diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128/lgamma_negl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/lgamma_negl.c | 82 |
1 files changed, 41 insertions, 41 deletions
diff --git a/sysdeps/ieee754/ldbl-128/lgamma_negl.c b/sysdeps/ieee754/ldbl-128/lgamma_negl.c index df46199b82..a624fc11b3 100644 --- a/sysdeps/ieee754/ldbl-128/lgamma_negl.c +++ b/sysdeps/ieee754/ldbl-128/lgamma_negl.c @@ -20,7 +20,7 @@ #include <math.h> #include <math_private.h> -static const long double lgamma_zeros[][2] = +static const _Float128 lgamma_zeros[][2] = { { -0x2.74ff92c01f0d82abec9f315f1a08p+0L, 0xe.d3ccb7fb2658634a2b9f6b2ba81p-116L }, { -0x2.bf6821437b20197995a4b4641eaep+0L, -0xb.f4b00b4829f961e428533e6ad048p-116L }, @@ -120,14 +120,14 @@ static const long double lgamma_zeros[][2] = { -0x3.2p+4L, 0x3.766dedc259af040be140a68a6c04p-216L }, }; -static const long double e_hi = 0x2.b7e151628aed2a6abf7158809cf4p+0L; -static const long double e_lo = 0xf.3c762e7160f38b4da56a784d9048p-116L; +static const _Float128 e_hi = 0x2.b7e151628aed2a6abf7158809cf4p+0L; +static const _Float128 e_lo = 0xf.3c762e7160f38b4da56a784d9048p-116L; /* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's approximation to lgamma function. */ -static const long double lgamma_coeff[] = +static const _Float128 lgamma_coeff[] = { 0x1.5555555555555555555555555555p-4L, -0xb.60b60b60b60b60b60b60b60b60b8p-12L, @@ -166,7 +166,7 @@ static const long double lgamma_coeff[] = polynomial is expressed in terms of x-xm, where xm is the midpoint of the interval for which the polynomial applies. */ -static const long double poly_coeff[] = +static const _Float128 poly_coeff[] = { /* Interval [-2.125, -2] (polynomial degree 23). */ -0x1.0b71c5c54d42eb6c17f30b7aa8f5p+0L, @@ -412,8 +412,8 @@ static const size_t poly_end[] = /* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ -static long double -lg_sinpi (long double x) +static _Float128 +lg_sinpi (_Float128 x) { if (x <= 0.25L) return __sinl (M_PIl * x); @@ -423,8 +423,8 @@ lg_sinpi (long double x) /* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ -static long double -lg_cospi (long double x) +static _Float128 +lg_cospi (_Float128 x) { if (x <= 0.25L) return __cosl (M_PIl * x); @@ -434,8 +434,8 @@ lg_cospi (long double x) /* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ -static long double -lg_cotpi (long double x) +static _Float128 +lg_cotpi (_Float128 x) { return lg_cospi (x) / lg_sinpi (x); } @@ -443,34 +443,34 @@ lg_cotpi (long double x) /* Compute lgamma of a negative argument -50 < X < -2, setting *SIGNGAMP accordingly. */ -long double -__lgamma_negl (long double x, int *signgamp) +_Float128 +__lgamma_negl (_Float128 x, int *signgamp) { /* Determine the half-integer region X lies in, handle exact integers and determine the sign of the result. */ int i = __floorl (-2 * x); if ((i & 1) == 0 && i == -2 * x) return 1.0L / 0.0L; - long double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + _Float128 xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); i -= 4; *signgamp = ((i & 2) == 0 ? -1 : 1); SET_RESTORE_ROUNDL (FE_TONEAREST); /* Expand around the zero X0 = X0_HI + X0_LO. */ - long double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; - long double xdiff = x - x0_hi - x0_lo; + _Float128 x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + _Float128 xdiff = x - x0_hi - x0_lo; /* For arguments in the range -3 to -2, use polynomial approximations to an adjusted version of the gamma function. */ if (i < 2) { int j = __floorl (-8 * x) - 16; - long double xm = (-33 - 2 * j) * 0.0625L; - long double x_adj = x - xm; + _Float128 xm = (-33 - 2 * j) * 