/* s_expm1f.c -- float version of s_expm1.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #ifndef lint static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.7 2002/05/28 18:15:04 alfred Exp $"; #endif #include "math.h" #include "math_private.h" static const float one = 1.0, huge = 1.0e+30, tiny = 1.0e-30, o_threshold = 8.8721679688e+01,/* 0x42b17180 */ ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ /* scaled coefficients related to expm1 */ Q1 = -3.3333335072e-02, /* 0xbd088889 */ Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ Q3 = -7.9365076090e-05, /* 0xb8a670cd */ Q4 = 4.0082177293e-06, /* 0x36867e54 */ Q5 = -2.0109921195e-07; /* 0xb457edbb */ float expm1f(float x) { float y,hi,lo,c,t,e,hxs,hfx,r1; int32_t k,xsb; u_int32_t hx; GET_FLOAT_WORD(hx,x); xsb = hx&0x80000000; /* sign bit of x */ if(xsb==0) y=x; else y= -x; /* y = |x| */ hx &= 0x7fffffff; /* high word of |x| */ /* filter out huge and non-finite argument */ if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ if(hx >= 0x42b17218) { /* if |x|>=88.721... */ if(hx>0x7f800000) return x+x; /* NaN */ if(hx==0x7f800000) return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ if(x > o_threshold) return huge*huge; /* overflow */ } if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ if(x+tiny<(float)0.0) /* raise inexact */ return tiny-one; /* return -1 */ } } /* argument reduction */ if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ if(xsb==0) {hi = x - ln2_hi; lo = ln2_lo; k = 1;} else {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} } else { k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); t = k; hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ lo = t*ln2_lo; } x = hi - lo; c = (hi-x)-lo; } else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ t = huge+x; /* return x with inexact flags when x!=0 */ return x - (t-(huge+x)); } else k = 0; /* x is now in primary range */ hfx = (float)0.5*x; hxs = x*hfx; r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); t = (float)3.0-r1*hfx; e = hxs*((r1-t)/((float)6.0 - x*t)); if(k==0) return x - (x*e-hxs); /* c is 0 */ else { e = (x*(e-c)-c); e -= hxs; if(k== -1) return (float)0.5*(x-e)-(float)0.5; if(k==1) if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); else return one+(float)2.0*(x-e); if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ int32_t i; y = one-(e-x); GET_FLOAT_WORD(i,y); SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ return y-one; } t = one; if(k<23) { int32_t i; SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ y = t-(e-x); GET_FLOAT_WORD(i,y); SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ } else { int32_t i; SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ y = x-(e+t); y += one; GET_FLOAT_WORD(i,y); SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ } } return y; }