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authorIan Lance Taylor <ian@gcc.gnu.org>2010-12-03 04:34:57 +0000
committerIan Lance Taylor <ian@gcc.gnu.org>2010-12-03 04:34:57 +0000
commit7a9389330e91acc3ed05deac2d198af25d13cf3c (patch)
tree38fe54a4f38ede5d949c915d66191f24a6fe5153 /libgo/go/cmath/sqrt.go
parent1aa6700378e5188a853c018256113ce6e1fb5c05 (diff)
downloadgcc-7a9389330e91acc3ed05deac2d198af25d13cf3c.tar.gz
Add Go frontend, libgo library, and Go testsuite.
gcc/: * gcc.c (default_compilers): Add entry for ".go". * common.opt: Add -static-libgo as a driver option. * doc/install.texi (Configuration): Mention libgo as an option for --enable-shared. Mention go as an option for --enable-languages. * doc/invoke.texi (Overall Options): Mention .go as a file name suffix. Mention go as a -x option. * doc/frontends.texi (G++ and GCC): Mention Go as a supported language. * doc/sourcebuild.texi (Top Level): Mention libgo. * doc/standards.texi (Standards): Add section on Go language. Move references for other languages into their own section. * doc/contrib.texi (Contributors): Mention that I contributed the Go frontend. gcc/testsuite/: * lib/go.exp: New file. * lib/go-dg.exp: New file. * lib/go-torture.exp: New file. * lib/target-supports.exp (check_compile): Match // Go. From-SVN: r167407
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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 cmath
+
+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.
+func Sqrt(x complex128) complex128 {
+ if imag(x) == 0 {
+ if real(x) == 0 {
+ return cmplx(0, 0)
+ }
+ if real(x) < 0 {
+ return cmplx(0, math.Sqrt(-real(x)))
+ }
+ return cmplx(math.Sqrt(real(x)), 0)
+ }
+ if real(x) == 0 {
+ if imag(x) < 0 {
+ r := math.Sqrt(-0.5 * imag(x))
+ return cmplx(r, -r)
+ }
+ r := math.Sqrt(0.5 * imag(x))
+ return cmplx(r, r)
+ }
+ a := real(x)
+ b := imag(x)
+ var scale float64
+ // Rescale to avoid internal overflow or underflow.
+ if math.Fabs(a) > 4 || math.Fabs(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.Fabs((0.5*b)/t)
+ t *= scale
+ } else {
+ r = math.Sqrt(0.5*r - 0.5*a)
+ t = scale * math.Fabs((0.5*b)/r)
+ r *= scale
+ }
+ if b < 0 {
+ return cmplx(t, -r)
+ }
+ return cmplx(t, r)
+}