src/cmd/compile/internal/gc: re-vendor math/big, manually adjust mparith3.go

The only unreviewed change is in mparith3.go.

Change-Id: Iec0885e7688981cbaed04c152dc9b1c7032677e6
Reviewed-on: https://go-review.googlesource.com/10665Reviewed-by: Alan Donovan <adonovan@google.com>
Run-TryBot: Robert Griesemer <gri@golang.org>

src/cmd/compile/internal/big/arith.go

@@ -107,11 +107,26 @@ func log2(x Word) int {
 	return bitLen(x) - 1
 }
 
-// Number of leading zeros in x.
-func leadingZeros(x Word) uint {
+// nlz returns the number of leading zeros in x.
+func nlz(x Word) uint {
 	return uint(_W - bitLen(x))
 }
 
+// nlz64 returns the number of leading zeros in x.
+func nlz64(x uint64) uint {
+	switch _W {
+	case 32:
+		w := x >> 32
+		if w == 0 {
+			return 32 + nlz(Word(x))
+		}
+		return nlz(Word(w))
+	case 64:
+		return nlz(Word(x))
+	}
+	panic("unreachable")
+}
+
 // q = (u1<<_W + u0 - r)/y
 // Adapted from Warren, Hacker's Delight, p. 152.
 func divWW_g(u1, u0, v Word) (q, r Word) {
@@ -119,7 +134,7 @@ func divWW_g(u1, u0, v Word) (q, r Word) {
 		return 1<<_W - 1, 1<<_W - 1
 	}
 
-	s := leadingZeros(v)
+	s := nlz(v)
 	v <<= s
 
 	vn1 := v >> _W2

src/cmd/compile/internal/big/bits_test.go

@@ -203,21 +203,21 @@ func TestFromBits(t *testing.T) {
 	}{
 		// all different bit numbers
 		{nil, "0"},
-		{Bits{0}, "0x.8p1"},
-		{Bits{1}, "0x.8p2"},
-		{Bits{-1}, "0x.8p0"},
-		{Bits{63}, "0x.8p64"},
-		{Bits{33, -30}, "0x.8000000000000001p34"},
-		{Bits{255, 0}, "0x.8000000000000000000000000000000000000000000000000000000000000001p256"},
+		{Bits{0}, "0x.8p+1"},
+		{Bits{1}, "0x.8p+2"},
+		{Bits{-1}, "0x.8p+0"},
+		{Bits{63}, "0x.8p+64"},
+		{Bits{33, -30}, "0x.8000000000000001p+34"},
+		{Bits{255, 0}, "0x.8000000000000000000000000000000000000000000000000000000000000001p+256"},
 
 		// multiple equal bit numbers
-		{Bits{0, 0}, "0x.8p2"},
-		{Bits{0, 0, 0, 0}, "0x.8p3"},
-		{Bits{0, 1, 0}, "0x.8p3"},
-		{append(Bits{2, 1, 0} /* 7 */, Bits{3, 1} /* 10 */ ...), "0x.88p5" /* 17 */},
+		{Bits{0, 0}, "0x.8p+2"},
+		{Bits{0, 0, 0, 0}, "0x.8p+3"},
+		{Bits{0, 1, 0}, "0x.8p+3"},
+		{append(Bits{2, 1, 0} /* 7 */, Bits{3, 1} /* 10 */ ...), "0x.88p+5" /* 17 */},
 	} {
 		f := test.bits.Float()
-		if got := f.Format('p', 0); got != test.want {
+		if got := f.Text('p', 0); got != test.want {
 			t.Errorf("setBits(%v) = %s; want %s", test.bits, got, test.want)
 		}
 	}

src/cmd/compile/internal/big/decimal.go

@@ -19,12 +19,14 @@
 
 package big
 
-// A decimal represents a floating-point number in decimal representation.
-// The value of a decimal x is x.mant * 10 ** x.exp with 0.5 <= x.mant < 1,
-// with the most-significant mantissa digit at index 0.
+// A decimal represents an unsigned floating-point number in decimal representation.
+// The value of a non-zero decimal x is x.mant * 10 ** x.exp with 0.5 <= x.mant < 1,
+// with the most-significant mantissa digit at index 0. For the zero decimal, the
+// mantissa length and exponent are 0.
+// The zero value for decimal represents a ready-to-use 0.0.
 type decimal struct {
 	mant []byte // mantissa ASCII digits, big-endian
-	exp  int    // exponent, valid if len(mant) > 0
+	exp  int    // exponent
 }
 
 // Maximum shift amount that can be done in one pass without overflow.
@@ -46,6 +48,7 @@ func (x *decimal) init(m nat, shift int) {
 	// special case 0
 	if len(m) == 0 {
 		x.mant = x.mant[:0]
+		x.exp = 0
 		return
 	}
 
@@ -255,4 +258,7 @@ func trim(x *decimal) {
 		i--
 	}
 	x.mant = x.mant[:i]
+	if i == 0 {
+		x.exp = 0
+	}
 }

src/cmd/compile/internal/big/float.go

@@ -16,7 +16,7 @@ import (
 	"math"
 )
 
