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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
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@ -958,6 +958,75 @@ var fabsSC = []float64{
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NaN(),
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}
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var vffdimSC = [][2]float64{
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{Inf(-1), Inf(-1)},
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{Inf(-1), Inf(1)},
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{Inf(-1), NaN()},
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{Copysign(0, -1), Copysign(0, -1)},
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{Copysign(0, -1), 0},
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{0, Copysign(0, -1)},
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{0, 0},
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{Inf(1), Inf(-1)},
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{Inf(1), Inf(1)},
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{Inf(1), NaN()},
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{NaN(), Inf(-1)},
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{NaN(), Copysign(0, -1)},
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{NaN(), 0},
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{NaN(), Inf(1)},
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{NaN(), NaN()},
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}
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var fdimSC = []float64{
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NaN(),
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0,
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NaN(),
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0,
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0,
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0,
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0,
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Inf(1),
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NaN(),
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NaN(),
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NaN(),
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NaN(),
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NaN(),
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NaN(),
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NaN(),
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}
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var fmaxSC = []float64{
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Inf(-1),
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Inf(1),
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NaN(),
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Copysign(0, -1),
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0,
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0,
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0,
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Inf(1),
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Inf(1),
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Inf(1),
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NaN(),
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NaN(),
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NaN(),
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Inf(1),
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NaN(),
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}
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var fminSC = []float64{
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Inf(-1),
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Inf(-1),
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Inf(-1),
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Copysign(0, -1),
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Copysign(0, -1),
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Copysign(0, -1),
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0,
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Inf(-1),
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Inf(1),
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NaN(),
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Inf(-1),
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NaN(),
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NaN(),
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NaN(),
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NaN(),
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}
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var vffmodSC = [][2]float64{
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{Inf(-1), Inf(-1)},
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{Inf(-1), -Pi},
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@ -1875,6 +1944,11 @@ func TestDim(t *testing.T) {
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t.Errorf("Dim(%g, %g) = %g, want %g", vf[i], 0.0, f, fdim[i])
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}
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}
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for i := 0; i < len(vffdimSC); i++ {
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if f := Dim(vffdimSC[i][0], vffdimSC[i][1]); !alike(fdimSC[i], f) {
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t.Errorf("Dim(%g, %g) = %g, want %g", vffdimSC[i][0], vffdimSC[i][1], f, fdimSC[i])
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}
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}
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}
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func TestFloor(t *testing.T) {
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@ -1896,6 +1970,11 @@ func TestMax(t *testing.T) {
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t.Errorf("Max(%g, %g) = %g, want %g", vf[i], ceil[i], f, ceil[i])
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}
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}
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for i := 0; i < len(vffdimSC); i++ {
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if f := Max(vffdimSC[i][0], vffdimSC[i][1]); !alike(fmaxSC[i], f) {
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t.Errorf("Max(%g, %g) = %g, want %g", vffdimSC[i][0], vffdimSC[i][1], f, fmaxSC[i])
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}
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}
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}
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func TestMin(t *testing.T) {
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@ -1904,6 +1983,11 @@ func TestMin(t *testing.T) {
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t.Errorf("Min(%g, %g) = %g, want %g", vf[i], floor[i], f, floor[i])
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}
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}
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for i := 0; i < len(vffdimSC); i++ {
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if f := Min(vffdimSC[i][0], vffdimSC[i][1]); !alike(fminSC[i], f) {
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t.Errorf("Min(%g, %g) = %g, want %g", vffdimSC[i][0], vffdimSC[i][1], f, fminSC[i])
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}
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}
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}
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func TestMod(t *testing.T) {
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@ -5,15 +5,37 @@
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package math
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// Dim returns the maximum of x-y or 0.
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//
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// Special cases are:
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// Dim(+Inf, +Inf) = NaN
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// Dim(-Inf, -Inf) = NaN
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// Dim(x, NaN) = Dim(NaN, x) = NaN
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func Dim(x, y float64) float64 {
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if x > y {
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return x - y
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}
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return 0
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return Max(x-y, 0)
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}
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// Max returns the larger of x or y.
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//
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// Special cases are:
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// Max(x, +Inf) = Max(+Inf, x) = +Inf
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// Max(x, NaN) = Max(NaN, x) = NaN
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// Max(+0, ±0) = Max(±0, +0) = +0
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// Max(-0, -0) = -0
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func Max(x, y float64) float64 {
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// TODO(rsc): Remove manual inlining of IsNaN, IsInf
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// when compiler does it for us
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// special cases
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switch {
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case x > MaxFloat64 || y > MaxFloat64: // IsInf(x, 1) || IsInf(y, 1):
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return Inf(1)
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case x != x || y != y: // IsNaN(x) || IsNaN(y):
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return NaN()
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case x == 0 && x == y:
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if Signbit(x) {
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return y
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}
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return x
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}
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if x > y {
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return x
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}
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@ -21,7 +43,26 @@ func Max(x, y float64) float64 {
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}
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// Min returns the smaller of x or y.
