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 #if defined(LIBM_SCCS) && !defined(lint) 18 __RCSID("$NetBSD: s_expm1f.c,v 1.10 2002/05/26 22:01:55 wiz Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float huge = 1.0e+30, tiny = 1.0e-30; 25 26 static const float 27 one = 1.0, 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 /* scaled coefficients related to expm1 */ 33 Q1 = -3.3333335072e-02, /* 0xbd088889 */ 34 Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ 35 Q3 = -7.9365076090e-05, /* 0xb8a670cd */ 36 Q4 = 4.0082177293e-06, /* 0x36867e54 */ 37 Q5 = -2.0109921195e-07; /* 0xb457edbb */ 38 39 float 40 expm1f(float x) 41 { 42 float y,hi,lo,c,t,e,hxs,hfx,r1; 43 int32_t k,xsb; 44 u_int32_t hx; 45 46 c = 0; 47 GET_FLOAT_WORD(hx,x); 48 xsb = hx&0x80000000; /* sign bit of x */ 49 if(xsb==0) y=x; else y= -x; /* y = |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 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+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 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 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 int32_t i; 106 y = one-(e-x); 107 GET_FLOAT_WORD(i,y); 108 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 109 return y-one; 110 } 111 t = one; 112 if(k<23) { 113 int32_t i; 114 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 115 y = t-(e-x); 116 GET_FLOAT_WORD(i,y); 117 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 118 } else { 119 int32_t i; 120 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 121 y = x-(e+t); 122 y += one; 123 GET_FLOAT_WORD(i,y); 124 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 125 } 126 } 127 return y; 128 } 129