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math: Atan2 special cases and tests; atan2_386
Added special cases, tests and benchmarks for Atan2; added 386 FPU version of Atan2. R=rsc CC=golang-dev https://golang.org/cl/201068
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@ -12,6 +12,7 @@ OFILES_amd64=\
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OFILES_386=\
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asin_386.$O\
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atan_386.$O\
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atan2_386.$O\
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exp_386.$O\
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fabs_386.$O\
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floor_386.$O\
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@ -100,6 +100,18 @@ var atanh = []float64{
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1.8459947964298794318714228e-01,
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-1.3273186910532645867272502e+00,
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}
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var atan2 = []float64{
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1.1088291730037004444527075e+00,
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9.1218183188715804018797795e-01,
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1.5984772603216203736068915e+00,
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2.0352918654092086637227327e+00,
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8.0391819139044720267356014e-01,
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1.2861075249894661588866752e+00,
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1.0889904479131695712182587e+00,
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1.3044821793397925293797357e+00,
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1.3902530903455392306872261e+00,
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2.2859857424479142655411058e+00,
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}
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var ceil = []float64{
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5.0000000000000000e+00,
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8.0000000000000000e+00,
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@ -427,6 +439,64 @@ var atanhSC = []float64{
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NaN(),
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NaN(),
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}
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var vfatan2SC = [][2]float64{
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[2]float64{Inf(-1), Inf(-1)},
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[2]float64{Inf(-1), -Pi},
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[2]float64{Inf(-1), 0},
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[2]float64{Inf(-1), +Pi},
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[2]float64{Inf(-1), Inf(1)},
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[2]float64{Inf(-1), NaN()},
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[2]float64{-Pi, Inf(-1)},
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[2]float64{-Pi, 0},
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[2]float64{-Pi, Inf(1)},
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[2]float64{-Pi, NaN()},
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[2]float64{0, Inf(-1)},
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[2]float64{0, -Pi},
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[2]float64{0, 0},
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[2]float64{0, +Pi},
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[2]float64{0, Inf(1)},
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[2]float64{0, NaN()},
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[2]float64{+Pi, Inf(-1)},
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[2]float64{+Pi, 0},
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[2]float64{+Pi, Inf(1)},
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[2]float64{+Pi, NaN()},
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[2]float64{Inf(1), Inf(-1)},
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[2]float64{Inf(1), -Pi},
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[2]float64{Inf(1), 0},
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[2]float64{Inf(1), +Pi},
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[2]float64{Inf(1), Inf(1)},
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[2]float64{Inf(1), NaN()},
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[2]float64{NaN(), NaN()},
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}
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var atan2SC = []float64{
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-3 * Pi / 4,
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-Pi / 2,
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-Pi / 2,
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-Pi / 2,
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-Pi / 4,
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NaN(),
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-Pi,
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-Pi / 2,
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-0,
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NaN(),
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Pi,
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Pi,
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0,
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0,
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0,
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NaN(),
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Pi,
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Pi / 2,
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0,
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NaN(),
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3 * Pi / 4,
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Pi / 2,
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Pi / 2,
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Pi / 2,
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Pi / 4,
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NaN(),
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NaN(),
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}
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var vfceilSC = []float64{
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Inf(-1),
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@ -851,6 +921,19 @@ func TestAtanh(t *testing.T) {
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}
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}
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func TestAtan2(t *testing.T) {
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for i := 0; i < len(vf); i++ {
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if f := Atan2(10, vf[i]); !veryclose(atan2[i], f) {
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t.Errorf("Atan2(10, %g) = %g, want %g\n", vf[i], f, atan2[i])
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}
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}
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for i := 0; i < len(vfatan2SC); i++ {
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if f := Atan2(vfatan2SC[i][0], vfatan2SC[i][1]); !alike(atan2SC[i], f) {
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t.Errorf("Atan2(%g, %g) = %g, want %g\n", vfatan2SC[i][0], vfatan2SC[i][1], f, atan2SC[i])
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}
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}
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}
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func TestCeil(t *testing.T) {
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for i := 0; i < len(vf); i++ {
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if f := Ceil(vf[i]); ceil[i] != f {
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@ -1254,6 +1337,12 @@ func BenchmarkAtanh(b *testing.B) {
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}
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}
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func BenchmarkAtan2(b *testing.B) {
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for i := 0; i < b.N; i++ {
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Atan2(.5, 1)
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}
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}
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func BenchmarkCeil(b *testing.B) {
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for i := 0; i < b.N; i++ {
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Ceil(.5)
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@ -7,14 +7,69 @@ package math
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// Atan2 returns the arc tangent of y/x, using
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// the signs of the two to determine the quadrant
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// of the return value.