-const debugFloat = true // enable for debugging
+const debugFloat = false // enable for debugging
 
 // A nonzero finite Float represents a multi-precision floating point number
 //
@@ -363,7 +363,7 @@ func (x *Float) validate() {
 	}
 	const msb = 1 << (_W - 1)
 	if x.mant[m-1]&msb == 0 {
-		panic(fmt.Sprintf("msb not set in last word %#x of %s", x.mant[m-1], x.Format('p', 0)))
+		panic(fmt.Sprintf("msb not set in last word %#x of %s", x.mant[m-1], x.Text('p', 0)))
 	}
 	if x.prec == 0 {
 		panic("zero precision finite number")
@@ -381,14 +381,11 @@ func (x *Float) validate() {
 func (z *Float) round(sbit uint) {
 	if debugFloat {
 		z.validate()
-		if z.form > finite {
-			panic(fmt.Sprintf("round called for non-finite value %s", z))
 	}
-	}
-	// z.form <= finite
 
 	z.acc = Exact
-	if z.form == zero {
+	if z.form != finite {
+		// ±0 or ±Inf => nothing left to do
 		return
 	}
 	// z.form == finite && len(z.mant) > 0
@@ -525,25 +522,6 @@ func (z *Float) round(sbit uint) {
 	return
 }
 
-// nlz returns the number of leading zero bits in x.
-func nlz(x Word) uint {
-	return _W - uint(bitLen(x))
-}
-
-func nlz64(x uint64) uint {
-	// TODO(gri) this can be done more nicely
-	if _W == 32 {
-		if x>>32 == 0 {
-			return 32 + nlz(Word(x))
-		}
-		return nlz(Word(x >> 32))
-	}
-	if _W == 64 {
-		return nlz(Word(x))
-	}
-	panic("unreachable")
-}
-
 func (z *Float) setBits64(neg bool, x uint64) *Float {
 	if z.prec == 0 {
 		z.prec = 64
@@ -732,25 +710,44 @@ func (z *Float) Copy(x *Float) *Float {
 	return z
 }
 
-func high32(x nat) uint32 {
-	// TODO(gri) This can be done more efficiently on 32bit platforms.
-	return uint32(high64(x) >> 32)
+// msb32 returns the 32 most significant bits of x.
+func msb32(x nat) uint32 {
+	i := len(x) - 1
+	if i < 0 {
+		return 0
+	}
+	if debugFloat && x[i]&(1<<(_W-1)) == 0 {
+		panic("x not normalized")
+	}
+	switch _W {
+	case 32:
+		return uint32(x[i])
+	case 64:
+		return uint32(x[i] >> 32)
+	}
+	panic("unreachable")
 }
 
-func high64(x nat) uint64 {
-	i := len(x)
-	if i == 0 {
+// msb64 returns the 64 most significant bits of x.
+func msb64(x nat) uint64 {
+	i := len(x) - 1
+	if i < 0 {
 		return 0
 	}
-	// i > 0
-	v := uint64(x[i-1])
-	if _W == 32 {
-		v <<= 32
-		if i > 1 {
-			v |= uint64(x[i-2])
+	if debugFloat && x[i]&(1<<(_W-1)) == 0 {
+		panic("x not normalized")
 	}
+	switch _W {
+	case 32:
+		v := uint64(x[i]) << 32
+		if i > 0 {
+			v |= uint64(x[i-1])
 		}
 		return v
+	case 64:
+		return uint64(x[i])
+	}
+	panic("unreachable")
 }
 
 // Uint64 returns the unsigned integer resulting from truncating x
@@ -776,7 +773,7 @@ func (x *Float) Uint64() (uint64, Accuracy) {
 		// 1 <= x < Inf
 		if x.exp <= 64 {
 			// u = trunc(x) fits into a uint64
-			u := high64(x.mant) >> (64 - uint32(x.exp))
+			u := msb64(x.mant) >> (64 - uint32(x.exp))
 			if x.MinPrec() <= 64 {
 				return u, Exact
 			}
@@ -821,7 +818,7 @@ func (x *Float) Int64() (int64, Accuracy) {
 		// 1 <= |x| < +Inf
 		if x.exp <= 63 {
 			// i = trunc(x) fits into an int64 (excluding math.MinInt64)
-			i := int64(high64(x.mant) >> (64 - uint32(x.exp)))
+			i := int64(msb64(x.mant) >> (64 - uint32(x.exp)))
 			if x.neg {
 				i = -i
 			}
@@ -913,6 +910,7 @@ func (x *Float) Float32() (float32, Accuracy) {
 			}
 			return float32(math.Inf(+1)), Above
 		}
+		// e <= emax
 
 		// Determine sign, biased exponent, and mantissa.
 		var sign, bexp, mant uint32
@@ -933,11 +931,11 @@ func (x *Float) Float32() (float32, Accuracy) {
 				return 0.0, Below
 			}
 			// bexp = 0
-			mant = high32(r.mant) >> (fbits - r.prec)
+			mant = msb32(r.mant) >> (fbits - r.prec)
 		} else {
 			// normal number: emin <= e <= emax
 			bexp = uint32(e+bias) << mbits
-			mant = high32(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
+			mant = msb32(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
 		}
 
 		return math.Float32frombits(sign | bexp | mant), r.acc
@@ -1019,6 +1017,7 @@ func (x *Float) Float64() (float64, Accuracy) {
 			}
 			return math.Inf(+1), Above
 		}
+		// e <= emax
 
