/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@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.
* ====================================================
*/
#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 */
static const float zero = 0.0;
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/zero; /* log1p(-1)=+inf */
return (x-x)/(x-x); /* log1p(x<-1)=NaN */
}
if (ax < 0x38000000) { /* |x| < 2**-15 */
/* raise inexact */
if (two25 + x > zero && ax < 0x33800000) /* |x| < 2**-24 */
return x;
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) {
STRICT_ASSIGN(float, u, 1.0f + 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 == zero) {
if (k == 0)
return zero;
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);
}
