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- /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
- /*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
- */
- /*
- * ====================================================
- * 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.
- * ====================================================
- */
- #include "libm.h"
- static const float
- ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
- ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
- two25 = 3.355443200e+07, /* 0x4c000000 */
- Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
- Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
- Lp3 = 2.8571429849e-01, /* 3E924925 */
- Lp4 = 2.2222198546e-01, /* 3E638E29 */
- Lp5 = 1.8183572590e-01, /* 3E3A3325 */
- Lp6 = 1.5313838422e-01, /* 3E1CD04F */
- Lp7 = 1.4798198640e-01; /* 3E178897 */
- float log1pf(float x)
- {
- float hfsq,f,c,s,z,R,u;
- int32_t k,hx,hu,ax;
- GET_FLOAT_WORD(hx, x);
- ax = hx & 0x7fffffff;
- k = 1;
- if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */
- if (ax >= 0x3f800000) { /* x <= -1.0 */
- if (x == -1.0f)
- return -two25/0.0f; /* log1p(-1)=+inf */
- return (x-x)/(x-x); /* log1p(x<-1)=NaN */
- }
- if (ax < 0x38000000) { /* |x| < 2**-15 */
- /* if 0x1p-126 <= |x| < 0x1p-24, avoid raising underflow */
- if (ax < 0x33800000 && ax >= 0x00800000)
- return x;
- #if FLT_EVAL_METHOD != 0
- FORCE_EVAL(x*x);
- #endif
- return x - x*x*0.5f;
- }
- if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
- k = 0;
- f = x;
- hu = 1;
- }
- }
- if (hx >= 0x7f800000)
- return x+x;
- if (k != 0) {
- if (hx < 0x5a000000) {
- u = 1 + x;
- GET_FLOAT_WORD(hu, u);
- k = (hu>>23) - 127;
- /* correction term */
- c = k > 0 ? 1.0f-(u-x) : x-(u-1.0f);
- c /= u;
- } else {
- u = x;
- GET_FLOAT_WORD(hu,u);
- k = (hu>>23) - 127;
- c = 0;
- }
- hu &= 0x007fffff;
- /*
- * The approximation to sqrt(2) used in thresholds is not
- * critical. However, the ones used above must give less
- * strict bounds than the one here so that the k==0 case is
- * never reached from here, since here we have committed to
- * using the correction term but don't use it if k==0.
- */
- if (hu < 0x3504f4) { /* u < sqrt(2) */
- SET_FLOAT_WORD(u, hu|0x3f800000); /* normalize u */
- } else {
- k += 1;
- SET_FLOAT_WORD(u, hu|0x3f000000); /* normalize u/2 */
- hu = (0x00800000-hu)>>2;
- }
- f = u - 1.0f;
- }
- hfsq = 0.5f * f * f;
- if (hu == 0) { /* |f| < 2**-20 */
- if (f == 0.0f) {
- if (k == 0)
- return 0.0f;
- c += k*ln2_lo;
- return k*ln2_hi+c;
- }
- R = hfsq*(1.0f - 0.66666666666666666f * f);
- if (k == 0)
- return f - R;
- return k*ln2_hi - ((R-(k*ln2_lo+c))-f);
- }
- s = f/(2.0f + 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));
- return k*ln2_hi - ((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
- }
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