 		// Determine sign, biased exponent, and mantissa.
 		var sign, bexp, mant uint64
@@ -1039,11 +1038,11 @@ func (x *Float) Float64() (float64, Accuracy) {
 				return 0.0, Below
 			}
 			// bexp = 0
-			mant = high64(r.mant) >> (fbits - r.prec)
+			mant = msb64(r.mant) >> (fbits - r.prec)
 		} else {
 			// normal number: emin <= e <= emax
 			bexp = uint64(e+bias) << mbits
-			mant = high64(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
+			mant = msb64(r.mant) >> ebits & (1<<mbits - 1) // cut off msb (implicit 1 bit)
 		}
 
 		return math.Float64frombits(sign | bexp | mant), r.acc

src/cmd/compile/internal/big/floatconv_test.go

@@ -5,15 +5,19 @@
 package big
 
 import (
+	"fmt"
 	"math"
 	"strconv"
 	"testing"
 )
 
 func TestFloatSetFloat64String(t *testing.T) {
+	inf := math.Inf(0)
+	nan := math.NaN()
+
 	for _, test := range []struct {
 		s string
-		x float64
+		x float64 // NaNs represent invalid inputs
 	}{
 		// basics
 		{"0", 0},
@@ -45,6 +49,25 @@ func TestFloatSetFloat64String(t *testing.T) {
 		{"1.E+10", 1e10},
 		{"+1E-10", 1e-10},
 
+		// infinities
+		{"Inf", inf},
+		{"+Inf", inf},
+		{"-Inf", -inf},
+		{"inf", inf},
+		{"+inf", inf},
+		{"-inf", -inf},
+
+		// invalid numbers
+		{"", nan},
+		{"-", nan},
+		{"0x", nan},
+		{"0e", nan},
+		{"1.2ef", nan},
+		{"2..3", nan},
+		{"123..", nan},
+		{"infinity", nan},
+		{"foobar", nan},
+
 		// misc decimal values
 		{"3.14159265", 3.14159265},
 		{"-687436.79457e-245", -687436.79457e-245},
@@ -96,8 +119,16 @@ func TestFloatSetFloat64String(t *testing.T) {
 		var x Float
 		x.SetPrec(53)
 		_, ok := x.SetString(test.s)
+		if math.IsNaN(test.x) {
+			// test.s is invalid
+			if ok {
+				t.Errorf("%s: want parse error", test.s)
+			}
+			continue
+		}
+		// test.s is valid
 		if !ok {
-			t.Errorf("%s: parse error", test.s)
+			t.Errorf("%s: got parse error", test.s)
 			continue
 		}
 		f, _ := x.Float64()
@@ -113,7 +144,7 @@ const (
 	above1e23 = 100000000000000008388608
 )
 
-func TestFloat64Format(t *testing.T) {
+func TestFloat64Text(t *testing.T) {
 	for _, test := range []struct {
 		x      float64
 		format byte
@@ -125,12 +156,16 @@ func TestFloat64Format(t *testing.T) {
 		{1, 'f', 0, "1"},
 		{-1, 'f', 0, "-1"},
 
+		{0.001, 'e', 0, "1e-03"},
+		{0.459, 'e', 0, "5e-01"},
 		{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"},
 
+		{0.001, 'f', 0, "0"},
+		{0.459, 'f', 0, "0"},
 		{1.459, 'f', 0, "1"},
 		{2.459, 'f', 1, "2.5"},
 		{3.459, 'f', 2, "3.46"},
@@ -145,8 +180,8 @@ func TestFloat64Format(t *testing.T) {
 
 		{0, 'p', 0, "0"},
 		{math.Copysign(0, -1), 'p', 0, "-0"},
-		{1024.0, 'p', 0, "0x.8p11"},
-		{-1024.0, 'p', 0, "-0x.8p11"},
+		{1024.0, 'p', 0, "0x.8p+11"},
+		{-1024.0, 'p', 0, "-0x.8p+11"},
 
 		// all test cases below from strconv/ftoa_test.go
 		{1, 'e', 5, "1.00000e+00"},
@@ -253,7 +288,7 @@ func TestFloat64Format(t *testing.T) {
 		// {383260575764816448, 'g', -1, "3.8326057576481645e+17"},
 	} {
 		f := new(Float).SetFloat64(test.x)
-		got := f.Format(test.format, test.prec)
+		got := f.Text(test.format, test.prec)
 		if got != test.want {
 			t.Errorf("%v: got %s; want %s", test, got, test.want)
 		}
@@ -273,7 +308,7 @@ func TestFloat64Format(t *testing.T) {
 	}
 }
 
