forked from libtom/libtomfloat
/
mpf_gamma.c
330 lines (305 loc) · 7.45 KB
/
mpf_gamma.c
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#include <tomfloat.h>
#include <math.h>
static mp_float *spougecache;
static size_t spougecache_len;
static long spougecache_eps;
// flag for handling precision for the cache
static int reflection;
static int fill_spougecache(size_t A, int accuracy, long eps)
{
int err, n;
mp_float factrl, e, t1, t2, t3, pi;
size_t start;
if ((err =
mpf_init_multi(eps, &factrl, &e, &t1, &t2, &t3, NULL)) != MP_OKAY) {
return err;
}
err = MP_OKAY;
if (spougecache_len < A || spougecache_eps < accuracy) {
//puts("filling spougecache");
if ((err = mpf_const_d(&factrl, 1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_const_e(&e)) != MP_OKAY) {
goto _ERR;
}
if (spougecache_len != 0) {
spougecache = realloc(spougecache, (A + 1) * sizeof(mp_float));
if (spougecache == NULL) {
return MP_MEM;
}
start = spougecache_len;
} else {
spougecache = malloc((A + 1) * sizeof(mp_float));
if (spougecache == NULL) {
return MP_MEM;
}
start = 1;
if ((err = mpf_init(&pi, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_const_pi(&pi)) != MP_OKAY) {
goto _ERR;
}
pi.exp += 1;
if ((err = mpf_init(&(spougecache[0]), eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sqrt(&pi, &(spougecache[0]))) != MP_OKAY) {
goto _ERR;
}
mpf_clear(&pi);
}
for (n = start; n < (int) A; n++) {
// to avoid the more expensive exp(log(a-n)*(n-0.5))
// TODO: check if exp() is fast enough now
if ((err = mpf_set_int(&t1, (int) (A - n))) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_pow_d(&t1, (int) (n - 1), &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sqrt(&t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&t2, &t1, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_pow_d(&e, (int) (A - n), &t3)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&t2, &t3, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_init(&(spougecache[n]), eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_div(&t2, &factrl, &(spougecache[n]))) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_set_int(&t1, -n)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&factrl, &t1, &factrl)) != MP_OKAY) {
goto _ERR;
}
}
spougecache_eps = accuracy;
spougecache_len = A;
}
_ERR:
mpf_clear_multi(&factrl, &e, &t1, &t2, &t3, NULL);
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;
}
void mpf_clear_spougecache()
{
size_t i;
for (i = 0; i < spougecache_len; i++) {
mpf_clear(&(spougecache[i]));
}
free(spougecache);
}
void mpf_dump_spougecache()
{
size_t i;
for (i = 0; i < spougecache_len; i++) {
printf("%u\n", i);
mpf_dump(&(spougecache[i]));
}
printf("eps = %ld\n", spougecache_eps);
}
// 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;
}