math: add functions Log2, Nextafter, Fdim, Fmax, Fmin

Add functions, tests and benchmarks. Fix typos in comments
in expm1 and hypot_386.  Fix Acosh domain error in benchmark
test.

R=rsc
CC=golang-dev
https://golang.org/cl/204069

src/pkg/math/Makefile

@@ -41,12 +41,14 @@ ALLGOFILES=\
 	exp.go\
 	expm1.go\
 	fabs.go\
+	fdim.go\
 	floor.go\
 	fmod.go\
 	hypot.go\
 	log.go\
 	log1p.go\
 	modf.go\
+	nextafter.go\
 	pow.go\
 	pow10.go\
 	sin.go\

src/pkg/math/all_test.go

@@ -208,6 +208,18 @@ var expm1 = []float64{
 	1.842068661871398836913874273e-02,
 	-8.3193870863553801814961137573e-02,
 }
+var fdim = []float64{
+	4.9790119248836735e+00,
+	7.7388724745781045e+00,
+	0.0000000000000000e+00,
+	0.0000000000000000e+00,
+	9.6362937071984173e+00,
+	2.9263772392439646e+00,
+	5.2290834314593066e+00,
+	2.7279399104360102e+00,
+	1.8253080916808550e+00,
+	0.0000000000000000e+00,
+}
 var floor = []float64{
 	4.0000000000000000e+00,
 	7.0000000000000000e+00,
@@ -287,6 +299,18 @@ var log1p = []float64{
 	1.8088493239630770262045333e-02,
 	-9.0865245631588989681559268e-02,
 }
+var log2 = []float64{
+	2.3158594707062190618898251e+00,
+	2.9521233862883917703341018e+00,
+	-1.8526669502700329984917062e+00,
+	2.3249844127278861543568029e+00,
+	3.268478366538305087466309e+00,
+	1.5491157592596970278166492e+00,
+	2.3865580889631732407886495e+00,
+	1.447811865817085365540347e+00,
+	8.6813999540425116282815557e-01,
+	3.118679457227342224364709e+00,
+}
 var modf = [][2]float64{
 	[2]float64{4.0000000000000000e+00, 9.7901192488367350108546816e-01},
 	[2]float64{7.0000000000000000e+00, 7.3887247457810456552351752e-01},
@@ -299,6 +323,18 @@ var modf = [][2]float64{
 	[2]float64{1.0000000000000000e+00, 8.2530809168085506044576505e-01},
 	[2]float64{-8.0000000000000000e+00, -6.8592476857560136238589621e-01},
 }
+var nextafter = []float64{
+	4.97901192488367438926388786e+00,
+	7.73887247457810545370193722e+00,
+	-2.7688005719200153853520874e-01,
+	-5.01060361827107403343006808e+00,
+	9.63629370719841915615688777e+00,
+	2.92637723924396508934364647e+00,
+	5.22908343145930754047867595e+00,
+	2.72793991043601069534929593e+00,
+	1.82530809168085528249036997e+00,
+	-8.68592476857559958602905681e+00,
+}
 var pow = []float64{
 	9.5282232631648411840742957e+04,
 	5.4811599352999901232411871e+07,
@@ -706,6 +742,17 @@ var modfSC = [][2]float64{
 	[2]float64{NaN(), NaN()},
 }
 
+var vfnextafterSC = [][2]float64{
+	[2]float64{0, NaN()},
+	[2]float64{NaN(), 0},
+	[2]float64{NaN(), NaN()},
+}
+var nextafterSC = []float64{
+	NaN(),
+	NaN(),
+	NaN(),
+}
+
 var vfpowSC = [][2]float64{
 	[2]float64{-Pi, Pi},
 	[2]float64{-Pi, -Pi},
@@ -1031,6 +1078,14 @@ func TestExpm1(t *testing.T) {
 	}
 }
 
+func TestFdim(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Fdim(vf[i], 0); fdim[i] != f {
+			t.Errorf("Fdim(%g, %g) = %g, want %g\n", vf[i], 0.0, f, fdim[i])
+		}
+	}
+}
+
 func TestFloor(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f := Floor(vf[i]); floor[i] != f {
@@ -1044,6 +1099,22 @@ func TestFloor(t *testing.T) {
 	}
 }
 
+func TestFmax(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Fmax(vf[i], ceil[i]); ceil[i] != f {
+			t.Errorf("Fmax(%g, %g) = %g, want %g\n", vf[i], ceil[i], f, ceil[i])
+		}
+	}
+}
+
+func TestFmin(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Fmin(vf[i], floor[i]); floor[i] != f {
+			t.Errorf("Fmin(%g, %g) = %g, want %g\n", vf[i], floor[i], f, floor[i])
+		}
+	}
+}
+
 func TestFmod(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f := Fmod(10, vf[i]); fmod[i] != f { /*!close(fmod[i], f)*/
@@ -1149,6 +1220,23 @@ func TestLog1p(t *testing.T) {
 	}
 }
 
+func TestLog2(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		a := Fabs(vf[i])
+		if f := Log2(a); !veryclose(log2[i], f) {
+			t.Errorf("Log2(%g) = %g, want %g\n", a, f, log2[i])
+		}
+	}
+	if f := Log2(E); f != Log2E {
+		t.Errorf("Log2(%g) = %g, want %g\n", E, f, Log2E)
+	}
+	for i := 0; i < len(vflogSC); i++ {
+		if f := Log2(vflogSC[i]); !alike(logSC[i], f) {
+			t.Errorf("Log2(%g) = %g, want %g\n", vflogSC[i], f, logSC[i])
+		}
+	}
+}
+
 func TestModf(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f, g := Modf(vf[i]); !veryclose(modf[i][0], f) || !veryclose(modf[i][1], g) {
@@ -1162,6 +1250,19 @@ func TestModf(t *testing.T) {
 	}
 }
 
