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 <float.h> 17 18 #include "math.h" 19 #include "math_private.h" 20 21 static const float 22 one = 1.0, 23 halF[2] = {0.5,-0.5,}, 24 o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 25 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 26 ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ 27 -6.9314575195e-01,}, /* 0xbf317200 */ 28 ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ 29 -1.4286067653e-06,}, /* 0xb5bfbe8e */ 30 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 31 /* 32 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: 33 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 34 */ 35 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ 36 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ 37 38 static volatile float 39 huge = 1.0e+30, 40 twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 41 42 float 43 expf(float x) 44 { 45 float y,hi=0.0,lo=0.0,c,t,twopk; 46 int32_t k=0,xsb; 47 u_int32_t hx; 48 49 GET_FLOAT_WORD(hx,x); 50 xsb = (hx>>31)&1; /* sign bit of x */ 51 hx &= 0x7fffffff; /* high word of |x| */ 52 53 /* filter out non-finite argument */ 54 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 55 if(hx>0x7f800000) 56 return x+x; /* NaN */ 57 if(hx==0x7f800000) 58 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 59 if(x > o_threshold) return huge*huge; /* overflow */ 60 if(x < u_threshold) return twom100*twom100; /* underflow */ 61 } 62 63 /* argument reduction */ 64 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 65 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 66 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 67 } else { 68 k = invln2*x+halF[xsb]; 69 t = k; 70 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 71 lo = t*ln2LO[0]; 72 } 73 STRICT_ASSIGN(float, x, hi - lo); 74 } 75 else if(hx < 0x39000000) { /* when |x|<2**-14 */ 76 if(huge+x>one) return one+x;/* trigger inexact */ 77 } 78 else k = 0; 79 80 /* x is now in primary range */ 81 t = x*x; 82 if(k >= -125) 83 SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23); 84 else 85 SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23); 86 c = x - t*(P1+t*P2); 87 if(k==0) return one-((x*c)/(c-(float)2.0)-x); 88 else y = one-((lo-(x*c)/((float)2.0-c))-hi); 89 if(k >= -125) { 90 if(k==128) return y*2.0F*0x1p127F; 91 return y*twopk; 92 } else { 93 return y*twopk*twom100; 94 } 95 } 96