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/src/gmpy_mpfr.c

http://gmpy.googlecode.com/
C | 2919 lines | 2354 code | 492 blank | 73 comment | 356 complexity | dc9c4e536aaf2cff3e22b6ad4dd1a020 MD5 | raw file

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   1/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
   2 * gmpy_mpfr.c                                                             *
   3 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
   4 * Python interface to the GMP or MPIR, MPFR, and MPC multiple precision   *
   5 * libraries.                                                              *
   6 *                                                                         *
   7 * Copyright 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007,               *
   8 *           2008, 2009 Alex Martelli                                      *
   9 *                                                                         *
  10 * Copyright 2008, 2009, 2010, 2011, 2012, 2013 Case Van Horsen            *
  11 *                                                                         *
  12 * This file is part of GMPY2.                                             *
  13 *                                                                         *
  14 * GMPY2 is free software: you can redistribute it and/or modify it under  *
  15 * the terms of the GNU Lesser General Public License as published by the  *
  16 * Free Software Foundation, either version 3 of the License, or (at your  *
  17 * option) any later version.                                              *
  18 *                                                                         *
  19 * GMPY2 is distributed in the hope that it will be useful, but WITHOUT    *
  20 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or   *
  21 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public    *
  22 * License for more details.                                               *
  23 *                                                                         *
  24 * You should have received a copy of the GNU Lesser General Public        *
  25 * License along with GMPY2; if not, see <http://www.gnu.org/licenses/>    *
  26 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
  27
  28PyDoc_STRVAR(doc_g_mpfr_f2q,
  29"f2q(x,[err]) -> mpq\n\n"
  30"Return the 'best' mpq approximating x to within relative error 'err'.\n"
  31"Default is the precision of x. Uses Stern-Brocot tree to find the\n"
  32"'best' approximation. An 'mpz' is returned if the the denominator\n"
  33"is 1. If 'err'<0, error sought is 2.0 ** err.");
  34
  35static PyObject *
  36Pympfr_f2q(PyObject *self, PyObject *args)
  37{
  38    PympfrObject *err = 0;
  39    PyObject *result;
  40
  41    if (!PyArg_ParseTuple(args, "O&|O&", Pympfr_convert_arg, &self,
  42                          Pympfr_convert_arg, &err)) {
  43        TYPE_ERROR("f2q() requires 'mpfr', ['mpfr'] arguments");
  44        return NULL;
  45    }
  46
  47    result = (PyObject*)stern_brocot((PympfrObject*)self, err, 0, 1);
  48    Py_DECREF(self);
  49    Py_XDECREF((PyObject*)err);
  50    return result;
  51}
  52
  53PyDoc_STRVAR(doc_mpfr,
  54"mpfr() -> mpfr(0.0)\n\n"
  55"     If no argument is given, return mpfr(0.0).\n\n"
  56"mpfr(n[, precison=0]) -> mpfr\n\n"
  57"     Return an 'mpfr' object after converting a numeric value. If\n"
  58"     no precision, or a precision of 0, is specified; the precison\n"
  59"     is taken from the current context.\n\n"
  60"mpfr(s[, precision=0[, [base=0]]) -> mpfr\n\n"
  61"     Return 'mpfr' object after converting a string 's' made up of\n"
  62"     digits in the given base, possibly with fraction-part (with\n"
  63"     period as a separator) and/or exponent-part (with exponent\n"
  64"     marker 'e' for base<=10, else '@'). If no precision, or a\n"
  65"     precision of 0, is specified; the precison is taken from the\n"
  66"     current context. The base of the string representation must\n"
  67"     be 0 or in the interval 2 ... 62. If the base is 0, the leading\n"
  68"     digits of the string are used to identify the base: 0b implies\n"
  69"     base=2, 0x implies base=16, otherwise base=10 is assumed.\n");
  70
  71static PyObject *
  72Pygmpy_mpfr(PyObject *self, PyObject *args, PyObject *keywds)
  73{
  74    PympfrObject *result = 0;
  75    PyObject *arg0;
  76    int base = 0;
  77    Py_ssize_t argc;
  78    /* Assumes mpfr_prec_t is the same as a long. */
  79    mpfr_prec_t bits = 0;
  80    static char *kwlist_s[] = {"s", "precision", "base", NULL};
  81    static char *kwlist_n[] = {"n", "precision", NULL};
  82
  83    argc = PyTuple_Size(args);
  84    if ((argc < 0) || (argc > 3)) {
  85        TYPE_ERROR("mpfr() requires 0 to 3 arguments");
  86        return NULL;
  87    }
  88
  89    if (argc == 0) {
  90        if ((result = (PympfrObject*)Pympfr_new(0))) {
  91            mpfr_set_ui(result->f, 0, context->ctx.mpfr_round);
  92        }
  93        return (PyObject*)result;
  94    }
  95    arg0 = PyTuple_GetItem(args, 0);
  96    if (PyStrOrUnicode_Check(arg0)) {
  97        /* Can have both precision and/or base as keyword arguments. */
  98        if (PyArg_ParseTupleAndKeywords(args, keywds, "O|li", kwlist_s,
  99                                        &arg0, &bits, &base)) {
 100            if ((base!=0) && ((base<2)||(base>62))) {
 101                VALUE_ERROR("base for mpfr() must be 0 or in the "
 102                            "interval 2 ... 62");
 103            }
 104            else if (bits < 0) {
 105                VALUE_ERROR("precision for mpfr() must be >= 0");
 106            }
 107            else {
 108                result = Pympfr_From_PyStr(arg0, base, bits);
 109            }
 110        }
 111        SUBNORMALIZE(result);
 112        return (PyObject*)result;
 113    }
 114
 115    /* Optimize the common case */
 116    if (isReal(arg0) && argc == 1 && !keywds) {
 117        result = Pympfr_From_Real(arg0, bits);
 118        SUBNORMALIZE(result);
 119        return (PyObject*)result;
 120    }
 121
 122    /* Can only have precision as keyword argument. */
 123    if (PyArg_ParseTupleAndKeywords(args, keywds, "O|l", kwlist_n, &arg0, &bits)) {
 124        if (bits < 0) {
 125            VALUE_ERROR("precision for mpfr() must be >= 0");
 126        }
 127        else {
 128            result = Pympfr_From_Real(arg0, bits);
 129            if (!result)
 130                TYPE_ERROR("mpfr() requires numeric or string argument");
 131        }
 132    }
 133    return (PyObject*)result;
 134}
 135
 136/* Implement the .precision attribute of an mpfr. */
 137
 138static PyObject *
 139Pympfr_getprec_attrib(PympfrObject *self, void *closure)
 140{
 141    return PyIntOrLong_FromSsize_t((Py_ssize_t)mpfr_get_prec(self->f));
 142}
 143
 144/* Implement the .rc attribute of an mpfr. */
 145
 146static PyObject *
 147Pympfr_getrc_attrib(PympfrObject *self, void *closure)
 148{
 149    return PyIntOrLong_FromLong((long)self->rc);
 150}
 151
 152/* Implement the .imag attribute of an mpfr. */
 153
 154static PyObject *
 155Pympfr_getimag_attrib(PympfrObject *self, void *closure)
 156{
 157    PympfrObject *result;
 158
 159    if ((result = (PympfrObject*)Pympfr_new(0)))
 160        mpfr_set_zero(result->f, 1);
 161    return (PyObject*)result;
 162}
 163
 164/* Implement the .real attribute of an mpfr. */
 165
 166static PyObject *
 167Pympfr_getreal_attrib(PympfrObject *self, void *closure)
 168{
 169    return (PyObject*)Pympfr_From_Pympfr((PyObject*)self, 0);
 170}
