// 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; }
// Computes q = exp(2 pi i tau). static void compute_q(mpc_t q, mpc_t tau) { mpc_t z0; mpf_t f0, f1; mpf_ptr fp0; pbc_mpui pwr; mpc_init(z0); mpf_init(f0); mpf_init(f1); //compute z0 = 2 pi i tau mpc_set(z0, tau); //first remove integral part of Re(tau) //since exp(2 pi i) = 1 //it seems |Re(tau)| < 1 anyway? fp0 = mpc_re(z0); mpf_trunc(f1, fp0); mpf_sub(fp0, fp0, f1); mpc_mul_mpf(z0, z0, pi); mpc_mul_ui(z0, z0, 2); mpc_muli(z0, z0); //compute q = exp(z0); //first write z0 = A + a + b i //where A is a (negative) integer //and a, b are in [-1, 1] //compute e^A separately fp0 = mpc_re(z0); pwr = mpf_get_ui(fp0); mpf_pow_ui(f0, recipeulere, pwr); mpf_add_ui(fp0, fp0, pwr); mpf_exp(f1, mpc_re(z0)); mpf_mul(f0, f1, f0); mpc_cis(q, mpc_im(z0)); /* old_mpc_exp(q, z0); */ mpc_mul_mpf(q, q, f0); mpc_clear(z0); mpf_clear(f0); mpf_clear(f1); }
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; }