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 #ifndef lint 17 static char rcsid[] = "$Id: s_expm1f.c,v 1.1.1.1 1994/08/19 09:39:58 jkh Exp $"; 18 #endif 19 20 #include "math.h" 21 #include "math_private.h" 22 23 #ifdef __STDC__ 24 static const float 25 #else 26 static float 27 #endif 28 one = 1.0, 29 huge = 1.0e+30, 30 tiny = 1.0e-30, 31 o_threshold = 8.8721679688e+01,/* 0x42b17180 */ 32 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 33 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 34 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 35 /* scaled coefficients related to expm1 */ 36 Q1 = -3.3333335072e-02, /* 0xbd088889 */ 37 Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ 38 Q3 = -7.9365076090e-05, /* 0xb8a670cd */ 39 Q4 = 4.0082177293e-06, /* 0x36867e54 */ 40 Q5 = -2.0109921195e-07; /* 0xb457edbb */ 41 42 #ifdef __STDC__ 43 float expm1f(float x) 44 #else 45 float expm1f(x) 46 float x; 47 #endif 48 { 49 float y,hi,lo,c,t,e,hxs,hfx,r1; 50 int32_t k,xsb; 51 u_int32_t hx; 52 53 GET_FLOAT_WORD(hx,x); 54 xsb = hx&0x80000000; /* sign bit of x */ 55 if(xsb==0) y=x; else y= -x; /* y = |x| */ 56 hx &= 0x7fffffff; /* high word of |x| */ 57 58 /* filter out huge and non-finite argument */ 59 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 60 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 61 if(hx>0x7f800000) 62 return x+x; /* NaN */ 63 if(hx==0x7f800000) 64 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 65 if(x > o_threshold) return huge*huge; /* overflow */ 66 } 67 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 68 if(x+tiny<(float)0.0) /* raise inexact */ 69 return tiny-one; /* return -1 */ 70 } 71 } 72 73 /* argument reduction */ 74 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 75 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 76 if(xsb==0) 77 {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 78 else 79 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 80 } else { 81 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 82 t = k; 83 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 84 lo = t*ln2_lo; 85 } 86 x = hi - lo; 87 c = (hi-x)-lo; 88 } 89 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 90 t = huge+x; /* return x with inexact flags when x!=0 */ 91 return x - (t-(huge+x)); 92 } 93 else k = 0; 94 95 /* x is now in primary range */ 96 hfx = (float)0.5*x; 97 hxs = x*hfx; 98 r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 99 t = (float)3.0-r1*hfx; 100 e = hxs*((r1-t)/((float)6.0 - x*t)); 101 if(k==0) return x - (x*e-hxs); /* c is 0 */ 102 else { 103 e = (x*(e-c)-c); 104 e -= hxs; 105 if(k== -1) return (float)0.5*(x-e)-(float)0.5; 106 if(k==1) 107 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 108 else return one+(float)2.0*(x-e); 109 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 110 int32_t i; 111 y = one-(e-x); 112 GET_FLOAT_WORD(i,y); 113 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 114 return y-one; 115 } 116 t = one; 117 if(k<23) { 118 int32_t i; 119 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 120 y = t-(e-x); 121 GET_FLOAT_WORD(i,y); 122 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 123 } else { 124 int32_t i; 125 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 126 y = x-(e+t); 127 y += one; 128 GET_FLOAT_WORD(i,y); 129 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 130 } 131 } 132 return y; 133 } 134