 171
 172/* Implement the nb_bool slot. */
 173
 174static int
 175Pympfr_nonzero(PympfrObject *self)
 176{
 177    return !mpfr_zero_p(self->f);
 178}
 179
 180/* Implement the conjugate() method. */
 181
 182PyDoc_STRVAR(doc_mpfr_conjugate,
 183"x.conjugate() -> mpfr\n\n"
 184"Return the conjugate of x (which is just a copy of x since x is\n"
 185"not a complex number).");
 186
 187static PyObject *
 188Pympfr_conjugate(PyObject *self, PyObject *args)
 189{
 190    return (PyObject*)Pympfr_From_Pympfr(self, 0);
 191}
 192
 193/* Implement the nb_positive slot. */
 194
 195/* TODO: can probably just call Pympfr_From_Real. */
 196
 197static PyObject *
 198Pympfr_pos(PympfrObject *self)
 199{
 200    PympfrObject *result;
 201
 202    if (!(result = (PympfrObject*)Pympfr_new(mpfr_get_prec(self->f))))
 203        return NULL;
 204
 205    mpfr_clear_flags();
 206
 207    /* Since result has the same precision as self, no rounding occurs. */
 208    mpfr_set(result->f, self->f, context->ctx.mpfr_round);
 209    result->round_mode = self->round_mode;
 210    result->rc = self->rc;
 211    /* Force the exponents to be valid. */
 212    result->rc = mpfr_check_range(result->f, result->rc, result->round_mode);
 213    /* Now round result to the current precision. */
 214    result->rc = mpfr_prec_round(result->f, context->ctx.mpfr_prec,
 215                                 context->ctx.mpfr_round);
 216
 217    SUBNORMALIZE(result);
 218    MERGE_FLAGS;
 219    CHECK_FLAGS("__pos__");
 220  done:
 221    if (PyErr_Occurred()) {
 222        Py_XDECREF((PyObject*)result);
 223        result = NULL;
 224    }
 225    return (PyObject*)result;
 226}
 227
 228PyDoc_STRVAR(doc_g_mpfr_get_emin_min,
 229"get_emin_min() -> integer\n\n"
 230"Return the minimum possible exponent that can be set for 'mpfr'.");
 231
 232static PyObject *
 233Pympfr_get_emin_min(PyObject *self, PyObject *args)
 234{
 235    return PyIntOrLong_FromSsize_t((Py_ssize_t)mpfr_get_emin_min());
 236}
 237
 238PyDoc_STRVAR(doc_g_mpfr_get_emax_max,
 239"get_emax_max() -> integer\n\n"
 240"Return the maximum possible exponent that can be set for 'mpfr'.");
 241
 242static PyObject *
 243Pympfr_get_emax_max(PyObject *self, PyObject *args)
 244{
 245    return PyIntOrLong_FromSsize_t((Py_ssize_t)mpfr_get_emax_max());
 246}
 247
 248PyDoc_STRVAR(doc_g_mpfr_get_max_precision,
 249"get_max_precision() -> integer\n\n"
 250"Return the maximum bits of precision that can be used for calculations.\n"
 251"Note: to allow extra precision for intermediate calculations, avoid\n"
 252"setting precision close the maximum precision.");
 253
 254static PyObject *
 255Pympfr_get_max_precision(PyObject *self, PyObject *args)
 256{
 257    return PyIntOrLong_FromSsize_t((Py_ssize_t)MPFR_PREC_MAX);
 258}
 259
 260PyDoc_STRVAR(doc_g_mpfr_get_exp,
 261"get_exp(mpfr) -> integer\n\n"
 262"Return the exponent of an mpfr. Returns 0 for NaN or Infinity and\n"
 263"sets the erange flag and will raise an exception if trap_erange\n"
 264"is set.");
 265
 266static PyObject *
 267Pympfr_get_exp(PyObject *self, PyObject *other)
 268{
 269    PyObject *result = 0;
 270    Py_ssize_t exp;
 271
 272    PARSE_ONE_MPFR_OTHER("get_exp() requires 'mpfr' argument");
 273
 274    if (mpfr_regular_p(Pympfr_AS_MPFR(self))) {
 275        exp = (Py_ssize_t)mpfr_get_exp(Pympfr_AS_MPFR(self));
 276        result = PyIntOrLong_FromSsize_t((Py_ssize_t)exp);
 277    }
 278    else if (mpfr_zero_p(Pympfr_AS_MPFR(self))) {
 279        Py_DECREF(self);
 280        result = PyIntOrLong_FromSsize_t(0);
 281    }
 282    else {
 283        context->ctx.erange = 1;
 284        if (context->ctx.trap_erange) {
 285            GMPY_ERANGE("Can not get exponent from NaN or Infinity.");
 286        }
 287        else {
 288            result = PyIntOrLong_FromSsize_t(0);
 289        }
 290    }
 291    Py_DECREF(self);
 292    return result;
 293}
 294
 295PyDoc_STRVAR(doc_g_mpfr_set_exp,
 296"set_exp(mpfr, n) -> mpfr\n\n"
 297"Set the exponent of an mpfr to n. If n is outside the range of\n"
 298"valid exponents, set_exp() will set the erange flag and either\n"
 299"return the original value or raise an exception if trap_erange\n"
 300"is set.");
 301
 302static PyObject *
 303Pympfr_set_exp(PyObject *self, PyObject *args)
 304{
 305    PympfrObject *result = 0;
 306    long exp = 0;
 307
 308    if (!PyArg_ParseTuple(args, "O&l", Pympfr_convert_arg, &self, &exp)) {
 309        TYPE_ERROR("set_exp() requires 'mpfr', 'integer' arguments");
 310        return NULL;
 311    }
 312
 313    if (!(result = Pympfr_From_Pympfr(self, 0)))
 314        return NULL;
 315    Py_DECREF(self);
 316
 317    result->rc = mpfr_set_exp(Pympfr_AS_MPFR(result), exp);
 318
 319    if (result->rc) {
 320        context->ctx.erange = 1;
 321        if (context->ctx.trap_erange) {
 322            GMPY_ERANGE("New exponent is out-of-bounds.");
 323            Py_DECREF(result);
 324            return NULL;
 325        }
 326    }
 327
 328    return (PyObject*)result;
 329}
 330
 331PyDoc_STRVAR(doc_g_mpfr_set_sign,
 332"set_sign(mpfr, bool) -> mpfr\n\n"
 333"If 'bool' is True, then return an 'mpfr' with the sign bit set.");
 334
 335static PyObject *
 336Pympfr_set_sign(PyObject *self, PyObject *args)
 337{
 338    PympfrObject *result = 0;
 339    PyObject *boolean = 0;
 340    int s;
 341
 342    if (!PyArg_ParseTuple(args, "O&O", Pympfr_convert_arg, &self, &boolean)) {
 343        TYPE_ERROR("set_sign() requires 'mpfr', 'boolean' arguments");
 344        return NULL;
 345    }
 346
 347    if (!(result = (PympfrObject*)Pympfr_new(0)))
 348        return NULL;
 349
 350    s = PyObject_IsTrue(boolean);
 351    if (s == -1) {
 352        TYPE_ERROR("set_sign() requires 'mpfr', 'boolean' arguments");
 353        Py_DECREF(self);
 354        Py_DECREF(boolean);
 355        Py_DECREF(result);
 356        return NULL;
 357    }
 358
 359    result->rc = mpfr_setsign(Pympfr_AS_MPFR(result), Pympfr_AS_MPFR(self),
 360                              s, context->ctx.mpfr_round);
 361
 362    Py_DECREF(self);
 363    Py_DECREF(boolean);
 364    return (PyObject*)result;
 365}
 366
 367PyDoc_STRVAR(doc_g_mpfr_copy_sign,
 368"copy_sign(mpfr, mpfr) -> mpfr\n\n"
 369"Return an 'mpfr' composed of the first argument with the sign of the\n"
 370"second argument.");
 371
 372static PyObject *
 373Pympfr_copy_sign(PyObject *self, PyObject *args)
 374{
 375    PympfrObject *result = 0;
 376    PyObject *other = 0;
 377
 378    if (!PyArg_ParseTuple(args, "O&O&", Pympfr_convert_arg, &self,
 379                          Pympfr_convert_arg, &other)) {
 380        TYPE_ERROR("copy_sign() requires 'mpfr', 'mpfr' arguments");
 381        return NULL;
 382    }
 383
 384    if (!(result = (PympfrObject*)Pympfr_new(0)))
 385        return NULL;
 386
 387    result->rc = mpfr_copysign(Pympfr_AS_MPFR(result), Pympfr_AS_MPFR(self),
 388                              Pympfr_AS_MPFR(other), context->ctx.mpfr_round);
 389
 390    Py_DECREF(self);
 391    Py_DECREF(other);
 392    return (PyObject*)result;
 393}
 394
 395static PyObject *
 396Pympfr_div_2exp(PyObject *self, PyObject *args)
 397{
 398    PympfrObject *result = 0;
 399    unsigned long exp = 0;
 400
 401    if (!PyArg_ParseTuple(args, "O&k", Pympfr_convert_arg, &self, &exp)) {
 402        TYPE_ERROR("div_2exp() requires 'mpfr', 'integer' arguments");
 403        return NULL;
 404    }
 405
 406    if (!(result = (PympfrObject*)Pympfr_new(0)))
 407        return NULL;
 408
 409    mpfr_clear_flags();
 410
 411    result->rc = mpfr_div_2ui(Pympfr_AS_MPFR(result), Pympfr_AS_MPFR(self),