0.0625L; + _Float128 x_adj = x - xm; size_t deg = poly_deg[j]; size_t end = poly_end[j]; - long double g = poly_coeff[end]; + _Float128 g = poly_coeff[end]; for (size_t j = 1; j <= deg; j++) g = g * x_adj + poly_coeff[end - j]; return __log1pl (g * xdiff / (x - xn)); @@ -478,8 +478,8 @@ __lgamma_negl (long double x, int *signgamp) /* The result we want is log (sinpi (X0) / sinpi (X)) + log (gamma (1 - X0) / gamma (1 - X)). */ - long double x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); - long double log_sinpi_ratio; + _Float128 x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); + _Float128 log_sinpi_ratio; if (x0_idiff < x_idiff * 0.5L) /* Use log not log1p to avoid inaccuracy from log1p of arguments close to -1. */ @@ -490,29 +490,29 @@ __lgamma_negl (long double x, int *signgamp) /* Use log1p not log to avoid inaccuracy from log of arguments close to 1. X0DIFF2 has positive sign if X0 is further from XN than X is from XN, negative sign otherwise. */ - long double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5L; - long double sx0d2 = lg_sinpi (x0diff2); - long double cx0d2 = lg_cospi (x0diff2); + _Float128 x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5L; + _Float128 sx0d2 = lg_sinpi (x0diff2); + _Float128 cx0d2 = lg_cospi (x0diff2); log_sinpi_ratio = __log1pl (2 * sx0d2 * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); } - long double log_gamma_ratio; - long double y0 = 1 - x0_hi; - long double y0_eps = -x0_hi + (1 - y0) - x0_lo; - long double y = 1 - x; - long double y_eps = -x + (1 - y); + _Float128 log_gamma_ratio; + _Float128 y0 = 1 - x0_hi; + _Float128 y0_eps = -x0_hi + (1 - y0) - x0_lo; + _Float128 y = 1 - x; + _Float128 y_eps = -x + (1 - y); /* We now wish to compute LOG_GAMMA_RATIO = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF accurately approximates the difference Y0 + Y0_EPS - Y - Y_EPS. Use Stirling's approximation. First, we may need to adjust into the range where Stirling's approximation is sufficiently accurate. */ - long double log_gamma_adj = 0; + _Float128 log_gamma_adj = 0; if (i < 20) { int n_up = (21 - i) / 2; - long double ny0, ny0_eps, ny, ny_eps; + _Float128 ny0, ny0_eps, ny, ny_eps; ny0 = y0 + n_up; ny0_eps = y0 - (ny0 - n_up) + y0_eps; y0 = ny0; @@ -521,28 +521,28 @@ __lgamma_negl (long double x, int *signgamp) ny_eps = y - (ny - n_up) + y_eps; y = ny; y_eps = ny_eps; - long double prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); + _Float128 prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); log_gamma_adj = -__log1pl (prodm1); } - long double log_gamma_high + _Float128 log_gamma_high = (xdiff * __log1pl ((y0 - e_hi - e_lo + y0_eps) / e_hi) + (y - 0.5L + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ - long double y0r = 1 / y0, yr = 1 / y; - long double y0r2 = y0r * y0r, yr2 = yr * yr; - long double rdiff = -xdiff / (y * y0); - long double bterm[NCOEFF]; - long double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + _Float128 y0r = 1 / y0, yr = 1 / y; + _Float128 y0r2 = y0r * y0r, yr2 = yr * yr; + _Float128 rdiff = -xdiff / (y * y0); + _Float128 bterm[NCOEFF]; + _Float128 dlast = rdiff, elast = rdiff * yr * (yr + y0r); bterm[0] = dlast * lgamma_coeff[0]; for (size_t j = 1; j < NCOEFF; j++) { - long double dnext = dlast * y0r2 + elast; - long double enext = elast * yr2; + _Float128 dnext = dlast * y0r2 + elast; + _Float128 enext = elast * yr2; bterm[j] = dnext * lgamma_coeff[j]; dlast = dnext; elast = enext; } - long double log_gamma_low = 0; + _Float128 log_gamma_low = 0; for (size_t j = 0; j < NCOEFF; j++) log_gamma_low += bterm[NCOEFF - 1 - j]; log_gamma_ratio = log_gamma_high + log_gamma_low; |