1 /* s_expm1f.c -- float version of s_expm1.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 __FBSDID("$FreeBSD$"); 18 19 #include "math.h" 20 #include "math_private.h" 21 22 static const float 23 one = 1.0, 24 huge = 1.0e+30, 25 tiny = 1.0e-30, 26 o_threshold = 8.8721679688e+01,/* 0x42b17180 */ 27 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 28 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 29 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 30 /* 31 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: 32 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 33 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): 34 */ 35 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ 36 Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ 37 38 float 39 expm1f(float x) 40 { 41 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 42 int32_t k,xsb; 43 u_int32_t hx; 44 45 GET_FLOAT_WORD(hx,x); 46 xsb = hx&0x80000000; /* sign bit of x */ 47 if(xsb==0) y=x; else y= -x; /* y = |x| */ 48 hx &= 0x7fffffff; /* high word of |x| */ 49 50 /* filter out huge and non-finite argument */ 51 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 52 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 53 if(hx>0x7f800000) 54 return x+x; /* NaN */ 55 if(hx==0x7f800000) 56 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 57 if(x > o_threshold) return huge*huge; /* overflow */ 58 } 59 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 60 if(x+tiny<(float)0.0) /* raise inexact */ 61 return tiny-one; /* return -1 */ 62 } 63 } 64 65 /* argument reduction */ 66 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 67 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 68 if(xsb==0) 69 {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 70 else 71 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 72 } else { 73 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 74 t = k; 75 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 76 lo = t*ln2_lo; 77 } 78 x = hi - lo; 79 c = (hi-x)-lo; 80 } 81 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 82 t = huge+x; /* return x with inexact flags when x!=0 */ 83 return x - (t-(huge+x)); 84 } 85 else k = 0; 86 87 /* x is now in primary range */ 88 hfx = (float)0.5*x; 89 hxs = x*hfx; 90 r1 = one+hxs*(Q1+hxs*Q2); 91 t = (float)3.0-r1*hfx; 92 e = hxs*((r1-t)/((float)6.0 - x*t)); 93 if(k==0) return x - (x*e-hxs); /* c is 0 */ 94 else { 95 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */ 96 e = (x*(e-c)-c); 97 e -= hxs; 98 if(k== -1) return (float)0.5*(x-e)-(float)0.5; 99 if(k==1) { 100 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 101 else return one+(float)2.0*(x-e); 102 } 103 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 104 y = one-(e-x); 105 if (k == 128) y = y*2.0F*0x1p127F; 106 else y = y*twopk; 107 return y-one; 108 } 109 t = one; 110 if(k<23) { 111 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 112 y = t-(e-x); 113 y = y*twopk; 114 } else { 115 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 116 y = x-(e+t); 117 y += one; 118 y = y*twopk; 119 } 120 } 121 return y; 122 } 123