 412                              exp, context->ctx.mpfr_round);
 413
 414    MPFR_CLEANUP_SELF("div_2exp()");
 415}
 416
 417static PyObject *
 418Pympfr_mul_2exp(PyObject *self, PyObject *args)
 419{
 420    PympfrObject *result = 0;
 421    unsigned long exp = 0;
 422
 423    if (!PyArg_ParseTuple(args, "O&k", Pympfr_convert_arg, &self, &exp)) {
 424        TYPE_ERROR("mul_2exp() requires 'mpfr', 'integer' arguments");
 425        return NULL;
 426    }
 427
 428    if (!(result = (PympfrObject*)Pympfr_new(0)))
 429        return NULL;
 430
 431    mpfr_clear_flags();
 432
 433    result->rc = mpfr_mul_2ui(Pympfr_AS_MPFR(result), Pympfr_AS_MPFR(self),
 434                              exp, context->ctx.mpfr_round);
 435
 436    MPFR_CLEANUP_SELF("mul_2exp()");
 437}
 438
 439PyDoc_STRVAR(doc_g_mpfr_set_nan,
 440"nan() -> mpfr\n\n"
 441"Return an 'mpfr' initialized to NaN (Not-A-Number).");
 442
 443static PyObject *
 444Pympfr_set_nan(PyObject *self, PyObject *other)
 445{
 446    PympfrObject *result;
 447
 448    if ((result = (PympfrObject*)Pympfr_new(0)))
 449        mpfr_set_nan(result->f);
 450    return (PyObject*)result;
 451}
 452
 453PyDoc_STRVAR(doc_g_mpfr_set_inf,
 454"inf(n) -> mpfr\n\n"
 455"Return an 'mpfr' initialized to Infinity with the same sign as n.\n"
 456"If n is not given, +Infinity is returned.");
 457
 458static PyObject *
 459Pympfr_set_inf(PyObject *self, PyObject *args)
 460{
 461    PympfrObject *result;
 462    long s = 1;
 463
 464    if (PyTuple_Size(args) == 1) {
 465        s = clong_From_Integer(PyTuple_GET_ITEM(args, 0));
 466        if (s == -1 && PyErr_Occurred()) {
 467            TYPE_ERROR("inf() requires 'int' argument");
 468            return NULL;
 469        }
 470    }
 471
 472    if ((result = (PympfrObject*)Pympfr_new(0)))
 473        mpfr_set_inf(result->f, s<0?-1:1);
 474    return (PyObject*)result;
 475}
 476
 477PyDoc_STRVAR(doc_g_mpfr_set_zero,
 478"zero(n) -> mpfr\n\n"
 479"Return an 'mpfr' inialized to 0.0 with the same sign as n.\n"
 480"If n is not given, +0.0 is returned.");
 481
 482static PyObject *
 483Pympfr_set_zero(PyObject *self, PyObject *args)
 484{
 485    PympfrObject *result;
 486    long s = 1;
 487
 488    if (PyTuple_Size(args) == 1) {
 489        s = clong_From_Integer(PyTuple_GET_ITEM(args, 0));
 490        if (s == -1 && PyErr_Occurred()) {
 491            TYPE_ERROR("zero() requires 'int' argument");
 492            return NULL;
 493        }
 494    }
 495
 496    if ((result = (PympfrObject*)Pympfr_new(0)))
 497        mpfr_set_zero(result->f, s<0?-1:1);
 498    return (PyObject*)result;
 499}
 500
 501PyDoc_STRVAR(doc_g_mpfr_is_signed,
 502"is_signed(x) -> boolean\n\n"
 503"Return True if the sign bit of x is set.");
 504
 505static PyObject *
 506Pympfr_is_signed(PyObject *self, PyObject *other)
 507{
 508    int res;
 509    if(self && Pympfr_Check(self)) {
 510        Py_INCREF(self);
 511    }
 512    else if(Pympfr_Check(other)) {
 513        self = other;
 514        Py_INCREF((PyObject*)self);
 515    }
 516    else if (!(self = (PyObject*)Pympfr_From_Real(other, 0))) {
 517        TYPE_ERROR("is_signed() requires 'mpfr' argument");
 518        return NULL;
 519    }
 520    res = mpfr_signbit(Pympfr_AS_MPFR(self));
 521    Py_DECREF(self);
 522    if (res)
 523        Py_RETURN_TRUE;
 524    else
 525        Py_RETURN_FALSE;
 526}
 527
 528#define MPFR_TEST_OTHER(NAME, msg) \
 529static PyObject * \
 530Pympfr_is_##NAME(PyObject *self, PyObject *other)\
 531{\
 532    int res;\
 533    if(self && Pympfr_Check(self)) {\
 534        Py_INCREF(self);\
 535    }\
 536    else if(Pympfr_Check(other)) {\
 537        self = other;\
 538        Py_INCREF((PyObject*)self);\
 539    }\
 540    else if (!(self = (PyObject*)Pympfr_From_Real(other, 0))) {\
 541        PyErr_SetString(PyExc_TypeError, msg);\
 542        return NULL;\
 543    }\
 544    res = mpfr_##NAME##_p(Pympfr_AS_MPFR(self));\
 545    Py_DECREF(self);\
 546    if (res)\
 547        Py_RETURN_TRUE;\
 548    else\
 549        Py_RETURN_FALSE;\
 550}
 551
 552MPFR_TEST_OTHER(nan, "is_nan() requires 'mpfr' argument");
 553
 554MPFR_TEST_OTHER(inf, "is_infinite() requires 'mpfr' argument");
 555
 556PyDoc_STRVAR(doc_g_mpfr_is_number,
 557"is_number(x) -> boolean\n\n"
 558"Return True if x is an actual number (i.e. not NaN or Infinity);\n"
 559"False otherwise.\n"
 560"Note: is_number() is deprecated; please use is_finite().");
 561
 562MPFR_TEST_OTHER(number, "is_finite() requires 'mpfr' argument");
 563
 564MPFR_TEST_OTHER(zero, "is_zero() requires 'mpfr' argument");
 565
 566PyDoc_STRVAR(doc_g_mpfr_is_regular,
 567"is_regular(x) -> boolean\n\n"
 568"Return True if x is not zero, NaN, or Infinity; False otherwise.");
 569
 570MPFR_TEST_OTHER(regular, "is_regular() requires 'mpfr' argument");
 571
 572PyDoc_STRVAR(doc_mpfr_is_integer,
 573"x.is_integer() -> boolean\n\n"
 574"Return True if x is an integer; False otherwise.");
 575
 576PyDoc_STRVAR(doc_g_mpfr_is_integer,
 577"is_integer(x) -> boolean\n\n"
 578"Return True if x is an integer; False otherwise.");
 579
 580MPFR_TEST_OTHER(integer, "is_integer() requires 'mpfr' argument");
 581
 582/* produce string for an mpfr with requested/defaulted parameters */
 583
 584PyDoc_STRVAR(doc_mpfr_digits,
 585"x.digits([base=10[, prec=0]]) -> (mantissa, exponent, bits)\n\n"
 586"Returns up to 'prec' digits in the given base. If 'prec' is 0, as many\n"
 587"digits that are available are returned. No more digits than available\n"
 588"given x's precision are returned. 'base' must be between 2 and 62,\n"
 589"inclusive. The result is a three element tuple containing the mantissa,\n"
 590"the exponent, and the number of bits of precision.");
 591
 592/* TODO: support keyword arguments. */
 593
 594static PyObject *
 595Pympfr_digits(PyObject *self, PyObject *args)
 596{
 597    int base = 10;
 598    int prec = 0;
 599    PyObject *result;
 600
 601    if (self && Pympfr_Check(self)) {
 602        if (!PyArg_ParseTuple(args, "|ii", &base, &prec))
 603            return NULL;
 604        Py_INCREF(self);
 605    }
 606    else {
 607        if(!PyArg_ParseTuple(args, "O&|ii", Pympfr_convert_arg, &self,
 608                            &base, &prec))
 609        return NULL;
 610    }
 611    result = Pympfr_To_PyStr((PympfrObject*)self, base, prec);
 612    Py_DECREF(self);
 613    return result;
 614}
 615
 616PyDoc_STRVAR(doc_mpfr_integer_ratio,
 617"x.as_integer_ratio() -> (num, den)\n\n"
 618"Return the exact rational equivalent of an mpfr. Value is a tuple\n"
 619"for compatibility with Python's float.as_integer_ratio().");
 620
 621static PyObject *
 622Pympfr_integer_ratio(PyObject *self, PyObject *args)
 623{
 624    PympzObject *num = 0, *den = 0;
 625    mpfr_exp_t temp, twocount;
 626    PyObject *result;
 627
 628    if (mpfr_nan_p(Pympfr_AS_MPFR(self))) {
 629        VALUE_ERROR("Cannot pass NaN to mpfr.as_integer_ratio.");
 630        return NULL;
 631    }
 632
 633    if (mpfr_inf_p(Pympfr_AS_MPFR(self))) {
 634        OVERFLOW_ERROR("Cannot pass Infinity to mpfr.as_integer_ratio.");
 635        return NULL;
 636    }
 637
 638    num = (PympzObject*)Pympz_new();
 639    den = (PympzObject*)Pympz_new();
 640    if (!num || !den) {
 641        Py_XDECREF((PyObject*)num);
 642        Py_XDECREF((PyObject*)den);
 643        return NULL;
 644    }
 645
 646    if (mpfr_zero_p(Pympfr_AS_MPFR(self))) {
 647        mpz_set_ui(num->z, 0);
 648        mpz_set_ui(den->z, 1);
 649    }
 650    else {
 651        temp = mpfr_get_z_2exp(num->z, Pympfr_AS_MPFR(self));
 652        twocount = (mpfr_exp_t)mpz_scan1(num->z, 0);
