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Source file src/math/cmplx/sin.go

  // Copyright 2010 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 cmplx
  
  import "math"
  
  // The original C code, the long comment, and the constants
  // below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
  // The go code is a simplified version of the original C.
  //
  // 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
  
  // Complex circular sine
  //
  // DESCRIPTION:
  //
  // If
  //     z = x + iy,
  //
  // then
  //
  //     w = sin x  cosh y  +  i cos x sinh y.
  //
  // csin(z) = -i csinh(iz).
  //
  // ACCURACY:
  //
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    DEC       -10,+10      8400       5.3e-17     1.3e-17
  //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
  // Also tested by csin(casin(z)) = z.
  
  // Sin returns the sine of x.
  func Sin(x complex128) complex128 {
  	s, c := math.Sincos(real(x))
  	sh, ch := sinhcosh(imag(x))
  	return complex(s*ch, c*sh)
  }
  
  // Complex hyperbolic sine
  //
  // DESCRIPTION:
  //
  // csinh z = (cexp(z) - cexp(-z))/2
  //         = sinh x * cos y  +  i cosh x * sin y .
  //
  // ACCURACY:
  //
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    IEEE      -10,+10     30000       3.1e-16     8.2e-17
  
  // Sinh returns the hyperbolic sine of x.
  func Sinh(x complex128) complex128 {
  	s, c := math.Sincos(imag(x))
  	sh, ch := sinhcosh(real(x))
  	return complex(c*sh, s*ch)
  }
  
  // Complex circular cosine
  //
  // DESCRIPTION:
  //
  // If
  //     z = x + iy,
  //
  // then
  //
  //     w = cos x  cosh y  -  i sin x sinh y.
  //
  // ACCURACY:
  //
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    DEC       -10,+10      8400       4.5e-17     1.3e-17
  //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
  
  // Cos returns the cosine of x.
  func Cos(x complex128) complex128 {
  	s, c := math.Sincos(real(x))
  	sh, ch := sinhcosh(imag(x))
  	return complex(c*ch, -s*sh)
  }
  
  // Complex hyperbolic cosine
  //
  // DESCRIPTION:
  //
  // ccosh(z) = cosh x  cos y + i sinh x sin y .
  //
  // ACCURACY:
  //
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    IEEE      -10,+10     30000       2.9e-16     8.1e-17
  
  // Cosh returns the hyperbolic cosine of x.
  func Cosh(x complex128) complex128 {
  	s, c := math.Sincos(imag(x))
  	sh, ch := sinhcosh(real(x))
  	return complex(c*ch, s*sh)
  }
  
  // calculate sinh and cosh
  func sinhcosh(x float64) (sh, ch float64) {
  	if math.Abs(x) <= 0.5 {
  		return math.Sinh(x), math.Cosh(x)
  	}
  	e := math.Exp(x)
  	ei := 0.5 / e
  	e *= 0.5
  	return e - ei, e + ei
  }
  

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