math: document special-cases behavior for Dim, Max and Min

Max returns +Inf if x or y is +Inf; else it returns NaN if either x or y is NaN. Max(-0, -0) returns -0.
Min returns -Inf if x or y is -Inf; else it returns NaN if either x or y is NaN. Min(+0, -0) returns -0.
Dim(+Inf, +Inf) = NaN, Dim(-Inf, -Inf) = NaN and Dim(NaN, anything) = NaN.
Also, change "conditions" to "cases" for Sin (missed it in previous CL).

R=rsc, dave
CC=golang-dev
https://golang.org/cl/5437137

src/pkg/math/all_test.go

@@ -958,6 +958,75 @@ var fabsSC = []float64{
 	NaN(),
 }
 
+var vffdimSC = [][2]float64{
+	{Inf(-1), Inf(-1)},
+	{Inf(-1), Inf(1)},
+	{Inf(-1), NaN()},
+	{Copysign(0, -1), Copysign(0, -1)},
+	{Copysign(0, -1), 0},
+	{0, Copysign(0, -1)},
+	{0, 0},
+	{Inf(1), Inf(-1)},
+	{Inf(1), Inf(1)},
+	{Inf(1), NaN()},
+	{NaN(), Inf(-1)},
+	{NaN(), Copysign(0, -1)},
+	{NaN(), 0},
+	{NaN(), Inf(1)},
+	{NaN(), NaN()},
+}
+var fdimSC = []float64{
+	NaN(),
+	0,
+	NaN(),
+	0,
+	0,
+	0,
+	0,
+	Inf(1),
+	NaN(),
+	NaN(),
+	NaN(),
+	NaN(),
+	NaN(),
+	NaN(),
+	NaN(),
+}
+var fmaxSC = []float64{
+	Inf(-1),
+	Inf(1),
+	NaN(),
+	Copysign(0, -1),
+	0,
+	0,
+	0,
+	Inf(1),
+	Inf(1),
+	Inf(1),
+	NaN(),
+	NaN(),
+	NaN(),
+	Inf(1),
+	NaN(),
+}
+var fminSC = []float64{
+	Inf(-1),
+	Inf(-1),
+	Inf(-1),
+	Copysign(0, -1),
+	Copysign(0, -1),
+	Copysign(0, -1),
+	0,
+	Inf(-1),
+	Inf(1),
+	NaN(),
+	Inf(-1),
+	NaN(),
+	NaN(),
+	NaN(),
+	NaN(),
+}
+
 var vffmodSC = [][2]float64{
 	{Inf(-1), Inf(-1)},
 	{Inf(-1), -Pi},
@@ -1875,6 +1944,11 @@ func TestDim(t *testing.T) {
 			t.Errorf("Dim(%g, %g) = %g, want %g", vf[i], 0.0, f, fdim[i])
 		}
 	}
+	for i := 0; i < len(vffdimSC); i++ {
+		if f := Dim(vffdimSC[i][0], vffdimSC[i][1]); !alike(fdimSC[i], f) {
+			t.Errorf("Dim(%g, %g) = %g, want %g", vffdimSC[i][0], vffdimSC[i][1], f, fdimSC[i])
+		}
+	}
 }
 
 func TestFloor(t *testing.T) {
@@ -1896,6 +1970,11 @@ func TestMax(t *testing.T) {
 			t.Errorf("Max(%g, %g) = %g, want %g", vf[i], ceil[i], f, ceil[i])
 		}
 	}
+	for i := 0; i < len(vffdimSC); i++ {
+		if f := Max(vffdimSC[i][0], vffdimSC[i][1]); !alike(fmaxSC[i], f) {
+			t.Errorf("Max(%g, %g) = %g, want %g", vffdimSC[i][0], vffdimSC[i][1], f, fmaxSC[i])
+		}
+	}
 }
 
