// TODO: adjust sign
int mpf_gamma(mp_float * a, mp_float * b)
{
int err;
long oldeps, eps;
mp_float t;
err = MP_OKAY;
oldeps = a->radix;
eps = oldeps + MP_DIGIT_BIT;
if ((err = mpf_init(&t, oldeps)) != MP_OKAY) {
return err;
}
if ((err = mpf_copy(a, &t)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&t, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_lngamma(&t, &t)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_exp(&t, &t)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&t, oldeps)) != MP_OKAY) {
goto _ERR;
}
mpf_exch(&t, b);
_ERR:
mpf_clear(&t);
return err;
}
// only (exp(log(gamma(a)))) for now
int mpf_lngamma(mp_float * a, mp_float * b)
{
int oldeps, eps, err, n, accuracy;
size_t A;
mp_float z, ONE, factrl, e, pi, t1, t2, t3, sum;
err = MP_OKAY;
if (mpf_iszero(a)) {
// raise singularity error
return MP_VAL;
}
// Check is expensive and inexact.
// if(mpf_isint(a){...}
// very near zero
if (a->exp + a->radix < -(a->radix)) {
if ((err = mpf_ln(a, b)) != MP_OKAY) {
return err;
}
return err;
}
oldeps = a->radix;
if (reflection == 1) {
// angst-allowance seemed not necessary
// TODO: check if that is really true
eps = oldeps;
} else {
accuracy = oldeps + MP_DIGIT_BIT;
A = (size_t) ceil(0.37714556279552730250018797240191093794 * accuracy);
// We need to compute the coefficients as exact as possible, so
// increase the working precision acccording to the largest coefficient
// TODO: probably too much
eps = ((accuracy * 116) / 100);
if ((err = fill_spougecache(A, accuracy, eps)) != MP_OKAY) {
return err;
}
}
if ((err =
mpf_init_multi(eps, &z, &ONE, &factrl, &e, &t1, &t2, &t3, &sum,
NULL)) != MP_OKAY) {
return err;
}
if ((err = mpf_copy(a, &z)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&z, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_set_int(&ONE, 1)) != MP_OKAY) {
goto _ERR;
}
// printf("splen = %u, A = %u, seps = %ld, acc = %d\n",
// spougecache_len , A , spougecache_eps , accuracy);
if (a->mantissa.sign == MP_NEG) {
// eps = oldeps + 10;
if ((err = mpf_copy(a, &z)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&z, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_init(&pi, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_const_pi(&pi)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&ONE, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sub(&ONE, &z, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&pi, &z, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sin(&t2, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_div(&pi, &t2, &t2)) != MP_OKAY) {
goto _ERR;
}
t2.mantissa.sign = MP_ZPOS;
if ((err = mpf_ln(&t2, &t2)) != MP_OKAY) {
goto _ERR;
}
reflection = 1;
if ((err = mpf_lngamma(&t1, &t1)) != MP_OKAY) {
goto _ERR;
}
reflection = 0;
if ((err = mpf_sub(&t2, &t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&t1, oldeps)) != MP_OKAY) {
goto _ERR;
}
mpf_exch(&t1, b);
goto _ERR;
}
if ((err = mpf_copy(&(spougecache[0]), &sum)) != MP_OKAY) {
goto _ERR;
}
for (n = 1; n < (int) spougecache_len; n++) {
if ((err = mpf_const_d(&t1, n)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_add(&z, &t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_div(&(spougecache[n]), &t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_add(&sum, &t1, &sum)) != MP_OKAY) {
goto _ERR;
}
}
