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 #include <float.h> 17 18 #include "math.h" 19 #include "math_private.h" 20 21 static const float 22 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 23 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 24 two25 = 3.355443200e+07, /* 0x4c000000 */ 25 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ 26 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ 27 Lp3 = 2.8571429849e-01, /* 3E924925 */ 28 Lp4 = 2.2222198546e-01, /* 3E638E29 */ 29 Lp5 = 1.8183572590e-01, /* 3E3A3325 */ 30 Lp6 = 1.5313838422e-01, /* 3E1CD04F */ 31 Lp7 = 1.4798198640e-01; /* 3E178897 */ 32 33 static const float zero = 0.0; 34 static volatile float vzero = 0.0; 35 36 float 37 log1pf(float x) 38 { 39 float hfsq,f,c,s,z,R,u; 40 int32_t k,hx,hu,ax; 41 42 GET_FLOAT_WORD(hx,x); 43 ax = hx&0x7fffffff; 44 45 k = 1; 46 if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ 47 if(ax>=0x3f800000) { /* x <= -1.0 */ 48 if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */ 49 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 50 } 51 if(ax<0x38000000) { /* |x| < 2**-15 */ 52 if(two25+x>zero /* raise inexact */ 53 &&ax<0x33800000) /* |x| < 2**-24 */ 54 return x; 55 else 56 return x - x*x*(float)0.5; 57 } 58 if(hx>0||hx<=((int32_t)0xbe95f619)) { 59 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ 60 } 61 if (hx >= 0x7f800000) return x+x; 62 if(k!=0) { 63 if(hx<0x5a000000) { 64 STRICT_ASSIGN(float,u,(float)1.0+x); 65 GET_FLOAT_WORD(hu,u); 66 k = (hu>>23)-127; 67 /* correction term */ 68 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 69 c /= u; 70 } else { 71 u = x; 72 GET_FLOAT_WORD(hu,u); 73 k = (hu>>23)-127; 74 c = 0; 75 } 76 hu &= 0x007fffff; 77 /* 78 * The approximation to sqrt(2) used in thresholds is not 79 * critical. However, the ones used above must give less 80 * strict bounds than the one here so that the k==0 case is 81 * never reached from here, since here we have committed to 82 * using the correction term but don't use it if k==0. 83 */ 84 if(hu<0x3504f4) { /* u < sqrt(2) */ 85 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 86 } else { 87 k += 1; 88 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 89 hu = (0x00800000-hu)>>2; 90 } 91 f = u-(float)1.0; 92 } 93 hfsq=(float)0.5*f*f; 94 if(hu==0) { /* |f| < 2**-20 */ 95 if(f==zero) { 96 if(k==0) { 97 return zero; 98 } else { 99 c += k*ln2_lo; 100 return k*ln2_hi+c; 101 } 102 } 103 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 104 if(k==0) return f-R; else 105 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 106 } 107 s = f/((float)2.0+f); 108 z = s*s; 109 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 110 if(k==0) return f-(hfsq-s*(hfsq+R)); else 111 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 112 } 113