diff options
Diffstat (limited to 'src/asin.c')
| -rw-r--r-- | src/asin.c | 136 |
1 files changed, 68 insertions, 68 deletions
@@ -29,117 +29,117 @@ mpc_asin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd) int inex; /* special values */ - if (mpfr_nan_p (MPC_RE (op)) || mpfr_nan_p (MPC_IM (op))) + if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op))) { - if (mpfr_inf_p (MPC_RE (op)) || mpfr_inf_p (MPC_IM (op))) + if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op))) { - mpfr_set_nan (MPC_RE (rop)); - mpfr_set_inf (MPC_IM (rop), mpfr_signbit (MPC_IM (op)) ? -1 : +1); + mpfr_set_nan (mpc_realref (rop)); + mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? -1 : +1); } - else if (mpfr_zero_p (MPC_RE (op))) + else if (mpfr_zero_p (mpc_realref (op))) { - mpfr_set (MPC_RE (rop), MPC_RE (op), GMP_RNDN); - mpfr_set_nan (MPC_IM (rop)); + mpfr_set (mpc_realref (rop), mpc_realref (op), GMP_RNDN); + mpfr_set_nan (mpc_imagref (rop)); } else { - mpfr_set_nan (MPC_RE (rop)); - mpfr_set_nan (MPC_IM (rop)); + mpfr_set_nan (mpc_realref (rop)); + mpfr_set_nan (mpc_imagref (rop)); } return 0; } - if (mpfr_inf_p (MPC_RE (op)) || mpfr_inf_p (MPC_IM (op))) + if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op))) { int inex_re; - if (mpfr_inf_p (MPC_RE (op))) + if (mpfr_inf_p (mpc_realref (op))) { - int inf_im = mpfr_inf_p (MPC_IM (op)); + int inf_im = mpfr_inf_p (mpc_imagref (op)); - inex_re = set_pi_over_2 (MPC_RE (rop), - (mpfr_signbit (MPC_RE (op)) ? -1 : 1), MPC_RND_RE (rnd)); - mpfr_set_inf (MPC_IM (rop), (mpfr_signbit (MPC_IM (op)) ? -1 : 1)); + inex_re = set_pi_over_2 (mpc_realref (rop), + (mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd)); + mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1)); if (inf_im) - mpfr_div_2ui (MPC_RE (rop), MPC_RE (rop), 1, GMP_RNDN); + mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN); } else { - mpfr_set_zero (MPC_RE (rop), (mpfr_signbit (MPC_RE (op)) ? -1 : 1)); + mpfr_set_zero (mpc_realref (rop), (mpfr_signbit (mpc_realref (op)) ? -1 : 1)); inex_re = 0; - mpfr_set_inf (MPC_IM (rop), (mpfr_signbit (MPC_IM (op)) ? -1 : 1)); + mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1)); } return MPC_INEX (inex_re, 0); } /* pure real argument */ - if (mpfr_zero_p (MPC_IM (op))) + if (mpfr_zero_p (mpc_imagref (op))) { int inex_re; int inex_im; int s_im; - s_im = mpfr_signbit (MPC_IM (op)); + s_im = mpfr_signbit (mpc_imagref (op)); - if (mpfr_cmp_ui (MPC_RE (op), 1) > 0) + if (mpfr_cmp_ui (mpc_realref (op), 1) > 0) { if (s_im) - inex_im = -mpfr_acosh (MPC_IM (rop), MPC_RE (op), + inex_im = -mpfr_acosh (mpc_imagref (rop), mpc_realref (op), INV_RND (MPC_RND_IM (rnd))); else - inex_im = mpfr_acosh (MPC_IM (rop), MPC_RE (op), + inex_im = mpfr_acosh (mpc_imagref (rop), mpc_realref (op), MPC_RND_IM (rnd)); - inex_re = set_pi_over_2 (MPC_RE (rop), - (mpfr_signbit (MPC_RE (op)) ? -1 : 1), MPC_RND_RE (rnd)); + inex_re = set_pi_over_2 (mpc_realref (rop), + (mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd)); if (s_im) mpc_conj (rop, rop, MPC_RNDNN); } - else if (mpfr_cmp_si (MPC_RE (op), -1) < 0) + else if (mpfr_cmp_si (mpc_realref (op), -1) < 0) { mpfr_t minus_op_re; - minus_op_re[0] = MPC_RE (op)[0]; + minus_op_re[0] = mpc_realref (op)[0]; MPFR_CHANGE_SIGN (minus_op_re); if (s_im) - inex_im = -mpfr_acosh (MPC_IM (rop), minus_op_re, + inex_im = -mpfr_acosh (mpc_imagref (rop), minus_op_re, INV_RND (MPC_RND_IM (rnd))); else - inex_im = mpfr_acosh (MPC_IM (rop), minus_op_re, + inex_im = mpfr_acosh (mpc_imagref (rop), minus_op_re, MPC_RND_IM (rnd)); - inex_re = set_pi_over_2 (MPC_RE (rop), - (mpfr_signbit (MPC_RE (op)) ? -1 : 1), MPC_RND_RE (rnd)); + inex_re = set_pi_over_2 (mpc_realref (rop), + (mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd)); if (s_im) mpc_conj (rop, rop, MPC_RNDNN); } else { - inex_im = mpfr_set_ui (MPC_IM (rop), 0, MPC_RND_IM (rnd)); + inex_im = mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd)); if (s_im) - mpfr_neg (MPC_IM (rop), MPC_IM (rop), GMP_RNDN); - inex_re = mpfr_asin (MPC_RE (rop), MPC_RE (op), MPC_RND_RE (rnd)); + mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), GMP_RNDN); + inex_re = mpfr_asin (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd)); } return MPC_INEX (inex_re, inex_im); } /* pure imaginary argument */ - if (mpfr_zero_p (MPC_RE (op))) + if (mpfr_zero_p (mpc_realref (op))) { int inex_im; int s; - s = mpfr_signbit (MPC_RE (op)); - mpfr_set_ui (MPC_RE (rop), 0, GMP_RNDN); + s = mpfr_signbit (mpc_realref (op)); + mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN); if (s) - mpfr_neg (MPC_RE (rop), MPC_RE (rop), GMP_RNDN); - inex_im = mpfr_asinh (MPC_IM (rop), MPC_IM (op), MPC_RND_IM (rnd)); + mpfr_neg (mpc_realref (rop), mpc_realref (rop), GMP_RNDN); + inex_im = mpfr_asinh (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd)); return MPC_INEX (0, inex_im); } /* regular complex: asin(z) = -i*log(i*z+sqrt(1-z^2)) */ - p_re = mpfr_get_prec (MPC_RE(rop)); - p_im = mpfr_get_prec (MPC_IM(rop)); + p_re = mpfr_get_prec (mpc_realref(rop)); + p_im = mpfr_get_prec (mpc_imagref(rop)); rnd_re = MPC_RND_RE(rnd); rnd_im = MPC_RND_IM(rnd); p = p_re >= p_im ? p_re : p_im; @@ -150,71 +150,71 @@ mpc_asin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd) p += mpc_ceil_log2 (p) + 3 + incr_p; /* incr_p is zero initially */ incr_p = p / 2; - mpfr_set_prec (MPC_RE(z1), p); - mpfr_set_prec (MPC_IM(z1), p); + mpfr_set_prec (mpc_realref(z1), p); + mpfr_set_prec (mpc_imagref(z1), p); /* z1 <- z^2 */ mpc_sqr (z1, op, MPC_RNDNN); /* err(x) <= 1/2 ulp(x), err(y) <= 1/2 ulp(y) */ /* z1 <- 1-z1 */ - ex = mpfr_get_exp (MPC_RE(z1)); - mpfr_ui_sub (MPC_RE(z1), 1, MPC_RE(z1), GMP_RNDN); - mpfr_neg (MPC_IM(z1), MPC_IM(z1), GMP_RNDN); - ex = ex - mpfr_get_exp (MPC_RE(z1)); + ex = mpfr_get_exp (mpc_realref(z1)); + mpfr_ui_sub (mpc_realref(z1), 1, mpc_realref(z1), GMP_RNDN); + mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN); + ex = ex - mpfr_get_exp (mpc_realref(z1)); ex = (ex <= 0) ? 0 : ex; /* err(x) <= 2^ex * ulp(x) */ - ex = ex + mpfr_get_exp (MPC_RE(z1)) - p; + ex = ex + mpfr_get_exp (mpc_realref(z1)) - p; /* err(x) <= 2^ex */ - ey = mpfr_get_exp (MPC_IM(z1)) - p - 1; + ey = mpfr_get_exp (mpc_imagref(z1)) - p - 1; /* err(y) <= 2^ey */ ex = (ex >= ey) ? ex : ey; /* err(x), err(y) <= 2^ex, i.e., the norm of the error is bounded by |h|<=2^(ex+1/2) */ /* z1 <- sqrt(z1): if z1 = z + h, then sqrt(z1) = sqrt(z) + h/2/sqrt(t) */ - ey = mpfr_get_exp (MPC_RE(z1)) >= mpfr_get_exp (MPC_IM(z1)) - ? mpfr_get_exp (MPC_RE(z1)) : mpfr_get_exp (MPC_IM(z1)); + ey = mpfr_get_exp (mpc_realref(z1)) >= mpfr_get_exp (mpc_imagref(z1)) + ? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1)); /* we have |z1| >= 2^(ey-1) thus 1/|z1| <= 2^(1-ey) */ mpc_sqrt (z1, z1, MPC_RNDNN); ex = (2 * ex + 1) - 2 - (ey - 1); /* |h^2/4/|t| <= 2^ex */ ex = (ex + 1) / 2; /* ceil(ex/2) */ /* express ex in terms of ulp(z1) */ - ey = mpfr_get_exp (MPC_RE(z1)) <= mpfr_get_exp (MPC_IM(z1)) - ? mpfr_get_exp (MPC_RE(z1)) : mpfr_get_exp (MPC_IM(z1)); + ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1)) + ? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1)); ex = ex - ey + p; /* take into account the rounding error in the mpc_sqrt call */ err = (ex <= 0) ? 1 : ex + 1; /* err(x) <= 2^err * ulp(x), err(y) <= 2^err * ulp(y) */ /* z1 <- i*z + z1 */ - ex = mpfr_get_exp (MPC_RE(z1)); - ey = mpfr_get_exp (MPC_IM(z1)); - mpfr_sub (MPC_RE(z1), MPC_RE(z1), MPC_IM(op), GMP_RNDN); - mpfr_add (MPC_IM(z1), MPC_IM(z1), MPC_RE(op), GMP_RNDN); - if (mpfr_cmp_ui (MPC_RE(z1), 0) == 0 || mpfr_cmp_ui (MPC_IM(z1), 0) == 0) + ex = mpfr_get_exp (mpc_realref(z1)); + ey = mpfr_get_exp (mpc_imagref(z1)); + mpfr_sub (mpc_realref(z1), mpc_realref(z1), mpc_imagref(op), GMP_RNDN); + mpfr_add (mpc_imagref(z1), mpc_imagref(z1), mpc_realref(op), GMP_RNDN); + if (mpfr_cmp_ui (mpc_realref(z1), 0) == 0 || mpfr_cmp_ui (mpc_imagref(z1), 0) == 0) continue; - ex -= mpfr_get_exp (MPC_RE(z1)); /* cancellation in x */ - ey -= mpfr_get_exp (MPC_IM(z1)); /* cancellation in y */ + ex -= mpfr_get_exp (mpc_realref(z1)); /* cancellation in x */ + ey -= mpfr_get_exp (mpc_imagref(z1)); /* cancellation in y */ ex = (ex >= ey) ? ex : ey; /* maximum cancellation */ err += ex; err = (err <= 0) ? 1 : err + 1; /* rounding error in sub/add */ /* z1 <- log(z1): if z1 = z + h, then log(z1) = log(z) + h/t with |t| >= min(|z1|,|z|) */ - ex = mpfr_get_exp (MPC_RE(z1)); - ey = mpfr_get_exp (MPC_IM(z1)); + ex = mpfr_get_exp (mpc_realref(z1)); + ey = mpfr_get_exp (mpc_imagref(z1)); ex = (ex >= ey) ? ex : ey; err += ex - p; /* revert to absolute error <= 2^err */ mpc_log (z1, z1, GMP_RNDN); err -= ex - 1; /* 1/|t| <= 1/|z| <= 2^(1-ex) */ /* express err in terms of ulp(z1) */ - ey = mpfr_get_exp (MPC_RE(z1)) <= mpfr_get_exp (MPC_IM(z1)) - ? mpfr_get_exp (MPC_RE(z1)) : mpfr_get_exp (MPC_IM(z1)); + ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1)) + ? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1)); err = err - ey + p; /* take into account the rounding error in the mpc_log call */ err = (err <= 0) ? 1 : err + 1; /* z1 <- -i*z1 */ - mpfr_swap (MPC_RE(z1), MPC_IM(z1)); - mpfr_neg (MPC_IM(z1), MPC_IM(z1), GMP_RNDN); - if (mpfr_can_round (MPC_RE(z1), p - err, GMP_RNDN, GMP_RNDZ, + mpfr_swap (mpc_realref(z1), mpc_imagref(z1)); + mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN); + if (mpfr_can_round (mpc_realref(z1), p - err, GMP_RNDN, GMP_RNDZ, p_re + (rnd_re == GMP_RNDN)) && - mpfr_can_round (MPC_IM(z1), p - err, GMP_RNDN, GMP_RNDZ, + mpfr_can_round (mpc_imagref(z1), p - err, GMP_RNDN, GMP_RNDZ, p_im + (rnd_im == GMP_RNDN))) break; } |