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

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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
This commit is contained in:
Charles L. Dorian 2011-12-07 14:52:17 -05:00 committed by Russ Cox
parent 69191553e7
commit e4de2e7fd0
4 changed files with 251 additions and 10 deletions
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84
src/pkg/math/all_test.go
View file

@ -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) {

49
src/pkg/math/dim.go
View file

@ -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 @@ 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
}

126
src/pkg/math/dim_amd64.s
View file

@ -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

2
src/pkg/math/sin.go
View file

@ -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