int mpf_const_1pi(mp_float *a)
{
int err;
if ((err = mpf_const_pi(a)) != MP_OKAY) {
return err;
}
return mpf_inv(a, a);
}
int mpf_div(mp_float *a, mp_float *b, mp_float *c)
{
mp_float tmp;
int err;
/* ensure b is not zero */
if (mp_iszero(&(b->mantissa)) == MP_YES) {
return MP_VAL;
}
/* find 1/b */
if ((err = mpf_init(&tmp, c->radix)) != MP_OKAY) {
return err;
}
if ((err = mpf_inv(b, &tmp)) != MP_OKAY) { goto __ERR; }
/* now multiply */
err = mpf_mul(&tmp, a, c);
__ERR: mpf_clear(&tmp);
return err;
}
/* 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;
}
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;
}
/* 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;
}