 653        if (twocount) {
 654            temp += twocount;
 655            mpz_div_2exp(num->z, num->z, twocount);
 656        }
 657        mpz_set_ui(den->z, 1);
 658        if (temp > 0)
 659            mpz_mul_2exp(num->z, num->z, temp);
 660        else if (temp < 0)
 661            mpz_mul_2exp(den->z, den->z, -temp);
 662    }
 663    result = Py_BuildValue("(NN)", (PyObject*)num, (PyObject*)den);
 664    if (!result) {
 665        Py_DECREF((PyObject*)num);
 666        Py_DECREF((PyObject*)den);
 667    }
 668    return result;
 669}
 670
 671PyDoc_STRVAR(doc_mpfr_mantissa_exp,
 672"x.as_mantissa_exp() -> (mantissa,exponent)\n\n"
 673"Return the mantissa and exponent of an mpfr.");
 674
 675static PyObject *
 676Pympfr_mantissa_exp(PyObject *self, PyObject *args)
 677{
 678    PympzObject *mantissa = 0, *exponent = 0;
 679    mpfr_exp_t temp;
 680    PyObject *result;
 681
 682    if (mpfr_nan_p(Pympfr_AS_MPFR(self))) {
 683        VALUE_ERROR("Cannot pass NaN to mpfr.as_mantissa_exp.");
 684        return NULL;
 685    }
 686
 687    if (mpfr_inf_p(Pympfr_AS_MPFR(self))) {
 688        OVERFLOW_ERROR("Cannot pass Infinity to mpfr.as_mantissa_exp.");
 689        return NULL;
 690    }
 691
 692    mantissa = (PympzObject*)Pympz_new();
 693    exponent = (PympzObject*)Pympz_new();
 694    if (!mantissa || !exponent) {
 695        Py_XDECREF((PyObject*)mantissa);
 696        Py_XDECREF((PyObject*)exponent);
 697        return NULL;
 698    }
 699
 700    if (mpfr_zero_p(Pympfr_AS_MPFR(self))) {
 701        mpz_set_ui(mantissa->z, 0);
 702        mpz_set_ui(exponent->z, 1);
 703    }
 704    else {
 705        temp = mpfr_get_z_2exp(mantissa->z, Pympfr_AS_MPFR(self));
 706        mpz_set_si(exponent->z, temp);
 707    }
 708    result = Py_BuildValue("(NN)", (PyObject*)mantissa, (PyObject*)exponent);
 709    if (!result) {
 710        Py_DECREF((PyObject*)mantissa);
 711        Py_DECREF((PyObject*)exponent);
 712    }
 713    return result;
 714}
 715
 716PyDoc_STRVAR(doc_mpfr_simple_fraction,
 717"x.as_simple_fraction([precision=0]) -> mpq\n\n"
 718"Return a simple rational approximation to x. The result will be\n"
 719"accurate to 'precision' bits. If 'precision' is 0, the precision\n"
 720"of 'x' will be used.");
 721
 722static PyObject *
 723Pympfr_simple_fraction(PyObject *self, PyObject *args, PyObject *keywds)
 724{
 725    mpfr_prec_t prec = 0;
 726    static char *kwlist[] = {"precision", NULL};
 727
 728    if (!PyArg_ParseTupleAndKeywords(args, keywds, "|l", kwlist, &prec))
 729        return NULL;
 730
 731    return (PyObject*)stern_brocot((PympfrObject*)self, 0, prec, 0);
 732}
 733
 734static Py_hash_t
 735_mpfr_hash(mpfr_t f)
 736{
 737#ifdef _PyHASH_MODULUS
 738    Py_uhash_t hash = 0;
 739    Py_ssize_t exp;
 740    size_t msize;
 741    int sign;
 742
 743    /* Handle special cases first */
 744    if (!mpfr_number_p(f)) {
 745        if (mpfr_inf_p(f))
 746            if (mpfr_sgn(f) > 0)
 747                return _PyHASH_INF;
 748            else
 749                return -_PyHASH_INF;
 750        else
 751            return _PyHASH_NAN;
 752    }
 753
 754    /* Calculate the number of limbs in the mantissa. */
 755    msize = (f->_mpfr_prec + mp_bits_per_limb - 1) / mp_bits_per_limb;
 756
 757    /* Calculate the hash of the mantissa. */
 758    if (mpfr_sgn(f) > 0) {
 759        hash = mpn_mod_1(f->_mpfr_d, msize, _PyHASH_MODULUS);
 760        sign = 1;
 761    }
 762    else if (mpfr_sgn(f) < 0) {
 763        hash = mpn_mod_1(f->_mpfr_d, msize, _PyHASH_MODULUS);
 764        sign = -1;
 765    }
 766    else {
 767        return 0;
 768    }
 769
 770    /* Calculate the final hash. */
 771    exp = f->_mpfr_exp - (msize * mp_bits_per_limb);
 772    exp = exp >= 0 ? exp % _PyHASH_BITS : _PyHASH_BITS-1-((-1-exp) % _PyHASH_BITS);
 773    hash = ((hash << exp) & _PyHASH_MODULUS) | hash >> (_PyHASH_BITS - exp);
 774
 775    hash *= sign;
 776    if (hash == (Py_uhash_t)-1)
 777        hash = (Py_uhash_t)-2;
 778    return (Py_hash_t)hash;
 779#else
 780    double temp;
 781    temp = mpfr_get_d(f, context->ctx.mpfr_round);
 782    return _Py_HashDouble(temp);
 783#endif
 784}
 785
 786static Py_hash_t
 787Pympfr_hash(PympfrObject *self)
 788{
 789    if (self->hash_cache == -1)
 790        self->hash_cache = _mpfr_hash(self->f);
 791    return self->hash_cache;
 792}
 793
 794/* This function is used in gmpy_mpany. */
 795
 796static PyObject *
 797Pympfr_pow(PyObject *base, PyObject *exp, PyObject *m)
 798{
 799    PympfrObject *tempb, *tempe, *result;
 800#ifdef WITHMPC
 801    PympcObject *mpc_result;
 802#endif
 803
 804    if (m != Py_None) {
 805        TYPE_ERROR("pow() 3rd argument not allowed unless all arguments are integers");
 806        return NULL;
 807    }
 808
 809    tempb = Pympfr_From_Real(base, 0);
 810    tempe = Pympfr_From_Real(exp, 0);
 811
 812    if (!tempe || !tempb) {
 813        Py_XDECREF((PyObject*)tempe);
 814        Py_XDECREF((PyObject*)tempb);
 815        Py_RETURN_NOTIMPLEMENTED;
 816    }
 817
 818    result = (PympfrObject*)Pympfr_new(0);
 819
 820    if (!result) {
 821        Py_DECREF((PyObject*)tempe);
 822        Py_DECREF((PyObject*)tempb);
 823        return NULL;
 824    }
 825
 826    if (mpfr_zero_p(tempb->f) && (mpfr_sgn(tempe->f) < 0)) {
 827        context->ctx.divzero = 1;
 828        if (context->ctx.trap_divzero) {
 829            GMPY_DIVZERO("zero cannot be raised to a negative power");
 830            goto done;
 831        }
 832    }
 833
 834    mpfr_clear_flags();
 835    result->rc = mpfr_pow(result->f, tempb->f,
 836                          tempe->f, context->ctx.mpfr_round);
 837#ifdef WITHMPC
 838    if (result && mpfr_nanflag_p() && context->ctx.allow_complex) {
 839        /* If we don't get a valid result, or the result is a nan, then just
 840         * return the original mpfr value. */
 841        if (!(mpc_result = (PympcObject*)Pympc_pow(base, exp, m)) ||
 842            MPC_IS_NAN_P(mpc_result)) {
 843
 844            Py_XDECREF((PyObject*)mpc_result);
 845            context->ctx.invalid = 1;
 846            GMPY_INVALID("invalid operation in 'mpfr' pow()");
 847            goto done;
 848        }
 849        /* return a valid complex result */
 850        Py_DECREF(result);
 851        result = (PympfrObject*)mpc_result;
 852        goto done;
 853    }
 854#endif
 855
 856    SUBNORMALIZE(result)
 857    MERGE_FLAGS
 858    CHECK_FLAGS("pow()")
 859  done:
 860    Py_DECREF((PyObject*)tempe);
 861    Py_DECREF((PyObject*)tempb);
 862    if (PyErr_Occurred()) {
 863        Py_XDECREF((PyObject*)result);
 864        result = NULL;
 865    }
 866    return (PyObject*)result;
 867}
 868
 869#define MPFR_CONST(NAME) \
 870static PyObject * \
 871Pympfr_##NAME(PyObject *self, PyObject *args, PyObject *keywds) \
 872{ \
 873    PympfrObject *result; \
 874    mpfr_prec_t bits = 0; \
 875    static char *kwlist[] = {"precision", NULL}; \
 876    if (!PyArg_ParseTupleAndKeywords(args, keywds, "|l", kwlist, &bits)) return NULL; \
 877    if ((result = (PympfrObject*)Pympfr_new(bits))) { \
 878        mpfr_clear_flags(); \
 879        result->rc = mpfr_##NAME(result->f, context->ctx.mpfr_round); \
 880        MERGE_FLAGS \
 881        CHECK_FLAGS(#NAME "()") \
 882    } \
 883  done: \
 884    return (PyObject*)result; \
 885}
 886
 887PyDoc_STRVAR(doc_mpfr_const_pi,
 888"const_pi([precision=0]) -> mpfr\n\n"
 889"Return the constant pi using the specified precision. If no\n"
 890"precision is specified, the default precision is used.");
 891
 892MPFR_CONST(const_pi)
