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https://github.com/fluencelabs/musl
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c599f4f4d7
for these functions f(x)=x for small inputs, because f(0)=0 and f'(0)=1, but for subnormal values they should raise the underflow flag (required by annex F), if they are approximated by a polynomial around 0 then spurious underflow should be avoided (not required by annex F) all these functions should raise inexact flag for small x if x!=0, but it's not required by the standard and it does not seem a worthy goal, so support for it is removed in some cases. raising underflow: - x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0 - x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0 - in case of double subnormal x, store x as float - in case of float subnormal x, store x*x as float
113 lines
2.9 KiB
C
113 lines
2.9 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "libm.h"
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static const float
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ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
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ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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two25 = 3.355443200e+07, /* 0x4c000000 */
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Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
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Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
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Lp3 = 2.8571429849e-01, /* 3E924925 */
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Lp4 = 2.2222198546e-01, /* 3E638E29 */
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Lp5 = 1.8183572590e-01, /* 3E3A3325 */
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Lp6 = 1.5313838422e-01, /* 3E1CD04F */
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Lp7 = 1.4798198640e-01; /* 3E178897 */
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float log1pf(float x)
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{
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float hfsq,f,c,s,z,R,u;
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int32_t k,hx,hu,ax;
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GET_FLOAT_WORD(hx, x);
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ax = hx & 0x7fffffff;
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k = 1;
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if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */
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if (ax >= 0x3f800000) { /* x <= -1.0 */
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if (x == -1.0f)
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return -two25/0.0f; /* log1p(-1)=+inf */
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return (x-x)/(x-x); /* log1p(x<-1)=NaN */
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}
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if (ax < 0x38000000) { /* |x| < 2**-15 */
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/* if 0x1p-126 <= |x| < 0x1p-24, avoid raising underflow */
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if (ax < 0x33800000 && ax >= 0x00800000)
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return x;
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#if FLT_EVAL_METHOD != 0
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FORCE_EVAL(x*x);
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#endif
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return x - x*x*0.5f;
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}
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if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
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k = 0;
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f = x;
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hu = 1;
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}
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}
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if (hx >= 0x7f800000)
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return x+x;
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if (k != 0) {
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if (hx < 0x5a000000) {
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STRICT_ASSIGN(float, u, 1.0f + x);
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GET_FLOAT_WORD(hu, u);
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k = (hu>>23) - 127;
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/* correction term */
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c = k > 0 ? 1.0f-(u-x) : x-(u-1.0f);
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c /= u;
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} else {
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u = x;
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GET_FLOAT_WORD(hu,u);
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k = (hu>>23) - 127;
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c = 0;
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}
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hu &= 0x007fffff;
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/*
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* The approximation to sqrt(2) used in thresholds is not
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* critical. However, the ones used above must give less
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* strict bounds than the one here so that the k==0 case is
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* never reached from here, since here we have committed to
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* using the correction term but don't use it if k==0.
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*/
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if (hu < 0x3504f4) { /* u < sqrt(2) */
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SET_FLOAT_WORD(u, hu|0x3f800000); /* normalize u */
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} else {
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k += 1;
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SET_FLOAT_WORD(u, hu|0x3f000000); /* normalize u/2 */
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hu = (0x00800000-hu)>>2;
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}
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f = u - 1.0f;
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}
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hfsq = 0.5f * f * f;
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if (hu == 0) { /* |f| < 2**-20 */
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if (f == 0.0f) {
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if (k == 0)
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return 0.0f;
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c += k*ln2_lo;
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return k*ln2_hi+c;
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}
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R = hfsq*(1.0f - 0.66666666666666666f * f);
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if (k == 0)
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return f - R;
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return k*ln2_hi - ((R-(k*ln2_lo+c))-f);
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}
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s = f/(2.0f + f);
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z = s*s;
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R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
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if (k == 0)
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return f - (hfsq-s*(hfsq+R));
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return k*ln2_hi - ((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
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}
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