 func TestMin(t *testing.T) {
@@ -1904,6 +1983,11 @@ func TestMin(t *testing.T) {
 			t.Errorf("Min(%g, %g) = %g, want %g", vf[i], floor[i], f, floor[i])
 		}
 	}
+	for i := 0; i < len(vffdimSC); i++ {
+		if f := Min(vffdimSC[i][0], vffdimSC[i][1]); !alike(fminSC[i], f) {
+			t.Errorf("Min(%g, %g) = %g, want %g", vffdimSC[i][0], vffdimSC[i][1], f, fminSC[i])
+		}
+	}
 }
 
 func TestMod(t *testing.T) {

src/pkg/math/dim.go

@@ -5,15 +5,37 @@
 package math
 
 // Dim returns the maximum of x-y or 0.
+//
+// Special cases are:
+//	Dim(+Inf, +Inf) = NaN
+//	Dim(-Inf, -Inf) = NaN
+//	Dim(x, NaN) = Dim(NaN, x) = NaN
 func Dim(x, y float64) float64 {
-	if x > y {
+	return Max(x-y, 0)
-		return x - y
-	}
-	return 0
 }
 
 // Max returns the larger of x or y.
+//
+// Special cases are:
+//	Max(x, +Inf) = Max(+Inf, x) = +Inf
+//	Max(x, NaN) = Max(NaN, x) = NaN
+//	Max(+0, ±0) = Max(±0, +0) = +0
+//	Max(-0, -0) = -0
 func Max(x, y float64) float64 {
+	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
+	// when compiler does it for us
+	// special cases
+	switch {
+	case x > MaxFloat64 || y > MaxFloat64: // IsInf(x, 1) || IsInf(y, 1):
+		return Inf(1)
+	case x != x || y != y: // IsNaN(x) || IsNaN(y):
+		return NaN()
+	case x == 0 && x == y:
+		if Signbit(x) {
+			return y
+		}
+		return x
+	}
 	if x > y {
 		return x
 	}
@@ -21,7 +43,26 @@ func Max(x, y float64) float64 {
 }
 
 // Min returns the smaller of x or y.
+//
+// Special cases are:
+//	Min(x, -Inf) = Min(-Inf, x) = -Inf
+//	Min(x, NaN) = Min(NaN, x) = NaN
+//	Min(-0, ±0) = Min(±0, -0) = -0
 func Min(x, y float64) float64 {
+	// TODO(rsc): Remove manual inlining of IsNaN, IsInf
+	// when compiler does it for us
+	// special cases
+	switch {
+	case x < -MaxFloat64 || y < -MaxFloat64: // IsInf(x, -1) || IsInf(y, -1):
+		return Inf(-1)
+	case x != x || y != y: // IsNaN(x) || IsNaN(y):
+		return NaN()
+	case x == 0 && x == y:
+		if Signbit(x) {
+			return x
+		}
+		return y
+	}
 	if x < y {
 		return x
 	}

src/pkg/math/dim_amd64.s

@@ -2,25 +2,141 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
+#define PosInf 0x7FF0000000000000
+#define NaN    0x7FF0000000000001
+#define NegInf 0xFFF0000000000000
+
 // func Dim(x, y float64) float64
 TEXT ·Dim(SB),7,$0
+	// (+Inf, +Inf) special case
+	MOVQ    x+0(FP), BX
+	MOVQ    y+8(FP), CX
+	MOVQ    $PosInf, AX
+	CMPQ    AX, BX
+	JNE     dim2
+	CMPQ    AX, CX
+	JEQ     bothInf
+dim2:	// (-Inf, -Inf) special case
+	MOVQ    $NegInf, AX
+	CMPQ    AX, BX
+	JNE     dim3
+	CMPQ    AX, CX
+	JEQ     bothInf
+dim3:	// (NaN, x) or (x, NaN)
+	MOVQ    $~(1<<63), DX
+	MOVQ    $NaN, AX
+	ANDQ    DX, BX // x = |x|
+	CMPQ    AX, BX
+	JLE     isDimNaN
+	ANDQ    DX, CX // y = |y|
+	CMPQ    AX, CX
+	JLE     isDimNaN
+
 	MOVSD x+0(FP), X0
 	SUBSD y+8(FP), X0
 	MOVSD $(0.0), X1
 	MAXSD X1, X0
 	MOVSD X0, r+16(FP)
 	RET
+bothInf: // Dim(-Inf, -Inf) or Dim(+Inf, +Inf)
+	MOVQ    $NaN, AX
+isDimNaN:
+	MOVQ    AX, r+16(FP)
+	RET
 
