diff options
Diffstat (limited to 'sysdeps/libm-ieee754/s_log1p.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_log1p.c | 44 |
1 files changed, 24 insertions, 20 deletions
diff --git a/sysdeps/libm-ieee754/s_log1p.c b/sysdeps/libm-ieee754/s_log1p.c index 1e58ccb039..cc380a1091 100644 --- a/sysdeps/libm-ieee754/s_log1p.c +++ b/sysdeps/libm-ieee754/s_log1p.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. * ==================================================== */ @@ -16,9 +16,9 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; /* double log1p(double x) * - * Method : - * 1. Argument Reduction: find k and f such that - * 1+x = 2^k * (1+f), + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), * where sqrt(2)/2 < 1+f < sqrt(2) . * * Note. If k=0, then f=x is exact. However, if k!=0, then f @@ -32,8 +32,8 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) * = 2s + 2/3 s**3 + 2/5 s**5 + ....., * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error * of this polynomial approximation is bounded by 2**-58.45. In * other words, * 2 4 6 8 10 12 14 @@ -41,21 +41,21 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; * (the values of Lp1 to Lp7 are listed in the program) * and * | 2 14 | -58.45 - * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 * | | * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. * In order to guarantee error in log below 1ulp, we compute log * by * log1p(f) = f - (hfsq - s*(hfsq+R)). - * - * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: + * Here ln2 is split into two floating point number: * ln2_hi + ln2_lo, * where n*ln2_hi is always exact for |n| < 2000. * * Special cases: - * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(x) is NaN with signal if x < -1 (including -INF) ; * log1p(+INF) is +INF; log1p(-1) is -INF with signal; * log1p(NaN) is that NaN with no signal. * @@ -64,14 +64,14 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 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. * * Note: Assuming log() return accurate answer, the following * algorithm can be used to compute log1p(x) to within a few ULP: - * + * * u = 1+x; * if(u==1.0) return x ; else * return log(u)*(x/(u-1.0)); @@ -132,11 +132,11 @@ static double zero = 0.0; } if(hx>0||hx<=((int32_t)0xbfd2bec3)) { k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ - } + } if (hx >= 0x7ff00000) return x+x; if(k!=0) { if(hx<0x43400000) { - u = 1.0+x; + u = 1.0+x; GET_HIGH_WORD(hu,u); k = (hu>>20)-1023; c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ @@ -151,7 +151,7 @@ static double zero = 0.0; if(hu<0x6a09e) { SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ } else { - k += 1; + k += 1; SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ hu = (0x00100000-hu)>>2; } @@ -159,16 +159,20 @@ static double zero = 0.0; } hfsq=0.5*f*f; if(hu==0) { /* |f| < 2**-20 */ - if(f==zero) if(k==0) return zero; + if(f==zero) if(k==0) return zero; else {c += k*ln2_lo; return k*ln2_hi+c;} R = hfsq*(1.0-0.66666666666666666*f); if(k==0) return f-R; else return k*ln2_hi-((R-(k*ln2_lo+c))-f); } - s = f/(2.0+f); + s = f/(2.0+f); z = s*s; R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); if(k==0) return f-(hfsq-s*(hfsq+R)); else return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); } weak_alias (__log1p, log1p) +#ifdef NO_LONG_DOUBLE +strong_alias (__log1p, __log1pl) +weak_alias (__log1p, log1pl) +#endif |