| The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame^] | 1 | /* e_expf.c -- float version of e_exp.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/e_expf.c,v 1.10 2005/11/30 04:56:49 bde Exp $"; |
| 18 | #endif |
| 19 | |
| 20 | #include "math.h" |
| 21 | #include "math_private.h" |
| 22 | |
| 23 | static const float |
| 24 | one = 1.0, |
| 25 | halF[2] = {0.5,-0.5,}, |
| 26 | huge = 1.0e+30, |
| 27 | twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ |
| 28 | o_threshold= 8.8721679688e+01, /* 0x42b17180 */ |
| 29 | u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ |
| 30 | ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ |
| 31 | -6.9314575195e-01,}, /* 0xbf317200 */ |
| 32 | ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ |
| 33 | -1.4286067653e-06,}, /* 0xb5bfbe8e */ |
| 34 | invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ |
| 35 | P1 = 1.6666667163e-01, /* 0x3e2aaaab */ |
| 36 | P2 = -2.7777778450e-03, /* 0xbb360b61 */ |
| 37 | P3 = 6.6137559770e-05, /* 0x388ab355 */ |
| 38 | P4 = -1.6533901999e-06, /* 0xb5ddea0e */ |
| 39 | P5 = 4.1381369442e-08; /* 0x3331bb4c */ |
| 40 | |
| 41 | float |
| 42 | __ieee754_expf(float x) /* default IEEE double exp */ |
| 43 | { |
| 44 | float y,hi=0.0,lo=0.0,c,t; |
| 45 | int32_t k=0,xsb; |
| 46 | u_int32_t hx; |
| 47 | |
| 48 | GET_FLOAT_WORD(hx,x); |
| 49 | xsb = (hx>>31)&1; /* sign bit of x */ |
| 50 | hx &= 0x7fffffff; /* high word of |x| */ |
| 51 | |
| 52 | /* filter out non-finite argument */ |
| 53 | if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
| 54 | if(hx>0x7f800000) |
| 55 | return x+x; /* NaN */ |
| 56 | if(hx==0x7f800000) |
| 57 | return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ |
| 58 | if(x > o_threshold) return huge*huge; /* overflow */ |
| 59 | if(x < u_threshold) return twom100*twom100; /* underflow */ |
| 60 | } |
| 61 | |
| 62 | /* argument reduction */ |
| 63 | if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
| 64 | if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
| 65 | hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; |
| 66 | } else { |
| 67 | k = invln2*x+halF[xsb]; |
| 68 | t = k; |
| 69 | hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ |
| 70 | lo = t*ln2LO[0]; |
| 71 | } |
| 72 | x = hi - lo; |
| 73 | } |
| 74 | else if(hx < 0x31800000) { /* when |x|<2**-28 */ |
| 75 | if(huge+x>one) return one+x;/* trigger inexact */ |
| 76 | } |
| 77 | else k = 0; |
| 78 | |
| 79 | /* x is now in primary range */ |
| 80 | t = x*x; |
| 81 | c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
| 82 | if(k==0) return one-((x*c)/(c-(float)2.0)-x); |
| 83 | else y = one-((lo-(x*c)/((float)2.0-c))-hi); |
| 84 | if(k >= -125) { |
| 85 | u_int32_t hy; |
| 86 | GET_FLOAT_WORD(hy,y); |
| 87 | SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ |
| 88 | return y; |
| 89 | } else { |
| 90 | u_int32_t hy; |
| 91 | GET_FLOAT_WORD(hy,y); |
| 92 | SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ |
| 93 | return y*twom100; |
| 94 | } |
| 95 | } |