tan.go

     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@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  //
    80  //	Tan(±0) = ±0
    81  //	Tan(±Inf) = NaN
    82  //	Tan(NaN) = NaN
    83  func Tan(x float64) float64 {
    84  	if haveArchTan {
    85  		return archTan(x)
    86  	}
    87  	return tan(x)
    88  }
    89  
    90  func tan(x float64) float64 {
    91  	const (
    92  		PI4A = 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
    93  		PI4B = 3.77489470793079817668e-8  // 0x3e64442d00000000,
    94  		PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
    95  	)
    96  	// special cases
    97  	switch {
    98  	case x == 0 || IsNaN(x):
    99  		return x // return ±0 || NaN()
   100  	case IsInf(x, 0):
   101  		return NaN()
   102  	}
   103  
   104  	// make argument positive but save the sign
   105  	sign := false
   106  	if x < 0 {
   107  		x = -x
   108  		sign = true
   109  	}
   110  	var j uint64
   111  	var y, z float64
   112  	if x >= reduceThreshold {
   113  		j, z = trigReduce(x)
   114  	} else {
   115  		j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
   116  		y = float64(j)           // integer part of x/(Pi/4), as float
   117  
   118  		/* map zeros and singularities to origin */
   119  		if j&1 == 1 {
   120  			j++
   121  			y++
   122  		}
   123  
   124  		z = ((x - y*PI4A) - y*PI4B) - y*PI4C
   125  	}
   126  	zz := z * z
   127  
   128  	if zz > 1e-14 {
   129  		y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
   130  	} else {
   131  		y = z
   132  	}
   133  	if j&2 == 2 {
   134  		y = -1 / y
   135  	}
   136  	if sign {
   137  		y = -y
   138  	}
   139  	return y
   140  }
   141
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