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 #ifndef lint 17 static char rcsid[] = "$FreeBSD$"; 18 #endif 19 20 #include "math.h" 21 #include "math_private.h" 22 23 static const float 24 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 25 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 26 two25 = 3.355443200e+07, /* 0x4c000000 */ 27 Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ 28 Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ 29 Lg3 = 2.8571429849e-01, /* 3E924925 */ 30 Lg4 = 2.2222198546e-01, /* 3E638E29 */ 31 Lg5 = 1.8183572590e-01, /* 3E3A3325 */ 32 Lg6 = 1.5313838422e-01, /* 3E1CD04F */ 33 Lg7 = 1.4798198640e-01; /* 3E178897 */ 34 35 static const float zero = 0.0; 36 37 float 38 __ieee754_logf(float x) 39 { 40 float hfsq,f,s,z,R,w,t1,t2,dk; 41 int32_t k,ix,i,j; 42 43 GET_FLOAT_WORD(ix,x); 44 45 k=0; 46 if (ix < 0x00800000) { /* x < 2**-126 */ 47 if ((ix&0x7fffffff)==0) 48 return -two25/zero; /* log(+-0)=-inf */ 49 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ 50 k -= 25; x *= two25; /* subnormal number, scale up x */ 51 GET_FLOAT_WORD(ix,x); 52 } 53 if (ix >= 0x7f800000) return x+x; 54 k += (ix>>23)-127; 55 ix &= 0x007fffff; 56 i = (ix+(0x95f64<<3))&0x800000; 57 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ 58 k += (i>>23); 59 f = x-(float)1.0; 60 if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ 61 if(f==zero) if(k==0) return zero; else {dk=(float)k; 62 return dk*ln2_hi+dk*ln2_lo;} 63 R = f*f*((float)0.5-(float)0.33333333333333333*f); 64 if(k==0) return f-R; else {dk=(float)k; 65 return dk*ln2_hi-((R-dk*ln2_lo)-f);} 66 } 67 s = f/((float)2.0+f); 68 dk = (float)k; 69 z = s*s; 70 i = ix-(0x6147a<<3); 71 w = z*z; 72 j = (0x6b851<<3)-ix; 73 t1= w*(Lg2+w*(Lg4+w*Lg6)); 74 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 75 i |= j; 76 R = t2+t1; 77 if(i>0) { 78 hfsq=(float)0.5*f*f; 79 if(k==0) return f-(hfsq-s*(hfsq+R)); else 80 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); 81 } else { 82 if(k==0) return f-s*(f-R); else 83 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); 84 } 85 } 86