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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 square root
-//
-// DESCRIPTION:
-//
-// If z = x + iy, r = |z|, then
-//
-// 1/2
-// Re w = [ (r + x)/2 ] ,
-//
-// 1/2
-// Im w = [ (r - x)/2 ] .
-//
-// Cancellation error in r-x or r+x is avoided by using the
-// identity 2 Re w Im w = y.
-//
-// Note that -w is also a square root of z. The root chosen
-// is always in the right half plane and Im w has the same sign as y.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 25000 3.2e-17 9.6e-18
-// IEEE -10,+10 1,000,000 2.9e-16 6.1e-17
-
-// Sqrt returns the square root of x.
-// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
-func Sqrt(x complex128) complex128 {
- if imag(x) == 0 {
- if real(x) == 0 {
- return complex(0, 0)
- }
- if real(x) < 0 {
- return complex(0, math.Sqrt(-real(x)))
- }
- return complex(math.Sqrt(real(x)), 0)
- }
- if real(x) == 0 {
- if imag(x) < 0 {
- r := math.Sqrt(-0.5 * imag(x))
- return complex(r, -r)
- }
- r := math.Sqrt(0.5 * imag(x))
- return complex(r, r)
- }
- a := real(x)
- b := imag(x)
- var scale float64
- // Rescale to avoid internal overflow or underflow.
- if math.Abs(a) > 4 || math.Abs(b) > 4 {
- a *= 0.25
- b *= 0.25
- scale = 2
- } else {
- a *= 1.8014398509481984e16 // 2**54
- b *= 1.8014398509481984e16
- scale = 7.450580596923828125e-9 // 2**-27
- }
- r := math.Hypot(a, b)
- var t float64
- if a > 0 {
- t = math.Sqrt(0.5*r + 0.5*a)
- r = scale * math.Abs((0.5*b)/t)
- t *= scale
- } else {
- r = math.Sqrt(0.5*r - 0.5*a)
- t = scale * math.Abs((0.5*b)/r)
- r *= scale
- }
- if b < 0 {
- return complex(t, -r)
- }
- return complex(t, r)
-}