 893
 894PyDoc_STRVAR(doc_mpfr_const_euler,
 895"const_euler([precision=0]) -> mpfr\n\n"
 896"Return the euler constant using the specified precision. If no\n"
 897"precision is specified, the default precision is used.");
 898
 899MPFR_CONST(const_euler)
 900
 901PyDoc_STRVAR(doc_mpfr_const_log2,
 902"const_log2([precision=0]) -> mpfr\n\n"
 903"Return the log2 constant  using the specified precision. If no\n"
 904"precision is specified, the default precision is used.");
 905
 906MPFR_CONST(const_log2)
 907
 908PyDoc_STRVAR(doc_mpfr_const_catalan,
 909"const_catalan([precision=0]) -> mpfr\n\n"
 910"Return the catalan constant  using the specified precision. If no\n"
 911"precision is specified, the default precision is used.");
 912
 913MPFR_CONST(const_catalan)
 914
 915static PyObject *
 916Pympfr_sqrt(PyObject *self, PyObject *other)
 917{
 918    PympfrObject *result;
 919
 920    PARSE_ONE_MPFR_OTHER("sqrt() requires 'mpfr' argument");
 921
 922#ifdef WITHMPC
 923    if (mpfr_sgn(Pympfr_AS_MPFR(self)) < 0 && context->ctx.allow_complex) {
 924        Py_DECREF(self);
 925        return Pympc_sqrt(self, other);
 926    }
 927#endif
 928
 929    if (!(result = (PympfrObject*)Pympfr_new(0))) {
 930        Py_DECREF(self);
 931        return NULL;
 932    }
 933
 934    mpfr_clear_flags();
 935    result->rc = mpfr_sqrt(result->f, Pympfr_AS_MPFR(self),
 936                           context->ctx.mpfr_round);
 937
 938    MPFR_CLEANUP_SELF("sqrt()");
 939}
 940
 941PyDoc_STRVAR(doc_g_mpfr_rec_sqrt,
 942"rec_sqrt(x) -> mpfr\n\n"
 943"Return the reciprocal of the square root of x.");
 944
 945static PyObject *
 946Pympfr_rec_sqrt(PyObject *self, PyObject *other)
 947{
 948    PympfrObject *result;
 949
 950    PARSE_ONE_MPFR_OTHER("rec_sqrt() requires 'mpfr' argument");
 951
 952    if (!(result = (PympfrObject*)Pympfr_new(0)))
 953        goto done;
 954
 955    mpfr_clear_flags();
 956    result->rc = mpfr_rec_sqrt(result->f, Pympfr_AS_MPFR(self),
 957                               context->ctx.mpfr_round);
 958
 959    MPFR_CLEANUP_SELF("rec_sqrt()");
 960}
 961
 962PyDoc_STRVAR(doc_mpfr_root,
 963"root(x, n) -> mpfr\n\n"
 964"Return n-th root of x. The result always an 'mpfr'.");
 965
 966static PyObject *
 967Pympfr_root(PyObject *self, PyObject *args)
 968{
 969    long n;
 970    PympfrObject *result;
 971
 972    PARSE_ONE_MPFR_REQ_CLONG(&n, "root() requires 'mpfr','int' arguments");
 973
 974    if (!(result = (PympfrObject*)Pympfr_new(0)))
 975        goto done;
 976
 977    if (n <= 0) {
 978        VALUE_ERROR("n must be > 0");
 979        goto done;
 980    }
 981
 982    mpfr_clear_flags();
 983    result->rc = mpfr_root(result->f, Pympfr_AS_MPFR(self), n,
 984                           context->ctx.mpfr_round);
 985
 986    MPFR_CLEANUP_SELF("root()");
 987}
 988
 989PyDoc_STRVAR(doc_g_mpfr_round2,
 990"round2(x[, n]) -> mpfr\n\n"
 991"Return x rounded to n bits. Uses default precision if n is not\n"
 992"specified. See round_away() to access the mpfr_round() function.");
 993
 994static PyObject *
 995Pympfr_round2(PyObject *self, PyObject *args)
 996{
 997    mpfr_prec_t prec = context->ctx.mpfr_prec;
 998    PympfrObject *result = 0;
 999
1000    PARSE_ONE_MPFR_OPT_CLONG(&prec,
1001            "round2() requires 'mpfr',['int'] arguments");
1002
1003    if (prec < MPFR_PREC_MIN || prec > MPFR_PREC_MAX) {
1004        VALUE_ERROR("invalid precision");
1005        goto done;
1006    }
1007
1008    if (!(result = (PympfrObject*)Pympfr_new(mpfr_get_prec(Pympfr_AS_MPFR(self))))) {
1009        goto done;
1010    }
1011
1012    mpfr_clear_flags();
1013    /* Duplicate the code from Pympfr_pos. */
1014    mpfr_set(result->f, Pympfr_AS_MPFR(self), context->ctx.mpfr_round);
1015    result->round_mode = ((PympfrObject*)self)->round_mode;
1016    result->rc = ((PympfrObject*)self)->rc;
1017    result->rc = mpfr_check_range(result->f, result->rc, result->round_mode);
1018    result->rc = mpfr_prec_round(result->f, prec, context->ctx.mpfr_round);
1019
1020    MPFR_CLEANUP_SELF("round2()");
1021}
1022
1023PyDoc_STRVAR(doc_g_mpfr_round10,
1024"__round__(x[, n = 0]) -> mpfr\n\n"
1025"Return x rounded to n decimal digits before (n < 0) or after (n > 0)\n"
1026"the decimal point. Rounds to an integer if n is not specified.");
1027
1028static PyObject *
1029Pympfr_round10(PyObject *self, PyObject *args)
1030{
1031    Py_ssize_t digits = 0;
1032    mpz_t temp;
1033    PympfrObject *resultf = 0;
1034    PympzObject *resultz;
1035
1036    /* If the size of args is 0, we just return an mpz. */
1037
1038    if (PyTuple_GET_SIZE(args) == 0) {
1039        if ((resultz = (PympzObject*)Pympz_new())) {
1040            if (mpfr_nan_p(Pympfr_AS_MPFR(self))) {
1041                Py_DECREF((PyObject*)resultz);
1042                VALUE_ERROR("'mpz' does not support NaN");
1043                return NULL;
1044            }
1045            if (mpfr_inf_p(Pympfr_AS_MPFR(self))) {
1046                Py_DECREF((PyObject*)resultz);
1047                OVERFLOW_ERROR("'mpz' does not support Infinity");
1048                return NULL;
1049            }
1050            /* return code is ignored */
1051            mpfr_get_z(resultz->z, Pympfr_AS_MPFR(self), MPFR_RNDN);
1052        }
1053        return (PyObject*)resultz;
1054    }
1055
1056    /* Now we need to return an mpfr, so handle the simple cases. */
1057
1058    if (!mpfr_regular_p(Pympfr_AS_MPFR(self))) {
1059        Py_INCREF(self);
1060        return self;
1061    }
1062
1063    if (PyTuple_GET_SIZE(args) > 1) {
1064        TYPE_ERROR("Too many arguments for __round__().");
1065        return NULL;
1066    }
1067
1068    if (PyTuple_GET_SIZE(args) == 1) {
1069        digits = ssize_t_From_Integer(PyTuple_GET_ITEM(args, 0));
1070        if (digits == -1 && PyErr_Occurred()) {
1071            TYPE_ERROR("__round__() requires 'int' argument");
1072            return NULL;
1073        }
1074    }
1075
1076    /* TODO: better error analysis, or else convert the mpfr to an exact
1077     * fraction, round the fraction, and then convert back to an mpfr.
1078     */
1079
1080    resultf = (PympfrObject*)Pympfr_new(mpfr_get_prec(Pympfr_AS_MPFR(self))+100);
1081    if (!resultf)
1082        return NULL;
1083
1084    mpz_inoc(temp);
1085    mpz_ui_pow_ui(temp, 10, digits > 0 ? digits : -digits);
1086    if (digits >= 0) {
1087        mpfr_mul_z(resultf->f, Pympfr_AS_MPFR(self), temp, MPFR_RNDN);
1088    }
1089    else {
1090        mpfr_div_z(resultf->f, Pympfr_AS_MPFR(self), temp, MPFR_RNDN);
1091    }
1092
1093    mpfr_rint(resultf->f, resultf->f, MPFR_RNDN);
1094
1095    if (digits >= 0) {
1096        mpfr_div_z(resultf->f, resultf->f, temp, MPFR_RNDN);
1097    }
1098    else {
1099        mpfr_mul_z(resultf->f, resultf->f, temp, MPFR_RNDN);
1100    }
1101    mpfr_prec_round(resultf->f, mpfr_get_prec(Pympfr_AS_MPFR(self)), MPFR_RNDN);
1102
1103    mpz_cloc(temp);
1104    return((PyObject*)resultf);
1105}
1106
1107PyDoc_STRVAR(doc_g_mpfr_reldiff,
1108"reldiff(x, y) -> mpfr\n\n"
1109"Return the relative difference between x and y. Result is equal to\n"
1110"abs(x-y)/x.");
1111
1112static PyObject *
1113Pympfr_reldiff(PyObject *self, PyObject *args)
1114{
1115    PympfrObject *result;
1116    PyObject *other;
1117
1118    PARSE_TWO_MPFR_ARGS(other, "reldiff() requires 'mpfr','mpfr' arguments");
1119
1120    if (!(result = (PympfrObject*)Pympfr_new(0))) {
1121        Py_DECREF(self);
1122        Py_DECREF(other);
1123        return NULL;
1124    }
1125
1126    /* mpfr_reldiff doesn't guarantee correct rounding and doesn't appear
1127     * to set any exceptions.