-func TestFloatFormat(t *testing.T) {
+func TestFloatText(t *testing.T) {
 	for _, test := range []struct {
 		x      string
 		prec   uint
@@ -331,8 +366,8 @@ func TestFloatFormat(t *testing.T) {
 		{"3e40", 100, 'g', 40, "3e+40"},
 
 		// make sure "stupid" exponents don't stall the machine
-		{"1e1000000", 64, 'p', 0, "0x.88b3a28a05eade3ap3321929"},
-		{"1e1000000000", 64, 'p', 0, "0x.ecc5f45aa573d3p1538481529"},
+		{"1e1000000", 64, 'p', 0, "0x.88b3a28a05eade3ap+3321929"},
+		{"1e1000000000", 64, 'p', 0, "0x.ecc5f45aa573d3p+1538481529"},
 		{"1e-1000000", 64, 'p', 0, "0x.efb4542cc8ca418ap-3321928"},
 		{"1e-1000000000", 64, 'p', 0, "0x.8a64dd983a4c7dabp-1538481528"},
 
@@ -352,20 +387,21 @@ func TestFloatFormat(t *testing.T) {
 		{"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"},
+		{"3", 350, 'p', 0, "0x.cp+2"},
+		{"03", 350, 'p', 0, "0x.cp+2"},
+		{"3.", 350, 'p', 0, "0x.cp+2"},
+		{"3.0", 350, 'p', 0, "0x.cp+2"},
+		{"3.00", 350, 'p', 0, "0x.cp+2"},
+		{"3.000", 350, 'p', 0, "0x.cp+2"},
 
 		{"0", 64, 'p', 0, "0"},
 		{"-0", 64, 'p', 0, "-0"},
-		{"1024.0", 64, 'p', 0, "0x.8p11"},
-		{"-1024.0", 64, 'p', 0, "-0x.8p11"},
+		{"1024.0", 64, 'p', 0, "0x.8p+11"},
+		{"-1024.0", 64, 'p', 0, "-0x.8p+11"},
 
 		// unsupported format
 		{"3.14", 64, 'x', 0, "%x"},
+		{"-3.14", 64, 'x', 0, "%x"},
 	} {
 		f, _, err := ParseFloat(test.x, 0, test.prec, ToNearestEven)
 		if err != nil {
@@ -373,7 +409,7 @@ func TestFloatFormat(t *testing.T) {
 			continue
 		}
 
