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 <sys/cdefs.h> 17 __FBSDID("$FreeBSD$"); 18 19 #include <float.h> 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float 25 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ 26 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ 27 two25 = 3.355443200e+07, /* 0x4c000000 */ 28 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ 29 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ 30 Lp3 = 2.8571429849e-01, /* 3E924925 */ 31 Lp4 = 2.2222198546e-01, /* 3E638E29 */ 32 Lp5 = 1.8183572590e-01, /* 3E3A3325 */ 33 Lp6 = 1.5313838422e-01, /* 3E1CD04F */ 34 Lp7 = 1.4798198640e-01; /* 3E178897 */ 35 36 static const float zero = 0.0; 37 38 float 39 log1pf(float x) 40 { 41 float hfsq,f,c,s,z,R,u; 42 int32_t k,hx,hu,ax; 43 44 GET_FLOAT_WORD(hx,x); 45 ax = hx&0x7fffffff; 46 47 k = 1; 48 if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ 49 if(ax>=0x3f800000) { /* x <= -1.0 */ 50 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ 51 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 52 } 53 if(ax<0x38000000) { /* |x| < 2**-15 */ 54 if(two25+x>zero /* raise inexact */ 55 &&ax<0x33800000) /* |x| < 2**-24 */ 56 return x; 57 else 58 return x - x*x*(float)0.5; 59 } 60 if(hx>0||hx<=((int32_t)0xbe95f619)) { 61 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ 62 } 63 if (hx >= 0x7f800000) return x+x; 64 if(k!=0) { 65 if(hx<0x5a000000) { 66 STRICT_ASSIGN(float,u,(float)1.0+x); 67 GET_FLOAT_WORD(hu,u); 68 k = (hu>>23)-127; 69 /* correction term */ 70 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 71 c /= u; 72 } else { 73 u = x; 74 GET_FLOAT_WORD(hu,u); 75 k = (hu>>23)-127; 76 c = 0; 77 } 78 hu &= 0x007fffff; 79 /* 80 * The approximation to sqrt(2) used in thresholds is not 81 * critical. However, the ones used above must give less 82 * strict bounds than the one here so that the k==0 case is 83 * never reached from here, since here we have committed to 84 * using the correction term but don't use it if k==0. 85 */ 86 if(hu<0x3504f4) { /* u < sqrt(2) */ 87 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 88 } else { 89 k += 1; 90 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 91 hu = (0x00800000-hu)>>2; 92 } 93 f = u-(float)1.0; 94 } 95 hfsq=(float)0.5*f*f; 96 if(hu==0) { /* |f| < 2**-20 */ 97 if(f==zero) { 98 if(k==0) { 99 return zero; 100 } else { 101 c += k*ln2_lo; 102 return k*ln2_hi+c; 103 } 104 } 105 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 106 if(k==0) return f-R; else 107 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 108 } 109 s = f/((float)2.0+f); 110 z = s*s; 111 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 112 if(k==0) return f-(hfsq-s*(hfsq+R)); else 113 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 114 } 115