if ((err = mpf_const_d(&t1, (int) spougecache_len)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_add(&z, &t1, &t1)) != MP_OKAY) {
goto _ERR;
}
// 1/2
ONE.exp -= 1;
//ret = log(sum) + (-(t1)) + log(t1) * (z + 1/2);
// = log(sum) + t2 + log(t1) * (z + 1/2);
// = log(sum) + t2 + log(t1) * t3
if ((err = mpf_neg(&t1, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_add(&z, &ONE, &t3)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_ln(&sum, &sum)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_ln(&t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&t1, &t3, &t3)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_add(&sum, &t2, &sum)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_add(&sum, &t3, &sum)) != MP_OKAY) {
goto _ERR;
}
// ret = ret - log(z)
if ((err = mpf_ln(&z, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sub(&sum, &t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_normalize_to(&t1, oldeps)) != MP_OKAY) {
goto _ERR;
}
mpf_exch(&t1, b);
_ERR:
mpf_clear_multi(&z, &ONE, &factrl, &e, &t1, &t2, &t3, &sum, NULL);
return err;
}
/* using sin x == \sum_{n=0}^{\infty} ((-1)^n/(2n+1)!) * x^(2n+1) */
int mpf_sin(mp_float *a, mp_float *b)
{
mp_float oldval, tmpovern, tmp, tmpx, res, sqr;
int oddeven, err, itts;
long n;
/* initialize temps */
if ((err = mpf_init_multi(b->radix, &oldval, &tmpx, &tmpovern, &tmp, &res, &sqr, NULL)) != MP_OKAY) {
return err;
}
/* initlialize temps */
/* this is the 1/n! which starts at 1 */
if ((err = mpf_const_d(&tmpovern, 1)) != MP_OKAY) { goto __ERR; }
/* the square of the input, used to save multiplications later */
if ((err = mpf_sqr(a, &sqr)) != MP_OKAY) { goto __ERR; }
/* tmpx starts at the input, so we copy and normalize */
if ((err = mpf_copy(a, &tmpx)) != MP_OKAY) { goto __ERR; }
tmpx.radix = b->radix;
if ((err = mpf_normalize(&tmpx)) != MP_OKAY) { goto __ERR; }
/* the result starts off at a as we skip a term in the series */
if ((err = mpf_copy(&tmpx, &res)) != MP_OKAY) { goto __ERR; }
/* this is the denom counter. Goes up by two per pass */
n = 1;
/* we alternate between adding and subtracting */
oddeven = 1;
/* get number of iterations */
itts = mpf_iterations(b);
while (itts-- > 0) {
if ((err = mpf_copy(&res, &oldval)) != MP_OKAY) { goto __ERR; }
/* compute 1/(2n)! from 1/(2(n-1))! by multiplying by (1/n)(1/(n+1)) */
if ((err = mpf_const_d(&tmp, ++n)) != MP_OKAY) { goto __ERR; }
if ((err = mpf_inv(&tmp, &tmp)) != MP_OKAY) { goto __ERR; }
if ((err = mpf_mul(&tmpovern, &tmp, &tmpovern)) != MP_OKAY) { goto __ERR; }
/* we do this twice */
if ((err = mpf_const_d(&tmp, ++n)) != MP_OKAY) { goto __ERR; }
if ((err = mpf_inv(&tmp, &tmp)) != MP_OKAY) { goto __ERR; }
if ((err = mpf_mul(&tmpovern, &tmp, &tmpovern)) != MP_OKAY) { goto __ERR; }
/* now multiply sqr into tmpx */
if ((err = mpf_mul(&tmpx, &sqr, &tmpx)) != MP_OKAY) { goto __ERR; }
/* now multiply the two */
if ((err = mpf_mul(&tmpx, &tmpovern, &tmp)) != MP_OKAY) { goto __ERR; }
/* now depending on if this is even or odd we add/sub */
oddeven ^= 1;
if (oddeven == 1) {
if ((err = mpf_add(&res, &tmp, &res)) != MP_OKAY) { goto __ERR; }
} else {
if ((err = mpf_sub(&res, &tmp, &res)) != MP_OKAY) { goto __ERR; }
}
if (mpf_cmp(&res, &oldval) == MP_EQ) {
break;
}
}
mpf_exch(&res, b);
__ERR: mpf_clear_multi(&oldval, &tmpx, &tmpovern, &tmp, &res, &sqr, NULL);
return err;
}