-		got := f.Format(test.format, test.digits)
+		got := f.Text(test.format, test.digits)
 		if got != test.want {
 			t.Errorf("%v: got %s; want %s", test, got, test.want)
 		}
@@ -395,3 +431,143 @@ func TestFloatFormat(t *testing.T) {
 		}
 	}
 }
+
+func TestFloatFormat(t *testing.T) {
+	for _, test := range []struct {
+		format string
+		value  interface{} // float32, float64, or string (== 512bit *Float)
+		want   string
+	}{
+		// TODO(gri) uncomment the disabled 'g'/'G' formats
+		// 	     below once (*Float).Text supports prec < 0
+
+		// from fmt/fmt_test.go
+		{"%+.3e", 0.0, "+0.000e+00"},
+		{"%+.3e", 1.0, "+1.000e+00"},
+		{"%+.3f", -1.0, "-1.000"},
+		{"%+.3F", -1.0, "-1.000"},
+		{"%+.3F", float32(-1.0), "-1.000"},
+		{"%+07.2f", 1.0, "+001.00"},
+		{"%+07.2f", -1.0, "-001.00"},
+		{"%+10.2f", +1.0, "     +1.00"},
+		{"%+10.2f", -1.0, "     -1.00"},
+		{"% .3E", -1.0, "-1.000E+00"},
+		{"% .3e", 1.0, " 1.000e+00"},
+		{"%+.3g", 0.0, "+0"},
+		{"%+.3g", 1.0, "+1"},
+		{"%+.3g", -1.0, "-1"},
+		{"% .3g", -1.0, "-1"},
+		{"% .3g", 1.0, " 1"},
+		{"%b", float32(1.0), "8388608p-23"},
+		{"%b", 1.0, "4503599627370496p-52"},
+
+		// from fmt/fmt_test.go: old test/fmt_test.go
+		{"%e", 1.0, "1.000000e+00"},
+		{"%e", 1234.5678e3, "1.234568e+06"},
+		{"%e", 1234.5678e-8, "1.234568e-05"},
+		{"%e", -7.0, "-7.000000e+00"},
+		{"%e", -1e-9, "-1.000000e-09"},
+		{"%f", 1234.5678e3, "1234567.800000"},
+		{"%f", 1234.5678e-8, "0.000012"},
+		{"%f", -7.0, "-7.000000"},
+		{"%f", -1e-9, "-0.000000"},
+		// {"%g", 1234.5678e3, "1.2345678e+06"},
+		// {"%g", float32(1234.5678e3), "1.2345678e+06"},
+		// {"%g", 1234.5678e-8, "1.2345678e-05"},
+		{"%g", -7.0, "-7"},
+		{"%g", -1e-9, "-1e-09"},
+		{"%g", float32(-1e-9), "-1e-09"},
+		{"%E", 1.0, "1.000000E+00"},
+		{"%E", 1234.5678e3, "1.234568E+06"},
+		{"%E", 1234.5678e-8, "1.234568E-05"},
+		{"%E", -7.0, "-7.000000E+00"},
+		{"%E", -1e-9, "-1.000000E-09"},
+		// {"%G", 1234.5678e3, "1.2345678E+06"},
+		// {"%G", float32(1234.5678e3), "1.2345678E+06"},
+		// {"%G", 1234.5678e-8, "1.2345678E-05"},
+		{"%G", -7.0, "-7"},
+		{"%G", -1e-9, "-1E-09"},
+		{"%G", float32(-1e-9), "-1E-09"},
+
+		{"%20.6e", 1.2345e3, "        1.234500e+03"},
+		{"%20.6e", 1.2345e-3, "        1.234500e-03"},
+		{"%20e", 1.2345e3, "        1.234500e+03"},
+		{"%20e", 1.2345e-3, "        1.234500e-03"},
+		{"%20.8e", 1.2345e3, "      1.23450000e+03"},
+		{"%20f", 1.23456789e3, "         1234.567890"},
+		{"%20f", 1.23456789e-3, "            0.001235"},
+		{"%20f", 12345678901.23456789, "  12345678901.234568"},
+		{"%-20f", 1.23456789e3, "1234.567890         "},
+		{"%20.8f", 1.23456789e3, "       1234.56789000"},
+		{"%20.8f", 1.23456789e-3, "          0.00123457"},
+		// {"%g", 1.23456789e3, "1234.56789"},
+		// {"%g", 1.23456789e-3, "0.00123456789"},
+		// {"%g", 1.23456789e20, "1.23456789e+20"},
+		{"%20e", math.Inf(1), "                +Inf"},
+		{"%-20f", math.Inf(-1), "-Inf                "},
+
+		// from fmt/fmt_test.go: comparison of padding rules with C printf
+		{"%.2f", 1.0, "1.00"},
+		{"%.2f", -1.0, "-1.00"},
+		{"% .2f", 1.0, " 1.00"},
+		{"% .2f", -1.0, "-1.00"},
+		{"%+.2f", 1.0, "+1.00"},
+		{"%+.2f", -1.0, "-1.00"},
+		{"%7.2f", 1.0, "   1.00"},
+		{"%7.2f", -1.0, "  -1.00"},
+		{"% 7.2f", 1.0, "   1.00"},
+		{"% 7.2f", -1.0, "  -1.00"},
+		{"%+7.2f", 1.0, "  +1.00"},
+		{"%+7.2f", -1.0, "  -1.00"},
+		{"%07.2f", 1.0, "0001.00"},
+		{"%07.2f", -1.0, "-001.00"},
+		{"% 07.2f", 1.0, " 001.00"},
+		{"% 07.2f", -1.0, "-001.00"},
+		{"%+07.2f", 1.0, "+001.00"},
+		{"%+07.2f", -1.0, "-001.00"},
+
+		// from fmt/fmt_test.go: zero padding does not apply to infinities
+		{"%020f", math.Inf(-1), "                -Inf"},
+		{"%020f", math.Inf(+1), "                +Inf"},
+		{"% 020f", math.Inf(-1), "                -Inf"},
+		{"% 020f", math.Inf(+1), "                 Inf"},
+		{"%+020f", math.Inf(-1), "                -Inf"},
+		{"%+020f", math.Inf(+1), "                +Inf"},
+		{"%20f", -1.0, "           -1.000000"},
+
+		// handle %v like %g
+		{"%v", 0.0, "0"},
+		{"%v", -7.0, "-7"},
+		{"%v", -1e-9, "-1e-09"},
+		{"%v", float32(-1e-9), "-1e-09"},
+		{"%010v", 0.0, "0000000000"},
+		{"%010v", 0.0, "0000000000"},
+
+		// *Float cases
+		{"%.20f", "1e-20", "0.00000000000000000001"},
+		{"%.20f", "-1e-20", "-0.00000000000000000001"},
+		{"%30.20f", "-1e-20", "       -0.00000000000000000001"},
+		{"%030.20f", "-1e-20", "-00000000.00000000000000000001"},
+		{"%030.20f", "+1e-20", "000000000.00000000000000000001"},
+		{"% 030.20f", "+1e-20", " 00000000.00000000000000000001"},
+
+		// erroneous formats
+		{"%s", 1.0, "%!s(*big.Float=1)"},
+	} {
+		value := new(Float)
+		switch v := test.value.(type) {
+		case float32:
+			value.SetPrec(24).SetFloat64(float64(v))
+		case float64:
+			value.SetPrec(53).SetFloat64(v)
+		case string:
+			value.SetPrec(512).Parse(v, 0)
+		default:
+			t.Fatalf("unsupported test value: %v (%T)", v, v)
+		}
+
+		if got := fmt.Sprintf(test.format, value); got != test.want {
+			t.Errorf("%v: got %q; want %q", test, got, test.want)
+		}
+	}
+}

