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// 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

}