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 #include <float.h> 18 19 #include "math.h" 20 #include "math_private.h" 21 22 static const float 23 one = 1.0, 24 halF[2] = {0.5,-0.5,}, 25 o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 26 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 27 ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ 28 -6.9314575195e-01,}, /* 0xbf317200 */ 29 ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ 30 -1.4286067653e-06,}, /* 0xb5bfbe8e */ 31 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 32 /* 33 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: 34 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 35 */ 36 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ 37 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ 38 39 static volatile float 40 huge = 1.0e+30, 41 twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 42 43 float 44 expf(float x) 45 { 46 float y,hi=0.0,lo=0.0,c,t,twopk; 47 int32_t k=0,xsb; 48 u_int32_t hx; 49 50 GET_FLOAT_WORD(hx,x); 51 xsb = (hx>>31)&1; /* sign bit of x */ 52 hx &= 0x7fffffff; /* high word of |x| */ 53 54 /* filter out non-finite argument */ 55 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 56 if(hx>0x7f800000) 57 return x+x; /* NaN */ 58 if(hx==0x7f800000) 59 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 60 if(x > o_threshold) return huge*huge; /* overflow */ 61 if(x < u_threshold) return twom100*twom100; /* underflow */ 62 } 63 64 /* argument reduction */ 65 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 66 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 67 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 68 } else { 69 k = invln2*x+halF[xsb]; 70 t = k; 71 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 72 lo = t*ln2LO[0]; 73 } 74 STRICT_ASSIGN(float, x, hi - lo); 75 } 76 else if(hx < 0x39000000) { /* when |x|<2**-14 */ 77 if(huge+x>one) return one+x;/* trigger inexact */ 78 } 79 else k = 0; 80 81 /* x is now in primary range */ 82 t = x*x; 83 if(k >= -125) 84 SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23); 85 else 86 SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23); 87 c = x - t*(P1+t*P2); 88 if(k==0) return one-((x*c)/(c-(float)2.0)-x); 89 else y = one-((lo-(x*c)/((float)2.0-c))-hi); 90 if(k >= -125) { 91 if(k==128) return y*2.0F*0x1p127F; 92 return y*twopk; 93 } else { 94 return y*twopk*twom100; 95 } 96 } 97