3a8617a83f
-- Begin comments from J.T. Conklin: The most significant improvement is the addition of "float" versions of the math functions that take float arguments, return floats, and do all operations in floating point. This doesn't help (performance) much on the i386, but they are still nice to have. The float versions were orginally done by Cygnus' Ian Taylor when fdlibm was integrated into the libm we support for embedded systems. I gave Ian a copy of my libm as a starting point since I had already fixed a lot of bugs & problems in Sun's original code. After he was done, I cleaned it up a bit and integrated the changes back into my libm. -- End comments Reviewed by: jkh Submitted by: jtc
134 lines
3.7 KiB
C
134 lines
3.7 KiB
C
/* s_expm1f.c -- float version of s_expm1.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#ifndef lint
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static char rcsid[] = "$Id: s_expm1f.c,v 1.2 1994/08/18 23:06:40 jtc Exp $";
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#endif
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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one = 1.0,
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huge = 1.0e+30,
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tiny = 1.0e-30,
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o_threshold = 8.8721679688e+01,/* 0x42b17180 */
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ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
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ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
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invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
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/* scaled coefficients related to expm1 */
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Q1 = -3.3333335072e-02, /* 0xbd088889 */
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Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
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Q3 = -7.9365076090e-05, /* 0xb8a670cd */
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Q4 = 4.0082177293e-06, /* 0x36867e54 */
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Q5 = -2.0109921195e-07; /* 0xb457edbb */
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#ifdef __STDC__
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float expm1f(float x)
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#else
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float expm1f(x)
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float x;
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#endif
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{
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float y,hi,lo,c,t,e,hxs,hfx,r1;
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int32_t k,xsb;
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u_int32_t hx;
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GET_FLOAT_WORD(hx,x);
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xsb = hx&0x80000000; /* sign bit of x */
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if(xsb==0) y=x; else y= -x; /* y = |x| */
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hx &= 0x7fffffff; /* high word of |x| */
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/* filter out huge and non-finite argument */
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if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
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if(hx >= 0x42b17218) { /* if |x|>=88.721... */
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if(hx>0x7f800000)
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return x+x; /* NaN */
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if(hx==0x7f800000)
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return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
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if(x > o_threshold) return huge*huge; /* overflow */
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}
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if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
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if(x+tiny<(float)0.0) /* raise inexact */
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return tiny-one; /* return -1 */
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}
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}
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/* argument reduction */
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if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
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if(xsb==0)
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{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
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else
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{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
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} else {
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k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
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t = k;
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hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
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lo = t*ln2_lo;
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}
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x = hi - lo;
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c = (hi-x)-lo;
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}
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else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
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t = huge+x; /* return x with inexact flags when x!=0 */
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return x - (t-(huge+x));
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}
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else k = 0;
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/* x is now in primary range */
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hfx = (float)0.5*x;
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hxs = x*hfx;
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r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
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t = (float)3.0-r1*hfx;
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e = hxs*((r1-t)/((float)6.0 - x*t));
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if(k==0) return x - (x*e-hxs); /* c is 0 */
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else {
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e = (x*(e-c)-c);
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e -= hxs;
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if(k== -1) return (float)0.5*(x-e)-(float)0.5;
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if(k==1)
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if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
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else return one+(float)2.0*(x-e);
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if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
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int32_t i;
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y = one-(e-x);
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GET_FLOAT_WORD(i,y);
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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return y-one;
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}
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t = one;
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if(k<23) {
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int32_t i;
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SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
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y = t-(e-x);
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GET_FLOAT_WORD(i,y);
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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} else {
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int32_t i;
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SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
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y = x-(e+t);
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y += one;
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GET_FLOAT_WORD(i,y);
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SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
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}
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}
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return y;
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}
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