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 "cdefs-compat.h" 17 //__FBSDID("$FreeBSD: src/lib/msun/src/e_expf.c,v 1.16 2011/10/21 06:26:38 das Exp $"); 18 19 #include <float.h> 20 21 #include "openlibm.h" 22 #include "math_private.h" 23 24 static const float 25 one = 1.0, 26 halF[2] = {0.5,-0.5,}, 27 huge = 1.0e+30, 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 /* 36 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: 37 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 38 */ 39 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ 40 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ 41 42 static volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 43 44 float 45 __ieee754_expf(float x) 46 { 47 float y,hi=0.0,lo=0.0,c,t,twopk; 48 int32_t k=0,xsb; 49 u_int32_t hx; 50 51 GET_FLOAT_WORD(hx,x); 52 xsb = (hx>>31)&1; /* sign bit of x */ 53 hx &= 0x7fffffff; /* high word of |x| */ 54 55 /* filter out non-finite argument */ 56 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 57 if(hx>0x7f800000) 58 return x+x; /* NaN */ 59 if(hx==0x7f800000) 60 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 61 if(x > o_threshold) return huge*huge; /* overflow */ 62 if(x < u_threshold) return twom100*twom100; /* underflow */ 63 } 64 65 /* argument reduction */ 66 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 67 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 68 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 69 } else { 70 k = invln2*x+halF[xsb]; 71 t = k; 72 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 73 lo = t*ln2LO[0]; 74 } 75 STRICT_ASSIGN(float, x, hi - lo); 76 } 77 else if(hx < 0x39000000) { /* when |x|<2**-14 */ 78 if(huge+x>one) return one+x;/* trigger inexact */ 79 } 80 else k = 0; 81 82 /* x is now in primary range */ 83 t = x*x; 84 if(k >= -125) 85 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); 86 else 87 SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23)); 88 c = x - t*(P1+t*P2); 89 if(k==0) return one-((x*c)/(c-(float)2.0)-x); 90 else y = one-((lo-(x*c)/((float)2.0-c))-hi); 91 if(k >= -125) { 92 if(k==128) return y*2.0F*0x1p127F; 93 return y*twopk; 94 } else { 95 return y*twopk*twom100; 96 } 97 } 98