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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / internal / cmplx64 / sqrt.go

diff --git a/vendor/gonum.org/v1/gonum/internal/cmplx64/sqrt.go b/vendor/gonum.org/v1/gonum/internal/cmplx64/sqrt.go
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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.
+
+// Copyright ©2017 The Gonum 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 cmplx64
+
+import math "gonum.org/v1/gonum/internal/math32"
+
+// 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 ]   .
+//
+// Cancelation 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 complex64) complex64 {
+       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 float32
+       // 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 float32
+       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)
+}