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Diffstat (limited to 'mpc/src/div.c')
| -rw-r--r-- | mpc/src/div.c | 449 |
1 files changed, 449 insertions, 0 deletions
diff --git a/mpc/src/div.c b/mpc/src/div.c new file mode 100644 index 0000000000..83584b8b5f --- /dev/null +++ b/mpc/src/div.c @@ -0,0 +1,449 @@ +/* mpc_div -- Divide two complex numbers. + +Copyright (C) 2002, 2003, 2004, 2005, 2008, 2009, 2010, 2011, 2012 INRIA + +This file is part of GNU MPC. + +GNU MPC is free software; you can redistribute it and/or modify it under +the terms of the GNU Lesser General Public License as published by the +Free Software Foundation; either version 3 of the License, or (at your +option) any later version. + +GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for +more details. + +You should have received a copy of the GNU Lesser General Public License +along with this program. If not, see http://www.gnu.org/licenses/ . +*/ + +#include "mpc-impl.h" + +/* this routine deals with the case where w is zero */ +static int +mpc_div_zero (mpc_ptr a, mpc_srcptr z, mpc_srcptr w, mpc_rnd_t rnd) +/* Assumes w==0, implementation according to C99 G.5.1.8 */ +{ + int sign = MPFR_SIGNBIT (mpc_realref (w)); + mpfr_t infty; + + mpfr_init2 (infty, MPFR_PREC_MIN); + mpfr_set_inf (infty, sign); + mpfr_mul (mpc_realref (a), infty, mpc_realref (z), MPC_RND_RE (rnd)); + mpfr_mul (mpc_imagref (a), infty, mpc_imagref (z), MPC_RND_IM (rnd)); + mpfr_clear (infty); + return MPC_INEX (0, 0); /* exact */ +} + +/* this routine deals with the case where z is infinite and w finite */ +static int +mpc_div_inf_fin (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w) +/* Assumes w finite and non-zero and z infinite; implementation + according to C99 G.5.1.8 */ +{ + int a, b, x, y; + + a = (mpfr_inf_p (mpc_realref (z)) ? MPFR_SIGNBIT (mpc_realref (z)) : 0); + b = (mpfr_inf_p (mpc_imagref (z)) ? MPFR_SIGNBIT (mpc_imagref (z)) : 0); + + /* a is -1 if Re(z) = -Inf, 1 if Re(z) = +Inf, 0 if Re(z) is finite + b is -1 if Im(z) = -Inf, 1 if Im(z) = +Inf, 0 if Im(z) is finite */ + + /* x = MPC_MPFR_SIGN (a * mpc_realref (w) + b * mpc_imagref (w)) */ + /* y = MPC_MPFR_SIGN (b * mpc_realref (w) - a * mpc_imagref (w)) */ + if (a == 0 || b == 0) { + /* only one of a or b can be zero, since z is infinite */ + x = a * MPC_MPFR_SIGN (mpc_realref (w)) + b * MPC_MPFR_SIGN (mpc_imagref (w)); + y = b * MPC_MPFR_SIGN (mpc_realref (w)) - a * MPC_MPFR_SIGN (mpc_imagref (w)); + } + else { + /* Both parts of z are infinite; x could be determined by sign + considerations and comparisons. Since operations with non-finite + numbers are not considered time-critical, we let mpfr do the work. */ + mpfr_t sign; + + mpfr_init2 (sign, 2); + /* This is enough to determine the sign of sums and differences. */ + + if (a == 1) + if (b == 1) { + mpfr_add (sign, mpc_realref (w), mpc_imagref (w), GMP_RNDN); + x = MPC_MPFR_SIGN (sign); + mpfr_sub (sign, mpc_realref (w), mpc_imagref (w), GMP_RNDN); + y = MPC_MPFR_SIGN (sign); + } + else { /* b == -1 */ + mpfr_sub (sign, mpc_realref (w), mpc_imagref (w), GMP_RNDN); + x = MPC_MPFR_SIGN (sign); + mpfr_add (sign, mpc_realref (w), mpc_imagref (w), GMP_RNDN); + y = -MPC_MPFR_SIGN (sign); + } + else /* a == -1 */ + if (b == 1) { + mpfr_sub (sign, mpc_imagref (w), mpc_realref (w), GMP_RNDN); + x = MPC_MPFR_SIGN (sign); + mpfr_add (sign, mpc_realref (w), mpc_imagref (w), GMP_RNDN); + y = MPC_MPFR_SIGN (sign); + } + else { /* b == -1 */ + mpfr_add (sign, mpc_realref (w), mpc_imagref (w), GMP_RNDN); + x = -MPC_MPFR_SIGN (sign); + mpfr_sub (sign, mpc_imagref (w), mpc_realref (w), GMP_RNDN); + y = MPC_MPFR_SIGN (sign); + } + mpfr_clear (sign); + } + + if (x == 0) + mpfr_set_nan (mpc_realref (rop)); + else + mpfr_set_inf (mpc_realref (rop), x); + if (y == 0) + mpfr_set_nan (mpc_imagref (rop)); + else + mpfr_set_inf (mpc_imagref (rop), y); + + return MPC_INEX (0, 0); /* exact */ +} + + +/* this routine deals with the case where z if finite and w infinite */ +static int +mpc_div_fin_inf (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w) +/* Assumes z finite and w infinite; implementation according to + C99 G.5.1.8 */ +{ + mpfr_t c, d, a, b, x, y, zero; + + mpfr_init2 (c, 2); /* needed to hold a signed zero, +1 or -1 */ + mpfr_init2 (d, 2); + mpfr_init2 (x, 2); + mpfr_init2 (y, 2); + mpfr_init2 (zero, 2); + mpfr_set_ui (zero, 0ul, GMP_RNDN); + mpfr_init2 (a, mpfr_get_prec (mpc_realref (z))); + mpfr_init2 (b, mpfr_get_prec (mpc_imagref (z))); + + mpfr_set_ui (c, (mpfr_inf_p (mpc_realref (w)) ? 1 : 0), GMP_RNDN); + MPFR_COPYSIGN (c, c, mpc_realref (w), GMP_RNDN); + mpfr_set_ui (d, (mpfr_inf_p (mpc_imagref (w)) ? 1 : 0), GMP_RNDN); + MPFR_COPYSIGN (d, d, mpc_imagref (w), GMP_RNDN); + + mpfr_mul (a, mpc_realref (z), c, GMP_RNDN); /* exact */ + mpfr_mul (b, mpc_imagref (z), d, GMP_RNDN); + mpfr_add (x, a, b, GMP_RNDN); + + mpfr_mul (b, mpc_imagref (z), c, GMP_RNDN); + mpfr_mul (a, mpc_realref (z), d, GMP_RNDN); + mpfr_sub (y, b, a, GMP_RNDN); + + MPFR_COPYSIGN (mpc_realref (rop), zero, x, GMP_RNDN); + MPFR_COPYSIGN (mpc_imagref (rop), zero, y, GMP_RNDN); + + mpfr_clear (c); + mpfr_clear (d); + mpfr_clear (x); + mpfr_clear (y); + mpfr_clear (zero); + mpfr_clear (a); + mpfr_clear (b); + + return MPC_INEX (0, 0); /* exact */ +} + + +static int +mpc_div_real (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w, mpc_rnd_t rnd) +/* Assumes z finite and w finite and non-zero, with imaginary part + of w a signed zero. */ +{ + int inex_re, inex_im; + /* save signs of operands in case there are overlaps */ + int zrs = MPFR_SIGNBIT (mpc_realref (z)); + int zis = MPFR_SIGNBIT (mpc_imagref (z)); + int wrs = MPFR_SIGNBIT (mpc_realref (w)); + int wis = MPFR_SIGNBIT (mpc_imagref (w)); + + /* warning: rop may overlap with z,w so treat the imaginary part first */ + inex_im = mpfr_div (mpc_imagref(rop), mpc_imagref(z), mpc_realref(w), MPC_RND_IM(rnd)); + inex_re = mpfr_div (mpc_realref(rop), mpc_realref(z), mpc_realref(w), MPC_RND_RE(rnd)); + + /* correct signs of zeroes if necessary, which does not affect the + inexact flags */ + if (mpfr_zero_p (mpc_realref (rop))) + mpfr_setsign (mpc_realref (rop), mpc_realref (rop), (zrs != wrs && zis != wis), + GMP_RNDN); /* exact */ + if (mpfr_zero_p (mpc_imagref (rop))) + mpfr_setsign (mpc_imagref (rop), mpc_imagref (rop), (zis != wrs && zrs == wis), + GMP_RNDN); + + return MPC_INEX(inex_re, inex_im); +} + + +static int +mpc_div_imag (mpc_ptr rop, mpc_srcptr z, mpc_srcptr w, mpc_rnd_t rnd) +/* Assumes z finite and w finite and non-zero, with real part + of w a signed zero. */ +{ + int inex_re, inex_im; + int overlap = (rop == z) || (rop == w); + int imag_z = mpfr_zero_p (mpc_realref (z)); + mpfr_t wloc; + mpc_t tmprop; + mpc_ptr dest = (overlap) ? tmprop : rop; + /* save signs of operands in case there are overlaps */ + int zrs = MPFR_SIGNBIT (mpc_realref (z)); + int zis = MPFR_SIGNBIT (mpc_imagref (z)); + int wrs = MPFR_SIGNBIT (mpc_realref (w)); + int wis = MPFR_SIGNBIT (mpc_imagref (w)); + + if (overlap) + mpc_init3 (tmprop, MPC_PREC_RE (rop), MPC_PREC_IM (rop)); + + wloc[0] = mpc_imagref(w)[0]; /* copies mpfr struct IM(w) into wloc */ + inex_re = mpfr_div (mpc_realref(dest), mpc_imagref(z), wloc, MPC_RND_RE(rnd)); + mpfr_neg (wloc, wloc, GMP_RNDN); + /* changes the sign only in wloc, not in w; no need to correct later */ + inex_im = mpfr_div (mpc_imagref(dest), mpc_realref(z), wloc, MPC_RND_IM(rnd)); + + if (overlap) { + /* Note: we could use mpc_swap here, but this might cause problems + if rop and tmprop have been allocated using different methods, since + it will swap the significands of rop and tmprop. See + http://lists.gforge.inria.fr/pipermail/mpc-discuss/2009-August/000504.html */ + mpc_set (rop, tmprop, MPC_RNDNN); /* exact */ + mpc_clear (tmprop); + } + + /* correct signs of zeroes if necessary, which does not affect the + inexact flags */ + if (mpfr_zero_p (mpc_realref (rop))) + mpfr_setsign (mpc_realref (rop), mpc_realref (rop), (zrs != wrs && zis != wis), + GMP_RNDN); /* exact */ + if (imag_z) + mpfr_setsign (mpc_imagref (rop), mpc_imagref (rop), (zis != wrs && zrs == wis), + GMP_RNDN); + + return MPC_INEX(inex_re, inex_im); +} + + +int +mpc_div (mpc_ptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd) +{ + int ok_re = 0, ok_im = 0; + mpc_t res, c_conj; + mpfr_t q; + mpfr_prec_t prec; + int inex, inexact_prod, inexact_norm, inexact_re, inexact_im, loops = 0; + int underflow_norm, overflow_norm, underflow_prod, overflow_prod; + int underflow_re = 0, overflow_re = 0, underflow_im = 0, overflow_im = 0; + mpfr_rnd_t rnd_re = MPC_RND_RE (rnd), rnd_im = MPC_RND_IM (rnd); + int saved_underflow, saved_overflow; + int tmpsgn; + + /* According to the C standard G.3, there are three types of numbers: */ + /* finite (both parts are usual real numbers; contains 0), infinite */ + /* (at least one part is a real infinity) and all others; the latter */ + /* are numbers containing a nan, but no infinity, and could reasonably */ + /* be called nan. */ + /* By G.5.1.4, infinite/finite=infinite; finite/infinite=0; */ + /* all other divisions that are not finite/finite return nan+i*nan. */ + /* Division by 0 could be handled by the following case of division by */ + /* a real; we handle it separately instead. */ + if (mpc_zero_p (c)) + return mpc_div_zero (a, b, c, rnd); + else if (mpc_inf_p (b) && mpc_fin_p (c)) + return mpc_div_inf_fin (a, b, c); + else if (mpc_fin_p (b) && mpc_inf_p (c)) + return mpc_div_fin_inf (a, b, c); + else if (!mpc_fin_p (b) || !mpc_fin_p (c)) { + mpc_set_nan (a); + return MPC_INEX (0, 0); + } + else if (mpfr_zero_p(mpc_imagref(c))) + return mpc_div_real (a, b, c, rnd); + else if (mpfr_zero_p(mpc_realref(c))) + return mpc_div_imag (a, b, c, rnd); + + prec = MPC_MAX_PREC(a); + + mpc_init2 (res, 2); + mpfr_init (q); + + /* create the conjugate of c in c_conj without allocating new memory */ + mpc_realref (c_conj)[0] = mpc_realref (c)[0]; + mpc_imagref (c_conj)[0] = mpc_imagref (c)[0]; + MPFR_CHANGE_SIGN (mpc_imagref (c_conj)); + + /* save the underflow or overflow flags from MPFR */ + saved_underflow = mpfr_underflow_p (); + saved_overflow = mpfr_overflow_p (); + + do { + loops ++; + prec += loops <= 2 ? mpc_ceil_log2 (prec) + 5 : prec / 2; + + mpc_set_prec (res, prec); + mpfr_set_prec (q, prec); + + /* first compute norm(c) */ + mpfr_clear_underflow (); + mpfr_clear_overflow (); + inexact_norm = mpc_norm (q, c, GMP_RNDU); + underflow_norm = mpfr_underflow_p (); + overflow_norm = mpfr_overflow_p (); + if (underflow_norm) + mpfr_set_ui (q, 0ul, GMP_RNDN); + /* to obtain divisions by 0 later on */ + + /* now compute b*conjugate(c) */ + mpfr_clear_underflow (); + mpfr_clear_overflow (); + inexact_prod = mpc_mul (res, b, c_conj, MPC_RNDZZ); + inexact_re = MPC_INEX_RE (inexact_prod); + inexact_im = MPC_INEX_IM (inexact_prod); + underflow_prod = mpfr_underflow_p (); + overflow_prod = mpfr_overflow_p (); + /* unfortunately, does not distinguish between under-/overflow + in real or imaginary parts + hopefully, the side-effects of mpc_mul do indeed raise the + mpfr exceptions */ + if (overflow_prod) { + int isinf = 0; + tmpsgn = mpfr_sgn (mpc_realref(res)); + if (tmpsgn > 0) + { + mpfr_nextabove (mpc_realref(res)); + isinf = mpfr_inf_p (mpc_realref(res)); + mpfr_nextbelow (mpc_realref(res)); + } + else if (tmpsgn < 0) + { + mpfr_nextbelow (mpc_realref(res)); + isinf = mpfr_inf_p (mpc_realref(res)); + mpfr_nextabove (mpc_realref(res)); + } + if (isinf) + { + mpfr_set_inf (mpc_realref(res), tmpsgn); + overflow_re = 1; + } + tmpsgn = mpfr_sgn (mpc_imagref(res)); + isinf = 0; + if (tmpsgn > 0) + { + mpfr_nextabove (mpc_imagref(res)); + isinf = mpfr_inf_p (mpc_imagref(res)); + mpfr_nextbelow (mpc_imagref(res)); + } + else if (tmpsgn < 0) + { + mpfr_nextbelow (mpc_imagref(res)); + isinf = mpfr_inf_p (mpc_imagref(res)); + mpfr_nextabove (mpc_imagref(res)); + } + if (isinf) + { + mpfr_set_inf (mpc_imagref(res), tmpsgn); + overflow_im = 1; + } + mpc_set (a, res, rnd); + goto end; + } + + /* divide the product by the norm */ + if (inexact_norm == 0 && (inexact_re == 0 || inexact_im == 0)) { + /* The division has good chances to be exact in at least one part. */ + /* Since this can cause problems when not rounding to the nearest, */ + /* we use the division code of mpfr, which handles the situation. */ + mpfr_clear_underflow (); + mpfr_clear_overflow (); + inexact_re |= mpfr_div (mpc_realref (res), mpc_realref (res), q, GMP_RNDZ); + underflow_re = mpfr_underflow_p (); + overflow_re = mpfr_overflow_p (); + ok_re = !inexact_re || underflow_re || overflow_re + || mpfr_can_round (mpc_realref (res), prec - 4, GMP_RNDN, + GMP_RNDZ, MPC_PREC_RE(a) + (rnd_re == GMP_RNDN)); + + if (ok_re) /* compute imaginary part */ { + mpfr_clear_underflow (); + mpfr_clear_overflow (); + inexact_im |= mpfr_div (mpc_imagref (res), mpc_imagref (res), q, GMP_RNDZ); + underflow_im = mpfr_underflow_p (); + overflow_im = mpfr_overflow_p (); + ok_im = !inexact_im || underflow_im || overflow_im + || mpfr_can_round (mpc_imagref (res), prec - 4, GMP_RNDN, + GMP_RNDZ, MPC_PREC_IM(a) + (rnd_im == GMP_RNDN)); + } + } + else { + /* The division is inexact, so for efficiency reasons we invert q */ + /* only once and multiply by the inverse. */ + if (mpfr_ui_div (q, 1ul, q, GMP_RNDZ) || inexact_norm) { + /* if 1/q is inexact, the approximations of the real and + imaginary part below will be inexact, unless RE(res) + or IM(res) is zero */ + inexact_re |= ~mpfr_zero_p (mpc_realref (res)); + inexact_im |= ~mpfr_zero_p (mpc_imagref (res)); + } + mpfr_clear_underflow (); + mpfr_clear_overflow (); + inexact_re |= mpfr_mul (mpc_realref (res), mpc_realref (res), q, GMP_RNDZ); + underflow_re = mpfr_underflow_p (); + overflow_re = mpfr_overflow_p (); + ok_re = !inexact_re || underflow_re || overflow_re + || mpfr_can_round (mpc_realref (res), prec - 4, GMP_RNDN, + GMP_RNDZ, MPC_PREC_RE(a) + (rnd_re == GMP_RNDN)); + + if (ok_re) /* compute imaginary part */ { + mpfr_clear_underflow (); + mpfr_clear_overflow (); + inexact_im |= mpfr_mul (mpc_imagref (res), mpc_imagref (res), q, GMP_RNDZ); + underflow_im = mpfr_underflow_p (); + overflow_im = mpfr_overflow_p (); + ok_im = !inexact_im || underflow_im || overflow_im + || mpfr_can_round (mpc_imagref (res), prec - 4, GMP_RNDN, + GMP_RNDZ, MPC_PREC_IM(a) + (rnd_im == GMP_RNDN)); + } + } + } while ((!ok_re || !ok_im) && !underflow_norm && !overflow_norm + && !underflow_prod && !overflow_prod); + + inex = mpc_set (a, res, rnd); + inexact_re = MPC_INEX_RE (inex); + inexact_im = MPC_INEX_IM (inex); + + end: + /* fix values and inexact flags in case of overflow/underflow */ + /* FIXME: heuristic, certainly does not cover all cases */ + if (overflow_re || (underflow_norm && !underflow_prod)) { + mpfr_set_inf (mpc_realref (a), mpfr_sgn (mpc_realref (res))); + inexact_re = mpfr_sgn (mpc_realref (res)); + } + else if (underflow_re || (overflow_norm && !overflow_prod)) { + inexact_re = mpfr_signbit (mpc_realref (res)) ? 1 : -1; + mpfr_set_zero (mpc_realref (a), -inexact_re); + } + if (overflow_im || (underflow_norm && !underflow_prod)) { + mpfr_set_inf (mpc_imagref (a), mpfr_sgn (mpc_imagref (res))); + inexact_im = mpfr_sgn (mpc_imagref (res)); + } + else if (underflow_im || (overflow_norm && !overflow_prod)) { + inexact_im = mpfr_signbit (mpc_imagref (res)) ? 1 : -1; + mpfr_set_zero (mpc_imagref (a), -inexact_im); + } + + mpc_clear (res); + mpfr_clear (q); + + /* restore underflow and overflow flags from MPFR */ + if (saved_underflow) + mpfr_set_underflow (); + if (saved_overflow) + mpfr_set_overflow (); + + return MPC_INEX (inexact_re, inexact_im); +} |