1 This is mpc.info, produced by makeinfo version 4.13 from mpc.texi.
3 This manual is for GNU MPC, a library for multiple precision complex
4 arithmetic, version 1.0 of July 2012.
6 Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
9 Permission is granted to copy, distribute and/or modify this
10 document under the terms of the GNU Free Documentation License,
11 Version 1.3 or any later version published by the Free Software
12 Foundation; with no Invariant Sections. A copy of the license is
13 included in the section entitled "GNU Free Documentation License."
15 INFO-DIR-SECTION GNU Packages
17 * mpc: (mpc)Multiple Precision Complex Library.
21 File: mpc.info, Node: Top, Next: Copying, Up: (dir)
26 This manual documents how to install and use the GNU Multiple Precision
27 Complex Library, version 1.0
31 * Copying:: GNU MPC Copying Conditions (LGPL).
32 * Introduction to GNU MPC:: Brief introduction to GNU MPC.
33 * Installing GNU MPC:: How to configure and compile the GNU MPC library.
34 * Reporting Bugs:: How to usefully report bugs.
35 * GNU MPC Basics:: What every GNU MPC user should know.
36 * Complex Functions:: Functions for arithmetic on complex numbers.
40 * GNU Free Documentation License::
43 File: mpc.info, Node: Copying, Next: Introduction to GNU MPC, Prev: Top, Up: Top
45 GNU MPC Copying Conditions
46 **************************
48 GNU MPC is free software; you can redistribute it and/or modify it under
49 the terms of the GNU Lesser General Public License as published by the
50 Free Software Foundation; either version 3 of the License, or (at your
51 option) any later version.
53 GNU MPC is distributed in the hope that it will be useful, but
54 WITHOUT ANY WARRANTY; without even the implied warranty of
55 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser
56 General Public License for more details.
58 You should have received a copy of the GNU Lesser General Public
59 License along with this program. If not, see
60 `http://www.gnu.org/licenses/'.
63 File: mpc.info, Node: Introduction to GNU MPC, Next: Installing GNU MPC, Prev: Copying, Up: Top
65 1 Introduction to GNU MPC
66 *************************
68 GNU MPC is a portable library written in C for arbitrary precision
69 arithmetic on complex numbers providing correct rounding. It implements
70 a multiprecision equivalent of the C99 standard. It builds upon the
71 GNU MP and the GNU MPFR libraries.
73 1.1 How to use this Manual
74 ==========================
76 Everyone should read *note GNU MPC Basics::. If you need to install
77 the library yourself, you need to read *note Installing GNU MPC::, too.
79 The remainder of the manual can be used for later reference,
80 although it is probably a good idea to skim through it.
83 File: mpc.info, Node: Installing GNU MPC, Next: Reporting Bugs, Prev: Introduction to GNU MPC, Up: Top
88 To build GNU MPC, you first have to install GNU MP (version 4.3.2 or
89 higher) and GNU MPFR (version 2.4.2 or higher) on your computer. You
90 need a C compiler; GCC version 4.4 or higher is recommended, since GNU
91 MPC may trigger a bug in previous versions, see the thread at
92 `http://lists.gforge.inria.fr/pipermail/mpc-discuss/2011-February/000823.html'.
93 And you need a standard Unix `make' program, plus some other standard
94 Unix utility programs.
96 Here are the steps needed to install the library on Unix systems:
98 1. `tar xzf mpc-1.0.tar.gz'
104 if GMP and GNU MPFR are installed into standard directories, that
105 is, directories that are searched by default by the compiler and
108 `./configure --with-gmp=<gmp_install_dir>'
110 is used to indicate a different location where GMP is installed.
111 Alternatively, you can specify directly GMP include and GMP lib
112 directories with `./configure --with-gmp-lib=<gmp_lib_dir>
113 --with-gmp-include=<gmp_include_dir>'.
115 `./configure --with-mpfr=<mpfr_install_dir>'
117 is used to indicate a different location where GNU MPFR is
118 installed. Alternatively, you can specify directly GNU MPFR
119 include and GNU MPFR lib directories with `./configure
120 --with-mpf-lib=<mpfr_lib_dir>
121 --with-mpfr-include=<mpfr_include_dir>'.
123 Another useful parameter is `--prefix', which can be used to
124 specify an alternative installation location instead of
125 `/usr/local'; see `make install' below.
127 To enable checking for memory leaks using `valgrind' during `make
128 check', add the parameter `--enable-valgrind-tests'.
130 If for debugging purposes you wish to log calls to GNU MPC
131 functions from within your code, add the parameter
132 `--enable-logging'. In your code, replace the inclusion of
133 `mpc.h' by `mpc-log.h' and link the executable dynamically. Then
134 all calls to functions with only complex arguments are printed to
135 `stderr' in the following form: First, the function name is given,
136 followed by its type such as `c_cc', meaning that the function has
137 one complex result (one `c' in front of the `_'), computed from
138 two complex arguments (two `c' after the `_'). Then, the
139 precisions of the real and the imaginary part of the first result
140 is given, followed by the second one and so on. Finally, for each
141 argument, the precisions of its real and imaginary part are
142 specified and the argument itself is printed in hexadecimal via
143 the function `mpc_out_str' (*note String and Stream Input and
144 Output::). The option requires a dynamic library, so it may not
145 be combined with `--disable-shared'.
147 Use `./configure --help' for an exhaustive list of parameters.
151 This compiles GNU MPC in the working directory.
155 This will make sure GNU MPC was built correctly.
157 If you get error messages, please report them to
158 `mpc-discuss@lists.gforge.inria.fr' (*Note Reporting Bugs::, for
159 information on what to include in useful bug reports).
163 This will copy the file `mpc.h' to the directory
164 `/usr/local/include', the file `libmpc.a' to the directory
165 `/usr/local/lib', and the file `mpc.info' to the directory
166 `/usr/local/share/info' (or if you passed the `--prefix' option to
167 `configure', using the prefix directory given as argument to
168 `--prefix' instead of `/usr/local'). Note: you need write
169 permissions on these directories.
172 2.1 Other `make' Targets
173 ========================
175 There are some other useful make targets:
179 Create an info version of the manual, in `mpc.info'.
183 Create a PDF version of the manual, in `doc/mpc.pdf'.
187 Create a DVI version of the manual, in `doc/mpc.dvi'.
191 Create a Postscript version of the manual, in `doc/mpc.ps'.
195 Create an HTML version of the manual, in several pages in the
196 directory `doc/mpc.html'; if you want only one output HTML file,
197 then type `makeinfo --html --no-split mpc.texi' instead.
201 Delete all object files and archive files, but not the
206 Delete all files not included in the distribution.
210 Delete all files copied by `make install'.
212 2.2 Known Build Problems
213 ========================
215 On AIX, if GMP was built with the 64-bit ABI, before building and
216 testing GNU MPC, it might be necessary to set the `OBJECT_MODE'
217 environment variable to 64 by, e.g.,
219 `export OBJECT_MODE=64'
221 This has been tested with the C compiler IBM XL C/C++ Enterprise
222 Edition V8.0 for AIX, version: 08.00.0000.0021, GMP 4.2.4 and GNU MPFR
225 Please report any other problems you encounter to
226 `mpc-discuss@lists.gforge.inria.fr'. *Note Reporting Bugs::.
