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
https://golang.org/cl/195052
diff --git a/src/pkg/math/asinh.go b/src/pkg/math/asinh.go
new file mode 100644
index 0000000..b38bbd7
--- /dev/null
+++ b/src/pkg/math/asinh.go
@@ -0,0 +1,72 @@
+// 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/s_asinh.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.
+// ====================================================
+//
+//
+// asinh(x)
+// Method :
+// Based on
+// asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
+// we have
+// asinh(x) := x if 1+x*x=1,
+// := sign(x)*(log(x)+ln2)) for large |x|, else
+// := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
+// := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
+//
+
+// Asinh(x) calculates the inverse hyperbolic sine of x.
+//
+// Special cases are:
+// Asinh(+Inf) = +Inf
+// Asinh(-Inf) = -Inf
+// Asinh(NaN) = NaN
+func Asinh(x float64) float64 {
+ const (
+ Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
+ NearZero = 1.0 / (1 << 28) // 2^-28
+ Large = 1 << 28 // 2^28
+ )
+ // TODO(rsc): Remove manual inlining of IsNaN, IsInf
+ // when compiler does it for us
+ // special cases
+ if x != x || x > MaxFloat64 || x < -MaxFloat64 { // IsNaN(x) || IsInf(x, 0)
+ return x
+ }
+ sign := false
+ if x < 0 {
+ x = -x
+ sign = true
+ }
+ var temp float64
+ switch {
+ case x > Large:
+ temp = Log(x) + Ln2 // |x| > 2^28
+ case x > 2:
+ temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2^28 > |x| > 2.0
+ case x < NearZero:
+ temp = x // |x| < 2^-28
+ default:
+ temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2^-28
+ }
+ if sign {
+ temp = -temp
+ }
+ return temp
+}
