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Diffstat (limited to 'src/pkg/math/log.go')
| -rw-r--r-- | src/pkg/math/log.go | 123 |
1 files changed, 0 insertions, 123 deletions
diff --git a/src/pkg/math/log.go b/src/pkg/math/log.go deleted file mode 100644 index a786c8ce3..000000000 --- a/src/pkg/math/log.go +++ /dev/null @@ -1,123 +0,0 @@ -// 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 { - 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 */ - ) - - // TODO(rsc): Remove manual inlining of IsNaN, IsInf - // when compiler does it for us - // special cases - switch { - case x != x || x > MaxFloat64: // 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) -} |