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Diffstat (limited to 'src/math/cmplx/pow.go')
-rw-r--r-- | src/math/cmplx/pow.go | 81 |
1 files changed, 81 insertions, 0 deletions
diff --git a/src/math/cmplx/pow.go b/src/math/cmplx/pow.go new file mode 100644 index 0000000..5a405f8 --- /dev/null +++ b/src/math/cmplx/pow.go @@ -0,0 +1,81 @@ +// 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. + if IsNaN(y) { + return NaN() + } + 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) +} |