Source file src/pkg/math/cmplx/sin.go

     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	//   [email protected]
    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	}