229 File: mpc.info, Node: Reporting Bugs, Next: GNU MPC Basics, Prev: Installing GNU MPC, Up: Top
234 If you think you have found a bug in the GNU MPC library, please
235 investigate and report it. We have made this library available to you,
236 and it is not to ask too much from you, to ask you to report the bugs
239 There are a few things you should think about when you put your bug
242 You have to send us a test case that makes it possible for us to
243 reproduce the bug. Include instructions on how to run the test case.
245 You also have to explain what is wrong; if you get a crash, or if
246 the results printed are incorrect and in that case, in what way.
248 Please include compiler version information in your bug report.
249 This can be extracted using `gcc -v', or `cc -V' on some machines.
250 Also, include the output from `uname -a'.
252 If your bug report is good, we will do our best to help you to get a
253 corrected version of the library; if the bug report is poor, we will
254 not do anything about it (aside of chiding you to send better bug
257 Send your bug report to: `mpc-discuss@lists.gforge.inria.fr'.
259 If you think something in this manual is unclear, or downright
260 incorrect, or if the language needs to be improved, please send a note
264 File: mpc.info, Node: GNU MPC Basics, Next: Complex Functions, Prev: Reporting Bugs, Up: Top
269 All declarations needed to use GNU MPC are collected in the include file
270 `mpc.h'. It is designed to work with both C and C++ compilers. You
271 should include that file in any program using the GNU MPC library by
275 4.1 Nomenclature and Types
276 ==========================
278 "Complex number" or "Complex" for short, is a pair of two arbitrary
279 precision floating-point numbers (for the real and imaginary parts).
280 The C data type for such objects is `mpc_t'.
282 The "Precision" is the number of bits used to represent the mantissa of
283 the real and imaginary parts; the corresponding C data type is
284 `mpfr_prec_t'. For more details on the allowed precision range, *note
285 Nomenclature and Types: (mpfr.info)Nomenclature and Types.
287 The "rounding mode" specifies the way to round the result of a complex
288 operation, in case the exact result can not be represented exactly in
289 the destination mantissa; the corresponding C data type is `mpc_rnd_t'.
290 A complex rounding mode is a pair of two rounding modes: one for the
291 real part, one for the imaginary part.
296 There is only one class of functions in the GNU MPC library, namely
297 functions for complex arithmetic. The function names begin with `mpc_'.
298 The associated type is `mpc_t'.
300 4.3 GNU MPC Variable Conventions
301 ================================
303 As a general rule, all GNU MPC functions expect output arguments before
304 input arguments. This notation is based on an analogy with the
307 GNU MPC allows you to use the same variable for both input and
308 output in the same expression. For example, the main function for
309 floating-point multiplication, `mpc_mul', can be used like this:
310 `mpc_mul (x, x, x, rnd_mode)'. This computes the square of X with
311 rounding mode `rnd_mode' and puts the result back in X.
313 Before you can assign to an GNU MPC variable, you need to initialize
314 it by calling one of the special initialization functions. When you
315 are done with a variable, you need to clear it out, using one of the
316 functions for that purpose.
318 A variable should only be initialized once, or at least cleared out
319 between each initialization. After a variable has been initialized, it
320 may be assigned to any number of times.
322 For efficiency reasons, avoid to initialize and clear out a variable
323 in loops. Instead, initialize it before entering the loop, and clear
324 it out after the loop has exited.
326 You do not need to be concerned about allocating additional space
327 for GNU MPC variables, since each of its real and imaginary part has a
328 mantissa of fixed size. Hence unless you change its precision, or
329 clear and reinitialize it, a complex variable will have the same
330 allocated space during all its life.
335 A complex rounding mode is of the form `MPC_RNDxy' where `x' and `y'
336 are one of `N' (to nearest), `Z' (towards zero), `U' (towards plus
337 infinity), `D' (towards minus infinity). The first letter refers to
338 the rounding mode for the real part, and the second one for the
339 imaginary part. For example `MPC_RNDZU' indicates to round the real
340 part towards zero, and the imaginary part towards plus infinity.
342 The `round to nearest' mode works as in the IEEE P754 standard: in
343 case the number to be rounded lies exactly in the middle of two
344 representable numbers, it is rounded to the one with the least
345 significant bit set to zero. For example, the number 5, which is
346 represented by (101) in binary, is rounded to (100)=4 with a precision
347 of two bits, and not to (110)=6.
352 Most GNU MPC functions have a return value of type `int', which is used
353 to indicate the position of the rounded real and imaginary parts with
354 respect to the exact (infinite precision) values. If this integer is
355 `i', the macros `MPC_INEX_RE(i)' and `MPC_INEX_IM(i)' give 0 if the
356 corresponding rounded value is exact, a negative value if the rounded
357 value is less than the exact one, and a positive value if it is greater
358 than the exact one. Similarly, functions computing a result of type
359 `mpfr_t' return an integer that is 0, positive or negative depending on
360 whether the rounded value is the same, larger or smaller then the exact
363 Some functions, such as `mpc_sin_cos', compute two complex results;
364 the macros `MPC_INEX1(i)' and `MPC_INEX2(i)', applied to the return
365 value `i' of such a function, yield the exactness value corresponding
366 to the first or the second computed value, respectively.
368 4.6 Branch Cuts And Special Values
369 ==================================
371 Some complex functions have branch cuts, across which the function is
372 discontinous. In GNU MPC, the branch cuts chosen are the same as those
373 specified for the corresponding functions in the ISO C99 standard.
375 Likewise, when evaluated at a point whose real or imaginary part is
376 either infinite or a NaN or a signed zero, a function returns the same
377 value as those specified for the corresponding function in the ISO C99
381 File: mpc.info, Node: Complex Functions, Next: References, Prev: GNU MPC Basics, Up: Top
386 The complex functions expect arguments of type `mpc_t'.
388 The GNU MPC floating-point functions have an interface that is
389 similar to the GNU MP integer functions. The function prefix for
390 operations on complex numbers is `mpc_'.
392 The precision of a computation is defined as follows: Compute the
393 requested operation exactly (with "infinite precision"), and round the
394 result to the destination variable precision with the given rounding
397 The GNU MPC complex functions are intended to be a smooth extension
398 of the IEEE P754 arithmetic. The results obtained on one computer
399 should not differ from the results obtained on a computer with a
404 * Initializing Complex Numbers::
405 * Assigning Complex Numbers::
406 * Converting Complex Numbers::
407 * String and Stream Input and Output::
408 * Complex Comparison::
409 * Projection & Decomposing::
411 * Power Functions and Logarithm::
412 * Trigonometric Functions::
413 * Miscellaneous Complex Functions::
414 * Advanced Functions::
418 File: mpc.info, Node: Initializing Complex Numbers, Next: Assigning Complex Numbers, Up: Complex Functions
420 5.1 Initialization Functions
421 ============================
423 An `mpc_t' object must be initialized before storing the first value in
424 it. The functions `mpc_init2' and `mpc_init3' are used for that
427 -- Function: void mpc_init2 (mpc_t Z, mpfr_prec_t PREC)
428 Initialize Z to precision PREC bits and set its real and imaginary
429 parts to NaN. Normally, a variable should be initialized once only
430 or at least be cleared, using `mpc_clear', between initializations.
