Date: Mon, 22 Oct 2012 13:20:31 +0000 (UTC) From: Warner Losh <imp@FreeBSD.org> To: src-committers@freebsd.org, svn-src-all@freebsd.org, svn-src-head@freebsd.org Subject: svn commit: r241886 - head/lib/msun/src Message-ID: <201210221320.q9MDKVTQ018108@svn.freebsd.org>
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Author: imp Date: Mon Oct 22 13:20:31 2012 New Revision: 241886 URL: http://svn.freebsd.org/changeset/base/241886 Log: Revert r241755 Modified: head/lib/msun/src/e_logf.c Modified: head/lib/msun/src/e_logf.c ============================================================================== --- head/lib/msun/src/e_logf.c Mon Oct 22 13:06:09 2012 (r241885) +++ head/lib/msun/src/e_logf.c Mon Oct 22 13:20:31 2012 (r241886) @@ -19,57 +19,6 @@ __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" -/* __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 8 to approximate R The maximum error - * of this polynomial approximation is bounded by 2**-34.24. In - * other words, - * 2 4 6 8 - * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s - * (the values of Lg1 to Lg7 are listed in the program) - * and - * | 2 8 | -34.24 - * | Lg1*s +...+Lg4*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. - */ - static const float ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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