diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_gamma_r.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_gamma_r.c | 140 |
1 files changed, 135 insertions, 5 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_gamma_r.c b/sysdeps/ieee754/dbl-64/e_gamma_r.c index 9873551757..5b17f7b5ad 100644 --- a/sysdeps/ieee754/dbl-64/e_gamma_r.c +++ b/sysdeps/ieee754/dbl-64/e_gamma_r.c @@ -19,14 +19,104 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const double gamma_coeff[] = + { + 0x1.5555555555555p-4, + -0xb.60b60b60b60b8p-12, + 0x3.4034034034034p-12, + -0x2.7027027027028p-12, + 0x3.72a3c5631fe46p-12, + -0x7.daac36664f1f4p-12, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 184, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static double +gamma_positive (double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam)); + } + else if (x < 6.5) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + double n = __ceil (x - 1.5); + double x_adj = x - n; + double eps; + double prod = __gamma_product (x_adj, 0, n, &eps); + return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam)) + * prod * (1.0 + eps)); + } + else + { + double eps = 0; + double x_eps = 0; + double x_adj = x; + double prod = 1; + if (x < 12.0) + { + /* Adjust into the range for applying Stirling's + approximation. */ + double n = __ceil (12.0 - x); +#if FLT_EVAL_METHOD != 0 + volatile +#endif + double x_tmp = x + n; + x_adj = x_tmp; + x_eps = (x - (x_adj - n)); + prod = __gamma_product (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + double exp_adj = -eps; + double x_adj_int = __round (x_adj); + double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + double x_adj_mant = __frexp (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2) + { + x_adj_log2--; + x_adj_mant *= 2.0; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + double ret = (__ieee754_pow (x_adj_mant, x_adj) + * __ieee754_exp2 (x_adj_log2 * x_adj_frac) + * __ieee754_exp (-x_adj) + * __ieee754_sqrt (2 * M_PI / x_adj) + / prod); + exp_adj += x_eps * __ieee754_log (x); + double bsum = gamma_coeff[NCOEFF - 1]; + double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1 (exp_adj); + } +} double __ieee754_gamma_r (double x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ int32_t hx; u_int32_t lx; @@ -51,8 +141,48 @@ __ieee754_gamma_r (double x, int *signgamp) *signgamp = 0; return x - x; } + if (__builtin_expect ((hx & 0x7ff00000) == 0x7ff00000, 0)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } - /* XXX FIXME. */ - return __ieee754_exp (__ieee754_lgamma_r (x, signgamp)); + if (x >= 172.0) + { + /* Overflow. */ + *signgamp = 0; + return DBL_MAX * DBL_MAX; + } + else if (x > 0.0) + { + *signgamp = 0; + int exp2_adj; + double ret = gamma_positive (x, &exp2_adj); + return __scalbn (ret, exp2_adj); + } + else if (x >= -DBL_EPSILON / 4.0) + { + *signgamp = 0; + return 1.0 / x; + } + else + { + double tx = __trunc (x); + *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1; + if (x <= -184.0) + /* Underflow. */ + return DBL_MIN * DBL_MIN; + double frac = tx - x; + if (frac > 0.5) + frac = 1.0 - frac; + double sinpix = (frac <= 0.25 + ? __sin (M_PI * frac) + : __cos (M_PI * (0.5 - frac))); + int exp2_adj; + double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj)); + return __scalbn (ret, -exp2_adj); + } } strong_alias (__ieee754_gamma_r, __gamma_r_finite) |