diff options
Diffstat (limited to 'src/pow.c')
| -rw-r--r-- | src/pow.c | 35 |
1 files changed, 20 insertions, 15 deletions
@@ -231,7 +231,7 @@ mpc_pow_exact (mpc_ptr z, mpc_srcptr x, mpfr_srcptr y, mpc_rnd_t rnd) } /* replace (c,d) by (c/(c^2-d^2), -d/(c^2-d^2)) */ mpz_neg (d, d); - ec -= t; + ec = -ec - t; } mpz_neg (my, my); } @@ -414,25 +414,30 @@ mpc_pow (mpc_ptr z, mpc_srcptr x, mpc_srcptr y, mpc_rnd_t rnd) if (mpfr_cmp_si (MPC_RE(x), -1) == 0 && mpfr_integer_p (MPC_RE(y))) z_real = 1; - /* x^y is imaginary when: + /* for x real, x^y is imaginary when: (a) x is negative and y is half-an-integer - (b) x = -1 and Re(y) is half-an-integer */ + (b) x = -1 and Re(y) is half-an-integer + */ if (mpfr_cmp_ui (MPC_RE(x), 0) < 0 && is_odd (MPC_RE(y), 1) && (y_real || mpfr_cmp_si (MPC_RE(x), -1) == 0)) z_imag = 1; } - - /* I^(t*I) and (-I)^(t*I) are real for t real, - I^(n+t*I) and (-I)^(n+t*I) are real for n even and t real, and - I^(n+t*I) and (-I)^(n+t*I) are imaginary for n odd and t real */ - if ((mpc_cmp_si_si (x, 0, 1) == 0 || mpc_cmp_si_si (x, 0, -1) == 0) && - mpfr_integer_p (MPC_RE(y))) - { /* x is I or -I, and Re(y) is an integer */ - if (is_odd (MPC_RE(y), 0)) - z_imag = 1; /* Re(y) odd: z is imaginary */ - else - z_real = 1; /* Re(y) even: z is real */ - } + else /* x non real */ + /* I^(t*I) and (-I)^(t*I) are real for t real, + I^(n+t*I) and (-I)^(n+t*I) are real for n even and t real, and + I^(n+t*I) and (-I)^(n+t*I) are imaginary for n odd and t real */ + if ((mpc_cmp_si_si (x, 0, 1) == 0 || mpc_cmp_si_si (x, 0, -1) == 0) && + mpfr_integer_p (MPC_RE(y))) + { /* x is I or -I, and Re(y) is an integer */ + if (is_odd (MPC_RE(y), 0)) + z_imag = 1; /* Re(y) odd: z is imaginary */ + else + z_real = 1; /* Re(y) even: z is real */ + } + else /* x^y is imaginary x is imaginary and y = -1 */ + if (mpfr_cmp_ui (MPC_RE(x), 0) == 0 && y_real && + mpfr_cmp_si (MPC_RE(y), -1) == 0) + z_imag = 1; /* first bound |Re(y log(x))|, |Im(y log(x)| < 2^q */ mpc_init2 (t, 64); |