* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITY
- * log domain: x < 0; returns NAN
*/
#include "libm.h"
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 2.32e-20
*/
-static long double P[] = {
+static const long double P[] = {
4.5270000862445199635215E-5L,
4.9854102823193375972212E-1L,
6.5787325942061044846969E0L,
5.7112963590585538103336E1L,
2.0039553499201281259648E1L,
};
-static long double Q[] = {
+static const long double Q[] = {
/* 1.0000000000000000000000E0,*/
1.5062909083469192043167E1L,
8.3047565967967209469434E1L,
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.16e-22
*/
-static long double R[4] = {
+static const long double R[4] = {
1.9757429581415468984296E-3L,
-7.1990767473014147232598E-1L,
1.0777257190312272158094E1L,
-3.5717684488096787370998E1L,
};
-static long double S[4] = {
+static const long double S[4] = {
/* 1.00000000000000000000E0L,*/
-2.6201045551331104417768E1L,
1.9361891836232102174846E2L,
return x;
if (x == INFINITY)
return x;
- if (x <= 0.0L) {
- if (x == 0.0L)
- return -INFINITY;
- return NAN;
+ if (x <= 0.0) {
+ if (x == 0.0)
+ return -1/(x+0); /* -inf with divbyzero */
+ return 0/0.0f; /* nan with invalid */
}
/* separate mantissa from exponent */
if (e > 2 || e < -2) {
if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
e -= 1;
- z = x - 0.5L;
- y = 0.5L * z + 0.5L;
+ z = x - 0.5;
+ y = 0.5 * z + 0.5;
} else { /* 2 (x-1)/(x+1) */
- z = x - 0.5L;
- z -= 0.5L;
- y = 0.5L * x + 0.5L;
+ z = x - 0.5;
+ z -= 0.5;
+ y = 0.5 * x + 0.5;
}
x = z / y;
z = x*x;
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH) {
e -= 1;
- x = ldexpl(x, 1) - 1.0L; /* 2x - 1 */
+ x = 2.0*x - 1.0;
} else {
- x = x - 1.0L;
+ x = x - 1.0;
}
z = x*x;
y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6));
y = y + e * C2;
- z = y - ldexpl(z, -1); /* y - 0.5 * z */
+ z = y - 0.5*z;
/* Note, the sum of above terms does not exceed x/4,
* so it contributes at most about 1/4 lsb to the error.
*/