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Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_log1p.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_log1p.c | 195 |
1 files changed, 0 insertions, 195 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_log1p.c b/sysdeps/ieee754/dbl-64/s_log1p.c deleted file mode 100644 index 340f6377f7..0000000000 --- a/sysdeps/ieee754/dbl-64/s_log1p.c +++ /dev/null @@ -1,195 +0,0 @@ -/* @(#)s_log1p.c 5.1 93/09/24 */ -/* - * ==================================================== - * 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. - * ==================================================== - */ -/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, - for performance improvement on pipelined processors. - */ - -/* double log1p(double x) - * - * 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 - * may not be representable exactly. In that case, a correction - * term is need. Let u=1+x rounded. Let c = (1+x)-u, then - * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), - * and add back the correction term c/u. - * (Note: when x > 2**53, one can simply return log(x)) - * - * 2. Approximation of log1p(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) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s - * (the values of Lp1 to Lp7 are listed in the program) - * and - * | 2 14 | -58.45 - * | 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). - * = 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: - * 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. - * - * 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. - * - * 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)); - * - * See HP-15C Advanced Functions Handbook, p.193. - */ - -#include <float.h> -#include <math.h> -#include <math_private.h> - -static const double - ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ - ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ - two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ - Lp[] = { 0.0, 6.666666666666735130e-01, /* 3FE55555 55555593 */ - 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ - 2.857142874366239149e-01, /* 3FD24924 94229359 */ - 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ - 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ - 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ - 1.479819860511658591e-01 }; /* 3FC2F112 DF3E5244 */ - -static const double zero = 0.0; - -double -__log1p (double x) -{ - double hfsq, f, c, s, z, R, u, z2, z4, z6, R1, R2, R3, R4; - int32_t k, hx, hu, ax; - - GET_HIGH_WORD (hx, x); - ax = hx & 0x7fffffff; - - k = 1; - if (hx < 0x3FDA827A) /* x < 0.41422 */ - { - if (__glibc_unlikely (ax >= 0x3ff00000)) /* x <= -1.0 */ - { - if (x == -1.0) - return -two54 / zero; /* log1p(-1)=-inf */ - else - return (x - x) / (x - x); /* log1p(x<-1)=NaN */ - } - if (__glibc_unlikely (ax < 0x3e200000)) /* |x| < 2**-29 */ - { - math_force_eval (two54 + x); /* raise inexact */ - if (ax < 0x3c900000) /* |x| < 2**-54 */ - { - math_check_force_underflow (x); - return x; - } - else - return x - x * x * 0.5; - } - if (hx > 0 || hx <= ((int32_t) 0xbfd2bec3)) - { - k = 0; f = x; hu = 1; - } /* -0.2929<x<0.41422 */ - } - else if (__glibc_unlikely (hx >= 0x7ff00000)) - return x + x; - if (k != 0) - { - if (hx < 0x43400000) - { - 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 */ - c /= u; - } - else - { - u = x; - GET_HIGH_WORD (hu, u); - k = (hu >> 20) - 1023; - c = 0; - } - hu &= 0x000fffff; - if (hu < 0x6a09e) - { - SET_HIGH_WORD (u, hu | 0x3ff00000); /* normalize u */ - } - else - { - k += 1; - SET_HIGH_WORD (u, hu | 0x3fe00000); /* normalize u/2 */ - hu = (0x00100000 - hu) >> 2; - } - f = u - 1.0; - } - hfsq = 0.5 * f * f; - if (hu == 0) /* |f| < 2**-20 */ - { - 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); - z = s * s; - R1 = z * Lp[1]; z2 = z * z; - R2 = Lp[2] + z * Lp[3]; z4 = z2 * z2; - R3 = Lp[4] + z * Lp[5]; z6 = z4 * z2; - R4 = Lp[6] + z * Lp[7]; - R = R1 + z2 * R2 + z4 * R3 + z6 * R4; - if (k == 0) - return f - (hfsq - s * (hfsq + R)); - else - return k * ln2_hi - ((hfsq - (s * (hfsq + R) + (k * ln2_lo + c))) - f); -} |