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Diffstat (limited to 'src/MSL_C.PPCEABI.bare.H/e_log.c')
| -rw-r--r-- | src/MSL_C.PPCEABI.bare.H/e_log.c | 158 |
1 files changed, 158 insertions, 0 deletions
diff --git a/src/MSL_C.PPCEABI.bare.H/e_log.c b/src/MSL_C.PPCEABI.bare.H/e_log.c new file mode 100644 index 0000000..abeb901 --- /dev/null +++ b/src/MSL_C.PPCEABI.bare.H/e_log.c @@ -0,0 +1,158 @@ +/* @(#)e_log.c 1.2 95/01/04 */ +/* + * ==================================================== + * 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 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 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*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. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif + ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ + ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ + 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 */ + +static double zero = 0.0; + +#ifdef __STDC__ +double __ieee754_log(double x) +#else +double __ieee754_log(x) +double x; +#endif +{ + double hfsq, f, s, z, R, w, t1, t2, dk; + _INT32 k, hx, i, j; + _UINT32 lx; + + hx = __HI(x); /* high word of x */ + lx = __LO(x); /* low word of x */ + + k = 0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx & 0x7fffffff) | lx) == 0) + return -two54 / zero; /* log(+-0)=-inf */ + if (hx < 0) { +#ifdef __STDC__ + errno = EDOM; +#endif + return (x - x) / zero; /* log(-#) = NaN */ + } + k -= 54; + x *= two54; /* subnormal number, scale up x */ + hx = __HI(x); /* high word of x */ + } + if (hx >= 0x7ff00000) + return x + x; + k += (hx >> 20) - 1023; + hx &= 0x000fffff; + i = (hx + 0x95f64) & 0x100000; + __HI(x) = hx | (i ^ 0x3ff00000); /* normalize x or x/2 */ + k += (i >> 20); + f = x - 1.0; + if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */ + if (f == zero) + if (k == 0) + return zero; + else { + dk = (double)k; + return dk * ln2_hi + dk * ln2_lo; + } + R = f * f * (0.5 - 0.33333333333333333 * f); + if (k == 0) + return f - R; + else { + dk = (double)k; + return dk * ln2_hi - ((R - dk * ln2_lo) - 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))); + i |= j; + R = t2 + t1; + if (i > 0) { + hfsq = 0.5 * f * f; + if (k == 0) + return f - (hfsq - s * (hfsq + R)); + else + return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - f); + } else { + if (k == 0) + return f - s * (f - R); + else + return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f); + } +} |