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//
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// Special cases are (in order):
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// Atan2(y, NaN) = NaN
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// Atan2(NaN, x) = NaN
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// Atan2(0, x>=0) = 0
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// Atan2(0, x<0) = Pi
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// Atan2(y>0, 0) = +Pi/2
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// Atan2(y<0, 0) = -Pi/2
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// Atan2(+Inf, +Inf) = +Pi/4
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// Atan2(-Inf, +Inf) = -Pi/4
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// Atan2(+Inf, -Inf) = 3Pi/4
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// Atan2(-Inf, -Inf) = -3Pi/4
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// Atan2(y, +Inf) = 0
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// Atan2(y>0, -Inf) = +Pi
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// Atan2(y<0, -Inf) = -Pi
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// Atan2(+Inf, x) = +Pi/2
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// Atan2(-Inf, x) = -Pi/2
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func Atan2(y, x float64) float64 {
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// Determine the quadrant and call atan.
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if y+x == y {
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if y >= 0 {
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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 y != y || x != x: // IsNaN(y) || IsNaN(x):
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return NaN()
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case y == 0:
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if x >= 0 {
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return 0
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}
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return Pi
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case x == 0:
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if y > 0 {
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return Pi / 2
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}
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return -Pi / 2
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case x < -MaxFloat64 || x > MaxFloat64: // IsInf(x, 0):
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if x > MaxFloat64 { // IsInf(x, 1) {
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switch {
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case y > MaxFloat64: // IsInf(y, 1):
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return Pi / 4
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case y < -MaxFloat64: // IsInf(y, -1):
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return -Pi / 4
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default:
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return 0
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}
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}
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switch {
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case y > MaxFloat64: //IsInf(y, 1):
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return 3 * Pi / 4
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case y < -MaxFloat64: //IsInf(y, -1):
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return -3 * Pi / 4
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case y > 0:
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return Pi
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default:
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return -Pi
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}
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case y < -MaxFloat64 || y > MaxFloat64: //IsInf(y, 0):
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if y > MaxFloat64 { // IsInf(y, 1) {
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return Pi / 2
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}
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return -Pi / 2
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}
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// Call atan and determine the quadrant.
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q := Atan(y / x)
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if x < 0 {
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if q <= 0 {
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11
src/pkg/math/atan2_386.s
Executable file
11
src/pkg/math/atan2_386.s
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@ -0,0 +1,11 @@
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// Copyright 2010 The Go Authors. All rights reserved.
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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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// func Atan2(y, x float64) float64 // =atan(y/x)
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TEXT ·Atan2(SB),7,$0
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FMOVD y+0(FP), F0 // F0=y
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FMOVD x+8(FP), F0 // F0=x, F1=y
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FPATAN // F0=atan(F1/F0)
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FMOVDP F0, r+16(FP)
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RET
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src/pkg/math/atan2_decl.go
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7
src/pkg/math/atan2_decl.go
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@ -0,0 +1,7 @@
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// Copyright 2010 The Go Authors. All rights reserved.
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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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package math
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func Atan2(y, x float64) float64
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