/* compute 1/x by (1/sqrt(x))^2 */ int mpf_inv_old(mp_float *a, mp_float *b) { int err, sign; /* get sign of input */ sign = a->mantissa.sign; /* force to positive */ a->mantissa.sign = MP_ZPOS; /* compute 1/sqrt(a) */ if ((err = mpf_invsqrt(a, b)) != MP_OKAY) { return err; } /* square 1/sqrt(a) to get 1/a */ err = mpf_sqr(b, b); /* now restore the sign */ b->mantissa.sign = a->mantissa.sign = sign; 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; }