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 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ 24 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ 25 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ 26 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ 27 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ 28 29 static const float zero = 0.0; 30 static volatile float vzero = 0.0; 31 32 float 33 logf(float x) 34 { 35 float hfsq,f,s,z,R,w,t1,t2,dk; 36 int32_t k,ix,i,j; 37 38 GET_FLOAT_WORD(ix,x); 39 40 k=0; 41 if (ix < 0x00800000) { /* x < 2**-126 */ 42 if ((ix&0x7fffffff)==0) 43 return -two25/vzero; /* log(+-0)=-inf */ 44 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ 45 k -= 25; x *= two25; /* subnormal number, scale up x */ 46 GET_FLOAT_WORD(ix,x); 47 } 48 if (ix >= 0x7f800000) return x+x; 49 k += (ix>>23)-127; 50 ix &= 0x007fffff; 51 i = (ix+(0x95f64<<3))&0x800000; 52 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ 53 k += (i>>23); 54 f = x-(float)1.0; 55 if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */ 56 if(f==zero) { 57 if(k==0) { 58 return zero; 59 } else { 60 dk=(float)k; 61 return dk*ln2_hi+dk*ln2_lo; 62 } 63 } 64 R = f*f*((float)0.5-(float)0.33333333333333333*f); 65 if(k==0) return f-R; else {dk=(float)k; 66 return dk*ln2_hi-((R-dk*ln2_lo)-f);} 67 } 68 s = f/((float)2.0+f); 69 dk = (float)k; 70 z = s*s; 71 i = ix-(0x6147a<<3); 72 w = z*z; 73 j = (0x6b851<<3)-ix; 74 t1= w*(Lg2+w*Lg4); 75 t2= z*(Lg1+w*Lg3); 76 i |= j; 77 R = t2+t1; 78 if(i>0) { 79 hfsq=(float)0.5*f*f; 80 if(k==0) return f-(hfsq-s*(hfsq+R)); else 81 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); 82 } else { 83 if(k==0) return f-s*(f-R); else 84 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); 85 } 86 } 87