diff options
Diffstat (limited to 'src/math/log1pf.c')
| -rw-r--r-- | src/math/log1pf.c | 125 |
1 files changed, 45 insertions, 80 deletions
diff --git a/src/math/log1pf.c b/src/math/log1pf.c index e6940d29..23985c35 100644 --- a/src/math/log1pf.c +++ b/src/math/log1pf.c @@ -1,8 +1,5 @@ /* 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. * @@ -18,95 +15,63 @@ 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 */ +/* |(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 -two25/0.0f; /* 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 */ - /* 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 (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) { - 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; + } 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 == 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); + /* 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; } |