char _lngamma( floatnum x, int digits) { floatstruct factor; int infinity; char result; if (float_cmp(x, &c1) == 0 || float_cmp(x, &c2) == 0) return _setzero(x); float_create(&factor); result = _lngamma_prim(x, &factor, &infinity, digits) && infinity == 0; if (result) { float_abs(&factor); _ln(&factor, digits + 1); result = float_sub(x, x, &factor, digits+1); } float_free(&factor); if (infinity != 0) return _seterror(x, ZeroDivide); if (!result) float_setnan(x); return result; }
/* evaluates ln(Gamma(x)) for all those x big enough to let the asymptotic series converge directly. Returns 0, if the result overflows relative error for a 100 gigit calculation < 5e-100 */ static char _lngammabigx( floatnum x, int digits) { floatstruct tmp1, tmp2; char result; result = 0; float_create(&tmp1); float_create(&tmp2); /* compute (ln x-1) * (x-0.5) - 0.5 + ln(sqrt(2*pi)) */ float_copy(&tmp2, x, digits+1); _ln(&tmp2, digits+1); float_sub(&tmp2, &tmp2, &c1, digits+2); float_sub(&tmp1, x, &c1Div2, digits+2); if (float_mul(&tmp1, &tmp1, &tmp2, digits+2)) { /* no overflow */ lngammaasymptotic(x, digits); float_add(x, &tmp1, x, digits+3); float_add(x, x, &cLnSqrt2PiMinusHalf, digits+3); result = 1; } float_free(&tmp2); float_free(&tmp1); return result; }
char float_ln(floatnum x, int digits) { if (!chckmathparam(x, digits)) return 0; if (float_getsign(x) <= 0) return _seterror(x, OutOfDomain); _ln(x, digits); return 1; }
char float_lg( floatnum x, int digits) { floatstruct tmp; int expx; if (!chckmathparam(x, digits)) return 0; if (float_getsign(x) <= 0) return _seterror(x, OutOfDomain); float_create(&tmp); expx = float_getexponent(x); float_setexponent(x, 0); _ln(x, digits); float_div(x, x, &cLn10, digits); float_setinteger(&tmp, expx); float_add(x, x, &tmp, digits); float_free(&tmp); return 1; }
REAL _pow2(REAL a, REAL b, QByteArray &error) { return _ln(a, b, error) * _pow(a, b, error); }