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/* 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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#include "math.h" |
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#include "math_private.h" |
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static const volatile float huge = 1.0e+30, tiny = 1.0e-30; |
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static const float |
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one = 1.0, |
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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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float |
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expm1f(float x) |
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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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} |
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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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DEF_STD(expm1f); |