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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 {
switch re, im := real(x), imag(x); {
case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
return complex(math.NaN(), im)
case math.IsInf(im, 0):
switch {
case re == 0:
return x
case math.IsInf(re, 0) || math.IsNaN(re):
return complex(math.NaN(), im)
}
case re == 0 && math.IsNaN(im):
return x
}
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 {
switch re, im := real(x), imag(x); {
case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)):
return complex(re, math.NaN())
case math.IsInf(re, 0):
switch {
case im == 0:
return complex(re, im)
case math.IsInf(im, 0) || math.IsNaN(im):
return complex(re, math.NaN())
}
case im == 0 && math.IsNaN(re):
return complex(math.NaN(), im)
}
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 {
switch re, im := real(x), imag(x); {
case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
return complex(math.NaN(), -im*math.Copysign(0, re))
case math.IsInf(im, 0):
switch {
case re == 0:
return complex(math.Inf(1), -re*math.Copysign(0, im))
case math.IsInf(re, 0) || math.IsNaN(re):
return complex(math.Inf(1), math.NaN())
}
case re == 0 && math.IsNaN(im):
return complex(math.NaN(), 0)
}
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 {
switch re, im := real(x), imag(x); {
case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)):
return complex(math.NaN(), re*math.Copysign(0, im))
case math.IsInf(re, 0):
switch {
case im == 0:
return complex(math.Inf(1), im*math.Copysign(0, re))
case math.IsInf(im, 0) || math.IsNaN(im):
return complex(math.Inf(1), math.NaN())
}
case im == 0 && math.IsNaN(re):
return complex(math.NaN(), im)
}
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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