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Diffstat (limited to 'src/pkg/math/log.go')
-rw-r--r-- | src/pkg/math/log.go | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/src/pkg/math/log.go b/src/pkg/math/log.go new file mode 100644 index 000000000..b24175b63 --- /dev/null +++ b/src/pkg/math/log.go @@ -0,0 +1,131 @@ +// 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 + +import "math" + +// 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 logrithm 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 { + 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); +} + +// Log10 returns the decimal logarthm of x. +// The special cases are the same as for Log. +func Log10(x float64) float64 { + if x <= 0 { + return NaN(); + } + return Log(x) * (1/Ln10); +} + |