diff options
Diffstat (limited to 'libm/e_log.c')
| -rw-r--r-- | libm/e_log.c | 38 |
1 files changed, 19 insertions, 19 deletions
diff --git a/libm/e_log.c b/libm/e_log.c index 9325903e0..0464014cb 100644 --- a/libm/e_log.c +++ b/libm/e_log.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -17,17 +17,17 @@ static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; /* __ieee754_log(x) * Return the logrithm of x * - * Method : - * 1. Argument Reduction: find k and f such that - * x = 2^k * (1+f), + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), * where sqrt(2)/2 < 1+f < sqrt(2) . * * 2. Approximation of log(1+f). * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) * = 2s + 2/3 s**3 + 2/5 s**5 + ....., * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error * of this polynomial approximation is bounded by 2**-58.45. In * other words, * 2 4 6 8 10 12 14 @@ -35,22 +35,22 @@ static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; * (the values of Lg1 to Lg7 are listed in the program) * and * | 2 14 | -58.45 - * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 * | | * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. * In order to guarantee error in log below 1ulp, we compute log * by * log(1+f) = f - s*(f - R) (if f is not too large) * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) - * - * 3. Finally, log(x) = k*ln2 + log(1+f). + * + * 3. Finally, log(x) = k*ln2 + log(1+f). * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: + * Here ln2 is split into two floating point number: * ln2_hi + ln2_lo, * where n*ln2_hi is always exact for |n| < 2000. * * Special cases: - * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(x) is NaN with signal if x < 0 (including -INF) ; * log(+INF) is +INF; log(0) is -INF with signal; * log(NaN) is that NaN with no signal. * @@ -59,9 +59,9 @@ static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; * 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 + * 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. */ @@ -105,12 +105,12 @@ static double zero = 0.0; k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) + if (((hx&0x7fffffff)|lx)==0) return -two54/zero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ k -= 54; x *= two54; /* subnormal number, scale up x */ GET_HIGH_WORD(hx,x); - } + } if (hx >= 0x7ff00000) return x+x; k += (hx>>20)-1023; hx &= 0x000fffff; @@ -126,14 +126,14 @@ static double zero = 0.0; if(k==0) return f-R; else {dk=(double)k; return dk*ln2_hi-((R-dk*ln2_lo)-f);} } - s = f/(2.0+f); + s = f/(2.0+f); dk = (double)k; z = s*s; i = hx-0x6147a; w = z*z; j = 0x6b851-hx; - t1= w*(Lg2+w*(Lg4+w*Lg6)); - t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); i |= j; R = t2+t1; if(i>0) { |