diff options
| -rw-r--r-- | libm/Makefile.in | 2 | ||||
| -rw-r--r-- | libm/e_log2.c | 130 | ||||
| -rw-r--r-- | libm/math_private.h | 1 |
3 files changed, 132 insertions, 1 deletions
diff --git a/libm/Makefile.in b/libm/Makefile.in index bcee5f35c..01c63d15a 100644 --- a/libm/Makefile.in +++ b/libm/Makefile.in @@ -57,7 +57,7 @@ ifeq ($(DO_C99_MATH),y) libm_CSRC := \ e_acos.c e_acosh.c e_asin.c e_atan2.c e_atanh.c e_cosh.c \ e_exp.c e_fmod.c e_gamma.c e_gamma_r.c e_hypot.c e_j0.c \ - e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c e_log.c e_log10.c \ + e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c e_log.c e_log2.c e_log10.c \ e_pow.c e_remainder.c e_rem_pio2.c e_scalb.c e_sinh.c \ e_sqrt.c k_cos.c k_rem_pio2.c k_sin.c k_standard.c k_tan.c \ s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c s_cos.c \ diff --git a/libm/e_log2.c b/libm/e_log2.c new file mode 100644 index 000000000..894a96df0 --- /dev/null +++ b/libm/e_log2.c @@ -0,0 +1,130 @@ +/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * 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_log2(x) + * Return the logarithm to base 2 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) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | 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 + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * 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. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2 = 0.69314718055994530942, +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_log2(double x) +#else + double __ieee754_log2(x) + double x; +#endif +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/(x-x); /* log(+-0)=-inf */ + if (hx<0) return (x-x)/(x-x); /* 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; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + dk = (double) k; + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) return dk; + R = f*f*(0.5-0.33333333333333333*f); + return dk-(R-f)/ln2; + } + s = f/(2.0+f); + 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))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + return dk-((hfsq-(s*(hfsq+R)))-f)/ln2; + } else { + return dk-((s*(f-R))-f)/ln2; + } +} diff --git a/libm/math_private.h b/libm/math_private.h index b0d948c07..f85db12a8 100644 --- a/libm/math_private.h +++ b/libm/math_private.h @@ -158,6 +158,7 @@ extern double __ieee754_sqrt (double) attribute_hidden; extern double __ieee754_acos (double) attribute_hidden; extern double __ieee754_acosh (double) attribute_hidden; extern double __ieee754_log (double) attribute_hidden; +extern double __ieee754_log2 (double) attribute_hidden; extern double __ieee754_atanh (double) attribute_hidden; extern double __ieee754_asin (double) attribute_hidden; extern double __ieee754_atan2 (double,double) attribute_hidden; |