1 /* e_expf.c -- float version of e_exp.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 __FBSDID("$FreeBSD$"); 18 19 #include <float.h> 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float 25 one = 1.0, 26 halF[2] = {0.5,-0.5,}, 27 o_threshold= 8.8721679688e+01, /* 0x42b17180 */ 28 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 29 ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ 30 -6.9314575195e-01,}, /* 0xbf317200 */ 31 ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ 32 -1.4286067653e-06,}, /* 0xb5bfbe8e */ 33 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 34 /* 35 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: 36 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 37 */ 38 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ 39 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ 40 41 static volatile float 42 huge = 1.0e+30, 43 twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 44 45 float 46 __ieee754_expf(float x) 47 { 48 float y,hi=0.0,lo=0.0,c,t,twopk; 49 int32_t k=0,xsb; 50 u_int32_t hx; 51 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 STRICT_ASSIGN(float, x, hi - lo); 77 } 78 else if(hx < 0x39000000) { /* when |x|<2**-14 */ 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 if(k >= -125) 86 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); 87 else 88 SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23)); 89 c = x - t*(P1+t*P2); 90 if(k==0) return one-((x*c)/(c-(float)2.0)-x); 91 else y = one-((lo-(x*c)/((float)2.0-c))-hi); 92 if(k >= -125) { 93 if(k==128) return y*2.0F*0x1p127F; 94 return y*twopk; 95 } else { 96 return y*twopk*twom100; 97 } 98 } 99