432 -- Function: void mpc_init3 (mpc_t Z, mpfr_prec_t PREC_R, mpfr_prec_t
434 Initialize Z with the precision of its real part being PREC_R bits
435 and the precision of its imaginary part being PREC_I bits, and set
436 the real and imaginary parts to NaN.
438 -- Function: void mpc_clear (mpc_t Z)
439 Free the space occupied by Z. Make sure to call this function for
440 all `mpc_t' variables when you are done with them.
442 Here is an example on how to initialize complex variables:
445 mpc_init2 (x, 256); /* precision _exactly_ 256 bits */
446 mpc_init3 (y, 100, 50); /* 100/50 bits for the real/imaginary part */
452 The following function is useful for changing the precision during a
453 calculation. A typical use would be for adjusting the precision
454 gradually in iterative algorithms like Newton-Raphson, making the
455 computation precision closely match the actual accurate part of the
458 -- Function: void mpc_set_prec (mpc_t X, mpfr_prec_t PREC)
459 Reset the precision of X to be *exactly* PREC bits, and set its
460 real/imaginary parts to NaN. The previous value stored in X is
461 lost. It is equivalent to a call to `mpc_clear(x)' followed by a
462 call to `mpc_init2(x, prec)', but more efficient as no allocation
463 is done in case the current allocated space for the mantissa of X
466 -- Function: mpfr_prec_t mpc_get_prec (mpc_t X)
467 If the real and imaginary part of X have the same precision, it is
468 returned, otherwise, 0 is returned.
470 -- Function: void mpc_get_prec2 (mpfr_prec_t* PR, mpfr_prec_t* PI,
472 Returns the precision of the real part of X via PR and of its
473 imaginary part via PI.
476 File: mpc.info, Node: Assigning Complex Numbers, Next: Converting Complex Numbers, Prev: Initializing Complex Numbers, Up: Complex Functions
478 5.2 Assignment Functions
479 ========================
481 These functions assign new values to already initialized complex numbers
482 (*note Initializing Complex Numbers::). When using any functions with
483 `intmax_t' or `uintmax_t' parameters, you must include `<stdint.h>' or
484 `<inttypes.h>' _before_ `mpc.h', to allow `mpc.h' to define prototypes
485 for these functions. Similarly, functions with parameters of type
486 `complex' or `long complex' are defined only if `<complex.h>' is
487 included _before_ `mpc.h'. If you need assignment functions that are
488 not in the current API, you can define them using the `MPC_SET_X_Y'
489 macro (*note Advanced Functions::).
491 -- Function: int mpc_set (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
492 Set the value of ROP from OP, rounded to the precision of ROP with
493 the given rounding mode RND.
495 -- Function: int mpc_set_ui (mpc_t ROP, unsigned long int OP,
497 -- Function: int mpc_set_si (mpc_t ROP, long int OP, mpc_rnd_t RND)
498 -- Function: int mpc_set_uj (mpc_t ROP, uintmax_t OP, mpc_rnd_t RND)
499 -- Function: int mpc_set_sj (mpc_t ROP, intmax_t OP, mpc_rnd_t RND)
500 -- Function: int mpc_set_d (mpc_t ROP, double OP, mpc_rnd_t RND)
501 -- Function: int mpc_set_ld (mpc_t ROP, long double OP, mpc_rnd_t RND)
502 -- Function: int mpc_set_dc (mpc_t ROP, double _Complex OP, mpc_rnd_t
504 -- Function: int mpc_set_ldc (mpc_t ROP, long double _Complex OP,
506 -- Function: int mpc_set_z (mpc_t ROP, mpz_t OP mpc_rnd_t RND)
507 -- Function: int mpc_set_q (mpc_t ROP, mpq_t OP mpc_rnd_t RND)
508 -- Function: int mpc_set_f (mpc_t ROP, mpf_t OP mpc_rnd_t RND)
509 -- Function: int mpc_set_fr (mpc_t ROP, mpfr_t OP, mpc_rnd_t RND)
510 Set the value of ROP from OP, rounded to the precision of ROP with
511 the given rounding mode RND. The argument OP is interpreted as
512 real, so the imaginary part of ROP is set to zero with a positive
513 sign. Please note that even a `long int' may have to be rounded,
514 if the destination precision is less than the machine word width.
515 For `mpc_set_d', be careful that the input number OP may not be
516 exactly representable as a double-precision number (this happens
517 for 0.1 for instance), in which case it is first rounded by the C
518 compiler to a double-precision number, and then only to a complex
521 -- Function: int mpc_set_ui_ui (mpc_t ROP, unsigned long int OP1,
522 unsigned long int OP2, mpc_rnd_t RND)
523 -- Function: int mpc_set_si_si (mpc_t ROP, long int OP1, long int OP2,
525 -- Function: int mpc_set_uj_uj (mpc_t ROP, uintmax_t OP1, uintmax_t
527 -- Function: int mpc_set_sj_sj (mpc_t ROP, intmax_t OP1, intmax_t OP2,
529 -- Function: int mpc_set_d_d (mpc_t ROP, double OP1, double OP2,
531 -- Function: int mpc_set_ld_ld (mpc_t ROP, long double OP1, long
532 double OP2, mpc_rnd_t RND)
533 -- Function: int mpc_set_z_z (mpc_t ROP, mpz_t OP1, mpz_t OP2,
535 -- Function: int mpc_set_q_q (mpc_t ROP, mpq_t OP1, mpq_t OP2,
537 -- Function: int mpc_set_f_f (mpc_t ROP, mpf_t OP1, mpf_t OP2,
539 -- Function: int mpc_set_fr_fr (mpc_t ROP, mpfr_t OP1, mpfr_t OP2,
541 Set the real part of ROP from OP1, and its imaginary part from
542 OP2, according to the rounding mode RND.
544 Beware that the behaviour of `mpc_set_fr_fr' is undefined if OP1
545 or OP2 is a pointer to the real or imaginary part of ROP. To
546 exchange the real and the imaginary part of a complex number,
547 either use `mpfr_swap (mpc_realref (rop), mpc_imagref (rop))',
548 which also exchanges the precisions of the two parts; or use a
551 For functions assigning complex variables from strings or input
552 streams, *note String and Stream Input and Output::.
