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
diff --git a/src/pkg/math/all_test.go b/src/pkg/math/all_test.go
index 7e63023..7256ca4 100644
--- a/src/pkg/math/all_test.go
+++ b/src/pkg/math/all_test.go
@@ -958,6 +958,75 @@
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 @@
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 @@
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 @@
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) {
diff --git a/src/pkg/math/dim.go b/src/pkg/math/dim.go
index d2eb52f..5701b14 100644
--- a/src/pkg/math/dim.go
+++ b/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 x - y
- }
- return 0
+ return Max(x-y, 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 @@
}
// 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
}
diff --git a/src/pkg/math/dim_amd64.s b/src/pkg/math/dim_amd64.s
index cfc8e05..c867db55 100644
--- a/src/pkg/math/dim_amd64.s
+++ b/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
- MAXSD y+8(FP), X0
- MOVSD X0, r+16(FP)
+ // +Inf special cases
+ 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
- MINSD y+8(FP), X0
+ // -Inf special cases
+ 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
+
diff --git a/src/pkg/math/sin.go b/src/pkg/math/sin.go
index b2a3f8a..18509d9 100644
--- a/src/pkg/math/sin.go
+++ b/src/pkg/math/sin.go
@@ -166,7 +166,7 @@
// Sin returns the sine of x.
//
-// Special conditions are:
+// Special cases are:
// Sin(±0) = ±0
// Sin(±Inf) = NaN
// Sin(NaN) = NaN
