diff options
Diffstat (limited to 'src/math')
| -rw-r--r-- | src/math/expl.c | 43 |
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 |