/* 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.
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;
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
+Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
+Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
+Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
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;
+ union {float f; uint32_t i;} u = {x};
+ float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
+ uint32_t ix,iu;
+ int k;
+ ix = u.i;
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 (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */
+ if (ix >= 0xbf800000) { /* x <= -1.0 */
+ if (x == -1)
+ return x/0.0f; /* log1p(-1)=+inf */
+ return (x-x)/0.0f; /* 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 (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */
+ /* underflow if subnormal */
+ if ((ix&0x7f800000) == 0)
+ FORCE_EVAL(x*x);
+ return x;
}
- if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+ if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
k = 0;
+ c = 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;
+ } else if (ix >= 0x7f800000)
+ return x;
+ if (k) {
+ u.f = 1 + x;
+ iu = u.i;
+ iu += 0x3f800000 - 0x3f3504f3;
+ k = (int)(iu>>23) - 0x7f;
+ /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+ if (k < 25) {
+ c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
+ c /= u.f;
+ } else
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);
+ /* reduce u into [sqrt(2)/2, sqrt(2)] */
+ iu = (iu&0x007fffff) + 0x3f3504f3;
+ u.i = iu;
+ f = u.f - 1;
}
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);
+ w = z*z;
+ t1= w*(Lg2+w*Lg4);
+ t2= z*(Lg1+w*Lg3);
+ R = t2 + t1;
+ hfsq = 0.5f*f*f;
+ dk = k;
+ return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
}
projects / musl / blobdiff