0,0 → 1,145 |
/* sf_expm1.c -- float version of s_expm1.c. |
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
*/ |
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/* |
* ==================================================== |
* 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. |
* ==================================================== |
*/ |
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#include "fdlibm.h" |
|
#ifdef __v810__ |
#define const |
#endif |
|
#ifdef __STDC__ |
static const float |
#else |
static float |
#endif |
one = 1.0, |
huge = 1.0e+30, |
tiny = 1.0e-30, |
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 */ |
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#ifdef __STDC__ |
float expm1f(float x) |
#else |
float expm1f(x) |
float x; |
#endif |
{ |
float y,hi,lo,c,t,e,hxs,hfx,r1; |
__int32_t k,xsb; |
__uint32_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(FLT_UWORD_IS_NAN(hx)) |
return x+x; |
if(FLT_UWORD_IS_INFINITE(hx)) |
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ |
if(xsb == 0 && hx > FLT_UWORD_LOG_MAX) /* 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; |
} |
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#ifdef _DOUBLE_IS_32BITS |
|
#ifdef __STDC__ |
double expm1(double x) |
#else |
double expm1(x) |
double x; |
#endif |
{ |
return (double) expm1f((float) x); |
} |
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#endif /* defined(_DOUBLE_IS_32BITS) */ |