+func TestNextafter(t *testing.T) {
+	for i := 0; i < len(vf); i++ {
+		if f := Nextafter(vf[i], 10); nextafter[i] != f {
+			t.Errorf("Nextafter(%g, %g) = %g want %g\n", vf[i], 10.0, f, nextafter[i])
+		}
+	}
+	for i := 0; i < len(vfmodfSC); i++ {
+		if f := Nextafter(vfnextafterSC[i][0], vfnextafterSC[i][1]); !alike(nextafterSC[i], f) {
+			t.Errorf("Nextafter(%g, %g) = %g want %g\n", vfnextafterSC[i][0], vfnextafterSC[i][1], f, nextafterSC[i])
+		}
+	}
+}
+
 func TestPow(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
 		if f := Pow(10, vf[i]); !close(pow[i], f) {
@@ -1309,7 +1410,7 @@ func BenchmarkAcos(b *testing.B) {
 
 func BenchmarkAcosh(b *testing.B) {
 	for i := 0; i < b.N; i++ {
-		Acosh(.5)
+		Acosh(1.5)
 	}
 }
 
@@ -1397,6 +1498,24 @@ func BenchmarkFloor(b *testing.B) {
 	}
 }
 
+func BenchmarkFdim(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Fdim(10, 3)
+	}
+}
+
+func BenchmarkFmax(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Fmax(10, 3)
+	}
+}
+
+func BenchmarkFmin(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Fmin(10, 3)
+	}
+}
+
 func BenchmarkFmod(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Fmod(10, 3)
@@ -1439,12 +1558,24 @@ func BenchmarkLog1p(b *testing.B) {
 	}
 }
 
+func BenchmarkLog2(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Log2(.5)
+	}
+}
+
 func BenchmarkModf(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Modf(1.5)
 	}
 }
 
+func BenchmarkNextafter(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Nextafter(.5, 1)
+	}
+}
+
 func BenchmarkPowInt(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		Pow(2, 2)

src/pkg/math/expm1.go

@@ -118,8 +118,8 @@ package math
 // It is more accurate than Exp(x) - 1 when x is near zero.
 //
 // Special cases are:
-//      Expm1(+Inf) = +Inf
-//      Expm1(-Inf) = -1
+//	Expm1(+Inf) = +Inf
+//	Expm1(-Inf) = -1
 //	Expm1(NaN) = NaN
 // Very large values overflow to -1 or +Inf.
 func Expm1(x float64) float64 {

src/pkg/math/fdim.go

+// Copyright 2010 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.
+
+package math
+
+// Fdim returns the maximum of x-y or 0.
+func Fdim(x, y float64) float64 {
+	if x > y {
+		return x - y
+	}
+	return 0
+}
+
+// Fmax returns the larger of x or y.
+func Fmax(x, y float64) float64 {
+	if x > y {
+		return x
+	}
+	return y
+}
+
+// Fmin returns the smaller of x or y.
+func Fmin(x, y float64) float64 {
+	if x < y {
+		return x
+	}
+	return y
+}

src/pkg/math/hypot_386.s

@@ -18,7 +18,7 @@ TEXT ·Hypot(SB),7,$0
 	FMOVD   y+8(FP), F0  // F0=y, F1=|x|
 	FABS                 // F0=|y|, F1=|x|
 	FUCOMI  F0, F1       // compare F0 to F1
-	JCC     2(PC)        // jump if F0 < F1
+	JCC     2(PC)        // jump if F0 >= F1
 	FXCHD   F0, F1       // F0=|x| (larger), F1=|y| (smaller)
 	FTST                 // compare F0 to 0
 	FSTSW	AX

src/pkg/math/log.go

@@ -125,3 +125,7 @@ func Log(x float64) float64 {
 // Log10 returns the decimal logarithm of x.
 // The special cases are the same as for Log.
 func Log10(x float64) float64 { return Log(x) * (1 / Ln10) }
+
+// Log2 returns the binary logarithm of x.
+// The special cases are the same as for Log.
+func Log2(x float64) float64 { return Log(x) * (1 / Ln2) }

src/pkg/math/log_386.s

@@ -17,3 +17,11 @@ TEXT ·Log10(SB),7,$0
 	FYL2X                // F0=log10(x)=log2(x)*log10(2)
 	FMOVDP  F0, r+8(FP)
 	RET
+	
+// func Log2(x float64) float64
+TEXT ·Log2(SB),7,$0
+	FLD1                 // F0=1
+	FMOVD   x+0(FP), F0  // F0=x, F1=1
+	FYL2X                // F0=log2(x)
+	FMOVDP  F0, r+8(FP)
+	RET

src/pkg/math/log_decl.go

@@ -6,3 +6,4 @@ package math
 
 func Log(x float64) float64
 func Log10(x float64) float64
+func Log2(x float64) float64

src/pkg/math/nextafter.go

+// Copyright 2010 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.
+
+package math
+
+// Nextafter returns the next representable value after x towards y.
+// If x == y, then x is returned.
+//
+// Special cases are:
+//	Nextafter(NaN, y) = NaN
+//	Nextafter(x, NaN) = NaN
+func Nextafter(x, y float64) (r float64) {
+	switch {
+	case IsNaN(x) || IsNaN(y): // special case
+		r = NaN()
+	case x == y:
+		r = x
+	case x == 0:
+		r = Copysign(Float64frombits(1), y)
+	case (y > x) == (x > 0):
+		r = Float64frombits(Float64bits(x) + 1)
+	default:
+		r = Float64frombits(Float64bits(x) - 1)
+	}
+	return r
+}