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
diff --git a/src/pkg/math/Makefile b/src/pkg/math/Makefile
index 0e89df7..7892371 100644
--- a/src/pkg/math/Makefile
+++ b/src/pkg/math/Makefile
@@ -12,6 +12,7 @@
OFILES_386=\
asin_386.$O\
atan_386.$O\
+ atan2_386.$O\
exp_386.$O\
fabs_386.$O\
floor_386.$O\
diff --git a/src/pkg/math/all_test.go b/src/pkg/math/all_test.go
index c0ac152..184d045 100644
--- a/src/pkg/math/all_test.go
+++ b/src/pkg/math/all_test.go
@@ -100,6 +100,18 @@
1.8459947964298794318714228e-01,
-1.3273186910532645867272502e+00,
}
+var atan2 = []float64{
+ 1.1088291730037004444527075e+00,
+ 9.1218183188715804018797795e-01,
+ 1.5984772603216203736068915e+00,
+ 2.0352918654092086637227327e+00,
+ 8.0391819139044720267356014e-01,
+ 1.2861075249894661588866752e+00,
+ 1.0889904479131695712182587e+00,
+ 1.3044821793397925293797357e+00,
+ 1.3902530903455392306872261e+00,
+ 2.2859857424479142655411058e+00,
+}
var ceil = []float64{
5.0000000000000000e+00,
8.0000000000000000e+00,
@@ -427,6 +439,64 @@
NaN(),
NaN(),
}
+var vfatan2SC = [][2]float64{
+ [2]float64{Inf(-1), Inf(-1)},
+ [2]float64{Inf(-1), -Pi},
+ [2]float64{Inf(-1), 0},
+ [2]float64{Inf(-1), +Pi},
+ [2]float64{Inf(-1), Inf(1)},
+ [2]float64{Inf(-1), NaN()},
+ [2]float64{-Pi, Inf(-1)},
+ [2]float64{-Pi, 0},
+ [2]float64{-Pi, Inf(1)},
+ [2]float64{-Pi, NaN()},
+ [2]float64{0, Inf(-1)},
+ [2]float64{0, -Pi},
+ [2]float64{0, 0},
+ [2]float64{0, +Pi},
+ [2]float64{0, Inf(1)},
+ [2]float64{0, NaN()},
+ [2]float64{+Pi, Inf(-1)},
+ [2]float64{+Pi, 0},
+ [2]float64{+Pi, Inf(1)},
+ [2]float64{+Pi, NaN()},
+ [2]float64{Inf(1), Inf(-1)},
+ [2]float64{Inf(1), -Pi},
+ [2]float64{Inf(1), 0},
+ [2]float64{Inf(1), +Pi},
+ [2]float64{Inf(1), Inf(1)},
+ [2]float64{Inf(1), NaN()},
+ [2]float64{NaN(), NaN()},
+}
+var atan2SC = []float64{
+ -3 * Pi / 4,
+ -Pi / 2,
+ -Pi / 2,
+ -Pi / 2,
+ -Pi / 4,
+ NaN(),
+ -Pi,
+ -Pi / 2,
+ -0,
+ NaN(),
+ Pi,
+ Pi,
+ 0,
+ 0,
+ 0,
+ NaN(),
+ Pi,
+ Pi / 2,
+ 0,
+ NaN(),
+ 3 * Pi / 4,
+ Pi / 2,
+ Pi / 2,
+ Pi / 2,
+ Pi / 4,
+ NaN(),
+ NaN(),
+}
var vfceilSC = []float64{
Inf(-1),
@@ -851,6 +921,19 @@
}
}
+func TestAtan2(t *testing.T) {
+ for i := 0; i < len(vf); i++ {
+ if f := Atan2(10, vf[i]); !veryclose(atan2[i], f) {
+ t.Errorf("Atan2(10, %g) = %g, want %g\n", vf[i], f, atan2[i])
+ }
+ }
+ for i := 0; i < len(vfatan2SC); i++ {
+ if f := Atan2(vfatan2SC[i][0], vfatan2SC[i][1]); !alike(atan2SC[i], f) {
+ t.Errorf("Atan2(%g, %g) = %g, want %g\n", vfatan2SC[i][0], vfatan2SC[i][1], f, atan2SC[i])
+ }
+ }
+}
+
func TestCeil(t *testing.T) {
for i := 0; i < len(vf); i++ {
if f := Ceil(vf[i]); ceil[i] != f {
@@ -1254,6 +1337,12 @@
}
}
+func BenchmarkAtan2(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Atan2(.5, 1)
+ }
+}
+
func BenchmarkCeil(b *testing.B) {
for i := 0; i < b.N; i++ {
Ceil(.5)
diff --git a/src/pkg/math/atan2.go b/src/pkg/math/atan2.go
index 80a28b1..a738fbc 100644
--- a/src/pkg/math/atan2.go
+++ b/src/pkg/math/atan2.go
@@ -7,14 +7,69 @@
// Atan2 returns the arc tangent of y/x, using
// the signs of the two to determine the quadrant
// of the return value.
