/* tan = sin/cos, prolly fix this up later */
int mpf_tan(mp_float *a, mp_float *b)
{
int err;
mp_float tmp;
/* get cos of a */
if ((err = mpf_init(&tmp, b->radix)) != MP_OKAY) {
return err;
}
if ((err = mpf_cos(a, &tmp)) != MP_OKAY) { goto __ERR; }
/* now make it upside down ;-) (this should catch domain errors too) */
if ((err = mpf_inv(&tmp, &tmp)) != MP_OKAY) { goto __ERR; }
/* put sin in b */
if ((err = mpf_sin(a, b)) != MP_OKAY) { goto __ERR; }
/* multiply the two and we done */
err = mpf_mul(b, &tmp, b);
__ERR: mpf_clear(&tmp);
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;
}
int main(void)
{
mp_float a, b, c, d, e;
int err;
mpf_init_multi(100, &a, &b, &c, &d, &e, NULL);
mpf_const_d(&a, 1);
draw(&a);
mpf_const_d(&b, 2);
draw(&b);
mpf_const_d(&c, 3);
draw(&c);
mpf_const_d(&d, 4);
draw(&d);
mpf_add(&b, &c, &e);
printf("2 + 3 == ");
draw(&e);
mpf_sub(&b, &c, &e);
printf("2 - 3 ==");
draw(&e);
mpf_mul(&b, &c, &e);
printf("2 * 3 == ");
draw(&e);
mpf_div(&b, &c, &e);
printf("2 / 3 == ");
draw(&e);
mpf_add_d(&b, 3, &e);
printf("2 + 3 == ");
draw(&e);
mpf_sub_d(&b, 3, &e);
printf("2 - 3 ==");
draw(&e);
mpf_mul_d(&b, 3, &e);
printf("2 * 3 == ");
draw(&e);
mpf_div_d(&b, 3, &e);
printf("2 / 3 == ");
draw(&e);
mpf_const_d(&e, 0);
mpf_add_d(&e, 1, &e);
printf("0 + 1 == ");
draw(&e);
mpf_const_d(&e, 0);
mpf_sub_d(&e, 1, &e);
printf("0 - 1 == ");
draw(&e);
printf("\n");
mpf_invsqrt(&d, &e);
printf("1/sqrt(4) == 1/2 == ");
draw(&e);
mpf_invsqrt(&c, &e);
printf("1/sqrt(3) == ");
draw(&e);
mpf_inv(&a, &e);
printf("1/1 == ");
draw(&e);
mpf_inv(&b, &e);
printf("1/2 == ");
draw(&e);
mpf_inv(&c, &e);
printf("1/3 == ");
draw(&e);
mpf_inv(&d, &e);
printf("1/4 == ");
draw(&e);
printf("\n");
mpf_const_pi(&e);
printf("Pi == ");
draw(&e);
printf("\n");
mpf_const_e(&e);
printf("e == ");
draw(&e);
mpf_exp(&c, &e);
printf("e^3 == ");
draw(&e);
mpf_sqrt(&e, &e);
printf("sqrt(e^3) == ");
draw(&e);
mpf_sqr(&e, &e);
printf("sqrt(e^3)^2 == ");
draw(&e);
printf("\n");
mpf_cos(&a, &e);
printf("cos(1) == ");
draw(&e);
mpf_cos(&b, &e);
printf("cos(2) == ");
draw(&e);
mpf_cos(&c, &e);
printf("cos(3) == ");
draw(&e);
mpf_cos(&d, &e);
printf("cos(4) == ");
draw(&e);
mpf_sin(&a, &e);
printf("sin(1) == ");
draw(&e);
mpf_sin(&b, &e);
printf("sin(2) == ");
draw(&e);
mpf_sin(&c, &e);
printf("sin(3) == ");
draw(&e);
mpf_sin(&d, &e);
printf("sin(4) == ");
draw(&e);
mpf_tan(&a, &e);
printf("tan(1) == ");
draw(&e);
mpf_tan(&b, &e);
printf("tan(2) == ");
draw(&e);
mpf_tan(&c, &e);
printf("tan(3) == ");
draw(&e);
mpf_tan(&d, &e);
printf("tan(4) == ");
draw(&e);
mpf_inv(&a, &e);
mpf_atan(&e, &e);
printf("atan(1/1) == ");
draw(&e);
mpf_inv(&b, &e);
mpf_atan(&e, &e);
printf("atan(1/2) == ");
draw(&e);
mpf_inv(&c, &e);
mpf_atan(&e, &e);
printf("atan(1/3) == ");
draw(&e);
mpf_inv(&d, &e);
mpf_atan(&e, &e);
printf("atan(1/4) == ");
draw(&e);
printf("\n");
#define lntest(x) if ((err = mpf_const_ln_d(&e, x)) != MP_OKAY) { printf("Failed ln(%3d), %d\n", x, err); } else { printf("ln(%3d) == ", x); draw(&e); };
lntest(0);
lntest(1);
lntest(2);
lntest(4);
lntest(8);
lntest(17);
lntest(1000);
lntest(100000);
lntest(250000);
return 0;
}
