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[] = "$FreeBSD$"; 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 } 96