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 <float.h> 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float 25 one = 1.0, 26 tiny = 1.0e-30, 27 o_threshold = 8.8721679688e+01,/* 0x42b17180 */ 28 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 29 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 30 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 31 /* 32 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: 33 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 34 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): 35 */ 36 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ 37 Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ 38 39 static volatile float huge = 1.0e+30; 40 41 float 42 expm1f(float x) 43 { 44 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 45 int32_t k,xsb; 46 u_int32_t hx; 47 48 GET_FLOAT_WORD(hx,x); 49 xsb = hx&0x80000000; /* sign bit of x */ 50 hx &= 0x7fffffff; /* high word of |x| */ 51 52 /* filter out huge and non-finite argument */ 53 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 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:-1.0;/* exp(+-inf)={inf,-1} */ 59 if(x > o_threshold) return huge*huge; /* overflow */ 60 } 61 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 62 if(x+tiny<(float)0.0) /* raise inexact */ 63 return tiny-one; /* return -1 */ 64 } 65 } 66 67 /* argument reduction */ 68 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 69 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 70 if(xsb==0) 71 {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 72 else 73 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 74 } else { 75 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 76 t = k; 77 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 78 lo = t*ln2_lo; 79 } 80 STRICT_ASSIGN(float, x, hi - lo); 81 c = (hi-x)-lo; 82 } 83 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 84 t = huge+x; /* return x with inexact flags when x!=0 */ 85 return x - (t-(huge+x)); 86 } 87 else k = 0; 88 89 /* x is now in primary range */ 90 hfx = (float)0.5*x; 91 hxs = x*hfx; 92 r1 = one+hxs*(Q1+hxs*Q2); 93 t = (float)3.0-r1*hfx; 94 e = hxs*((r1-t)/((float)6.0 - x*t)); 95 if(k==0) return x - (x*e-hxs); /* c is 0 */ 96 else { 97 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */ 98 e = (x*(e-c)-c); 99 e -= hxs; 100 if(k== -1) return (float)0.5*(x-e)-(float)0.5; 101 if(k==1) { 102 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 103 else return one+(float)2.0*(x-e); 104 } 105 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 106 y = one-(e-x); 107 if (k == 128) y = y*2.0F*0x1p127F; 108 else y = y*twopk; 109 return y-one; 110 } 111 t = one; 112 if(k<23) { 113 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 114 y = t-(e-x); 115 y = y*twopk; 116 } else { 117 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 118 y = x-(e+t); 119 y += one; 120 y = y*twopk; 121 } 122 } 123 return y; 124 } 125