554 -- Function: void mpc_set_nan (mpc_t ROP)
555 Set ROP to Nan+i*NaN.
557 -- Function: void mpc_swap (mpc_t OP1, mpc_t OP2)
558 Swap the values of OP1 and OP2 efficiently. Warning: The
559 precisions are exchanged, too; in case these are different,
560 `mpc_swap' is thus not equivalent to three `mpc_set' calls using a
561 third auxiliary variable.
564 File: mpc.info, Node: Converting Complex Numbers, Next: String and Stream Input and Output, Prev: Assigning Complex Numbers, Up: Complex Functions
566 5.3 Conversion Functions
567 ========================
569 The following functions are available only if `<complex.h>' is included
572 -- Function: double _Complex mpc_get_dc (mpc_t OP, mpc_rnd_t RND)
573 -- Function: long double _Complex mpc_get_ldc (mpc_t OP, mpc_rnd_t RND)
574 Convert OP to a C complex number, using the rounding mode RND.
576 For functions converting complex variables to strings or stream
577 output, *note String and Stream Input and Output::.
580 File: mpc.info, Node: String and Stream Input and Output, Next: Complex Comparison, Prev: Converting Complex Numbers, Up: Complex Functions
582 5.4 String and Stream Input and Output
583 ======================================
585 -- Function: int mpc_strtoc (mpc_t ROP, const char *NPTR, char
586 **ENDPTR, int BASE, mpc_rnd_t RND)
587 Read a complex number from a string NPTR in base BASE, rounded to
588 the precision of ROP with the given rounding mode RND. The BASE
589 must be either 0 or a number from 2 to 36 (otherwise the behaviour
590 is undefined). If NPTR starts with valid data, the result is
591 stored in ROP, the usual inexact value is returned (*note Return
592 Value: return-value.) and, if ENDPTR is not the null pointer,
593 *ENDPTR points to the character just after the valid data.
594 Otherwise, ROP is set to `NaN + i * NaN', -1 is returned and, if
595 ENDPTR is not the null pointer, the value of NPTR is stored in the
596 location referenced by ENDPTR.
598 The expected form of a complex number string is either a real
599 number (an optional leading whitespace, an optional sign followed
600 by a floating-point number), or a pair of real numbers in
601 parentheses separated by whitespace. If a real number is read, the
602 missing imaginary part is set to +0. The form of a floating-point
603 number depends on the base and is described in the documentation
604 of `mpfr_strtofr' (*note Assignment Functions:
605 (mpfr.info)Assignment Functions.). For instance, `"3.1415926"',
606 `"(1.25e+7 +.17)"', `"(@nan@ 2)"' and `"(-0 -7)"' are valid
607 strings for BASE = 10. If BASE = 0, then a prefix may be used to
608 indicate the base in which the floating-point number is written.
609 Use prefix '0b' for binary numbers, prefix '0x' for hexadecimal
610 numbers, and no prefix for decimal numbers. The real and
611 imaginary part may then be written in different bases. For
612 instance, `"(1.024e+3 +2.05e+3)"' and `"(0b1p+10 +0x802)"' are
613 valid strings for `base'=0 and represent the same value.
615 -- Function: int mpc_set_str (mpc_t ROP, const char *S, int BASE,
617 Set ROP to the value of the string S in base BASE, rounded to the
618 precision of ROP with the given rounding mode RND. See the
619 documentation of `mpc_strtoc' for a detailed description of the
620 valid string formats. Contrarily to `mpc_strtoc', `mpc_set_str'
621 requires the _whole_ string to represent a valid complex number
622 (potentially followed by additional white space). This function
623 returns the usual inexact value (*note Return Value:
624 return-value.) if the entire string up to the final null character
625 is a valid number in base BASE; otherwise it returns -1, and ROP
628 -- Function: char * mpc_get_str (int B, size_t N, mpc_t OP, mpc_rnd_t
630 Convert OP to a string containing its real and imaginary parts,
631 separated by a space and enclosed in a pair of parentheses. The
632 numbers are written in base B (which may vary from 2 to 36) and
633 rounded according to RND. The number of significant digits, at
634 least 2, is given by N. It is also possible to let N be zero, in
635 which case the number of digits is chosen large enough so that
636 re-reading the printed value with the same precision, assuming
637 both output and input use rounding to nearest, will recover the
638 original value of OP. Note that `mpc_get_str' uses the decimal
639 point of the current locale if available, and `.' otherwise.
641 The string is generated using the current memory allocation
642 function (`malloc' by default, unless it has been modified using
643 the custom memory allocation interface of `gmp'); once it is not
644 needed any more, it should be freed by calling `mpc_free_str'.
646 -- Function: void mpc_free_str (char *STR)
647 Free the string STR, which needs to have been allocated by a call
650 The following two functions read numbers from input streams and write
651 them to output streams. When using any of these functions, you need to
652 include `stdio.h' _before_ `mpc.h'.
654 -- Function: int mpc_inp_str (mpc_t ROP, FILE *STREAM, size_t *READ,
655 int BASE, mpc_rnd_t RND)
656 Input a string in base BASE in the same format as for `mpc_strtoc'
657 from stdio stream STREAM, rounded according to RND, and put the
658 read complex number into ROP. If STREAM is the null pointer, ROP
659 is read from `stdin'. Return the usual inexact value; if an error
660 occurs, set ROP to `NaN + i * NaN' and return -1. If READ is not
661 the null pointer, it is set to the number of read characters.
663 Unlike `mpc_strtoc', the function `mpc_inp_str' does not possess
664 perfect knowledge of the string to transform and has to read it
665 character by character, so it behaves slightly differently: It
666 tries to read a string describing a complex number and processes
667 this string through a call to `mpc_set_str'. Precisely, after
668 skipping optional whitespace, a minimal string is read according
669 to the regular expression `mpfr | '(' \s* mpfr \s+ mpfr \s* ')'',
670 where `\s' denotes a whitespace, and `mpfr' is either a string
671 containing neither whitespaces nor parentheses, or
672 `nan(n-char-sequence)' or `@nan@(n-char-sequence)' (regardless of
673 capitalisation) with `n-char-sequence' a string of ascii letters,
676 For instance, upon input of `"nan(13 1)"', the function
677 `mpc_inp_str' starts to recognise a value of NaN followed by an
678 n-char-sequence indicated by the opening parenthesis; as soon as
679 the space is reached, it becocmes clear that the expression in
680 parentheses is not an n-char-sequence, and the error flag -1 is
681 returned after 6 characters have been consumed from the stream
682 (the whitespace itself remaining in the stream). The function
683 `mpc_strtoc', on the other hand, may track back when reaching the
684 whitespace; it treats the string as the two successive complex
685 numbers `NaN + i * 0' and `13 + i'. It is thus recommended to
686 have a whitespace follow each floating point number to avoid this
689 -- Function: size_t mpc_out_str (FILE *STREAM, int BASE, size_t
690 N_DIGITS, mpc_t OP, mpc_rnd_t RND)
691 Output OP on stdio stream STREAM in base BASE, rounded according
692 to RND, in the same format as for `mpc_strtoc' If STREAM is the
693 null pointer, ROP is written to `stdout'.
