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- // Copyright 2011 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
- /*
- Floating-point tangent.
- */
- // The original C code, the long comment, and the constants
- // below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
- // available from http://www.netlib.org/cephes/cmath.tgz.
- // The go code is a simplified version of the original C.
- //
- // tan.c
- //
- // Circular tangent
- //
- // SYNOPSIS:
- //
- // double x, y, tan();
- // y = tan( x );
- //
- // DESCRIPTION:
- //
- // Returns the circular tangent of the radian argument x.
- //
- // Range reduction is modulo pi/4. A rational function
- // x + x**3 P(x**2)/Q(x**2)
- // is employed in the basic interval [0, pi/4].
- //
- // ACCURACY:
- // Relative error:
- // arithmetic domain # trials peak rms
- // DEC +-1.07e9 44000 4.1e-17 1.0e-17
- // IEEE +-1.07e9 30000 2.9e-16 8.1e-17
- //
- // Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9. The loss
- // is not gradual, but jumps suddenly to about 1 part in 10e7. Results may
- // be meaningless for x > 2**49 = 5.6e14.
- // [Accuracy loss statement from sin.go comments.]
- //
- // Cephes Math Library Release 2.8: June, 2000
- // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
- //
- // The readme file at http://netlib.sandia.gov/cephes/ says:
- // Some software in this archive may be from the book _Methods and
- // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
- // International, 1989) or from the Cephes Mathematical Library, a
- // commercial product. In either event, it is copyrighted by the author.
- // What you see here may be used freely but it comes with no support or
- // guarantee.
- //
- // The two known misprints in the book are repaired here in the
- // source listings for the gamma function and the incomplete beta
- // integral.
- //
- // Stephen L. Moshier
- // moshier@na-net.ornl.gov
- // tan coefficients
- var _tanP = [...]float64{
- -1.30936939181383777646e4, // 0xc0c992d8d24f3f38
- 1.15351664838587416140e6, // 0x413199eca5fc9ddd
- -1.79565251976484877988e7, // 0xc1711fead3299176
- }
- var _tanQ = [...]float64{
- 1.00000000000000000000e0,
- 1.36812963470692954678e4, //0x40cab8a5eeb36572
- -1.32089234440210967447e6, //0xc13427bc582abc96
- 2.50083801823357915839e7, //0x4177d98fc2ead8ef
- -5.38695755929454629881e7, //0xc189afe03cbe5a31
- }
- // Tan returns the tangent of the radian argument x.
- //
- // Special cases are:
- // Tan(±0) = ±0
- // Tan(±Inf) = NaN
- // Tan(NaN) = NaN
- func Tan(x float64) float64 {
- return libc_tan(x)
- }
- //extern tan
- func libc_tan(float64) float64
- func tan(x float64) float64 {
- const (
- PI4A = 7.85398125648498535156e-1 // 0x3fe921fb40000000, Pi/4 split into three parts
- PI4B = 3.77489470793079817668e-8 // 0x3e64442d00000000,
- PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
- )
- // special cases
- switch {
- case x == 0 || IsNaN(x):
- return x // return ±0 || NaN()
- case IsInf(x, 0):
- return NaN()
- }
- // make argument positive but save the sign
- sign := false
- if x < 0 {
- x = -x
- sign = true
- }
- var j uint64
- var y, z float64
- if x >= reduceThreshold {
- j, z = trigReduce(x)
- } else {
- j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
- y = float64(j) // integer part of x/(Pi/4), as float
- /* map zeros and singularities to origin */
- if j&1 == 1 {
- j++
- y++
- }
- z = ((x - y*PI4A) - y*PI4B) - y*PI4C
- }
- zz := z * z
- if zz > 1e-14 {
- y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
- } else {
- y = z
- }
- if j&2 == 2 {
- y = -1 / y
- }
- if sign {
- y = -y
- }
- return y
- }
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