1128     */
1129    mpfr_reldiff(result->f, Pympfr_AS_MPFR(self), Pympfr_AS_MPFR(other),
1130                 context->ctx.mpfr_round);
1131    result->rc = 0;
1132    Py_DECREF(self);
1133    Py_DECREF(other);
1134    return (PyObject*)result;
1135}
1136
1137static PyObject *
1138Pympfr_sign(PyObject *self, PyObject *other)
1139{
1140    long sign;
1141
1142    PARSE_ONE_MPFR_OTHER("sign() requires 'mpfr' argument");
1143
1144    mpfr_clear_flags();
1145    sign = mpfr_sgn(Pympfr_AS_MPFR(self));
1146
1147    MERGE_FLAGS;
1148    CHECK_ERANGE("range error in 'mpfr' sign(), NaN argument");
1149
1150  done:
1151    Py_DECREF((PyObject*)self);
1152    if (PyErr_Occurred())
1153        return NULL;
1154    else
1155        return PyIntOrLong_FromLong(sign);
1156}
1157
1158#define MPFR_MONOP(NAME) \
1159static PyObject * \
1160Py##NAME(PympfrObject *x) \
1161{ \
1162    PympfrObject *r; \
1163    if (!(r = (PympfrObject*)Pympfr_new(0))) \
1164        return NULL; \
1165    if (Pympfr_CheckAndExp(x)) { \
1166        r->rc = NAME(r->f, x->f, context->ctx.mpfr_round); \
1167    } \
1168    else { \
1169        mpfr_set(r->f, x->f, context->ctx.mpfr_round); \
1170        r->round_mode = x->round_mode; \
1171        r->rc = x->rc; \
1172        mpfr_clear_flags(); \
1173        mpfr_check_range(r->f, r->rc, r->round_mode); \
1174        r->rc = NAME(r->f, r->f, context->ctx.mpfr_round); \
1175        MERGE_FLAGS; \
1176        CHECK_FLAGS(#NAME "()"); \
1177    } \
1178  done: \
1179    return (PyObject *) r; \
1180}
1181
1182MPFR_MONOP(mpfr_abs)
1183MPFR_MONOP(mpfr_neg)
1184
1185#define MPFR_UNIOP_NOROUND(NAME) \
1186static PyObject * \
1187Pympfr_##NAME(PyObject* self, PyObject *other) \
1188{ \
1189    PympfrObject *result; \
1190    PARSE_ONE_MPFR_OTHER(#NAME "() requires 'mpfr' argument"); \
1191    if (!(result = (PympfrObject*)Pympfr_new(0))) goto done; \
1192    mpfr_clear_flags(); \
1193    result->rc = mpfr_##NAME(result->f, Pympfr_AS_MPFR(self)); \
1194    MPFR_CLEANUP_SELF(#NAME "()"); \
1195}
1196
1197PyDoc_STRVAR(doc_mpfr_ceil,
1198"x.__ceil__() -> mpfr\n\n"
1199"Return an 'mpfr' that is the smallest integer >= x.");
1200
1201PyDoc_STRVAR(doc_g_mpfr_ceil,
1202"ceil(x) ->mpfr\n\n"
1203"Return an 'mpfr' that is the smallest integer >= x.");
1204
1205MPFR_UNIOP_NOROUND(ceil)
1206
1207PyDoc_STRVAR(doc_mpfr_floor,
1208"x.__floor__() -> mpfr\n\n"
1209"Return an 'mpfr' that is the smallest integer <= x.");
1210
1211PyDoc_STRVAR(doc_g_mpfr_floor,
1212"floor(x) -> mpfr\n\n"
1213"Return an 'mpfr' that is the smallest integer <= x.");
1214
1215MPFR_UNIOP_NOROUND(floor);
1216
1217PyDoc_STRVAR(doc_mpfr_trunc,
1218"x.__trunc__() -> mpfr\n\n"
1219"Return an 'mpfr' that is truncated towards 0. Same as\n"
1220"x.floor() if x>=0 or x.ceil() if x<0.");
1221
1222PyDoc_STRVAR(doc_g_mpfr_trunc,
1223"trunc(x) -> mpfr\n\n"
1224"Return an 'mpfr' that is x truncated towards 0. Same as\n"
1225"x.floor() if x>=0 or x.ceil() if x<0.");
1226
1227MPFR_UNIOP_NOROUND(trunc)
1228
1229PyDoc_STRVAR(doc_g_mpfr_round_away,
1230"round_away(x) -> mpfr\n\n"
1231"Return an 'mpfr' that is x rounded to the nearest integer,\n"
1232"with ties rounded away from 0.");
1233
1234static PyObject *
1235Pympfr_round_away(PyObject* self, PyObject *other)
1236{
1237    PympfrObject *result;
1238
1239    PARSE_ONE_MPFR_OTHER("round_away() requires 'mpfr' argument");
1240    if (!(result = (PympfrObject*)Pympfr_new(0)))
1241        goto done;
1242    mpfr_clear_flags();
1243    result->rc = mpfr_round(result->f, Pympfr_AS_MPFR(self));
1244    MPFR_CLEANUP_SELF("round_away()");
1245}
1246
1247#define MPFR_UNIOP(NAME) \
1248static PyObject * \
1249Pympfr_##NAME(PyObject* self, PyObject *other) \
1250{ \
1251    PympfrObject *result; \
1252    PARSE_ONE_MPFR_OTHER(#NAME "() requires 'mpfr' argument"); \
1253    if (!(result = (PympfrObject*)Pympfr_new(0))) goto done; \
1254    mpfr_clear_flags(); \
1255    result->rc = mpfr_##NAME(result->f, Pympfr_AS_MPFR(self), context->ctx.mpfr_round); \
1256    MPFR_CLEANUP_SELF(#NAME "()"); \
1257}
1258
1259PyDoc_STRVAR(doc_g_mpfr_rint,
1260"rint(x) -> mpfr\n\n"
1261"Return x rounded to the nearest integer using the current rounding\n"
1262"mode.");
1263
1264MPFR_UNIOP(rint)
1265
1266PyDoc_STRVAR(doc_g_mpfr_rint_ceil,
1267"rint_ceil(x) -> mpfr\n\n"
1268"Return x rounded to the nearest integer by first rounding to the\n"
1269"next higher or equal integer and then, if needed, using the current\n"
1270"rounding mode.");
1271
1272MPFR_UNIOP(rint_ceil)
1273
1274PyDoc_STRVAR(doc_g_mpfr_rint_floor,
1275"rint_floor(x) -> mpfr\n\n"
1276"Return x rounded to the nearest integer by first rounding to the\n"
1277"next lower or equal integer and then, if needed, using the current\n"
1278"rounding mode.");
1279
1280MPFR_UNIOP(rint_floor)
1281
1282PyDoc_STRVAR(doc_g_mpfr_rint_round,
1283"rint_round(x) -> mpfr\n\n"
1284"Return x rounded to the nearest integer by first rounding to the\n"
1285"nearest integer (ties away from 0) and then, if needed, using\n"
1286"the current rounding mode.");
1287
1288MPFR_UNIOP(rint_round)
1289
1290PyDoc_STRVAR(doc_g_mpfr_rint_trunc,
1291"rint_trunc(x) -> mpfr\n\n"
1292"Return x rounded to the nearest integer by first rounding towards\n"
1293"zero and then, if needed, using the current rounding mode.");
1294
1295MPFR_UNIOP(rint_trunc)
1296
1297PyDoc_STRVAR(doc_g_mpfr_frac,
1298"frac(x) -> mpfr\n\n"
1299"Return fractional part of x.");
1300
1301MPFR_UNIOP(frac)
1302
1303PyDoc_STRVAR(doc_g_mpfr_modf,
1304"modf(x) -> (mpfr, mpfr)\n\n"
1305"Return a tuple containing the integer and fractional portions\n"
1306"of x.");
1307
1308static PyObject *
1309Pympfr_modf(PyObject *self, PyObject *other)
1310{
1311    PympfrObject *s, *c;
1312    PyObject *result;
1313    int code;
1314
1315    PARSE_ONE_MPFR_OTHER("modf() requires 'mpfr' argument");
1316
1317    s = (PympfrObject*)Pympfr_new(0);
1318    c = (PympfrObject*)Pympfr_new(0);
1319    result = PyTuple_New(2);
1320    if (!s || !c || !result)
1321        goto done;
1322
1323    mpfr_clear_flags();
1324    code = mpfr_modf(s->f, c->f, Pympfr_AS_MPFR(self),
1325                     context->ctx.mpfr_round);
1326    s->rc = code & 0x03;
1327    c->rc = code >> 2;
1328    if (s->rc == 2) s->rc = -1;
1329    if (c->rc == 2) c->rc = -1;
1330    SUBNORMALIZE(s);
1331    SUBNORMALIZE(c);
1332    MERGE_FLAGS;
1333    CHECK_FLAGS("modf()");
1334
1335  done:
1336    Py_DECREF(self);
1337    if (PyErr_Occurred()) {
