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math: expf.c cleanup

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similar to exp.c cleanup: use scalbnf, don't return excess precision,
drop some optimizatoins.
exp.c was changed to be more consistent with expf.c code.
This commit is contained in:
Szabolcs Nagy 2012-11-18 03:42:09 +01:00
parent 159c7655d0
commit ab1772c597
2 changed files with 55 additions and 63 deletions
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20
src/math/exp.c
View File

@ -80,7 +80,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
double exp(double x)
{
double hi, lo, c, z;
double hi, lo, c, xx;
int k, sign;
uint32_t hx;
@ -92,24 +92,26 @@ double exp(double x)
if (hx >= 0x40862e42) { /* if |x| >= 709.78... */
if (isnan(x))
return x;
if (hx == 0x7ff00000 && sign) /* -inf */
return 0;
if (x > 709.782712893383973096) {
/* overflow if x!=inf */
STRICT_ASSIGN(double, x, 0x1p1023 * x);
return x;
}
if (x < -745.13321910194110842) {
/* underflow if x!=-inf */
STRICT_ASSIGN(double, x, 0x1p-1000 / -x * 0x1p-1000);
/* underflow */
STRICT_ASSIGN(double, x, 0x1p-1000 * 0x1p-1000);
return x;
}
}
/* argument reduction */
if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if (hx < 0x3ff0a2b2) /* if |x| < 1.5 ln2 */
k = 1 - sign - sign; /* optimization */
else
if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */
k = (int)(invln2*x + half[sign]);
else
k = 1 - sign - sign;
hi = x - k*ln2hi; /* k*ln2hi is exact here */
lo = k*ln2lo;
STRICT_ASSIGN(double, x, hi - lo);
@ -124,9 +126,9 @@ double exp(double x)
}
/* x is now in primary range */
z = x*x;
c = x - z*(P1+z*(P2+z*(P3+z*(P4+z*P5))));
x = 1 + ((x*c/(2-c) - lo) + hi);
xx = x*x;
c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5))));
x = 1 + (x*c/(2-c) - lo + hi);
if (k == 0)
return x;
return scalbn(x, k);

98
src/math/expf.c
View File

@ -16,79 +16,69 @@
#include "libm.h"
static const float
halF[2] = {0.5,-0.5,},
huge = 1.0e+30,
o_threshold = 8.8721679688e+01, /* 0x42b17180 */
u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
ln2HI[2] = { 6.9314575195e-01, /* 0x3f317200 */
-6.9314575195e-01,},/* 0xbf317200 */
ln2LO[2] = { 1.4286067653e-06, /* 0x35bfbe8e */
-1.4286067653e-06,},/* 0xb5bfbe8e */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
half[2] = {0.5,-0.5},
ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
*/
P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
static const volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
float expf(float x)
{
float y,hi=0.0,lo=0.0,c,t,twopk;
int32_t k=0,xsb;
float hi, lo, c, xx;
int k, sign;
uint32_t hx;
GET_FLOAT_WORD(hx, x);
xsb = (hx>>31)&1; /* sign bit of x */
sign = hx >> 31; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out non-finite argument */
if (hx >= 0x42b17218) { /* if |x|>=88.721... */
/* special cases */
if (hx >= 0x42b17218) { /* if |x| >= 88.722839f or NaN */
if (hx > 0x7f800000) /* NaN */
return x+x;
if (hx == 0x7f800000) /* exp(+-inf)={inf,0} */
return xsb==0 ? x : 0.0;
if (x > o_threshold)
return huge*huge; /* overflow */
if (x < u_threshold)
return twom100*twom100; /* underflow */
return x;
if (!sign) {
/* overflow if x!=inf */
STRICT_ASSIGN(float, x, x * 0x1p127f);
return x;
}
if (hx == 0x7f800000) /* -inf */
return 0;
if (hx >= 0x42cff1b5) { /* x <= -103.972084f */
/* underflow */
STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
return x;
}
}
/* 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;
} else {
k = invln2*x + halF[xsb];
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
}
if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
k = invln2*x + half[sign];
else
k = 1 - sign - sign;
hi = x - k*ln2hi; /* k*ln2hi is exact here */
lo = k*ln2lo;
STRICT_ASSIGN(float, x, hi - lo);
} else if(hx < 0x39000000) { /* |x|<2**-14 */
/* raise inexact */
if (huge+x > 1.0f)
return 1.0f + x;
} else
} else if (hx > 0x39000000) { /* |x| > 2**-14 */
k = 0;
hi = x;
lo = 0;
} else {
/* raise inexact */
FORCE_EVAL(0x1p127f + x);
return 1 + x;
}
/* x is now in primary range */
t = x*x;
if (k >= -125)
SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
else
SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
c = x - t*(P1+t*P2);
xx = x*x;
c = x - xx*(P1+xx*P2);
x = 1 + (x*c/(2-c) - lo + hi);
if (k == 0)
return 1.0f - ((x*c)/(c - 2.0f) - x);
y = 1.0f - ((lo - (x*c)/(2.0f - c)) - hi);
if (k < -125)
return y*twopk*twom100;
if (k == 128)
return y*2.0f*0x1p127f;
return y*twopk;
return x;
return scalbnf(x, k);
}