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math: improved accuracy for Tan
R=rsc CC=golang-dev https://golang.org/cl/5298087
This commit is contained in:
Charles L. Dorian
Russ Cox
parent
7df9ff5594
commit
cefee3c919
@ -7,7 +7,6 @@ package math_test
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import (
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"fmt"
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. "math"
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"runtime"
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"testing"
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)
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@ -2247,7 +2246,7 @@ func TestSqrt(t *testing.T) {
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func TestTan(t *testing.T) {
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for i := 0; i < len(vf); i++ {
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if f := Tan(vf[i]); !close(tan[i], f) {
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if f := Tan(vf[i]); !veryclose(tan[i], f) {
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t.Errorf("Tan(%g) = %g, want %g", vf[i], f, tan[i])
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}
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}
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@ -2257,16 +2256,6 @@ func TestTan(t *testing.T) {
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t.Errorf("Tan(%g) = %g, want %g", vfsinSC[i], f, sinSC[i])
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}
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}
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// Make sure portable Tan(Pi/2) doesn't panic (it used to).
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// The portable implementation returns NaN.
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// Assembly implementations might not,
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// because Pi/2 is not exactly representable.
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if runtime.GOARCH != "386" {
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if f := Tan(Pi / 2); !alike(f, NaN()) {
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t.Errorf("Tan(%g) = %g, want %g", Pi/2, f, NaN())
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}
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}
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}
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func TestTanh(t *testing.T) {
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@ -1,64 +1,130 @@
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// Copyright 2009 The Go Authors. All rights reserved.
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// Copyright 2011 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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/*
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Floating point tangent.
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Floating-point tangent.
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*/
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// Tan returns the tangent of x.
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func Tan(x float64) float64 {
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// Coefficients are #4285 from Hart & Cheney. (19.74D)
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const (
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P0 = -.1306820264754825668269611177e+5
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P1 = .1055970901714953193602353981e+4
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P2 = -.1550685653483266376941705728e+2
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P3 = .3422554387241003435328470489e-1
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P4 = .3386638642677172096076369e-4
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Q0 = -.1663895238947119001851464661e+5
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Q1 = .4765751362916483698926655581e+4
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Q2 = -.1555033164031709966900124574e+3
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)
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// The original C code, the long comment, and the constants
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// below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
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// available from http://www.netlib.org/cephes/cmath.tgz.
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// The go code is a simplified version of the original C.
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//
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// tan.c
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//
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// Circular tangent
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//
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// SYNOPSIS:
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//
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// double x, y, tan();
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// y = tan( x );
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//
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// DESCRIPTION:
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//
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// Returns the circular tangent of the radian argument x.
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//
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// Range reduction is modulo pi/4. A rational function
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// x + x**3 P(x**2)/Q(x**2)
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// is employed in the basic interval [0, pi/4].
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//
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// ACCURACY:
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// Relative error:
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// arithmetic domain # trials peak rms
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// DEC +-1.07e9 44000 4.1e-17 1.0e-17
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// IEEE +-1.07e9 30000 2.9e-16 8.1e-17
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//
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// Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9. The loss
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// is not gradual, but jumps suddenly to about 1 part in 10e7. Results may
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// be meaningless for x > 2**49 = 5.6e14.
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// [Accuracy loss statement from sin.go comments.]
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//
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// Cephes Math Library Release 2.8: June, 2000
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// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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//
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// The readme file at http://netlib.sandia.gov/cephes/ says:
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// Some software in this archive may be from the book _Methods and
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// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
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// International, 1989) or from the Cephes Mathematical Library, a
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// commercial product. In either event, it is copyrighted by the author.
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// What you see here may be used freely but it comes with no support or
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// guarantee.
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//
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// The two known misprints in the book are repaired here in the
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// source listings for the gamma function and the incomplete beta
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// integral.
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//
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// Stephen L. Moshier
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// moshier@na-net.ornl.gov
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flag := false
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// tan coefficients
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var _tanP = [...]float64{
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-1.30936939181383777646E4, // 0xc0c992d8d24f3f38
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1.15351664838587416140E6, // 0x413199eca5fc9ddd
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-1.79565251976484877988E7, // 0xc1711fead3299176
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}
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var _tanQ = [...]float64{
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1.00000000000000000000E0,
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1.36812963470692954678E4, //0x40cab8a5eeb36572
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-1.32089234440210967447E6, //0xc13427bc582abc96
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2.50083801823357915839E7, //0x4177d98fc2ead8ef
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-5.38695755929454629881E7, //0xc189afe03cbe5a31
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}
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// Tan returns the tangent of x.
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//
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// Special conditions are:
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// Tan(±0) = ±0
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// Tan(±Inf) = NaN
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// Tan(NaN) = NaN
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func Tan(x float64) float64 {
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const (
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PI4A = 7.85398125648498535156E-1 // 0x3fe921fb40000000, Pi/4 split into three parts
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PI4B = 3.77489470793079817668E-8 // 0x3e64442d00000000,
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PI4C = 2.69515142907905952645E-15 // 0x3ce8469898cc5170,
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M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
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)
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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 == 0 || x != x: // x == 0 || IsNaN():
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return x // return ±0 || NaN()
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case x < -MaxFloat64 || x > MaxFloat64: // IsInf(x, 0):
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return NaN()
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}
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// make argument positive but save the sign
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sign := false
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if x < 0 {
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x = -x
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sign = true
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}
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x = x * (4 / Pi) /* overflow? */
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var e float64
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e, x = Modf(x)
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i := int32(e)
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switch i & 3 {
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case 1:
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x = 1 - x
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flag = true
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j := int64(x * M4PI) // integer part of x/(Pi/4), as integer for tests on the phase angle
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y := float64(j) // integer part of x/(Pi/4), as float
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case 2:
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sign = !sign
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flag = true
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case 3:
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x = 1 - x
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sign = !sign
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/* map zeros and singularities to origin */
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if j&1 == 1 {
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j += 1
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y += 1
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}
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xsq := x * x
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temp := ((((P4*xsq+P3)*xsq+P2)*xsq+P1)*xsq + P0) * x
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temp = temp / (((xsq+Q2)*xsq+Q1)*xsq + Q0)
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z := ((x - y*PI4A) - y*PI4B) - y*PI4C
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zz := z * z
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if flag {
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if temp == 0 {
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return NaN()
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}
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temp = 1 / temp
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if zz > 1e-14 {
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y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
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} else {
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y = z
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}
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if j&2 == 2 {
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y = -1 / y
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}
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if sign {
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temp = -temp
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y = -y
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}
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return temp
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return y
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}
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