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 static volatile float vzero = 0.0; 38 39 float 40 log1pf(float x) 41 { 42 float hfsq,f,c,s,z,R,u; 43 int32_t k,hx,hu,ax; 44 45 GET_FLOAT_WORD(hx,x); 46 ax = hx&0x7fffffff; 47 48 k = 1; 49 if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ 50 if(ax>=0x3f800000) { /* x <= -1.0 */ 51 if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */ 52 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ 53 } 54 if(ax<0x38000000) { /* |x| < 2**-15 */ 55 if(two25+x>zero /* raise inexact */ 56 &&ax<0x33800000) /* |x| < 2**-24 */ 57 return x; 58 else 59 return x - x*x*(float)0.5; 60 } 61 if(hx>0||hx<=((int32_t)0xbe95f619)) { 62 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ 63 } 64 if (hx >= 0x7f800000) return x+x; 65 if(k!=0) { 66 if(hx<0x5a000000) { 67 STRICT_ASSIGN(float,u,(float)1.0+x); 68 GET_FLOAT_WORD(hu,u); 69 k = (hu>>23)-127; 70 /* correction term */ 71 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); 72 c /= u; 73 } else { 74 u = x; 75 GET_FLOAT_WORD(hu,u); 76 k = (hu>>23)-127; 77 c = 0; 78 } 79 hu &= 0x007fffff; 80 /* 81 * The approximation to sqrt(2) used in thresholds is not 82 * critical. However, the ones used above must give less 83 * strict bounds than the one here so that the k==0 case is 84 * never reached from here, since here we have committed to 85 * using the correction term but don't use it if k==0. 86 */ 87 if(hu<0x3504f4) { /* u < sqrt(2) */ 88 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ 89 } else { 90 k += 1; 91 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ 92 hu = (0x00800000-hu)>>2; 93 } 94 f = u-(float)1.0; 95 } 96 hfsq=(float)0.5*f*f; 97 if(hu==0) { /* |f| < 2**-20 */ 98 if(f==zero) { 99 if(k==0) { 100 return zero; 101 } else { 102 c += k*ln2_lo; 103 return k*ln2_hi+c; 104 } 105 } 106 R = hfsq*((float)1.0-(float)0.66666666666666666*f); 107 if(k==0) return f-R; else 108 return k*ln2_hi-((R-(k*ln2_lo+c))-f); 109 } 110 s = f/((float)2.0+f); 111 z = s*s; 112 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); 113 if(k==0) return f-(hfsq-s*(hfsq+R)); else 114 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); 115 } 116