 // func ·Max(x, y float64) float64
 TEXT ·Max(SB),7,$0
-	MOVSD x+0(FP), X0
+	// +Inf special cases
-	MAXSD y+8(FP), X0
+	MOVQ    $PosInf, AX
+	MOVQ    x+0(FP), R8
+	CMPQ    AX, R8
+	JEQ     isPosInf
+	MOVQ    y+8(FP), R9
+	CMPQ    AX, R9
+	JEQ     isPosInf
+	// NaN special cases
+	MOVQ    $~(1<<63), DX // bit mask
+	MOVQ    $NaN, AX
+	MOVQ    R8, BX
+	ANDQ    DX, BX // x = |x|
+	CMPQ    AX, BX
+	JLE     isMaxNaN
+	MOVQ    R9, CX
+	ANDQ    DX, CX // y = |y|
+	CMPQ    AX, CX
+	JLE     isMaxNaN
+	// ±0 special cases
+	ORQ     CX, BX
+	JEQ     isMaxZero
+
+	MOVQ    R8, X0
+	MOVQ    R9, X1
+	MAXSD   X1, X0
 	MOVSD   X0, r+16(FP)
 	RET
+isMaxNaN: // return NaN
+isPosInf: // return +Inf
+	MOVQ    AX, r+16(FP)
+	RET
+isMaxZero:
+	MOVQ    $(1<<63), AX // -0.0
+	CMPQ    AX, R8
+	JEQ     +3(PC)
+	MOVQ    R8, r+16(FP) // return 0
+	RET
+	MOVQ    R9, r+16(FP) // return other 0
+	RET
+
+/*
+	MOVQ    $0, AX
+	CMPQ    AX, R8
+	JNE     +3(PC)
+	MOVQ    R8, r+16(FP) // return 0
+	RET
+	MOVQ    R9, r+16(FP) // return other 0
+	RET
+*/
 
 // func Min(x, y float64) float64
 TEXT ·Min(SB),7,$0
-	MOVSD x+0(FP), X0
+	// -Inf special cases
-	MINSD y+8(FP), X0
+	MOVQ    $NegInf, AX
+	MOVQ    x+0(FP), R8
+	CMPQ    AX, R8
+	JEQ     isNegInf
+	MOVQ    y+8(FP), R9
+	CMPQ    AX, R9
+	JEQ     isNegInf
+	// NaN special cases
+	MOVQ    $~(1<<63), DX
+	MOVQ    $NaN, AX
+	MOVQ    R8, BX
+	ANDQ    DX, BX // x = |x|
+	CMPQ    AX, BX
+	JLE     isMinNaN
+	MOVQ    R9, CX
+	ANDQ    DX, CX // y = |y|
+	CMPQ    AX, CX
+	JLE     isMinNaN
+	// ±0 special cases
+	ORQ     CX, BX
+	JEQ     isMinZero
+
+	MOVQ    R8, X0
+	MOVQ    R9, X1
+	MINSD   X1, X0
 	MOVSD X0, r+16(FP)
 	RET
+isMinNaN: // return NaN
+isNegInf: // return -Inf
+	MOVQ    AX, r+16(FP)
+	RET
+isMinZero:
+	MOVQ    $(1<<63), AX // -0.0
+	CMPQ    AX, R8
+	JEQ     +3(PC)
+	MOVQ    R9, r+16(FP) // return other 0
+	RET
+	MOVQ    R8, r+16(FP) // return -0
+	RET
+

src/pkg/math/sin.go

@@ -166,7 +166,7 @@ func Cos(x float64) float64 {
 
 // Sin returns the sine of x.
 //
-// Special conditions are:
+// Special cases are:
 //	Sin(±0) = ±0
 //	Sin(±Inf) = NaN
 //	Sin(NaN) = NaN