mirror of
https://github.com/autc04/Retro68.git
synced 2024-11-30 19:53:46 +00:00
79 lines
2.2 KiB
Go
79 lines
2.2 KiB
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 power function
|
|
//
|
|
// DESCRIPTION:
|
|
//
|
|
// Raises complex A to the complex Zth power.
|
|
// Definition is per AMS55 # 4.2.8,
|
|
// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
|
|
//
|
|
// ACCURACY:
|
|
//
|
|
// Relative error:
|
|
// arithmetic domain # trials peak rms
|
|
// IEEE -10,+10 30000 9.4e-15 1.5e-15
|
|
|
|
// Pow returns x**y, the base-x exponential of y.
|
|
// For generalized compatibility with math.Pow:
|
|
// Pow(0, ±0) returns 1+0i
|
|
// Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
|
|
func Pow(x, y complex128) complex128 {
|
|
if x == 0 { // Guaranteed also true for x == -0.
|
|
r, i := real(y), imag(y)
|
|
switch {
|
|
case r == 0:
|
|
return 1
|
|
case r < 0:
|
|
if i == 0 {
|
|
return complex(math.Inf(1), 0)
|
|
}
|
|
return Inf()
|
|
case r > 0:
|
|
return 0
|
|
}
|
|
panic("not reached")
|
|
}
|
|
modulus := Abs(x)
|
|
if modulus == 0 {
|
|
return complex(0, 0)
|
|
}
|
|
r := math.Pow(modulus, real(y))
|
|
arg := Phase(x)
|
|
theta := real(y) * arg
|
|
if imag(y) != 0 {
|
|
r *= math.Exp(-imag(y) * arg)
|
|
theta += imag(y) * math.Log(modulus)
|
|
}
|
|
s, c := math.Sincos(theta)
|
|
return complex(r*c, r*s)
|
|
}
|