Adding upstream version 1.20.14.upstream/1.20.14upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 129 insertions, 0 deletions

diff --git a/src/math/log.go b/src/math/log.go
new file mode 100644
index 0000000..695a545
--- /dev/null
+++ b/src/math/log.go
@@ -0,0 +1,129 @@
+// Copyright 2009 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
+
+/*
+	Floating-point logarithm.
+*/
+
+// The original C code, the long comment, and the constants
+// below are from FreeBSD's /usr/src/lib/msun/src/e_log.c
+// and came with this notice. The go code is a simpler
+// 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_log(x)
+// Return the logarithm of x
+//
+// Method :
+//   1. Argument Reduction: find k and f such that
+//			x = 2**k * (1+f),
+//	   where  sqrt(2)/2 < 1+f < sqrt(2) .
+//
+//   2. Approximation of log(1+f).
+//	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+//		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+//	     	 = 2s + s*R
+//      We use a special Reme algorithm on [0,0.1716] to generate
+//	a polynomial of degree 14 to approximate R.  The maximum error
+//	of this polynomial approximation is bounded by 2**-58.45. In
+//	other words,
+//		        2      4      6      8      10      12      14
+//	    R(z) ~ L1*s +L2*s +L3*s +L4*s +L5*s  +L6*s  +L7*s
+//	(the values of L1 to L7 are listed in the program) and
+//	    |      2          14          |     -58.45
+//	    | L1*s +...+L7*s    -  R(z) | <= 2
+//	    |                             |
+//	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+//	In order to guarantee error in log below 1ulp, we compute log by
+//		log(1+f) = f - s*(f - R)		(if f is not too large)
+//		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
+//
+//	3. Finally,  log(x) = k*Ln2 + log(1+f).
+//			    = k*Ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*Ln2_lo)))
+//	   Here Ln2 is split into two floating point number:
+//			Ln2_hi + Ln2_lo,
+//	   where n*Ln2_hi is always exact for |n| < 2000.
+//
+// Special cases:
+//	log(x) is NaN with signal if x < 0 (including -INF) ;
+//	log(+INF) is +INF; log(0) is -INF with signal;
+//	log(NaN) is that NaN with no signal.
+//
+// Accuracy:
+//	according to an error analysis, the error is always less than
+//	1 ulp (unit in the last place).
+//
+// Constants:
+// The hexadecimal values are the intended ones for the following
+// constants. The decimal values may be used, provided that the
+// compiler will convert from decimal to binary accurately enough
+// to produce the hexadecimal values shown.
+
+// Log returns the natural logarithm of x.
+//
+// Special cases are:
+//
+//	Log(+Inf) = +Inf
+//	Log(0) = -Inf
+//	Log(x < 0) = NaN
+//	Log(NaN) = NaN
+func Log(x float64) float64 {
+	if haveArchLog {
+		return archLog(x)
+	}
+	return log(x)
+}
+
+func log(x float64) float64 {
+	const (
+		Ln2Hi = 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
+		Ln2Lo = 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
+		L1    = 6.666666666666735130e-01   /* 3FE55555 55555593 */
+		L2    = 3.999999999940941908e-01   /* 3FD99999 9997FA04 */
+		L3    = 2.857142874366239149e-01   /* 3FD24924 94229359 */
+		L4    = 2.222219843214978396e-01   /* 3FCC71C5 1D8E78AF */
+		L5    = 1.818357216161805012e-01   /* 3FC74664 96CB03DE */
+		L6    = 1.531383769920937332e-01   /* 3FC39A09 D078C69F */
+		L7    = 1.479819860511658591e-01   /* 3FC2F112 DF3E5244 */
+	)
+
+	// special cases
+	switch {
+	case IsNaN(x) || IsInf(x, 1):
+		return x
+	case x < 0:
+		return NaN()
+	case x == 0:
+		return Inf(-1)
+	}
+
+	// reduce
+	f1, ki := Frexp(x)
+	if f1 < Sqrt2/2 {
+		f1 *= 2
+		ki--
+	}
+	f := f1 - 1
+	k := float64(ki)
+
+	// compute
+	s := f / (2 + f)
+	s2 := s * s
+	s4 := s2 * s2
+	t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))
+	t2 := s4 * (L2 + s4*(L4+s4*L6))
+	R := t1 + t2
+	hfsq := 0.5 * f * f
+	return k*Ln2Hi - ((hfsq - (s*(hfsq+R) + k*Ln2Lo)) - f)
+}