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Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/exp.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/exp.c | 134 |
1 files changed, 0 insertions, 134 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/exp.c b/lib/mlibc/options/ansi/musl-generic-math/exp.c deleted file mode 100644 index 9ea672f..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/exp.c +++ /dev/null @@ -1,134 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_exp.c */ -/* - * ==================================================== - * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* exp(x) - * Returns the exponential of x. - * - * Method - * 1. Argument reduction: - * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. - * Given x, find r and integer k such that - * - * x = k*ln2 + r, |r| <= 0.5*ln2. - * - * Here r will be represented as r = hi-lo for better - * accuracy. - * - * 2. Approximation of exp(r) by a special rational function on - * the interval [0,0.34658]: - * Write - * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... - * We use a special Remez algorithm on [0,0.34658] to generate - * a polynomial of degree 5 to approximate R. The maximum error - * of this polynomial approximation is bounded by 2**-59. In - * other words, - * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 - * (where z=r*r, and the values of P1 to P5 are listed below) - * and - * | 5 | -59 - * | 2.0+P1*z+...+P5*z - R(z) | <= 2 - * | | - * The computation of exp(r) thus becomes - * 2*r - * exp(r) = 1 + ---------- - * R(r) - r - * r*c(r) - * = 1 + r + ----------- (for better accuracy) - * 2 - c(r) - * where - * 2 4 10 - * c(r) = r - (P1*r + P2*r + ... + P5*r ). - * - * 3. Scale back to obtain exp(x): - * From step 1, we have - * exp(x) = 2^k * exp(r) - * - * Special cases: - * exp(INF) is INF, exp(NaN) is NaN; - * exp(-INF) is 0, and - * for finite argument, only exp(0)=1 is exact. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * Misc. info. - * For IEEE double - * if x > 709.782712893383973096 then exp(x) overflows - * if x < -745.133219101941108420 then exp(x) underflows - */ - -#include "libm.h" - -static const double -half[2] = {0.5,-0.5}, -ln2hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ -ln2lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ -invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ -P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ -P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ -P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ -P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ -P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ - -double exp(double x) -{ - double_t hi, lo, c, xx, y; - int k, sign; - uint32_t hx; - - GET_HIGH_WORD(hx, x); - sign = hx>>31; - hx &= 0x7fffffff; /* high word of |x| */ - - /* special cases */ - if (hx >= 0x4086232b) { /* if |x| >= 708.39... */ - if (isnan(x)) - return x; - if (x > 709.782712893383973096) { - /* overflow if x!=inf */ - x *= 0x1p1023; - return x; - } - if (x < -708.39641853226410622) { - /* underflow if x!=-inf */ - FORCE_EVAL((float)(-0x1p-149/x)); - if (x < -745.13321910194110842) - return 0; - } - } - - /* argument reduction */ - if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ - if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */ - k = (int)(invln2*x + half[sign]); - else - k = 1 - sign - sign; - hi = x - k*ln2hi; /* k*ln2hi is exact here */ - lo = k*ln2lo; - x = hi - lo; - } else if (hx > 0x3e300000) { /* if |x| > 2**-28 */ - k = 0; - hi = x; - lo = 0; - } else { - /* inexact if x!=0 */ - FORCE_EVAL(0x1p1023 + x); - return 1 + x; - } - - /* x is now in primary range */ - xx = x*x; - c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5)))); - y = 1 + (x*c/(2-c) - lo + hi); - if (k == 0) - return y; - return scalbn(y, k); -} |