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Use double arithmetic instead of simulating it with two floats. This

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results in a performance gain on the order of 10% for amd64 (sledge),
ia64 (pluto1), i386+SSE (Pentium 4), and sparc64 (panther), and a
negligible improvement for i386 without SSE.  (The i386 port still
uses the hardware instruction, though.)
This commit is contained in:
David Schultz 2005-02-21 17:44:57 +00:00
parent 473156220d
commit 96efaf6c36
1 changed files with 8 additions and 13 deletions
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21
lib/msun/src/e_expf.c
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@ -27,27 +27,24 @@ huge = 1.0e+30,
twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
-6.9313812256e-01,}, /* 0xbf317180 */
ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
-9.0580006145e-06,}, /* 0xb717f7d1 */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08; /* 0x3331bb4c */
double ln2[2] = { 6.93147180369123816490e-01, -6.93147180369123816490e-01 };
float
__ieee754_expf(float x) /* default IEEE double exp */
__ieee754_expf(float x) /* IEEE float exp */
{
float y,hi=0.0,lo=0.0,c,t;
float y,c,t;
int32_t k=0,xsb;
u_int32_t hx;
GET_FLOAT_WORD(hx,x);
xsb = (hx>>31)&1; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
hx &= 0x7fffffff; /* |x| */
/* filter out non-finite argument */
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
@ -62,14 +59,12 @@ __ieee754_expf(float x) /* default IEEE double exp */
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
x = x-ln2[xsb]; k = 1-xsb-xsb;
} else {
k = invln2*x+halF[xsb];
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
x = x - t*ln2[0];
}
x = hi - lo;
}
else if(hx < 0x31800000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
@ -79,8 +74,8 @@ __ieee754_expf(float x) /* default IEEE double exp */
/* x is now in primary range */
t = x*x;
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
y = one-(((double)x*c)/(c-2.0)-x);
if(k==0) return y;
if(k >= -125) {
u_int32_t hy;
GET_FLOAT_WORD(hy,y);