1338        Py_XDECREF((PyObject*)s);
1339        Py_XDECREF((PyObject*)c);
1340        Py_XDECREF(result);
1341        result = NULL;
1342    }
1343    else {
1344        PyTuple_SET_ITEM(result, 0, (PyObject*)s);
1345        PyTuple_SET_ITEM(result, 1, (PyObject*)c);
1346    }
1347    return result;
1348}
1349
1350/* Needed for square() in mpz_mpany.c */
1351
1352MPFR_UNIOP(sqr)
1353
1354PyDoc_STRVAR(doc_g_mpfr_cbrt,
1355"cbrt(x) -> mpfr\n\n"
1356"Return the cube root of x.");
1357
1358MPFR_UNIOP(cbrt)
1359
1360/* Called via gmpy_mpany so doc-string is there. */
1361
1362MPFR_UNIOP(log)
1363
1364PyDoc_STRVAR(doc_g_mpfr_log2,
1365"log2(x) -> mpfr\n\n"
1366"Return base-2 logarithm of x.");
1367
1368MPFR_UNIOP(log2)
1369
1370/* Called via gmpy_mpany so doc-string is there. */
1371
1372MPFR_UNIOP(log10)
1373
1374/* Called via gmpy_mpany so doc-string is there. */
1375
1376MPFR_UNIOP(exp)
1377
1378PyDoc_STRVAR(doc_g_mpfr_exp2,
1379"exp2(x) -> mpfr\n\n"
1380"Return 2**x.");
1381
1382MPFR_UNIOP(exp2)
1383
1384PyDoc_STRVAR(doc_g_mpfr_exp10,
1385"exp10(x) -> mpfr\n\n"
1386"Return 10**x.");
1387
1388MPFR_UNIOP(exp10)
1389
1390MPFR_UNIOP(sin)
1391
1392MPFR_UNIOP(cos)
1393
1394MPFR_UNIOP(tan)
1395
1396PyDoc_STRVAR(doc_g_mpfr_sec,
1397"sec(x) -> mpfr\n\n"
1398"Return secant of x; x in radians.");
1399
1400MPFR_UNIOP(sec)
1401
1402PyDoc_STRVAR(doc_g_mpfr_csc,
1403"csc(x) -> mpfr\n\n"
1404"Return cosecant of x; x in radians.");
1405
1406MPFR_UNIOP(csc)
1407
1408PyDoc_STRVAR(doc_g_mpfr_cot,
1409"cot(x) -> mpfr\n\n"
1410"Return cotangent of x; x in radians.");
1411
1412MPFR_UNIOP(cot)
1413
1414static PyObject *
1415Pympfr_acos(PyObject* self, PyObject *other)
1416{
1417    PympfrObject *result;
1418
1419    PARSE_ONE_MPFR_OTHER("acos() requires 'mpfr' argument");
1420
1421#ifdef WITHMPC
1422    if (!mpfr_nan_p(Pympfr_AS_MPFR(self)) &&
1423            (mpfr_cmp_si(Pympfr_AS_MPFR(self), 1) > 0 ||
1424            mpfr_cmp_si(Pympfr_AS_MPFR(self), -1) < 0) &&
1425            context->ctx.allow_complex) {
1426        Py_DECREF(self);
1427        return Pympc_acos(self, other);
1428    }
1429#endif
1430
1431    if (!(result = (PympfrObject*)Pympfr_new(0))) {
1432        Py_DECREF(self);
1433        return NULL;
1434    }
1435    mpfr_clear_flags();
1436    result->rc = mpfr_acos(result->f, Pympfr_AS_MPFR(self),
1437                           context->ctx.mpfr_round);
1438    MPFR_CLEANUP_SELF("acos()");
1439}
1440
1441static PyObject *
1442Pympfr_asin(PyObject* self, PyObject *other)
1443{
1444    PympfrObject *result;
1445
1446    PARSE_ONE_MPFR_OTHER("asin() requires 'mpfr' argument");
1447
1448#ifdef WITHMPC
1449    if (!mpfr_nan_p(Pympfr_AS_MPFR(self)) &&
1450            (mpfr_cmp_si(Pympfr_AS_MPFR(self), 1) > 0 ||
1451            mpfr_cmp_si(Pympfr_AS_MPFR(self), -1) < 0) &&
1452            context->ctx.allow_complex) {
1453        Py_DECREF(self);
1454        return Pympc_asin(self, other);
1455    }
1456#endif
1457
1458    if (!(result = (PympfrObject*)Pympfr_new(0))) {
1459        Py_DECREF(self);
1460        return NULL;
1461    }
1462    mpfr_clear_flags();
1463    result->rc = mpfr_asin(result->f, Pympfr_AS_MPFR(self),
1464                           context->ctx.mpfr_round);
1465    MPFR_CLEANUP_SELF("asin()");
1466}
1467
1468MPFR_UNIOP(atan)
1469
1470MPFR_UNIOP(cosh)
1471
1472MPFR_UNIOP(sinh)
1473
1474MPFR_UNIOP(tanh)
1475
1476PyDoc_STRVAR(doc_g_mpfr_sech,
1477"sech(x) -> mpfr\n\n"
1478"Returns hyperbolic secant of x.");
1479
1480MPFR_UNIOP(sech)
1481
1482PyDoc_STRVAR(doc_g_mpfr_csch,
1483"csch(x) -> mpfr\n\n"
1484"Return hyperbolic cosecant of x.");
1485
1486MPFR_UNIOP(csch)
1487
1488PyDoc_STRVAR(doc_g_mpfr_coth,
1489"coth(x) -> mpfr\n\n"
1490"Return hyperbolic cotangent of x.");
1491
1492MPFR_UNIOP(coth)
1493
1494MPFR_UNIOP(acosh)
1495
1496MPFR_UNIOP(asinh)
1497
1498static PyObject *
1499Pympfr_atanh(PyObject* self, PyObject *other)
1500{
1501    PympfrObject *result;
1502
1503    PARSE_ONE_MPFR_OTHER("atanh() requires 'mpfr' argument");
1504
1505#ifdef WITHMPC
1506    if (!mpfr_nan_p(Pympfr_AS_MPFR(self)) &&
1507            (mpfr_cmp_si(Pympfr_AS_MPFR(self), 1) > 0 ||
1508            mpfr_cmp_si(Pympfr_AS_MPFR(self), -1) < 0) &&
1509            context->ctx.allow_complex) {
1510        Py_DECREF(self);
1511        return Pympc_atanh(self, other);
1512    }
1513#endif
1514
1515    if (!(result = (PympfrObject*)Pympfr_new(0))) {
1516        Py_DECREF(self);
1517        return NULL;
1518    }
1519    mpfr_clear_flags();
1520    result->rc = mpfr_asin(result->f, Pympfr_AS_MPFR(self),
1521                           context->ctx.mpfr_round);
1522    MPFR_CLEANUP_SELF("atanh()");
1523}
1524
1525
1526PyDoc_STRVAR(doc_g_mpfr_log1p,
1527"log1p(x) -> mpfr\n\n"
1528"Return logarithm of (1+x).");
1529
1530MPFR_UNIOP(log1p)
1531
1532PyDoc_STRVAR(doc_g_mpfr_expm1,
1533"expm1(x) -> mpfr\n\n"
1534"Return exponential(x) - 1.");
1535
1536MPFR_UNIOP(expm1)
1537
1538PyDoc_STRVAR(doc_g_mpfr_eint,
1539"eint(x) -> mpfr\n\n"
1540"Return exponential integral of x.");
1541
1542MPFR_UNIOP(eint)
1543
1544PyDoc_STRVAR(doc_g_mpfr_li2,
1545"li2(x) -> mpfr\n\n"
1546"Return real part of dilogarithm of x.");
1547
1548MPFR_UNIOP(li2)
1549
1550PyDoc_STRVAR(doc_g_mpfr_gamma,
1551"gamma(x) -> mpfr\n\n"
1552"Return gamma of x.");
1553
1554MPFR_UNIOP(gamma)
1555
1556PyDoc_STRVAR(doc_g_mpfr_lngamma,
1557"lngamma(x) -> mpfr\n\n"
1558"Return logarithm of gamma(x).");
1559
1560MPFR_UNIOP(lngamma)
1561
1562PyDoc_STRVAR(doc_g_mpfr_lgamma,
1563"lgamma(x) -> (mpfr, int)\n\n"
1564"Return a tuple containing the logarithm of the absolute value of\n"
1565"gamma(x) and the sign of gamma(x)");
1566
1567static PyObject *
1568Pympfr_lgamma(PyObject* self, PyObject *other)
1569{
1570    PyObject *result;
1571    PympfrObject *value;
1572    int signp = 0;
1573
1574    PARSE_ONE_MPFR_OTHER("lgamma() requires 'mpfr' argument");
1575
1576    value = (PympfrObject*)Pympfr_new(0);
1577    result = PyTuple_New(2);
1578    if (!value || !result)
1579        goto done;
1580
1581    mpfr_clear_flags();
1582    value->rc = mpfr_lgamma(value->f, &signp, Pympfr_AS_MPFR(self),
1583                            context->ctx.mpfr_round);
1584    SUBNORMALIZE(value);
1585    MERGE_FLAGS;
1586    CHECK_FLAGS("lgamma()");
1587
1588  done:
1589    Py_DECREF(self);
1590    if (PyErr_Occurred()) {
1591        Py_XDECREF(result);
1592        Py_XDECREF((PyObject*)value);
1593        result = NULL;
1594    }
