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-rw-r--r--src/math/expl.c43
1 files changed, 19 insertions, 24 deletions
diff --git a/src/math/expl.c b/src/math/expl.c
index b289ffec..50a04297 100644
--- a/src/math/expl.c
+++ b/src/math/expl.c
@@ -35,7 +35,7 @@
* x k f
* e = 2 e.
*
- * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
+ * A Pade' form of degree 5/6 is used to approximate exp(f) - 1
* in the basic range [-0.5 ln 2, 0.5 ln 2].
*
*
@@ -86,42 +86,37 @@ static const long double Q[4] = {
2.0000000000000000000897E0L,
};
static const long double
-C1 = 6.9314575195312500000000E-1L,
-C2 = 1.4286068203094172321215E-6L,
-MAXLOGL = 1.1356523406294143949492E4L,
-MINLOGL = -1.13994985314888605586758E4L,
-LOG2EL = 1.4426950408889634073599E0L;
+LN2HI = 6.9314575195312500000000E-1L,
+LN2LO = 1.4286068203094172321215E-6L,
+LOG2E = 1.4426950408889634073599E0L;
long double expl(long double x)
{
long double px, xx;
- int n;
+ int k;
if (isnan(x))
return x;
- if (x > MAXLOGL)
- return INFINITY;
- if (x < MINLOGL)
- return 0.0;
+ if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */
+ return x * 0x1p16383L;
+ if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */
+ return 0x1p-10000L * 0x1p-10000L;
- /* Express e**x = e**g 2**n
- * = e**g e**(n loge(2))
- * = e**(g + n loge(2))
+ /* Express e**x = e**f 2**k
+ * = e**(f + k ln(2))
*/
- px = floorl(LOG2EL * x + 0.5); /* floor() truncates toward -infinity. */
- n = px;
- x -= px * C1;
- x -= px * C2;
+ px = floorl(LOG2E * x + 0.5);
+ k = px;
+ x -= px * LN2HI;
+ x -= px * LN2LO;
- /* rational approximation for exponential
- * of the fractional part:
- * e**x = 1 + 2x P(x**2)/(Q(x**2) - P(x**2))
+ /* rational approximation of the fractional part:
+ * e**x = 1 + 2x P(x**2)/(Q(x**2) - x P(x**2))
*/
xx = x * x;
px = x * __polevll(xx, P, 2);
- x = px/(__polevll(xx, Q, 3) - px);
+ x = px/(__polevll(xx, Q, 3) - px);
x = 1.0 + 2.0 * x;
- x = scalbnl(x, n);
- return x;
+ return scalbnl(x, k);
}
#endif