695 Return the number of characters written.
698 File: mpc.info, Node: Complex Comparison, Next: Projection & Decomposing, Prev: String and Stream Input and Output, Up: Complex Functions
700 5.5 Comparison Functions
701 ========================
703 -- Function: int mpc_cmp (mpc_t OP1, mpc_t OP2)
704 -- Function: int mpc_cmp_si_si (mpc_t OP1, long int OP2R, long int
706 -- Macro: int mpc_cmp_si (mpc_t OP1, long int OP2)
707 Compare OP1 and OP2, where in the case of `mpc_cmp_si_si', OP2 is
708 taken to be OP2R + i OP2I. The return value C can be decomposed
709 into `x = MPC_INEX_RE(c)' and `y = MPC_INEX_IM(c)', such that X is
710 positive if the real part of OP1 is greater than that of OP2, zero
711 if both real parts are equal, and negative if the real part of OP1
712 is less than that of OP2, and likewise for Y. Both OP1 and OP2
713 are considered to their full own precision, which may differ. It
714 is not allowed that one of the operands has a NaN (Not-a-Number)
717 The storage of the return value is such that equality can be
718 simply checked with `mpc_cmp (op1, op2) == 0'.
721 File: mpc.info, Node: Projection & Decomposing, Next: Basic Arithmetic, Prev: Complex Comparison, Up: Complex Functions
723 5.6 Projection and Decomposing Functions
724 ========================================
726 -- Function: int mpc_real (mpfr_t ROP, mpc_t OP, mpfr_rnd_t RND)
727 Set ROP to the value of the real part of OP rounded in the
730 -- Function: int mpc_imag (mpfr_t ROP, mpc_t OP, mpfr_rnd_t RND)
731 Set ROP to the value of the imaginary part of OP rounded in the
734 -- Macro: mpfr_t mpc_realref (mpc_t OP)
735 -- Macro: mpfr_t mpc_imagref (mpc_t OP)
736 Return a reference to the real part and imaginary part of OP,
737 respectively. The `mpfr' functions can be used on the result of
738 these macros (note that the `mpfr_t' type is itself a pointer).
740 -- Function: int mpc_arg (mpfr_t ROP, mpc_t OP, mpfr_rnd_t RND)
741 Set ROP to the argument of OP, with a branch cut along the
744 -- Function: int mpc_proj (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
745 Compute a projection of OP onto the Riemann sphere. Set ROP to OP
746 rounded in the direction RND, except when at least one part of OP
747 is infinite (even if the other part is a NaN) in which case the
748 real part of ROP is set to plus infinity and its imaginary part to
749 a signed zero with the same sign as the imaginary part of OP.
752 File: mpc.info, Node: Basic Arithmetic, Next: Power Functions and Logarithm, Prev: Projection & Decomposing, Up: Complex Functions
754 5.7 Basic Arithmetic Functions
755 ==============================
757 All the following functions are designed in such a way that, when
758 working with real numbers instead of complex numbers, their complexity
759 should essentially be the same as with the GNU MPFR library, with only
760 a marginal overhead due to the GNU MPC layer.
762 -- Function: int mpc_add (mpc_t ROP, mpc_t OP1, mpc_t OP2, mpc_rnd_t
764 -- Function: int mpc_add_ui (mpc_t ROP, mpc_t OP1, unsigned long int
766 -- Function: int mpc_add_fr (mpc_t ROP, mpc_t OP1, mpfr_t OP2,
768 Set ROP to OP1 + OP2 rounded according to RND.
770 -- Function: int mpc_sub (mpc_t ROP, mpc_t OP1, mpc_t OP2, mpc_rnd_t
772 -- Function: int mpc_sub_fr (mpc_t ROP, mpc_t OP1, mpfr_t OP2,
774 -- Function: int mpc_fr_sub (mpc_t ROP, mpfr_t OP1, mpc_t OP2,
776 -- Function: int mpc_sub_ui (mpc_t ROP, mpc_t OP1, unsigned long int
778 -- Macro: int mpc_ui_sub (mpc_t ROP, unsigned long int OP1, mpc_t OP2,
780 -- Function: int mpc_ui_ui_sub (mpc_t ROP, unsigned long int RE1,
781 unsigned long int IM1, mpc_t OP2, mpc_rnd_t RND)
782 Set ROP to OP1 - OP2 rounded according to RND. For
783 `mpc_ui_ui_sub', OP1 is RE1 + IM1.
785 -- Function: int mpc_neg (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
786 Set ROP to -OP rounded according to RND. Just changes the sign if
787 ROP and OP are the same variable.
789 -- Function: int mpc_mul (mpc_t ROP, mpc_t OP1, mpc_t OP2, mpc_rnd_t
791 -- Function: int mpc_mul_ui (mpc_t ROP, mpc_t OP1, unsigned long int
793 -- Function: int mpc_mul_si (mpc_t ROP, mpc_t OP1, long int OP2,
795 -- Function: int mpc_mul_fr (mpc_t ROP, mpc_t OP1, mpfr_t OP2,
797 Set ROP to OP1 times OP2 rounded according to RND. Note: for
798 `mpc_mul', in case OP1 and OP2 have the same value, use `mpc_sqr'
799 for better efficiency.
801 -- Function: int mpc_mul_i (mpc_t ROP, mpc_t OP, int SGN, mpc_rnd_t
803 Set ROP to OP times the imaginary unit i if SGN is non-negative,
804 set ROP to OP times -i otherwise, in both cases rounded according
807 -- Function: int mpc_sqr (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
808 Set ROP to the square of OP rounded according to RND.
810 -- Function: int mpc_fma (mpc_t ROP, mpc_t OP1, mpc_t OP2, mpc_t OP3,
812 Set ROP to OP1*OP2+OP3, rounded according to RND, with only one
815 -- Function: int mpc_div (mpc_t ROP, mpc_t OP1, mpc_t OP2, mpc_rnd_t
817 -- Function: int mpc_div_ui (mpc_t ROP, mpc_t OP1, unsigned long int
819 -- Function: int mpc_div_fr (mpc_t ROP, mpc_t OP1, mpfr_t OP2,
821 -- Function: int mpc_ui_div (mpc_t ROP, unsigned long int OP1, mpc_t
823 -- Function: int mpc_fr_div (mpc_t ROP, mpfr_t OP1, mpc_t OP2,
825 Set ROP to OP1/OP2 rounded according to RND.
827 -- Function: int mpc_conj (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
828 Set ROP to the conjugate of OP rounded according to RND. Just
829 changes the sign of the imaginary part if ROP and OP are the same
832 -- Function: int mpc_abs (mpfr_t ROP, mpc_t OP, mpfr_rnd_t RND)
833 Set the floating-point number ROP to the absolute value of OP,
834 rounded in the direction RND.
836 -- Function: int mpc_norm (mpfr_t ROP, mpc_t OP, mpfr_rnd_t RND)
837 Set the floating-point number ROP to the norm of OP (i.e., the
838 square of its absolute value), rounded in the direction RND.
