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
| 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
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17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_expf.c 142181 2005-02-21 17:44:57Z das $";
| 17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_expf.c 142369 2005-02-24 06:32:13Z das $";
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18#endif 19 20#include "math.h" 21#include "math_private.h" 22 23static const float 24one = 1.0, 25halF[2] = {0.5,-0.5,}, 26huge = 1.0e+30, 27twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ 28o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 29u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
| 18#endif 19 20#include "math.h" 21#include "math_private.h" 22 23static const float 24one = 1.0, 25halF[2] = {0.5,-0.5,}, 26huge = 1.0e+30, 27twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ 28o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 29u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
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| 30ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ 31 -6.9313812256e-01,}, /* 0xbf317180 */ 32ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ 33 -9.0580006145e-06,}, /* 0xb717f7d1 */
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30invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 31P1 = 1.6666667163e-01, /* 0x3e2aaaab */ 32P2 = -2.7777778450e-03, /* 0xbb360b61 */ 33P3 = 6.6137559770e-05, /* 0x388ab355 */ 34P4 = -1.6533901999e-06, /* 0xb5ddea0e */ 35P5 = 4.1381369442e-08; /* 0x3331bb4c */
| 34invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 35P1 = 1.6666667163e-01, /* 0x3e2aaaab */ 36P2 = -2.7777778450e-03, /* 0xbb360b61 */ 37P3 = 6.6137559770e-05, /* 0x388ab355 */ 38P4 = -1.6533901999e-06, /* 0xb5ddea0e */ 39P5 = 4.1381369442e-08; /* 0x3331bb4c */
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36double ln2[2] = { 6.93147180369123816490e-01, -6.93147180369123816490e-01 };
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37 38float
| 40 41float
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39__ieee754_expf(float x) /* IEEE float exp */
| 42__ieee754_expf(float x) /* default IEEE double exp */
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40{
| 43{
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41 float y,c,t;
| 44 float y,hi=0.0,lo=0.0,c,t;
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42 int32_t k=0,xsb; 43 u_int32_t hx; 44 45 GET_FLOAT_WORD(hx,x); 46 xsb = (hx>>31)&1; /* sign bit of x */
| 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 */
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47 hx &= 0x7fffffff; /* |x| */
| 50 hx &= 0x7fffffff; /* high word of |x| */
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48 49 /* filter out non-finite argument */ 50 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 51 if(hx>0x7f800000) 52 return x+x; /* NaN */ 53 if(hx==0x7f800000) 54 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 55 if(x > o_threshold) return huge*huge; /* overflow */ 56 if(x < u_threshold) return twom100*twom100; /* underflow */ 57 } 58 59 /* argument reduction */ 60 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 61 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
| 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 */
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62 x = x-ln2[xsb]; k = 1-xsb-xsb;
| 65 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
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63 } else { 64 k = invln2*x+halF[xsb]; 65 t = k;
| 66 } else { 67 k = invln2*x+halF[xsb]; 68 t = k;
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66 x = x - t*ln2[0];
| 69 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 70 lo = t*ln2LO[0];
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67 }
| 71 }
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| 72 x = hi - lo;
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68 } 69 else if(hx < 0x31800000) { /* when |x|<2**-28 */ 70 if(huge+x>one) return one+x;/* trigger inexact */ 71 } 72 else k = 0; 73 74 /* x is now in primary range */ 75 t = x*x; 76 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
| 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))));
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77 y = one-(((double)x*c)/(c-2.0)-x); 78 if(k==0) return y;
| 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);
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79 if(k >= -125) { 80 u_int32_t hy; 81 GET_FLOAT_WORD(hy,y); 82 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ 83 return y; 84 } else { 85 u_int32_t hy; 86 GET_FLOAT_WORD(hy,y); 87 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ 88 return y*twom100; 89 } 90}
| 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}
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