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 #include "math.h" 17 #include "math_private.h" 18 19 static const volatile float huge = 1.0e+30; 20 21 static const float 22 one = 1.0, 23 halF[2] = {0.5,-0.5,}, 24 twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ 25 o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 26 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 27 ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ 28 -6.9313812256e-01,}, /* 0xbf317180 */ 29 ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ 30 -9.0580006145e-06,}, /* 0xb717f7d1 */ 31 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 32 P1 = 1.6666667163e-01, /* 0x3e2aaaab */ 33 P2 = -2.7777778450e-03, /* 0xbb360b61 */ 34 P3 = 6.6137559770e-05, /* 0x388ab355 */ 35 P4 = -1.6533901999e-06, /* 0xb5ddea0e */ 36 P5 = 4.1381369442e-08; /* 0x3331bb4c */ 37 38 float 39 expf(float x) /* default IEEE double exp */ 40 { 41 float y,hi,lo,c,t; 42 int32_t k,xsb; 43 u_int32_t hx; 44 45 GET_FLOAT_WORD(hx,x); 46 xsb = (hx>>31)&1; /* sign bit of x */ 47 hx &= 0x7fffffff; /* high word of |x| */ 48 k = 0; 49 50 /* filter out non-finite argument */ 51 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 52 if(hx>0x7f800000) 53 return x+x; /* NaN */ 54 if(hx==0x7f800000) 55 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 56 if(x > o_threshold) return huge*huge; /* overflow */ 57 if(x < u_threshold) return twom100*twom100; /* underflow */ 58 } 59 60 /* argument reduction */ 61 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 62 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 63 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 64 } else { 65 k = invln2*x+halF[xsb]; 66 t = k; 67 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 68 lo = t*ln2LO[0]; 69 } 70 x = hi - lo; 71 } 72 else if(hx < 0x31800000) { /* when |x|<2**-28 */ 73 if(huge+x>one) return one+x;/* trigger inexact */ 74 } 75 76 /* x is now in primary range */ 77 t = x*x; 78 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 79 if(k==0) return one-((x*c)/(c-(float)2.0)-x); 80 else y = one-((lo-(x*c)/((float)2.0-c))-hi); 81 if(k >= -125) { 82 u_int32_t hy; 83 GET_FLOAT_WORD(hy,y); 84 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ 85 return y; 86 } else { 87 u_int32_t hy; 88 GET_FLOAT_WORD(hy,y); 89 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ 90 return y*twom100; 91 } 92 } 93