840 -- Function: int mpc_mul_2ui (mpc_t ROP, mpc_t OP1, unsigned long int
842 -- Function: int mpc_mul_2si (mpc_t ROP, mpc_t OP1, long int OP2,
844 Set ROP to OP1 times 2 raised to OP2 rounded according to RND.
845 Just modifies the exponents of the real and imaginary parts by OP2
846 when ROP and OP1 are identical.
848 -- Function: int mpc_div_2ui (mpc_t ROP, mpc_t OP1, unsigned long int
850 -- Function: int mpc_div_2ui (mpc_t ROP, mpc_t OP1, long int OP2,
852 Set ROP to OP1 divided by 2 raised to OP2 rounded according to
853 RND. Just modifies the exponents of the real and imaginary parts
854 by OP2 when ROP and OP1 are identical.
857 File: mpc.info, Node: Power Functions and Logarithm, Next: Trigonometric Functions, Prev: Basic Arithmetic, Up: Complex Functions
859 5.8 Power Functions and Logarithm
860 =================================
862 -- Function: int mpc_sqrt (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
863 Set ROP to the square root of OP rounded according to RND. The
864 returned value ROP has a non-negative real part, and if its real
865 part is zero, a non-negative imaginary part.
867 -- Function: int mpc_pow (mpc_t ROP, mpc_t OP1, mpc_t OP2, mpc_rnd_t
869 -- Function: int mpc_pow_d (mpc_t ROP, mpc_t OP1, double OP2,
871 -- Function: int mpc_pow_ld (mpc_t ROP, mpc_t OP1, long double OP2,
873 -- Function: int mpc_pow_si (mpc_t ROP, mpc_t OP1, long OP2, mpc_rnd_t
875 -- Function: int mpc_pow_ui (mpc_t ROP, mpc_t OP1, unsigned long OP2,
877 -- Function: int mpc_pow_z (mpc_t ROP, mpc_t OP1, mpz_t OP2, mpc_rnd_t
879 -- Function: int mpc_pow_fr (mpc_t ROP, mpc_t OP1, mpfr_t OP2,
881 Set ROP to OP1 raised to the power OP2, rounded according to RND.
882 For `mpc_pow_d', `mpc_pow_ld', `mpc_pow_si', `mpc_pow_ui',
883 `mpc_pow_z' and `mpc_pow_fr', the imaginary part of OP2 is
884 considered as +0. When both OP1 and OP2 are zero, the result has
885 real part 1, and imaginary part 0, with sign being the opposite of
888 -- Function: int mpc_exp (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
889 Set ROP to the exponential of OP, rounded according to RND with
890 the precision of ROP.
892 -- Function: int mpc_log (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
893 -- Function: int mpc_log10 (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
894 Set ROP to the natural and base-10 logarithm of OP respectively,
895 rounded according to RND with the precision of ROP. The principal
896 branch is chosen, with the branch cut on the negative real axis,
897 so that the imaginary part of the result lies in ]-\pi , \pi] and
898 ]-\pi/log(10) , \pi/log(10)] respectively.
901 File: mpc.info, Node: Trigonometric Functions, Next: Miscellaneous Complex Functions, Prev: Power Functions and Logarithm, Up: Complex Functions
903 5.9 Trigonometric Functions
904 ===========================
906 -- Function: int mpc_sin (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
907 Set ROP to the sine of OP, rounded according to RND with the
910 -- Function: int mpc_cos (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
911 Set ROP to the cosine of OP, rounded according to RND with the
914 -- Function: int mpc_sin_cos (mpc_t ROP_SIN, mpc_t ROP_COS, mpc_t OP,
915 mpc_rnd_t RND_SIN, mpc_rnd_t RND_COS)
916 Set ROP_SIN to the sine of OP, rounded according to RND_SIN with
917 the precision of ROP_SIN, and ROP_COS to the cosine of OP, rounded
918 according to RND_COS with the precision of ROP_COS.
920 -- Function: int mpc_tan (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
921 Set ROP to the tangent of OP, rounded according to RND with the
924 -- Function: int mpc_sinh (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
925 Set ROP to the hyperbolic sine of OP, rounded according to RND
926 with the precision of ROP.
928 -- Function: int mpc_cosh (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
929 Set ROP to the hyperbolic cosine of OP, rounded according to RND
930 with the precision of ROP.
932 -- Function: int mpc_tanh (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
933 Set ROP to the hyperbolic tangent of OP, rounded according to RND
934 with the precision of ROP.
936 -- Function: int mpc_asin (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
937 -- Function: int mpc_acos (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
938 -- Function: int mpc_atan (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
939 Set ROP to the inverse sine, inverse cosine, inverse tangent of OP,
940 rounded according to RND with the precision of ROP.
942 -- Function: int mpc_asinh (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
943 -- Function: int mpc_acosh (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
944 -- Function: int mpc_atanh (mpc_t ROP, mpc_t OP, mpc_rnd_t RND)
945 Set ROP to the inverse hyperbolic sine, inverse hyperbolic cosine,
946 inverse hyperbolic tangent of OP, rounded according to RND with
947 the precision of ROP. The branch cut of MPC_ACOSH is (-\infty, 1).
950 File: mpc.info, Node: Miscellaneous Complex Functions, Next: Advanced Functions, Prev: Trigonometric Functions, Up: Complex Functions
952 5.10 Miscellaneous Functions
953 ============================
955 -- Function: int mpc_urandom (mpc_t ROP, gmp_randstate_t STATE)
956 Generate a uniformly distributed random complex in the unit square
957 [0, 1] x [0, 1]. Return 0, unless an exponent in the real or
958 imaginary part is not in the current exponent range, in which case
959 that part is set to NaN and a zero value is returned. The second
960 argument is a `gmp_randstate_t' structure which should be created
961 using the GMP `rand_init' function, see the GMP manual.
963 -- Function: const char * mpc_get_version (void)
964 Return the GNU MPC version, as a null-terminated string.
966 -- Macro: MPC_VERSION
967 -- Macro: MPC_VERSION_MAJOR
968 -- Macro: MPC_VERSION_MINOR
969 -- Macro: MPC_VERSION_PATCHLEVEL
970 -- Macro: MPC_VERSION_STRING
971 `MPC_VERSION' is the version of GNU MPC as a preprocessing
972 constant. `MPC_VERSION_MAJOR', `MPC_VERSION_MINOR' and
973 `MPC_VERSION_PATCHLEVEL' are respectively the major, minor and
974 patch level of GNU MPC version, as preprocessing constants.
975 `MPC_VERSION_STRING' is the version as a string constant, which
976 can be compared to the result of `mpc_get_version' to check at run
977 time the header file and library used match:
978 if (strcmp (mpc_get_version (), MPC_VERSION_STRING))
979 fprintf (stderr, "Warning: header and library do not match\n");
980 Note: Obtaining different strings is not necessarily an error, as
981 in general, a program compiled with some old GNU MPC version can be
982 dynamically linked with a newer GNU MPC library version (if
983 allowed by the library versioning system).
