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package math_cmplx
import "base:builtin"
import "core: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
acos :: proc{
acos_complex32,
acos_complex64,
acos_complex128,
}
acosh :: proc{
acosh_complex32,
acosh_complex64,
acosh_complex128,
}
asin :: proc{
asin_complex32,
asin_complex64,
asin_complex128,
}
asinh :: proc{
asinh_complex32,
asinh_complex64,
asinh_complex128,
}
atan :: proc{
atan_complex32,
atan_complex64,
atan_complex128,
}
atanh :: proc{
atanh_complex32,
atanh_complex64,
atanh_complex128,
}
acos_complex32 :: proc "contextless" (x: complex32) -> complex32 {
return complex32(acos_complex64(complex64(x)))
}
acos_complex64 :: proc "contextless" (x: complex64) -> complex64 {
w := asin(x)
return complex(math.PI/2 - real(w), -imag(w))
}
acos_complex128 :: proc "contextless" (x: complex128) -> complex128 {
w := asin(x)
return complex(math.PI/2 - real(w), -imag(w))
}
acosh_complex32 :: proc "contextless" (x: complex32) -> complex32 {
return complex32(acosh_complex64(complex64(x)))
}
acosh_complex64 :: proc "contextless" (x: complex64) -> complex64 {
if x == 0 {
return complex(0, math.copy_sign(math.PI/2, imag(x)))
}
w := acos(x)
if imag(w) <= 0 {
return complex(-imag(w), real(w))
}
return complex(imag(w), -real(w))
}
acosh_complex128 :: proc "contextless" (x: complex128) -> complex128 {
if x == 0 {
return complex(0, math.copy_sign(math.PI/2, imag(x)))
}
w := acos(x)
if imag(w) <= 0 {
return complex(-imag(w), real(w))
}
return complex(imag(w), -real(w))
}
asin_complex32 :: proc "contextless" (x: complex32) -> complex32 {
return complex32(asin_complex128(complex128(x)))
}
asin_complex64 :: proc "contextless" (x: complex64) -> complex64 {
return complex64(asin_complex128(complex128(x)))
}
asin_complex128 :: proc "contextless" (x: complex128) -> complex128 {
switch re, im := real(x), imag(x); {
case im == 0 && abs(re) <= 1:
return complex(math.asin(re), im)
case re == 0 && abs(im) <= 1:
return complex(re, math.asinh(im))
case math.is_nan(im):
switch {
case re == 0:
return complex(re, math.nan_f64())
case math.is_inf(re, 0):
return complex(math.nan_f64(), re)
case:
return nan_complex128()
}
case math.is_inf(im, 0):
switch {
case math.is_nan(re):
return x
case math.is_inf(re, 0):
return complex(math.copy_sign(math.PI/4, re), im)
case:
return complex(math.copy_sign(0, re), im)
}
case math.is_inf(re, 0):
return complex(math.copy_sign(math.PI/2, re), math.copy_sign(re, im))
}
ct := complex(-imag(x), real(x)) // i * x
xx := x * x
x1 := complex(1-real(xx), -imag(xx)) // 1 - x*x
x2 := sqrt(x1) // x2 = sqrt(1 - x*x)
w := ln(ct + x2)
return complex(imag(w), -real(w)) // -i * w
}
asinh_complex32 :: proc "contextless" (x: complex32) -> complex32 {
return complex32(asinh_complex128(complex128(x)))
}
asinh_complex64 :: proc "contextless" (x: complex64) -> complex64 {
return complex64(asinh_complex128(complex128(x)))
}
asinh_complex128 :: proc "contextless" (x: complex128) -> complex128 {
switch re, im := real(x), imag(x); {
case im == 0 && abs(re) <= 1:
return complex(math.asinh(re), im)
case re == 0 && abs(im) <= 1:
return complex(re, math.asin(im))
case math.is_inf(re, 0):
switch {
case math.is_inf(im, 0):
return complex(re, math.copy_sign(math.PI/4, im))
case math.is_nan(im):
return x
case:
return complex(re, math.copy_sign(0.0, im))
}
case math.is_nan(re):
switch {
case im == 0:
return x
case math.is_inf(im, 0):
return complex(im, re)
case:
return nan_complex128()
}
case math.is_inf(im, 0):
return complex(math.copy_sign(im, re), math.copy_sign(math.PI/2, im))
}
xx := x * x
x1 := complex(1+real(xx), imag(xx)) // 1 + x*x
return ln(x + sqrt(x1)) // log(x + sqrt(1 + x*x))
}
atan_complex32 :: proc "contextless" (x: complex32) -> complex32 {
return complex32(atan_complex128(complex128(x)))
}
atan_complex64 :: proc "contextless" (x: complex64) -> complex64 {
return complex64(atan_complex128(complex128(x)))
}
atan_complex128 :: proc "contextless" (x: complex128) -> complex128 {
// Complex circular arc tangent
//
// DESCRIPTION:
//
// If
// z = x + iy,
//
// then
// 1 ( 2x )
// Re w = - arctan(-----------) + k PI
// 2 ( 2 2)
// (1 - x - y )
//
// ( 2 2)
// 1 (x + (y+1) )
// Im w = - log(------------)
// 4 ( 2 2)
// (x + (y-1) )
//
// Where k is an arbitrary integer.
//
// catan(z) = -i catanh(iz).
//
// ACCURACY:
//
// Relative error:
// arithmetic domain # trials peak rms
// DEC -10,+10 5900 1.3e-16 7.8e-18
// IEEE -10,+10 30000 2.3e-15 8.5e-17
// The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
// had peak relative error 1.5e-16, rms relative error
// 2.9e-17. See also clog().
switch re, im := real(x), imag(x); {
case im == 0:
return complex(math.atan(re), im)
case re == 0 && abs(im) <= 1:
return complex(re, math.atanh(im))
case math.is_inf(im, 0) || math.is_inf(re, 0):
if math.is_nan(re) {
return complex(math.nan_f64(), math.copy_sign(0, im))
}
return complex(math.copy_sign(math.PI/2, re), math.copy_sign(0, im))
case math.is_nan(re) || math.is_nan(im):
return nan_complex128()
}
x2 := real(x) * real(x)
a := 1 - x2 - imag(x)*imag(x)
if a == 0 {
return nan_complex128()
}
t := 0.5 * math.atan2(2*real(x), a)
w := _reduce_pi_f64(t)
t = imag(x) - 1
b := x2 + t*t
if b == 0 {
return nan_complex128()
}
t = imag(x) + 1
c := (x2 + t*t) / b
return complex(w, 0.25*math.ln(c))
}
atanh_complex32 :: proc "contextless" (x: complex32) -> complex32 {
return complex32(atanh_complex64(complex64(x)))
}
atanh_complex64 :: proc "contextless" (x: complex64) -> complex64 {
z := complex(-imag(x), real(x)) // z = i * x
z = atan(z)
return complex(imag(z), -real(z)) // z = -i * z
}
atanh_complex128 :: proc "contextless" (x: complex128) -> complex128 {
z := complex(-imag(x), real(x)) // z = i * x
z = atan(z)
return complex(imag(z), -real(z)) // z = -i * z
}
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