1595    else {
1596        PyTuple_SET_ITEM(result, 0, (PyObject*)value);
1597        PyTuple_SET_ITEM(result, 1, PyIntOrLong_FromLong((long)signp));
1598    }
1599    return result;
1600}
1601
1602PyDoc_STRVAR(doc_g_mpfr_digamma,
1603"digamma(x) -> mpfr\n\n"
1604"Return digamma of x.");
1605
1606MPFR_UNIOP(digamma)
1607
1608PyDoc_STRVAR(doc_g_mpfr_zeta,
1609"zeta(x) -> mpfr\n\n"
1610"Return Riemann zeta of x.");
1611
1612MPFR_UNIOP(zeta)
1613
1614PyDoc_STRVAR(doc_g_mpfr_erf,
1615"erf(x) -> mpfr\n\n"
1616"Return error function of x.");
1617
1618MPFR_UNIOP(erf)
1619
1620PyDoc_STRVAR(doc_g_mpfr_erfc,
1621"erfc(x) -> mpfr\n\n"
1622"Return complementary error function of x.");
1623
1624MPFR_UNIOP(erfc)
1625
1626PyDoc_STRVAR(doc_g_mpfr_j0,
1627"j0(x) -> mpfr\n\n"
1628"Return first kind Bessel function of order 0 of x.");
1629
1630MPFR_UNIOP(j0)
1631
1632PyDoc_STRVAR(doc_g_mpfr_j1,
1633"j1(x) -> mpfr\n\n"
1634"Return first kind Bessel function of order 1 of x.");
1635
1636MPFR_UNIOP(j1)
1637
1638PyDoc_STRVAR(doc_g_mpfr_jn,
1639"jn(x,n) -> mpfr\n\n"
1640"Return the first kind Bessel function of order n of x.");
1641
1642static PyObject *
1643Pympfr_jn(PyObject *self, PyObject *args)
1644{
1645    PympfrObject *result;
1646    long n = 0;
1647
1648    PARSE_ONE_MPFR_REQ_CLONG(&n, "jn() requires 'mpfr','int' arguments");
1649
1650    if (!(result = (PympfrObject*)Pympfr_new(0)))
1651        goto done;
1652
1653    mpfr_clear_flags();
1654    result->rc = mpfr_jn(result->f, n, Pympfr_AS_MPFR(self),
1655                         context->ctx.mpfr_round);
1656    MPFR_CLEANUP_SELF("jn()");
1657}
1658
1659PyDoc_STRVAR(doc_g_mpfr_y0,
1660"y0(x) -> mpfr\n\n"
1661"Return second kind Bessel function of order 0 of x.");
1662
1663MPFR_UNIOP(y0)
1664
1665PyDoc_STRVAR(doc_g_mpfr_y1,
1666"y1(x) -> mpfr\n\n"
1667"Return second kind Bessel function of order 1 of x.");
1668
1669MPFR_UNIOP(y1)
1670
1671PyDoc_STRVAR(doc_g_mpfr_yn,
1672"yn(x,n) -> mpfr\n\n"
1673"Return the second kind Bessel function of order n of x.");
1674
1675static PyObject *
1676Pympfr_yn(PyObject *self, PyObject *args)
1677{
1678    PympfrObject *result;
1679    long n = 0;
1680
1681    PARSE_ONE_MPFR_REQ_CLONG(&n, "yn() requires 'mpfr','int' arguments");
1682
1683    if (!(result = (PympfrObject*)Pympfr_new(0)))
1684        goto done;
1685
1686    mpfr_clear_flags();
1687    result->rc = mpfr_yn(result->f, n, Pympfr_AS_MPFR(self),
1688                         context->ctx.mpfr_round);
1689    MPFR_CLEANUP_SELF("yn()");
1690}
1691
1692PyDoc_STRVAR(doc_g_mpfr_ai,
1693"ai(x) -> mpfr\n\n"
1694"Return Airy function of x.");
1695
1696MPFR_UNIOP(ai)
1697
1698static PyObject *
1699Pympfr_add_fast(PyObject *x, PyObject *y)
1700{
1701    PympfrObject *result;
1702
1703    if (Pympfr_CheckAndExp(x) && Pympfr_CheckAndExp(y)) {
1704        if (!(result = (PympfrObject*)Pympfr_new(0))) {
1705            return NULL;
1706        }
1707        mpfr_clear_flags();
1708        result->rc = mpfr_add(result->f,
1709                              Pympfr_AS_MPFR(x),
1710                              Pympfr_AS_MPFR(y),
1711                              context->ctx.mpfr_round);
1712        MPFR_CLEANUP_RESULT("addition");
1713        return (PyObject*)result;
1714    }
1715    else {
1716        return Pybasic_add(x, y);
1717    }
1718}
1719
1720static PyObject *
1721Pympfr_add(PyObject *self, PyObject *args)
1722{
1723    PympfrObject *result;
1724    PyObject *other;
1725
1726    PARSE_TWO_MPFR_ARGS(other, "add() requires 'mpfr','mpfr' arguments");
1727
1728    if (!(result = (PympfrObject*)Pympfr_new(0)))
1729        goto done;
1730
1731    mpfr_clear_flags();
1732    result->rc = mpfr_add(result->f, Pympfr_AS_MPFR(self),
1733                          Pympfr_AS_MPFR(other), context->ctx.mpfr_round);
1734    MPFR_CLEANUP_SELF_OTHER("add()");
1735}
1736
1737static PyObject *
1738Pympfr_sub_fast(PyObject *x, PyObject *y)
1739{
1740    PympfrObject *result;
1741
1742    if (Pympfr_CheckAndExp(x) && Pympfr_CheckAndExp(y)) {
1743        if (!(result = (PympfrObject*)Pympfr_new(0))) {
1744            return NULL;
1745        }
1746        mpfr_clear_flags();
1747        result->rc = mpfr_sub(result->f,
1748                              Pympfr_AS_MPFR(x),
1749                              Pympfr_AS_MPFR(y),
1750                              context->ctx.mpfr_round);
1751        MPFR_CLEANUP_RESULT("subtraction");
1752        return (PyObject*)result;
1753    }
1754    else {
1755        return Pybasic_sub(x, y);
1756    }
1757}
1758
1759static PyObject *
1760Pympfr_sub(PyObject *self, PyObject *args)
1761{
1762    PympfrObject *result;
1763    PyObject *other;
1764
1765    PARSE_TWO_MPFR_ARGS(other, "sub() requires 'mpfr','mpfr' arguments");
1766
1767    if (!(result = (PympfrObject*)Pympfr_new(0)))
1768        goto done;
1769
1770    mpfr_clear_flags();
1771    result->rc = mpfr_sub(result->f, Pympfr_AS_MPFR(self),
1772                          Pympfr_AS_MPFR(other), context->ctx.mpfr_round);
1773    MPFR_CLEANUP_SELF_OTHER("sub()");
1774}
1775
1776static PyObject *
1777Pympfr_mul_fast(PyObject *x, PyObject *y)
1778{
1779    PympfrObject *result;
1780
1781    if (Pympfr_CheckAndExp(x) && Pympfr_CheckAndExp(y)) {
1782        if (!(result = (PympfrObject*)Pympfr_new(0))) {
1783            return NULL;
1784        }
1785        mpfr_clear_flags();
1786        result->rc = mpfr_mul(result->f,
1787                              Pympfr_AS_MPFR(x),
1788                              Pympfr_AS_MPFR(y),
1789                              context->ctx.mpfr_round);
1790        MPFR_CLEANUP_RESULT("multiplication");
1791        return (PyObject*)result;
1792    }
1793    else {
1794        return Pybasic_mul(x, y);
1795    }
1796}
1797
1798static PyObject *
1799Pympfr_mul(PyObject *self, PyObject *args)
1800{
1801    PympfrObject *result;
1802    PyObject *other;
1803
1804    PARSE_TWO_MPFR_ARGS(other, "mul() requires 'mpfr','mpfr' arguments");
1805
1806    if (!(result = (PympfrObject*)Pympfr_new(0)))
1807        goto done;
1808
1809    mpfr_clear_flags();
1810    result->rc = mpfr_mul(result->f, Pympfr_AS_MPFR(self),
1811                          Pympfr_AS_MPFR(other), context->ctx.mpfr_round);
1812    MPFR_CLEANUP_SELF_OTHER("mul()");
1813}
1814
1815static PyObject *
1816Pympfr_truediv_fast(PyObject *x, PyObject *y)
1817{
1818    PympfrObject *result;
1819
1820    if (Pympfr_Check…

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