985 -- Macro: long MPC_VERSION_NUM (MAJOR, MINOR, PATCHLEVEL)
986 Create an integer in the same format as used by `MPC_VERSION' from
987 the given MAJOR, MINOR and PATCHLEVEL. Here is an example of how
988 to check the GNU MPC version at compile time:
989 #if (!defined(MPC_VERSION) || (MPC_VERSION<MPC_VERSION_NUM(2,1,0)))
990 # error "Wrong GNU MPC version."
994 File: mpc.info, Node: Advanced Functions, Next: Internals, Prev: Miscellaneous Complex Functions, Up: Complex Functions
996 5.11 Advanced Functions
997 =======================
999 -- Macro: MPC_SET_X_Y (REAL_SUFFIX, IMAG_SUFFIX, ROP, REAL, IMAG, RND)
1000 The macro MPC_SET_X_Y is designed to serve as the body of an
1001 assignment function and cannot be used by itself. The REAL_SUFFIX
1002 and IMAG_SUFFIX parameters are the types of the real and imaginary
1003 part, that is, the `x' in the `mpfr_set_x' function one would use
1004 to set the part; for the mpfr type, use `fr'. REAL (respectively
1005 IMAG) is the value you want to assign to the real (resp.
1006 imaginary) part, its type must conform to REAL_SUFFIX (resp.
1007 IMAG_SUFFIX). RND is the `mpc_rnd_t' rounding mode. The return
1008 value is the usual inexact value (*note Return Value:
1011 For instance, you can define mpc_set_ui_fr as follows:
1012 int mpc_set_ui_fr (mpc_t rop, long int re, double im, mpc_rnd_t rnd)
1013 MPC_SET_X_Y (ui, fr, rop, re, im, rnd);
1016 File: mpc.info, Node: Internals, Prev: Advanced Functions, Up: Complex Functions
1021 These macros and functions are mainly designed for the implementation
1022 of GNU MPC, but may be useful for users too. However, no upward
1023 compatibility is guaranteed. You need to include `mpc-impl.h' to use
1026 The macro `MPC_MAX_PREC(z)' gives the maximum of the precisions of
1027 the real and imaginary parts of a complex number.
1030 File: mpc.info, Node: References, Next: Concept Index, Prev: Complex Functions, Up: Top
1035 * Torbjo"rn Granlund et al. `gmp' - GNU multiprecision library.
1036 Version 4.2.4, `http://gmplib.org/'.
1038 * Guillaume Hanrot, Vincent Lefe`vre, Patrick Pe'lissier, Paul
1039 Zimmermann et al. `mpfr' - A library for multiple-precision
1040 floating-point computations with exact rounding. Version 2.4.1,
1041 `http://www.mpfr.org'.
1043 * IEEE standard for binary floating-point arithmetic, Technical
1044 Report ANSI-IEEE Standard 754-1985, New York, 1985. Approved
1045 March 21, 1985: IEEE Standards Board; approved July 26, 1985:
1046 American National Standards Institute, 18 pages.
1048 * Donald E. Knuth, "The Art of Computer Programming", vol 2,
1049 "Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
1051 * ISO/IEC 9899:1999, Programming languages — C.
1055 File: mpc.info, Node: Concept Index, Next: Function Index, Prev: References, Up: Top
1063 * Arithmetic functions: Basic Arithmetic. (line 6)
1064 * Comparison functions: Complex Comparison. (line 6)
1065 * Complex arithmetic functions: Basic Arithmetic. (line 6)
1066 * Complex assignment functions: Assigning Complex Numbers.
1068 * Complex comparisons functions: Complex Comparison. (line 6)
1069 * Complex functions: Complex Functions. (line 6)
1070 * Complex number: GNU MPC Basics. (line 15)
1071 * Conditions for copying GNU MPC: Copying. (line 6)
1072 * Conversion functions: Converting Complex Numbers.
1074 * Copying conditions: Copying. (line 6)
1075 * Installation: Installing GNU MPC. (line 6)
1076 * Logarithm: Power Functions and Logarithm.
1078 * Miscellaneous complex functions: Miscellaneous Complex Functions.
1080 * mpc.h: GNU MPC Basics. (line 6)
1081 * Power functions: Power Functions and Logarithm.
1083 * Precision: GNU MPC Basics. (line 19)
1084 * Projection and Decomposing Functions: Projection & Decomposing.
1086 * Reporting bugs: Reporting Bugs. (line 6)
1087 * Rounding Mode: GNU MPC Basics. (line 24)
1088 * String and stream input and output: String and Stream Input and Output.
1090 * Trigonometric functions: Trigonometric Functions.
1092 * User-defined precision: Complex Functions. (line 12)
1095 File: mpc.info, Node: Function Index, Next: GNU Free Documentation License, Prev: Concept Index, Up: Top
1103 * _Complex: Converting Complex Numbers.
1105 * mpc_abs: Basic Arithmetic. (line 82)
1106 * mpc_acos: Trigonometric Functions.
1108 * mpc_acosh: Trigonometric Functions.
1110 * mpc_add: Basic Arithmetic. (line 13)
1111 * mpc_add_fr: Basic Arithmetic. (line 17)
1112 * mpc_add_ui: Basic Arithmetic. (line 15)
1113 * mpc_arg: Projection & Decomposing.
1115 * mpc_asin: Trigonometric Functions.
1117 * mpc_asinh: Trigonometric Functions.
1119 * mpc_atan: Trigonometric Functions.
1121 * mpc_atanh: Trigonometric Functions.
1123 * mpc_clear: Initializing Complex Numbers.
1125 * mpc_cmp: Complex Comparison. (line 7)
1126 * mpc_cmp_si: Complex Comparison. (line 10)
1127 * mpc_cmp_si_si: Complex Comparison. (line 9)
1128 * mpc_conj: Basic Arithmetic. (line 77)
1129 * mpc_cos: Trigonometric Functions.
1131 * mpc_cosh: Trigonometric Functions.
1133 * mpc_div: Basic Arithmetic. (line 66)
1134 * mpc_div_2ui: Basic Arithmetic. (line 99)
1135 * mpc_div_fr: Basic Arithmetic. (line 70)
1136 * mpc_div_ui: Basic Arithmetic. (line 68)
1137 * mpc_exp: Power Functions and Logarithm.
1139 * mpc_fma: Basic Arithmetic. (line 61)
1140 * mpc_fr_div: Basic Arithmetic. (line 74)
1141 * mpc_fr_sub: Basic Arithmetic. (line 25)
1142 * mpc_free_str: String and Stream Input and Output.
1144 * mpc_get_ldc: Converting Complex Numbers.
1146 * mpc_get_prec: Initializing Complex Numbers.
1148 * mpc_get_prec2: Initializing Complex Numbers.
1150 * mpc_get_str: String and Stream Input and Output.