src/cmd/compile/internal/big/floatexample_test.go

@@ -17,13 +17,13 @@ func ExampleFloat_Add() {
 	y.SetFloat64(2.718281828) // y is automatically set to 53bit precision
 	z.SetPrec(32)
 	z.Add(&x, &y)
-	fmt.Printf("x = %s (%s, prec = %d, acc = %s)\n", &x, x.Format('p', 0), x.Prec(), x.Acc())
-	fmt.Printf("y = %s (%s, prec = %d, acc = %s)\n", &y, y.Format('p', 0), y.Prec(), y.Acc())
-	fmt.Printf("z = %s (%s, prec = %d, acc = %s)\n", &z, z.Format('p', 0), z.Prec(), z.Acc())
+	fmt.Printf("x = %.10g (%s, prec = %d, acc = %s)\n", &x, x.Text('p', 0), x.Prec(), x.Acc())
+	fmt.Printf("y = %.10g (%s, prec = %d, acc = %s)\n", &y, y.Text('p', 0), y.Prec(), y.Acc())
+	fmt.Printf("z = %.10g (%s, prec = %d, acc = %s)\n", &z, z.Text('p', 0), z.Prec(), z.Acc())
 	// Output:
-	// x = 1000 (0x.fap10, prec = 64, acc = Exact)
-	// y = 2.718281828 (0x.adf85458248cd8p2, prec = 53, acc = Exact)
-	// z = 1002.718282 (0x.faadf854p10, prec = 32, acc = Below)
+	// x = 1000 (0x.fap+10, prec = 64, acc = Exact)
+	// y = 2.718281828 (0x.adf85458248cd8p+2, prec = 53, acc = Exact)
+	// z = 1002.718282 (0x.faadf854p+10, prec = 32, acc = Below)
 }
 
 func Example_Shift() {
@@ -59,7 +59,7 @@ func ExampleFloat_Cmp() {
 		x := big.NewFloat(x64)
 		for _, y64 := range operands {
 			y := big.NewFloat(y64)
-			fmt.Printf("%4s  %4s  %3d\n", x, y, x.Cmp(y))
+			fmt.Printf("%4g  %4g  %3d\n", x, y, x.Cmp(y))
 		}
 		fmt.Println()
 	}

src/cmd/compile/internal/big/ftoa.go

@@ -2,34 +2,89 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// This file implements the 'e', 'f', 'g' floating-point formats.
-// It is closely following the corresponding implementation in
-// strconv/ftoa.go, but modified and simplified for big.Float.
-
-// Algorithm:
-//   1) convert Float to multiprecision decimal
-//   2) round to desired precision
-//   3) read digits out and format
+// This file implements Float-to-string conversion functions.
+// It is closely following the corresponding implementation
+// in strconv/ftoa.go, but modified and simplified for Float.
 
 package big
 
-import "strconv"
+import (
+	"fmt"
+	"strconv"
+	"strings"
+)
 
-// TODO(gri) Consider moving sign into decimal - could make the signatures below cleaner.
+// Text converts the floating-point number x to a string according
+// to the given format and precision prec. The format is one of:
+//
+//	'e'	-d.dddde±dd, decimal exponent, at least two (possibly 0) exponent digits
+//	'E'	-d.ddddE±dd, decimal exponent, at least two (possibly 0) exponent digits
+//	'f'	-ddddd.dddd, no exponent
+//	'g'	like 'e' for large exponents, like 'f' otherwise
+//	'G'	like 'E' for large exponents, like 'f' otherwise
+//	'b'	-ddddddp±dd, binary exponent
+//	'p'	-0x.dddp±dd, binary exponent, hexadecimal mantissa
+//
+// For the binary exponent formats, the mantissa is printed in normalized form:
+//
+//	'b'	decimal integer mantissa using x.Prec() bits, or -0
+//	'p'	hexadecimal fraction with 0.5 <= 0.mantissa < 1.0, or -0
+//
+// If format is a different character, Text returns a "%" followed by the
+// unrecognized format character.
+//
+// The precision prec controls the number of digits (excluding the exponent)
+// printed by the 'e', 'E', 'f', 'g', and 'G' formats. For 'e', 'E', and 'f'
+// it is the number of digits after the decimal point. For 'g' and 'G' it is
+// the total number of digits. A negative precision selects the smallest
+// number of digits necessary to identify the value x uniquely.
+// The prec value is ignored for the 'b' or 'p' format.
+//
+// BUG(gri) Float.Text does not accept negative precisions (issue #10991).
+func (x *Float) Text(format byte, prec int) string {
+	const extra = 10 // TODO(gri) determine a good/better value here
+	return string(x.Append(make([]byte, 0, prec+extra), format, prec))
+}
 
-// bigFtoa formats a float for the %e, %E, %f, %g, and %G formats.
-func (f *Float) bigFtoa(buf []byte, fmt byte, prec int) []byte {
-	if debugFloat && f.IsInf() {
-		panic("non-finite float")
+// String formats x like x.Text('g', 10).
+func (x *Float) String() string {
+	return x.Text('g', 10)
+}
+
+// Append appends to buf the string form of the floating-point number x,
+// as generated by x.Text, and returns the extended buffer.
+func (x *Float) Append(buf []byte, fmt byte, prec int) []byte {
+	// sign
+	if x.neg {
+		buf = append(buf, '-')
+	}
+
+	// Inf
+	if x.form == inf {
+		if !x.neg {
+			buf = append(buf, '+')
+		}
+		return append(buf, "Inf"...)
+	}
+
+	// pick off easy formats
+	switch fmt {
+	case 'b':
+		return x.fmtB(buf)
+	case 'p':
+		return x.fmtP(buf)
 	}
 
