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 <sys/cdefs.h> 17 #if defined(LIBM_SCCS) && !defined(lint) 18 __RCSID("$NetBSD: e_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float huge = 1.0e+30; 25 26 static const float 27 one = 1.0, 28 halF[2] = {0.5,-0.5,}, 29 twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ 30 o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 31 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 32 ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ 33 -6.9313812256e-01,}, /* 0xbf317180 */ 34 ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ 35 -9.0580006145e-06,}, /* 0xb717f7d1 */ 36 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 37 P1 = 1.6666667163e-01, /* 0x3e2aaaab */ 38 P2 = -2.7777778450e-03, /* 0xbb360b61 */ 39 P3 = 6.6137559770e-05, /* 0x388ab355 */ 40 P4 = -1.6533901999e-06, /* 0xb5ddea0e */ 41 P5 = 4.1381369442e-08; /* 0x3331bb4c */ 42 43 float 44 __ieee754_expf(float x) /* default IEEE double exp */ 45 { 46 float y,hi,lo,c,t; 47 int32_t k,xsb; 48 u_int32_t hx; 49 50 hi = lo = 0; 51 k = 0; 52 GET_FLOAT_WORD(hx,x); 53 xsb = (hx>>31)&1; /* sign bit of x */ 54 hx &= 0x7fffffff; /* high word of |x| */ 55 56 /* filter out non-finite argument */ 57 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 58 if(hx>0x7f800000) 59 return x+x; /* NaN */ 60 if(hx==0x7f800000) 61 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 62 if(x > o_threshold) return huge*huge; /* overflow */ 63 if(x < u_threshold) return twom100*twom100; /* underflow */ 64 } 65 66 /* argument reduction */ 67 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 68 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 69 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 70 } else { 71 k = invln2*x+halF[xsb]; 72 t = k; 73 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 74 lo = t*ln2LO[0]; 75 } 76 x = hi - lo; 77 } 78 else if(hx < 0x31800000) { /* when |x|<2**-28 */ 79 if(huge+x>one) return one+x;/* trigger inexact */ 80 } 81 else k = 0; 82 83 /* x is now in primary range */ 84 t = x*x; 85 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 86 if(k==0) return one-((x*c)/(c-(float)2.0)-x); 87 else y = one-((lo-(x*c)/((float)2.0-c))-hi); 88 if(k >= -125) { 89 u_int32_t hy; 90 GET_FLOAT_WORD(hy,y); 91 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ 92 return y; 93 } else { 94 u_int32_t hy; 95 GET_FLOAT_WORD(hy,y); 96 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ 97 return y*twom100; 98 } 99 } 100