| The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 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: src/lib/msun/src/s_log1pf.c,v 1.9 2005/12/04 12:30:44 bde Exp $"; |
| 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 | } |