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Diffstat (limited to 'src/pkg/math/cmplx/sqrt.go')
-rw-r--r-- | src/pkg/math/cmplx/sqrt.go | 104 |
1 files changed, 0 insertions, 104 deletions
diff --git a/src/pkg/math/cmplx/sqrt.go b/src/pkg/math/cmplx/sqrt.go deleted file mode 100644 index 4ef6807ad..000000000 --- a/src/pkg/math/cmplx/sqrt.go +++ /dev/null @@ -1,104 +0,0 @@ -// 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) -} |