math: add functions; update tests and special cases

Added special cases to comments for asin.go and fabs.go.
Added Trunc() to floor.go and floor_386.s.  Fixed formatting
error in hypot_386.s  Added new functions Acosh, Asinh,
Atanh, Copysign, Erf, Erfc, Expm1, and Log1p.  Added
386 FPU version of Fmod.  Added tests, benchmarks, and
precision to expected results in all_test.go.  Edited
makefile so it all compiles.

R=rsc
CC=golang-dev
http://codereview.appspot.com/195052

Committer: Russ Cox <rsc@golang.org>

1 files changed, 59 insertions, 0 deletions

diff --git a/src/pkg/math/acosh.go b/src/pkg/math/acosh.go
new file mode 100644
index 000000000..1f0d3f338
--- /dev/null
+++ b/src/pkg/math/acosh.go
@@ -0,0 +1,59 @@
+// 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 math
+
+
+// The original C code, the long comment, and the constants
+// below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
+// and came with this notice.  The go code is a simplified
+// version of the original C.
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+//
+//
+// __ieee754_acosh(x)
+// Method :
+//	Based on
+//	        acosh(x) = log [ x + sqrt(x*x-1) ]
+//	we have
+//	        acosh(x) := log(x)+ln2,	if x is large; else
+//	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+//	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+//
+// Special cases:
+//	acosh(x) is NaN with signal if x<1.
+//	acosh(NaN) is NaN without signal.
+//
+
+// Acosh(x) calculates the inverse hyperbolic cosine of x.
+//
+// Special cases are:
+//	Acosh(x) = NaN if x < 1
+//	Acosh(NaN) = NaN
+func Acosh(x float64) float64 {
+	const (
+		Ln2   = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
+		Large = 1 << 28                    // 2^28
+	)
+	switch {
+	case x < 1 || IsNaN(x):
+		return NaN()
+	case x == 1:
+		return 0
+	case x >= Large:
+		return Log(x) + Ln2 // x > 2^28
+	case x > 2:
+		return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2^28 > x > 2
+	}
+	t := x - 1
+	return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
+}