| 1 | /* s_log1pf.c -- float version of s_log1p.c.
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| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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| 3 | */
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| 4 |
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| 5 | /*
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| 6 | * ====================================================
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 8 | *
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 10 | * Permission to use, copy, modify, and distribute this
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| 11 | * software is freely granted, provided that this notice
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| 12 | * is preserved.
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| 13 | * ====================================================
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| 14 | */
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| 15 |
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| 16 | #ifndef lint
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| 17 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_log1pf.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
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| 18 | #endif
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| 19 |
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| 20 | #include "math.h"
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| 21 | #include "math_private.h"
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| 22 |
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| 23 | static const float
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| 24 | ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
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| 25 | ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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| 26 | two25 = 3.355443200e+07, /* 0x4c000000 */
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| 27 | Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
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| 28 | Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
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| 29 | Lp3 = 2.8571429849e-01, /* 3E924925 */
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| 30 | Lp4 = 2.2222198546e-01, /* 3E638E29 */
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| 31 | Lp5 = 1.8183572590e-01, /* 3E3A3325 */
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| 32 | Lp6 = 1.5313838422e-01, /* 3E1CD04F */
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| 33 | Lp7 = 1.4798198640e-01; /* 3E178897 */
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| 34 |
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| 35 | static const float zero = 0.0;
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| 36 |
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| 37 | float
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| 38 | log1pf(float x)
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| 39 | {
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| 40 | float hfsq,f,c,s,z,R,u;
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| 41 | int32_t k,hx,hu,ax;
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| 42 |
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| 43 | GET_FLOAT_WORD(hx,x);
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| 44 | ax = hx&0x7fffffff;
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| 45 |
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| 46 | k = 1;
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| 47 | if (hx < 0x3ed413d7) { /* x < 0.41422 */
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| 48 | if(ax>=0x3f800000) { /* x <= -1.0 */
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| 49 | if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
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| 50 | else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
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| 51 | }
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| 52 | if(ax<0x31000000) { /* |x| < 2**-29 */
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| 53 | if(two25+x>zero /* raise inexact */
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| 54 | &&ax<0x24800000) /* |x| < 2**-54 */
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| 55 | return x;
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| 56 | else
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| 57 | return x - x*x*(float)0.5;
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| 58 | }
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| 59 | if(hx>0||hx<=((int32_t)0xbe95f61f)) {
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| 60 | k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
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| 61 | }
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| 62 | if (hx >= 0x7f800000) return x+x;
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| 63 | if(k!=0) {
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| 64 | if(hx<0x5a000000) {
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| 65 | u = (float)1.0+x;
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| 66 | GET_FLOAT_WORD(hu,u);
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| 67 | k = (hu>>23)-127;
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| 68 | /* correction term */
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| 69 | c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
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| 70 | c /= u;
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| 71 | } else {
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| 72 | u = x;
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| 73 | GET_FLOAT_WORD(hu,u);
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| 74 | k = (hu>>23)-127;
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| 75 | c = 0;
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| 76 | }
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| 77 | hu &= 0x007fffff;
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| 78 | if(hu<0x3504f7) {
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| 79 | SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
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| 80 | } else {
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| 81 | k += 1;
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| 82 | SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
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| 83 | hu = (0x00800000-hu)>>2;
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| 84 | }
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| 85 | f = u-(float)1.0;
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| 86 | }
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| 87 | hfsq=(float)0.5*f*f;
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| 88 | if(hu==0) { /* |f| < 2**-20 */
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| 89 | if(f==zero) if(k==0) return zero;
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| 90 | else {c += k*ln2_lo; return k*ln2_hi+c;}
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| 91 | R = hfsq*((float)1.0-(float)0.66666666666666666*f);
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| 92 | if(k==0) return f-R; else
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| 93 | return k*ln2_hi-((R-(k*ln2_lo+c))-f);
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| 94 | }
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| 95 | s = f/((float)2.0+f);
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| 96 | z = s*s;
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| 97 | R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
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| 98 | if(k==0) return f-(hfsq-s*(hfsq+R)); else
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| 99 | return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
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| 100 | }
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