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 "cdefs-compat.h" 17 //__FBSDID("$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.12 2011/10/21 06:26:38 das Exp $"); 18 19 #include <float.h> 20 #include <openlibm.h> 21 22 #include "math_private.h" 23 24 static const float 25 one = 1.0, 26 huge = 1.0e+30, 27 tiny = 1.0e-30, 28 o_threshold = 8.8721679688e+01,/* 0x42b17180 */ 29 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 30 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 31 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 32 /* 33 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: 34 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 35 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): 36 */ 37 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ 38 Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ 39 40 DLLEXPORT float 41 expm1f(float x) 42 { 43 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 44 int32_t k,xsb; 45 u_int32_t hx; 46 47 GET_FLOAT_WORD(hx,x); 48 xsb = hx&0x80000000; /* sign bit of x */ 49 hx &= 0x7fffffff; /* high word of |x| */ 50 51 /* filter out huge and non-finite argument */ 52 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 53 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 54 if(hx>0x7f800000) 55 return x+x; /* NaN */ 56 if(hx==0x7f800000) 57 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 58 if(x > o_threshold) return huge*huge; /* overflow */ 59 } 60 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 61 if(x+tiny<(float)0.0) /* raise inexact */ 62 return tiny-one; /* return -1 */ 63 } 64 } 65 66 /* argument reduction */ 67 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 68 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 69 if(xsb==0) 70 {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 71 else 72 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 73 } else { 74 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 75 t = k; 76 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 77 lo = t*ln2_lo; 78 } 79 STRICT_ASSIGN(float, x, hi - lo); 80 c = (hi-x)-lo; 81 } 82 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 83 t = huge+x; /* return x with inexact flags when x!=0 */ 84 return x - (t-(huge+x)); 85 } 86 else k = 0; 87 88 /* x is now in primary range */ 89 hfx = (float)0.5*x; 90 hxs = x*hfx; 91 r1 = one+hxs*(Q1+hxs*Q2); 92 t = (float)3.0-r1*hfx; 93 e = hxs*((r1-t)/((float)6.0 - x*t)); 94 if(k==0) return x - (x*e-hxs); /* c is 0 */ 95 else { 96 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */ 97 e = (x*(e-c)-c); 98 e -= hxs; 99 if(k== -1) return (float)0.5*(x-e)-(float)0.5; 100 if(k==1) { 101 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 102 else return one+(float)2.0*(x-e); 103 } 104 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 105 y = one-(e-x); 106 if (k == 128) y = y*2.0F*0x1p127F; 107 else y = y*twopk; 108 return y-one; 109 } 110 t = one; 111 if(k<23) { 112 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 113 y = t-(e-x); 114 y = y*twopk; 115 } else { 116 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 117 y = x-(e+t); 118 y += one; 119 y = y*twopk; 120 } 121 } 122 return y; 123 } 124