1 /* e_logf.c -- float version of e_log.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include "math.h" 17 #include "math_private.h" 18 19 static const float 20 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 21 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 22 two25 = 3.355443200e+07, /* 0x4c000000 */ 23 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ 24 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ 25 Lg3 = 2.8571429849e-01, /* 3E924925 */ 26 Lg4 = 2.2222198546e-01, /* 3E638E29 */ 27 Lg5 = 1.8183572590e-01, /* 3E3A3325 */ 28 Lg6 = 1.5313838422e-01, /* 3E1CD04F */ 29 Lg7 = 1.4798198640e-01; /* 3E178897 */ 30 31 static const float zero = 0.0; 32 33 float 34 logf(float x) 35 { 36 float hfsq,f,s,z,R,w,t1,t2,dk; 37 int32_t k,ix,i,j; 38 39 GET_FLOAT_WORD(ix,x); 40 41 k=0; 42 if (ix < 0x00800000) { /* x < 2**-126 */ 43 if ((ix&0x7fffffff)==0) 44 return -two25/zero; /* log(+-0)=-inf */ 45 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ 46 k -= 25; x *= two25; /* subnormal number, scale up x */ 47 GET_FLOAT_WORD(ix,x); 48 } 49 if (ix >= 0x7f800000) return x+x; 50 k += (ix>>23)-127; 51 ix &= 0x007fffff; 52 i = (ix+(0x95f64<<3))&0x800000; 53 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ 54 k += (i>>23); 55 f = x-(float)1.0; 56 if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ 57 if(f==zero) {if(k==0) return zero; else {dk=(float)k; 58 return dk*ln2_hi+dk*ln2_lo;}} 59 R = f*f*((float)0.5-(float)0.33333333333333333*f); 60 if(k==0) return f-R; else {dk=(float)k; 61 return dk*ln2_hi-((R-dk*ln2_lo)-f);} 62 } 63 s = f/((float)2.0+f); 64 dk = (float)k; 65 z = s*s; 66 i = ix-(0x6147a<<3); 67 w = z*z; 68 j = (0x6b851<<3)-ix; 69 t1= w*(Lg2+w*(Lg4+w*Lg6)); 70 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 71 i |= j; 72 R = t2+t1; 73 if(i>0) { 74 hfsq=(float)0.5*f*f; 75 if(k==0) return f-(hfsq-s*(hfsq+R)); else 76 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); 77 } else { 78 if(k==0) return f-s*(f-R); else 79 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); 80 } 81 } 82