+//
+// Special cases are (in order):
+// Atan2(y, NaN) = NaN
+// Atan2(NaN, x) = NaN
+// Atan2(0, x>=0) = 0
+// Atan2(0, x<0) = Pi
+// Atan2(y>0, 0) = +Pi/2
+// Atan2(y<0, 0) = -Pi/2
+// Atan2(+Inf, +Inf) = +Pi/4
+// Atan2(-Inf, +Inf) = -Pi/4
+// Atan2(+Inf, -Inf) = 3Pi/4
+// Atan2(-Inf, -Inf) = -3Pi/4
+// Atan2(y, +Inf) = 0
+// Atan2(y>0, -Inf) = +Pi
+// Atan2(y<0, -Inf) = -Pi
+// Atan2(+Inf, x) = +Pi/2
+// Atan2(-Inf, x) = -Pi/2
func Atan2(y, x float64) float64 {
- // Determine the quadrant and call atan.
- if y+x == y {
- if y >= 0 {
+ // TODO(rsc): Remove manual inlining of IsNaN, IsInf
+ // when compiler does it for us
+ // special cases
+ switch {
+ case y != y || x != x: // IsNaN(y) || IsNaN(x):
+ return NaN()
+ case y == 0:
+ if x >= 0 {
+ return 0
+ }
+ return Pi
+ case x == 0:
+ if y > 0 {
+ return Pi / 2
+ }
+ return -Pi / 2
+ case x < -MaxFloat64 || x > MaxFloat64: // IsInf(x, 0):
+ if x > MaxFloat64 { // IsInf(x, 1) {
+ switch {
+ case y > MaxFloat64: // IsInf(y, 1):
+ return Pi / 4
+ case y < -MaxFloat64: // IsInf(y, -1):
+ return -Pi / 4
+ default:
+ return 0
+ }
+ }
+ switch {
+ case y > MaxFloat64: //IsInf(y, 1):
+ return 3 * Pi / 4
+ case y < -MaxFloat64: //IsInf(y, -1):
+ return -3 * Pi / 4
+ case y > 0:
+ return Pi
+ default:
+ return -Pi
+ }
+ case y < -MaxFloat64 || y > MaxFloat64: //IsInf(y, 0):
+ if y > MaxFloat64 { // IsInf(y, 1) {
return Pi / 2
}
return -Pi / 2
}
+
+ // Call atan and determine the quadrant.
q := Atan(y / x)
if x < 0 {
if q <= 0 {
diff --git a/src/pkg/math/atan2_386.s b/src/pkg/math/atan2_386.s
new file mode 100755
index 0000000..9a66492
--- /dev/null
+++ b/src/pkg/math/atan2_386.s
@@ -0,0 +1,11 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// func Atan2(y, x float64) float64 // =atan(y/x)
+TEXT ·Atan2(SB),7,$0
+ FMOVD y+0(FP), F0 // F0=y
+ FMOVD x+8(FP), F0 // F0=x, F1=y
+ FPATAN // F0=atan(F1/F0)
+ FMOVDP F0, r+16(FP)
+ RET
diff --git a/src/pkg/math/atan2_decl.go b/src/pkg/math/atan2_decl.go
new file mode 100755
index 0000000..3932ed6
--- /dev/null
+++ b/src/pkg/math/atan2_decl.go
@@ -0,0 +1,7 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+func Atan2(y, x float64) float64
