf, "0x."...)
 	buf = append(buf, strings.TrimRight(x.mant.hexString(), "0")...)
 	buf = append(buf, 'p')

src/math/big/floatconv_test.go

@@ -240,86 +240,112 @@ func TestFloat64Format(t *testing.T) {
 func TestFloatFormat(t *testing.T) {
 	for _, test := range []struct {
 		x      string
+		prec   uint
 		format byte
-		prec   int
+		digits int
 		want   string
 	}{
-		{"0", 'f', 0, "0"},
-		{"-0", 'f', 0, "-0"},
-		{"1", 'f', 0, "1"},
-		{"-1", 'f', 0, "-1"},
-
-		{"1.459", 'e', 0, "1e+00"},
-		{"2.459", 'e', 1, "2.5e+00"},
-		{"3.459", 'e', 2, "3.46e+00"},
-		{"4.459", 'e', 3, "4.459e+00"},
-		{"5.459", 'e', 4, "5.4590e+00"},
-
-		{"1.459", 'E', 0, "1E+00"},
-		{"2.459", 'E', 1, "2.5E+00"},
-		{"3.459", 'E', 2, "3.46E+00"},
-		{"4.459", 'E', 3, "4.459E+00"},
-		{"5.459", 'E', 4, "5.4590E+00"},
-
-		{"1.459", 'f', 0, "1"},
-		{"2.459", 'f', 1, "2.5"},
-		{"3.459", 'f', 2, "3.46"},
-		{"4.459", 'f', 3, "4.459"},
-		{"5.459", 'f', 4, "5.4590"},
-
-		{"1.459", 'g', 0, "1"},
-		{"2.459", 'g', 1, "2"},
-		{"3.459", 'g', 2, "3.5"},
-		{"4.459", 'g', 3, "4.46"},
-		{"5.459", 'g', 4, "5.459"},
-
-		{"1459", 'g', 0, "1e+03"},
-		{"2459", 'g', 1, "2e+03"},
-		{"3459", 'g', 2, "3.5e+03"},
-		{"4459", 'g', 3, "4.46e+03"},
-		{"5459", 'g', 4, "5459"},
-
-		{"1459", 'G', 0, "1E+03"},
-		{"2459", 'G', 1, "2E+03"},
-		{"3459", 'G', 2, "3.5E+03"},
-		{"4459", 'G', 3, "4.46E+03"},
-		{"5459", 'G', 4, "5459"},
-
-		{"3", 'e', 40, "3.0000000000000000000000000000000000000000e+00"},
-		{"3", 'f', 40, "3.0000000000000000000000000000000000000000"},
-		{"3", 'g', 40, "3"},
-
-		{"3e40", 'e', 40, "3.0000000000000000000000000000000000000000e+40"},
-		{"3e40", 'f', 4, "30000000000000000000000000000000000000000.0000"},
-		{"3e40", 'g', 40, "3e+40"},
+		{"0", 10, 'f', 0, "0"},
+		{"-0", 10, 'f', 0, "-0"},
+		{"1", 10, 'f', 0, "1"},
+		{"-1", 10, 'f', 0, "-1"},
+
+		{"1.459", 100, 'e', 0, "1e+00"},
+		{"2.459", 100, 'e', 1, "2.5e+00"},
+		{"3.459", 100, 'e', 2, "3.46e+00"},
+		{"4.459", 100, 'e', 3, "4.459e+00"},
+		{"5.459", 100, 'e', 4, "5.4590e+00"},
+
+		{"1.459", 100, 'E', 0, "1E+00"},
+		{"2.459", 100, 'E', 1, "2.5E+00"},
+		{"3.459", 100, 'E', 2, "3.46E+00"},
+		{"4.459", 100, 'E', 3, "4.459E+00"},
+		{"5.459", 100, 'E', 4, "5.4590E+00"},
+
+		{"1.459", 100, 'f', 0, "1"},
+		{"2.459", 100, 'f', 1, "2.5"},
+		{"3.459", 100, 'f', 2, "3.46"},
+		{"4.459", 100, 'f', 3, "4.459"},
+		{"5.459", 100, 'f', 4, "5.4590"},
+
+		{"1.459", 100, 'g', 0, "1"},
+		{"2.459", 100, 'g', 1, "2"},
+		{"3.459", 100, 'g', 2, "3.5"},
+		{"4.459", 100, 'g', 3, "4.46"},
+		{"5.459", 100, 'g', 4, "5.459"},
+
+		{"1459", 53, 'g', 0, "1e+03"},
+		{"2459", 53, 'g', 1, "2e+03"},
+		{"3459", 53, 'g', 2, "3.5e+03"},
+		{"4459", 53, 'g', 3, "4.46e+03"},
+		{"5459", 53, 'g', 4, "5459"},
+
+		{"1459", 53, 'G', 0, "1E+03"},
+		{"2459", 53, 'G', 1, "2E+03"},
+		{"3459", 53, 'G', 2, "3.5E+03"},
+		{"4459", 53, 'G', 3, "4.46E+03"},
+		{"5459", 53, 'G', 4, "5459"},
+
+		{"3", 10, 'e', 40, "3.0000000000000000000000000000000000000000e+00"},
+		{"3", 10, 'f', 40, "3.0000000000000000000000000000000000000000"},
+		{"3", 10, 'g', 40, "3"},
+
+		{"3e40", 100, 'e', 40, "3.0000000000000000000000000000000000000000e+40"},
+		{"3e40", 100, 'f', 4, "30000000000000000000000000000000000000000.0000"},
+		{"3e40", 100, 'g', 40, "3e+40"},
 
