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| Rev | Author | Line No. | Line |
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| 2 | pj | 1 | /* e_expf.c -- float version of e_exp.c. |
| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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| 3 | */ |
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| 4 | |||
| 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 | |||
| 16 | #ifndef lint |
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| 17 | static char rcsid[] = "$\Id: e_expf.c,v 1.3 1996/07/12 18:57:56 jkh Exp $"; |
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| 18 | #endif |
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| 19 | |||
| 20 | #include "math.h" |
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| 21 | #include "math_private.h" |
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| 22 | |||
| 23 | #ifdef __STDC__ |
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| 24 | static const float |
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| 25 | #else |
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| 26 | static float |
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| 27 | #endif |
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| 28 | one = 1.0, |
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| 29 | halF[2] = {0.5,-0.5,}, |
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| 30 | huge = 1.0e+30, |
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| 31 | twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ |
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| 32 | o_threshold= 8.8721679688e+01, /* 0x42b17180 */ |
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| 33 | u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ |
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| 34 | ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ |
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| 35 | -6.9313812256e-01,}, /* 0xbf317180 */ |
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| 36 | ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ |
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| 37 | -9.0580006145e-06,}, /* 0xb717f7d1 */ |
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| 38 | invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ |
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| 39 | P1 = 1.6666667163e-01, /* 0x3e2aaaab */ |
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| 40 | P2 = -2.7777778450e-03, /* 0xbb360b61 */ |
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| 41 | P3 = 6.6137559770e-05, /* 0x388ab355 */ |
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| 42 | P4 = -1.6533901999e-06, /* 0xb5ddea0e */ |
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| 43 | P5 = 4.1381369442e-08; /* 0x3331bb4c */ |
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| 44 | |||
| 45 | #ifdef __STDC__ |
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| 46 | float __ieee754_expf(float x) /* default IEEE double exp */ |
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| 47 | #else |
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| 48 | float __ieee754_expf(x) /* default IEEE double exp */ |
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| 49 | float x; |
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| 50 | #endif |
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| 51 | { |
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| 52 | float y,hi=0.0,lo=0.0,c,t; |
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| 53 | int32_t k=0,xsb; |
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| 54 | u_int32_t hx; |
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| 55 | |||
| 56 | GET_FLOAT_WORD(hx,x); |
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| 57 | xsb = (hx>>31)&1; /* sign bit of x */ |
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| 58 | hx &= 0x7fffffff; /* high word of |x| */ |
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| 59 | |||
| 60 | /* filter out non-finite argument */ |
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| 61 | if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
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| 62 | if(hx>0x7f800000) |
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| 63 | return x+x; /* NaN */ |
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| 64 | if(hx==0x7f800000) |
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| 65 | return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ |
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| 66 | if(x > o_threshold) return huge*huge; /* overflow */ |
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| 67 | if(x < u_threshold) return twom100*twom100; /* underflow */ |
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| 68 | } |
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| 69 | |||
| 70 | /* argument reduction */ |
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| 71 | if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
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| 72 | if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
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| 73 | hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; |
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| 74 | } else { |
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| 75 | k = invln2*x+halF[xsb]; |
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| 76 | t = k; |
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| 77 | hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ |
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| 78 | lo = t*ln2LO[0]; |
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| 79 | } |
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| 80 | x = hi - lo; |
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| 81 | } |
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| 82 | else if(hx < 0x31800000) { /* when |x|<2**-28 */ |
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| 83 | if(huge+x>one) return one+x;/* trigger inexact */ |
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| 84 | } |
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| 85 | else k = 0; |
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| 86 | |||
| 87 | /* x is now in primary range */ |
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| 88 | t = x*x; |
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| 89 | c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
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| 90 | if(k==0) return one-((x*c)/(c-(float)2.0)-x); |
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| 91 | else y = one-((lo-(x*c)/((float)2.0-c))-hi); |
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| 92 | if(k >= -125) { |
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| 93 | u_int32_t hy; |
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| 94 | GET_FLOAT_WORD(hy,y); |
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| 95 | SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ |
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| 96 | return y; |
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| 97 | } else { |
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| 98 | u_int32_t hy; |
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| 99 | GET_FLOAT_WORD(hy,y); |
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| 100 | SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ |
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| 101 | return y*twom100; |
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| 102 | } |
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| 103 | } |