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      1 // Copyright 2011 The Go Authors. All rights reserved.
      2 // Use of this source code is governed by a BSD-style
      3 // license that can be found in the LICENSE file.
      4 
      5 package math
      6 
      7 /*
      8 	Floating-point tangent.
      9 */
     10 
     11 // The original C code, the long comment, and the constants
     12 // below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
     13 // available from http://www.netlib.org/cephes/cmath.tgz.
     14 // The go code is a simplified version of the original C.
     15 //
     16 //      tan.c
     17 //
     18 //      Circular tangent
     19 //
     20 // SYNOPSIS:
     21 //
     22 // double x, y, tan();
     23 // y = tan( x );
     24 //
     25 // DESCRIPTION:
     26 //
     27 // Returns the circular tangent of the radian argument x.
     28 //
     29 // Range reduction is modulo pi/4.  A rational function
     30 //       x + x**3 P(x**2)/Q(x**2)
     31 // is employed in the basic interval [0, pi/4].
     32 //
     33 // ACCURACY:
     34 //                      Relative error:
     35 // arithmetic   domain     # trials      peak         rms
     36 //    DEC      +-1.07e9      44000      4.1e-17     1.0e-17
     37 //    IEEE     +-1.07e9      30000      2.9e-16     8.1e-17
     38 //
     39 // Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9.  The loss
     40 // is not gradual, but jumps suddenly to about 1 part in 10e7.  Results may
     41 // be meaningless for x > 2**49 = 5.6e14.
     42 // [Accuracy loss statement from sin.go comments.]
     43 //
     44 // Cephes Math Library Release 2.8:  June, 2000
     45 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
     46 //
     47 // The readme file at http://netlib.sandia.gov/cephes/ says:
     48 //    Some software in this archive may be from the book _Methods and
     49 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
     50 // International, 1989) or from the Cephes Mathematical Library, a
     51 // commercial product. In either event, it is copyrighted by the author.
     52 // What you see here may be used freely but it comes with no support or
     53 // guarantee.
     54 //
     55 //   The two known misprints in the book are repaired here in the
     56 // source listings for the gamma function and the incomplete beta
     57 // integral.
     58 //
     59 //   Stephen L. Moshier
     60 //   moshier (a] na-net.ornl.gov
     61 
     62 // tan coefficients
     63 var _tanP = [...]float64{
     64 	-1.30936939181383777646E4, // 0xc0c992d8d24f3f38
     65 	1.15351664838587416140E6,  // 0x413199eca5fc9ddd
     66 	-1.79565251976484877988E7, // 0xc1711fead3299176
     67 }
     68 var _tanQ = [...]float64{
     69 	1.00000000000000000000E0,
     70 	1.36812963470692954678E4,  //0x40cab8a5eeb36572
     71 	-1.32089234440210967447E6, //0xc13427bc582abc96
     72 	2.50083801823357915839E7,  //0x4177d98fc2ead8ef
     73 	-5.38695755929454629881E7, //0xc189afe03cbe5a31
     74 }
     75 
     76 // Tan returns the tangent of the radian argument x.
     77 //
     78 // Special cases are:
     79 //	Tan(0) = 0
     80 //	Tan(Inf) = NaN
     81 //	Tan(NaN) = NaN
     82 func Tan(x float64) float64
     83 
     84 func tan(x float64) float64 {
     85 	const (
     86 		PI4A = 7.85398125648498535156E-1                             // 0x3fe921fb40000000, Pi/4 split into three parts
     87 		PI4B = 3.77489470793079817668E-8                             // 0x3e64442d00000000,
     88 		PI4C = 2.69515142907905952645E-15                            // 0x3ce8469898cc5170,
     89 		M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
     90 	)
     91 	// special cases
     92 	switch {
     93 	case x == 0 || IsNaN(x):
     94 		return x // return 0 || NaN()
     95 	case IsInf(x, 0):
     96 		return NaN()
     97 	}
     98 
     99 	// make argument positive but save the sign
    100 	sign := false
    101 	if x < 0 {
    102 		x = -x
    103 		sign = true
    104 	}
    105 
    106 	j := int64(x * M4PI) // integer part of x/(Pi/4), as integer for tests on the phase angle
    107 	y := float64(j)      // integer part of x/(Pi/4), as float
    108 
    109 	/* map zeros and singularities to origin */
    110 	if j&1 == 1 {
    111 		j++
    112 		y++
    113 	}
    114 
    115 	z := ((x - y*PI4A) - y*PI4B) - y*PI4C
    116 	zz := z * z
    117 
    118 	if zz > 1e-14 {
    119 		y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
    120 	} else {
    121 		y = z
    122 	}
    123 	if j&2 == 2 {
    124 		y = -1 / y
    125 	}
    126 	if sign {
    127 		y = -y
    128 	}
    129 	return y
    130 }
    131