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Source file src/math/cmplx/sin.go

Documentation: math/cmplx

     1  // Copyright 2010 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 cmplx
     6  
     7  import "math"
     8  
     9  // The original C code, the long comment, and the constants
    10  // below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
    11  // The go code is a simplified version of the original C.
    12  //
    13  // Cephes Math Library Release 2.8:  June, 2000
    14  // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
    15  //
    16  // The readme file at http://netlib.sandia.gov/cephes/ says:
    17  //    Some software in this archive may be from the book _Methods and
    18  // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
    19  // International, 1989) or from the Cephes Mathematical Library, a
    20  // commercial product. In either event, it is copyrighted by the author.
    21  // What you see here may be used freely but it comes with no support or
    22  // guarantee.
    23  //
    24  //   The two known misprints in the book are repaired here in the
    25  // source listings for the gamma function and the incomplete beta
    26  // integral.
    27  //
    28  //   Stephen L. Moshier
    29  //   moshier@na-net.ornl.gov
    30  
    31  // Complex circular sine
    32  //
    33  // DESCRIPTION:
    34  //
    35  // If
    36  //     z = x + iy,
    37  //
    38  // then
    39  //
    40  //     w = sin x  cosh y  +  i cos x sinh y.
    41  //
    42  // csin(z) = -i csinh(iz).
    43  //
    44  // ACCURACY:
    45  //
    46  //                      Relative error:
    47  // arithmetic   domain     # trials      peak         rms
    48  //    DEC       -10,+10      8400       5.3e-17     1.3e-17
    49  //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
    50  // Also tested by csin(casin(z)) = z.
    51  
    52  // Sin returns the sine of x.
    53  func Sin(x complex128) complex128 {
    54  	s, c := math.Sincos(real(x))
    55  	sh, ch := sinhcosh(imag(x))
    56  	return complex(s*ch, c*sh)
    57  }
    58  
    59  // Complex hyperbolic sine
    60  //
    61  // DESCRIPTION:
    62  //
    63  // csinh z = (cexp(z) - cexp(-z))/2
    64  //         = sinh x * cos y  +  i cosh x * sin y .
    65  //
    66  // ACCURACY:
    67  //
    68  //                      Relative error:
    69  // arithmetic   domain     # trials      peak         rms
    70  //    IEEE      -10,+10     30000       3.1e-16     8.2e-17
    71  
    72  // Sinh returns the hyperbolic sine of x.
    73  func Sinh(x complex128) complex128 {
    74  	s, c := math.Sincos(imag(x))
    75  	sh, ch := sinhcosh(real(x))
    76  	return complex(c*sh, s*ch)
    77  }
    78  
    79  // Complex circular cosine
    80  //
    81  // DESCRIPTION:
    82  //
    83  // If
    84  //     z = x + iy,
    85  //
    86  // then
    87  //
    88  //     w = cos x  cosh y  -  i sin x sinh y.
    89  //
    90  // ACCURACY:
    91  //
    92  //                      Relative error:
    93  // arithmetic   domain     # trials      peak         rms
    94  //    DEC       -10,+10      8400       4.5e-17     1.3e-17
    95  //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
    96  
    97  // Cos returns the cosine of x.
    98  func Cos(x complex128) complex128 {
    99  	s, c := math.Sincos(real(x))
   100  	sh, ch := sinhcosh(imag(x))
   101  	return complex(c*ch, -s*sh)
   102  }
   103  
   104  // Complex hyperbolic cosine
   105  //
   106  // DESCRIPTION:
   107  //
   108  // ccosh(z) = cosh x  cos y + i sinh x sin y .
   109  //
   110  // ACCURACY:
   111  //
   112  //                      Relative error:
   113  // arithmetic   domain     # trials      peak         rms
   114  //    IEEE      -10,+10     30000       2.9e-16     8.1e-17
   115  
   116  // Cosh returns the hyperbolic cosine of x.
   117  func Cosh(x complex128) complex128 {
   118  	s, c := math.Sincos(imag(x))
   119  	sh, ch := sinhcosh(real(x))
   120  	return complex(c*ch, s*sh)
   121  }
   122  
   123  // calculate sinh and cosh
   124  func sinhcosh(x float64) (sh, ch float64) {
   125  	if math.Abs(x) <= 0.5 {
   126  		return math.Sinh(x), math.Cosh(x)
   127  	}
   128  	e := math.Exp(x)
   129  	ei := 0.5 / e
   130  	e *= 0.5
   131  	return e - ei, e + ei
   132  }
   133  

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