1 /* s_log1pf.c -- float version of s_log1p.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 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ 28 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ 29 Lp3 = 2.8571429849e-01, /* 3E924925 */ 30 Lp4 = 2.2222198546e-01, /* 3E638E29 */ 31 Lp5 = 1.8183572590e-01, /* 3E3A3325 */ 32 Lp6 = 1.5313838422e-01, /* 3E1CD04F */ 33 Lp7 = 1.4798198640e-01; /* 3E178897 */ 34 35 static const float zero = 0.0; 36 37 float 38 log1pf(float x) 39 { 40 float hfsq,f,c,s,z,R,u; 41 int32_t k,hx,hu,ax; 42 43 GET_FLOAT_WORD(hx,x); 44 ax = hx&0x7fffffff; 45 46 k = 1; 47 if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ 48 if(ax>=0x3f800000) { /* x <= -1.0 */ 49 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ 50 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 51 } 52 if(ax<0x31000000) { /* |x| < 2**-29 */ 53 if(two25+x>zero /* raise inexact */ 54 &&ax<0x24800000) /* |x| < 2**-54 */ 55 return x; 56 else 57 return x - x*x*(float)0.5; 58 } 59 if(hx>0||hx<=((int32_t)0xbe95f619)) { 60 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ 61 } 62 if (hx >= 0x7f800000) return x+x; 63 if(k!=0) { 64 if(hx<0x5a000000) { 65 *(volatile float *)&u = (float)1.0+x; 66 GET_FLOAT_WORD(hu,u); 67 k = (hu>>23)-127; 68 /* correction term */ 69 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 70 c /= u; 71 } else { 72 u = x; 73 GET_FLOAT_WORD(hu,u); 74 k = (hu>>23)-127; 75 c = 0; 76 } 77 hu &= 0x007fffff; 78 /* 79 * The approximation to sqrt(2) used in thresholds is not 80 * critical. However, the ones used above must give less 81 * strict bounds than the one here so that the k==0 case is 82 * never reached from here, since here we have committed to 83 * using the correction term but don't use it if k==0. 84 */ 85 if(hu<0x3504f4) { /* u < sqrt(2) */ 86 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 87 } else { 88 k += 1; 89 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 90 hu = (0x00800000-hu)>>2; 91 } 92 f = u-(float)1.0; 93 } 94 hfsq=(float)0.5*f*f; 95 if(hu==0) { /* |f| < 2**-20 */ 96 if(f==zero) if(k==0) return zero; 97 else {c += k*ln2_lo; return k*ln2_hi+c;} 98 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 99 if(k==0) return f-R; else 100 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 101 } 102 s = f/((float)2.0+f); 103 z = s*s; 104 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 105 if(k==0) return f-(hfsq-s*(hfsq+R)); else 106 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 107 } 108