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//
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// Special cases are:
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// Min(x, -Inf) = Min(-Inf, x) = -Inf
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// Min(x, NaN) = Min(NaN, x) = NaN
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// Min(-0, ±0) = Min(±0, -0) = -0
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func Min(x, y float64) float64 {
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// TODO(rsc): Remove manual inlining of IsNaN, IsInf
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// when compiler does it for us
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// special cases
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switch {
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case x < -MaxFloat64 || y < -MaxFloat64: // IsInf(x, -1) || IsInf(y, -1):
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return Inf(-1)
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case x != x || y != y: // IsNaN(x) || IsNaN(y):
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return NaN()
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case x == 0 && x == y:
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if Signbit(x) {
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return x
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}
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return y
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}
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if x < y {
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return x
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}
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@ -2,25 +2,141 @@
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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#define PosInf 0x7FF0000000000000
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#define NaN 0x7FF0000000000001
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#define NegInf 0xFFF0000000000000
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// func Dim(x, y float64) float64
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TEXT ·Dim(SB),7,$0
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// (+Inf, +Inf) special case
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MOVQ x+0(FP), BX
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MOVQ y+8(FP), CX
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MOVQ $PosInf, AX
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CMPQ AX, BX
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JNE dim2
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CMPQ AX, CX
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JEQ bothInf
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dim2: // (-Inf, -Inf) special case
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MOVQ $NegInf, AX
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CMPQ AX, BX
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JNE dim3
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CMPQ AX, CX
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JEQ bothInf
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dim3: // (NaN, x) or (x, NaN)
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MOVQ $~(1<<63), DX
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MOVQ $NaN, AX
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ANDQ DX, BX // x = |x|
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CMPQ AX, BX
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JLE isDimNaN
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ANDQ DX, CX // y = |y|
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CMPQ AX, CX
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JLE isDimNaN
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MOVSD x+0(FP), X0
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SUBSD y+8(FP), X0
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MOVSD $(0.0), X1
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MAXSD X1, X0
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MOVSD X0, r+16(FP)
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RET
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bothInf: // Dim(-Inf, -Inf) or Dim(+Inf, +Inf)
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MOVQ $NaN, AX
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isDimNaN:
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MOVQ AX, r+16(FP)
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RET
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// func ·Max(x, y float64) float64
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TEXT ·Max(SB),7,$0
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MOVSD x+0(FP), X0
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MAXSD y+8(FP), X0
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MOVSD X0, r+16(FP)
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// +Inf special cases
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MOVQ $PosInf, AX
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MOVQ x+0(FP), R8
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CMPQ AX, R8
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JEQ isPosInf
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MOVQ y+8(FP), R9
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CMPQ AX, R9
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JEQ isPosInf
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// NaN special cases
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MOVQ $~(1<<63), DX // bit mask
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MOVQ $NaN, AX
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MOVQ R8, BX
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ANDQ DX, BX // x = |x|
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CMPQ AX, BX
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JLE isMaxNaN
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MOVQ R9, CX
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ANDQ DX, CX // y = |y|
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CMPQ AX, CX
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JLE isMaxNaN
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// ±0 special cases
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ORQ CX, BX
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JEQ isMaxZero
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MOVQ R8, X0
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MOVQ R9, X1
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MAXSD X1, X0
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MOVSD X0, r+16(FP)
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RET
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isMaxNaN: // return NaN
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isPosInf: // return +Inf
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MOVQ AX, r+16(FP)
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RET
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isMaxZero:
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MOVQ $(1<<63), AX // -0.0
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CMPQ AX, R8
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JEQ +3(PC)
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MOVQ R8, r+16(FP) // return 0
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RET
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MOVQ R9, r+16(FP) // return other 0
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RET
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/*
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MOVQ $0, AX
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CMPQ AX, R8
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JNE +3(PC)
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MOVQ R8, r+16(FP) // return 0
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RET
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MOVQ R9, r+16(FP) // return other 0
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RET
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*/
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// func Min(x, y float64) float64
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TEXT ·Min(SB),7,$0
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MOVSD x+0(FP), X0
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MINSD y+8(FP), X0
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// -Inf special cases
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MOVQ $NegInf, AX
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MOVQ x+0(FP), R8
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CMPQ AX, R8
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JEQ isNegInf
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MOVQ y+8(FP), R9
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CMPQ AX, R9
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JEQ isNegInf
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// NaN special cases
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MOVQ $~(1<<63), DX
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MOVQ $NaN, AX
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MOVQ R8, BX
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ANDQ DX, BX // x = |x|
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CMPQ AX, BX
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JLE isMinNaN
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MOVQ R9, CX
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ANDQ DX, CX // y = |y|
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CMPQ AX, CX
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JLE isMinNaN
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// ±0 special cases
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ORQ CX, BX
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JEQ isMinZero
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MOVQ R8, X0
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MOVQ R9, X1
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MINSD X1, X0
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MOVSD X0, r+16(FP)
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RET
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isMinNaN: // return NaN
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isNegInf: // return -Inf
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MOVQ AX, r+16(FP)
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RET
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isMinZero:
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MOVQ $(1<<63), AX // -0.0
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CMPQ AX, R8
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JEQ +3(PC)
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MOVQ R9, r+16(FP) // return other 0
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RET
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MOVQ R8, r+16(FP) // return -0
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RET
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@ -166,7 +166,7 @@ func Cos(x float64) float64 {
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// Sin returns the sine of x.
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//
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// Special conditions are:
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// Special cases are:
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// Sin(±0) = ±0
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// Sin(±Inf) = NaN
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// Sin(NaN) = NaN
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