float __cbrtf (float x) { float xm, ym, u, t2; int xe; /* Reduce X. XM now is an range 1.0 to 0.5. */ xm = __frexpf (fabsf (x), &xe); /* If X is not finite or is null return it (with raising exceptions if necessary. Note: *Our* version of `frexp' sets XE to zero if the argument is Inf or NaN. This is not portable but faster. */ if (xe == 0 && fpclassify (x) <= FP_ZERO) return x + x; u = (0.492659620528969547 + (0.697570460207922770 - 0.191502161678719066 * xm) * xm); t2 = u * u * u; ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; return __ldexpf (x > 0.0 ? ym : -ym, xe / 3); }
static float gammaf_positive (float x, int *exp2_adj) { int local_signgam; if (x < 0.5f) { *exp2_adj = 0; return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x; } else if (x <= 1.5f) { *exp2_adj = 0; return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam)); } else if (x < 2.5f) { *exp2_adj = 0; float x_adj = x - 1; return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam)) * x_adj); } else { float eps = 0; float x_eps = 0; float x_adj = x; float prod = 1; if (x < 4.0f) { /* Adjust into the range for applying Stirling's approximation. */ float n = __ceilf (4.0f - x); x_adj = math_narrow_eval (x + n); x_eps = (x - (x_adj - n)); prod = __gamma_productf (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. */ float exp_adj = -eps; float x_adj_int = __roundf (x_adj); float x_adj_frac = x_adj - x_adj_int; int x_adj_log2; float x_adj_mant = __frexpf (x_adj, &x_adj_log2); if (x_adj_mant < (float) M_SQRT1_2) { x_adj_log2--; x_adj_mant *= 2.0f; } *exp2_adj = x_adj_log2 * (int) x_adj_int; float ret = (__ieee754_powf (x_adj_mant, x_adj) * __ieee754_exp2f (x_adj_log2 * x_adj_frac) * __ieee754_expf (-x_adj) * __ieee754_sqrtf (2 * (float) M_PI / x_adj) / prod); exp_adj += x_eps * __ieee754_logf (x_adj); float bsum = gamma_coeff[NCOEFF - 1]; float 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 * __expm1f (exp_adj); } }