golang log 代码
文件路径：/src/math/log.go
/ 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)
}