+	// Algorithm:
 	//   1) convert Float to multiprecision decimal
-	var mant nat
-	if f.form == finite {
-		mant = f.mant
+	//   2) round to desired precision
+	//   3) read digits out and format
+
+	// 1) convert Float to multiprecision decimal
+	var d decimal // == 0.0
+	if x.form == finite {
+		d.init(x.mant, int(x.exp)-x.mant.bitLen())
 	}
-	var d decimal
-	d.init(mant, int(f.exp)-f.mant.bitLen())
 
 	// 2) round to desired precision
 	shortest := false
@@ -67,9 +122,9 @@ func (f *Float) bigFtoa(buf []byte, fmt byte, prec int) []byte {
 	// 3) read digits out and format
 	switch fmt {
 	case 'e', 'E':
-		return fmtE(buf, fmt, prec, f.neg, d)
+		return fmtE(buf, fmt, prec, d)
 	case 'f':
-		return fmtF(buf, prec, f.neg, d)
+		return fmtF(buf, prec, d)
 	case 'g', 'G':
 		// trim trailing fractional zeros in %e format
 		eprec := prec
@@ -88,25 +143,23 @@ func (f *Float) bigFtoa(buf []byte, fmt byte, prec int) []byte {
 			if prec > len(d.mant) {
 				prec = len(d.mant)
 			}
-			return fmtE(buf, fmt+'e'-'g', prec-1, f.neg, d)
+			return fmtE(buf, fmt+'e'-'g', prec-1, d)
 		}
 		if prec > d.exp {
 			prec = len(d.mant)
 		}
-		return fmtF(buf, max(prec-d.exp, 0), f.neg, d)
+		return fmtF(buf, max(prec-d.exp, 0), d)
 	}
 
 	// unknown format
+	if x.neg {
+		buf = buf[:len(buf)-1] // sign was added prematurely - remove it again
+	}
 	return append(buf, '%', fmt)
 }
 
-// %e: -d.ddddde±dd
-func fmtE(buf []byte, fmt byte, prec int, neg bool, d decimal) []byte {
-	// sign
-	if neg {
-		buf = append(buf, '-')
-	}
-
+// %e: d.ddddde±dd
+func fmtE(buf []byte, fmt byte, prec int, d decimal) []byte {
 	// first digit
 	ch := byte('0')
 	if len(d.mant) > 0 {
@@ -149,13 +202,8 @@ func fmtE(buf []byte, fmt byte, prec int, neg bool, d decimal) []byte {
 	return strconv.AppendInt(buf, exp, 10)
 }
 
-// %f: -ddddddd.ddddd
-func fmtF(buf []byte, prec int, neg bool, d decimal) []byte {
-	// sign
-	if neg {
-		buf = append(buf, '-')
-	}
-
+// %f: ddddddd.ddddd
+func fmtF(buf []byte, prec int, d decimal) []byte {
 	// integer, padded with zeros as needed
 	if d.exp > 0 {
 		m := min(len(d.mant), d.exp)
@@ -182,9 +230,164 @@ func fmtF(buf []byte, prec int, neg bool, d decimal) []byte {
 	return buf
 }
 