1152 * mpc_get_version: Miscellaneous Complex Functions.
1154 * mpc_imag: Projection & Decomposing.
1156 * mpc_imagref: Projection & Decomposing.
1158 * mpc_init2: Initializing Complex Numbers.
1160 * mpc_init3: Initializing Complex Numbers.
1162 * mpc_inp_str: String and Stream Input and Output.
1164 * mpc_log: Power Functions and Logarithm.
1166 * mpc_log10: Power Functions and Logarithm.
1168 * mpc_mul: Basic Arithmetic. (line 40)
1169 * mpc_mul_2si: Basic Arithmetic. (line 93)
1170 * mpc_mul_2ui: Basic Arithmetic. (line 91)
1171 * mpc_mul_fr: Basic Arithmetic. (line 46)
1172 * mpc_mul_i: Basic Arithmetic. (line 52)
1173 * mpc_mul_si: Basic Arithmetic. (line 44)
1174 * mpc_mul_ui: Basic Arithmetic. (line 42)
1175 * mpc_neg: Basic Arithmetic. (line 35)
1176 * mpc_norm: Basic Arithmetic. (line 86)
1177 * mpc_out_str: String and Stream Input and Output.
1179 * mpc_pow: Power Functions and Logarithm.
1181 * mpc_pow_d: Power Functions and Logarithm.
1183 * mpc_pow_fr: Power Functions and Logarithm.
1185 * mpc_pow_ld: Power Functions and Logarithm.
1187 * mpc_pow_si: Power Functions and Logarithm.
1189 * mpc_pow_ui: Power Functions and Logarithm.
1191 * mpc_pow_z: Power Functions and Logarithm.
1193 * mpc_proj: Projection & Decomposing.
1195 * mpc_real: Projection & Decomposing.
1197 * mpc_realref: Projection & Decomposing.
1199 * mpc_rnd_t: GNU MPC Basics. (line 24)
1200 * mpc_set: Assigning Complex Numbers.
1202 * mpc_set_d: Assigning Complex Numbers.
1204 * mpc_set_d_d: Assigning Complex Numbers.
1206 * mpc_set_dc: Assigning Complex Numbers.
1208 * mpc_set_f: Assigning Complex Numbers.
1210 * mpc_set_f_f: Assigning Complex Numbers.
1212 * mpc_set_fr: Assigning Complex Numbers.
1214 * mpc_set_fr_fr: Assigning Complex Numbers.
1216 * mpc_set_ld: Assigning Complex Numbers.
1218 * mpc_set_ld_ld: Assigning Complex Numbers.
1220 * mpc_set_ldc: Assigning Complex Numbers.
1222 * mpc_set_nan: Assigning Complex Numbers.
1224 * mpc_set_prec: Initializing Complex Numbers.
1226 * mpc_set_q: Assigning Complex Numbers.
1228 * mpc_set_q_q: Assigning Complex Numbers.
1230 * mpc_set_si: Assigning Complex Numbers.
1232 * mpc_set_si_si: Assigning Complex Numbers.
1234 * mpc_set_sj: Assigning Complex Numbers.
1236 * mpc_set_sj_sj: Assigning Complex Numbers.
1238 * mpc_set_str: String and Stream Input and Output.
1240 * mpc_set_ui: Assigning Complex Numbers.
1242 * mpc_set_ui_ui: Assigning Complex Numbers.
1244 * mpc_set_uj: Assigning Complex Numbers.
1246 * mpc_set_uj_uj: Assigning Complex Numbers.
1248 * MPC_SET_X_Y: Advanced Functions. (line 7)
1249 * mpc_set_z: Assigning Complex Numbers.
1251 * mpc_set_z_z: Assigning Complex Numbers.
1253 * mpc_sin: Trigonometric Functions.
1255 * mpc_sin_cos: Trigonometric Functions.
1257 * mpc_sinh: Trigonometric Functions.
1259 * mpc_sqr: Basic Arithmetic. (line 57)
1260 * mpc_sqrt: Power Functions and Logarithm.
1262 * mpc_strtoc: String and Stream Input and Output.
1264 * mpc_sub: Basic Arithmetic. (line 21)
1265 * mpc_sub_fr: Basic Arithmetic. (line 23)
1266 * mpc_sub_ui: Basic Arithmetic. (line 27)
1267 * mpc_swap: Assigning Complex Numbers.
1269 * mpc_t: GNU MPC Basics. (line 15)
1270 * mpc_tan: Trigonometric Functions.
1272 * mpc_tanh: Trigonometric Functions.
1274 * mpc_ui_div: Basic Arithmetic. (line 72)
1275 * mpc_ui_sub: Basic Arithmetic. (line 29)
1276 * mpc_ui_ui_sub: Basic Arithmetic. (line 31)
1277 * mpc_urandom: Miscellaneous Complex Functions.
1279 * MPC_VERSION: Miscellaneous Complex Functions.
1281 * MPC_VERSION_MAJOR: Miscellaneous Complex Functions.
1283 * MPC_VERSION_MINOR: Miscellaneous Complex Functions.
1285 * MPC_VERSION_NUM: Miscellaneous Complex Functions.
1287 * MPC_VERSION_PATCHLEVEL: Miscellaneous Complex Functions.
1289 * MPC_VERSION_STRING: Miscellaneous Complex Functions.
1291 * mpfr_prec_t: GNU MPC Basics. (line 19)
1294 File: mpc.info, Node: GNU Free Documentation License, Prev: Function Index, Up: Top
1296 Anhang A GNU Free Documentation License
1297 ***************************************
1299 Version 1.3, 3 November 2008
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1749 ====================================================
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1755 Copyright (C) YEAR YOUR NAME.
1756 Permission is granted to copy, distribute and/or modify this document
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1777 permit their use in free software.
1783 Node: Copying
\7f1436
1784 Node: Introduction to GNU MPC
\7f2207
1785 Node: Installing GNU MPC
\7f2925
1786 Node: Reporting Bugs
\7f8003
1787 Node: GNU MPC Basics
\7f9344
1788 Ref: return-value
\7f13042
1789 Node: Complex Functions
\7f14492
1790 Node: Initializing Complex Numbers
\7f15651
1791 Node: Assigning Complex Numbers
\7f18039
1792 Node: Converting Complex Numbers
\7f22438
1793 Node: String and Stream Input and Output
\7f23063
1794 Node: Complex Comparison
\7f29642
1795 Node: Projection & Decomposing
\7f30721
1796 Node: Basic Arithmetic
\7f32096
1797 Node: Power Functions and Logarithm
\7f36669
1798 Node: Trigonometric Functions
\7f38736
1799 Node: Miscellaneous Complex Functions
\7f40961
1800 Node: Advanced Functions
\7f43135
1801 Node: Internals
\7f44208
1802 Node: References
\7f44659
1803 Node: Concept Index
\7f45565
1804 Node: Function Index
\7f47879
1805 Node: GNU Free Documentation License
\7f61590
projects / platform / upstream / mpc.git / blob