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/* e_logf.c -- float version of e_log.c. |
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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 "math.h" |
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#include "math_private.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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Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ |
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Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ |
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Lg3 = 2.8571429849e-01, /* 3E924925 */ |
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Lg4 = 2.2222198546e-01, /* 3E638E29 */ |
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Lg5 = 1.8183572590e-01, /* 3E3A3325 */ |
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Lg6 = 1.5313838422e-01, /* 3E1CD04F */ |
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Lg7 = 1.4798198640e-01; /* 3E178897 */ |
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static const float zero = 0.0; |
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float |
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logf(float x) |
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{ |
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float hfsq,f,s,z,R,w,t1,t2,dk; |
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int32_t k,ix,i,j; |
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GET_FLOAT_WORD(ix,x); |
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k=0; |
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✗✓ |
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if (ix < 0x00800000) { /* x < 2**-126 */ |
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if ((ix&0x7fffffff)==0) |
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return -two25/zero; /* log(+-0)=-inf */ |
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if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ |
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k -= 25; x *= two25; /* subnormal number, scale up x */ |
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GET_FLOAT_WORD(ix,x); |
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} |
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✗✓ |
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if (ix >= 0x7f800000) return x+x; |
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k += (ix>>23)-127; |
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ix &= 0x007fffff; |
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i = (ix+(0x95f64<<3))&0x800000; |
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SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ |
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k += (i>>23); |
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f = x-(float)1.0; |
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✓✗ |
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if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ |
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✓✗✗✓
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if(f==zero) {if(k==0) return zero; else {dk=(float)k; |
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return dk*ln2_hi+dk*ln2_lo;}} |
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R = f*f*((float)0.5-(float)0.33333333333333333*f); |
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if(k==0) return f-R; else {dk=(float)k; |
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return dk*ln2_hi-((R-dk*ln2_lo)-f);} |
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} |
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s = f/((float)2.0+f); |
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dk = (float)k; |
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z = s*s; |
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i = ix-(0x6147a<<3); |
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w = z*z; |
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j = (0x6b851<<3)-ix; |
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t1= w*(Lg2+w*(Lg4+w*Lg6)); |
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t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); |
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i |= j; |
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R = t2+t1; |
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if(i>0) { |
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hfsq=(float)0.5*f*f; |
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if(k==0) return f-(hfsq-s*(hfsq+R)); else |
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return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); |
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} else { |
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if(k==0) return f-s*(f-R); else |
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return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); |
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} |
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} |
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DEF_STD(logf); |