+// fmtB 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.Prec() bits in binary
+// representation.
+// The sign of x is ignored, and x must not be an Inf.
+func (x *Float) fmtB(buf []byte) []byte {
+	if x.form == zero {
+		return append(buf, '0')
+	}
+
+	if debugFloat && x.form != finite {
+		panic("non-finite float")
+	}
+	// x != 0
+
+	// adjust mantissa to use exactly x.prec bits
+	m := x.mant
+	switch w := uint32(len(x.mant)) * _W; {
+	case w < x.prec:
+		m = nat(nil).shl(m, uint(x.prec-w))
+	case w > x.prec:
+		m = nat(nil).shr(m, uint(w-x.prec))
+	}
+
+	buf = append(buf, m.decimalString()...)
+	buf = append(buf, 'p')
+	e := int64(x.exp) - int64(x.prec)
+	if e >= 0 {
+		buf = append(buf, '+')
+	}
+	return strconv.AppendInt(buf, e, 10)
+}
+
+// fmtP appends the string of x in the format 0x." mantissa "p" exponent
+// with a hexadecimal mantissa and a binary exponent, or 0" if x is zero,
+// ad returns the extended buffer.
+// The mantissa is normalized such that 0.5 <= 0.mantissa < 1.0.
+// The sign of x is ignored, and x must not be an Inf.
+func (x *Float) fmtP(buf []byte) []byte {
+	if x.form == zero {
+		return append(buf, '0')
+	}
+
+	if debugFloat && x.form != finite {
+		panic("non-finite float")
+	}
+	// x != 0
+
+	// 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(m.hexString(), "0")...)
+	buf = append(buf, 'p')
+	if x.exp >= 0 {
+		buf = append(buf, '+')
+	}
+	return strconv.AppendInt(buf, int64(x.exp), 10)
+}
+
 func min(x, y int) int {
 	if x < y {
 		return x
 	}
 	return y
 }
+
+// Format implements fmt.Formatter. It accepts all the regular
+// formats for floating-point numbers ('e', 'E', 'f', 'F', 'g',
+// 'G') as well as 'b', 'p', and 'v'. See (*Float).Text for the
+// interpretation of 'b' and 'p'. The 'v' format is handled like
+// 'g'.
+// Format also supports specification of the minimum precision
+// in digits, the output field width, as well as the format verbs
+// '+' and ' ' for sign control, '0' for space or zero padding,
+// and '-' for left or right justification. See the fmt package
+// for details.
+//
+// BUG(gri) A missing precision for the 'g' format, or a negative
+//          (via '*') precision is not yet supported. Instead the
+//          default precision (6) is used in that case (issue #10991).
+func (x *Float) Format(s fmt.State, format rune) {
+	prec, hasPrec := s.Precision()
+	if !hasPrec {
+		prec = 6 // default precision for 'e', 'f'
+	}
+
+	switch format {
+	case 'e', 'E', 'f', 'b', 'p':
+		// nothing to do
+	case 'F':
+		// (*Float).Text doesn't support 'F'; handle like 'f'
+		format = 'f'
+	case 'v':
+		// handle like 'g'
+		format = 'g'
+		fallthrough
+	case 'g', 'G':
+		if !hasPrec {
+			// TODO(gri) uncomment once (*Float).Text handles prec < 0
+			// prec = -1 // default precision for 'g', 'G'
+		}
+	default:
+		fmt.Fprintf(s, "%%!%c(*big.Float=%s)", format, x.String())
+		return
+	}
+	var buf []byte
+	buf = x.Append(buf, byte(format), prec)
+	if len(buf) == 0 {
+		buf = []byte("?") // should never happen, but don't crash
+	}
+	// len(buf) > 0
+
+	var sign string
+	switch {
+	case buf[0] == '-':
+		sign = "-"
+		buf = buf[1:]
+	case buf[0] == '+':
+		// +Inf
+		sign = "+"
+		if s.Flag(' ') {
+			sign = " "
+		}
+		buf = buf[1:]
+	case s.Flag('+'):
+		sign = "+"
+	case s.Flag(' '):
+		sign = " "
+	}
+
+	var padding int
+	if width, hasWidth := s.Width(); hasWidth && width > len(sign)+len(buf) {
+		padding = width - len(sign) - len(buf)
+	}
+
+	switch {
+	case s.Flag('0') && !x.IsInf():
+		// 0-padding on left
+		writeMultiple(s, sign, 1)
+		writeMultiple(s, "0", padding)
+		s.Write(buf)
+	case s.Flag('-'):
+		// padding on right
+		writeMultiple(s, sign, 1)
+		s.Write(buf)
+		writeMultiple(s, " ", padding)
+	default:
+		// padding on left
+		writeMultiple(s, " ", padding)
+		writeMultiple(s, sign, 1)
+		s.Write(buf)
+	}
+}

src/cmd/compile/internal/big/nat.go

@@ -572,7 +572,7 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
 	u.clear() // TODO(gri) no need to clear if we allocated a new u
 
 	// D1.
-	shift := leadingZeros(v[n-1])
+	shift := nlz(v[n-1])
 	if shift > 0 {
 		// do not modify v, it may be used by another goroutine simultaneously
 		v1 := make(nat, n)
@@ -942,7 +942,7 @@ func (z nat) expNN(x, y, m nat) nat {
 	}
 
 	v := y[len(y)-1] // v > 0 because y is normalized and y > 0
-	shift := leadingZeros(v) + 1
+	shift := nlz(v) + 1
 	v <<= shift
 	var q nat
 

src/cmd/compile/internal/big/nat_test.go

@@ -205,11 +205,11 @@ func BenchmarkMul(b *testing.B) {
 	}
 }
 
-func TestLeadingZeros(t *testing.T) {
+func TestNLZ(t *testing.T) {
 	var x Word = _B >> 1
 	for i := 0; i <= _W; i++ {
-		if int(leadingZeros(x)) != i {
-			t.Errorf("failed at %x: got %d want %d", x, leadingZeros(x), i)
+		if int(nlz(x)) != i {
+			t.Errorf("failed at %x: got %d want %d", x, nlz(x), i)
 		}
 		x >>= 1
 	}

src/cmd/compile/internal/gc/mparith3.go

@@ -178,7 +178,7 @@ func (f *Mpflt) String() string {
 
 func Fconv(fvp *Mpflt, flag int) string {
 	if flag&obj.FmtSharp == 0 {
-		return fvp.Val.Format('b', 0)
+		return fvp.Val.Text('b', 0)
 	}
 
 	// use decimal format for error messages