 		// TODO(gri) need tests for actual large Floats
 
-		// These depend on the selected mantissa length to match strconv.FormatFloat.
-		// Disabled for now.
-		// {"0", 'b', 0, "0"},
-		// {"-0", 'b', 0, "-0"},
-		// {"1.0", 'b', 0, "4503599627370496p-52"},
-		// {"-1.0", 'b', 0, "-4503599627370496p-52"},
-		// {"4503599627370496", 'b', 0, "4503599627370496p+0"},
-
-		{"0", 'p', 0, "0"},
-		{"-0", 'p', 0, "-0"},
-		{"1024.0", 'p', 0, "0x.8p11"},
-		{"-1024.0", 'p', 0, "-0x.8p11"},
+		{"0", 53, 'b', 0, "0"},
+		{"-0", 53, 'b', 0, "-0"},
+		{"1.0", 53, 'b', 0, "4503599627370496p-52"},
+		{"-1.0", 53, 'b', 0, "-4503599627370496p-52"},
+		{"4503599627370496", 53, 'b', 0, "4503599627370496p+0"},
+
+		// issue 9939
+		{"3", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
+		{"03", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
+		{"3.", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
+		{"3.0", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
+		{"3.00", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
+		{"3.000", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
+
+		{"3", 350, 'p', 0, "0x.cp2"},
+		{"03", 350, 'p', 0, "0x.cp2"},
+		{"3.", 350, 'p', 0, "0x.cp2"},
+		{"3.0", 350, 'p', 0, "0x.cp2"},
+		{"3.00", 350, 'p', 0, "0x.cp2"},
+		{"3.000", 350, 'p', 0, "0x.cp2"},
+
+		{"0", 64, 'p', 0, "0"},
+		{"-0", 64, 'p', 0, "-0"},
+		{"1024.0", 64, 'p', 0, "0x.8p11"},
+		{"-1024.0", 64, 'p', 0, "-0x.8p11"},
 
 		// unsupported format
-		{"3.14", 'x', 0, "%x"},
+		{"3.14", 64, 'x', 0, "%x"},
 	} {
-		f, _, err := ParseFloat(test.x, 0, 1000, ToNearestEven)
+		f, _, err := ParseFloat(test.x, 0, test.prec, ToNearestEven)
 		if err != nil {
 			t.Errorf("%v: %s", test, err)
 			continue
 		}
 
-		got := f.Format(test.format, test.prec)
+		got := f.Format(test.format, test.digits)
 		if got != test.want {
 			t.Errorf("%v: got %s; want %s", test, got, test.want)
 		}
+
+		// compare with strconv.FormatFloat output if possible
+		// ('p' format is not supported by strconv.FormatFloat,
+		// and its output for 0.0 prints a biased exponent value
+		// as in 0p-1074 which makes no sense to emulate here)
+		if test.prec == 53 && test.format != 'p' && f.Sign() != 0 {
+			f64, _ := f.Float64()
+			got := strconv.FormatFloat(f64, test.format, test.digits, 64)
+			if got != test.want {
+				t.Errorf("%v: got %s; want %s", test, got, test.want)
+			}
+		}
 	}
 }