# flint.h – global definitions

## Macros

The file `flint.h` contains various useful macros.

__FLINT_VERSION
__FLINT_VERSION_MINOR
__FLINT_VERSION_PATCHLEVEL

  The major, minor and patch for current version of FLINT.

__FLINT_RELEASE

  Equivalent to `10000 * __FLINT_VERSION + 100 * __FLINT_VERSION_MINOR + __FLINT_VERSION_PATCHLEVEL`.

FLINT_VERSION

  A static text string giving the version number, e.g. `3.1.0` or `3.2.0-dev`.

FLINT_BITS

  The constant defining how many bits per limb on the machine. We require this to be either 32 or 64. This constant is set during the configuration.

FLINT_D_BITS

  A constant set at compile time to be the number of bits per double on the machine or one less than the number of bits per limb, whichever is smaller. This will have the value 31 on 32-bit systems and 53 on 64-bit systems. Numerous internal functions using precomputed inverses only support operands up to `FLINT_D_BITS` bits, hence the macro.

FLINT_ABS(x)

  Returns the absolute value of x for primitive signed numerical types. It might fail for least negative values such as INT_MIN and LONG_MIN.

FLINT_UABS(x)

  Returns the absolute value of x for primitive signed numerical types, casting the result to an ulong. The result is well-defined for least negative values.

FLINT_MIN(x, y)
FLINT_MAX(x, y)

  Returns the minimum or maximum of x and y for primitive types. This macro is only safe to use when x and y are of the same type, to avoid problems with integer promotion.

FLINT_SWAP(T, x, y)

  Swaps x and y, both of types T. For instance, with x and y of type `fmpz_poly_t`, one can write `FLINT_SWAP(fmpz_poly_struct, *x, *y)` to swap the content of x with the content of y.

FLINT_SGN(x)

  Returns the sign of \(x\) where \(x\) is interpreted as a `slong`, that is, returns \(-1\) if \(x < 0\), \(0\) if \(x = 0\) and \(1\) if \(x > 0\).

## Integer types

The char, short and int types are assumed to be two’s complement types with exactly 8, 16 and 32 bits. Although this is not guaranteed prior to C23, it is true on all mainstream platforms prior to this.

Since the C types long and unsigned long do not have a standardised size in practice, FLINT defines slong and ulong types which are guaranteed to be 32 bits on a 32-bit system and 64 bits on a 64-bit system. They are also guaranteed to have the same size as GMP’s mp_limb_t. GMP builds with a different limb size configuration are not supported at all.

type ulong

  The ulong type is used for integer-valued coefficients that are known to be unsigned, and for values that require the full 32-bit or 64-bit range. In method names, a ulong parameter is denoted by ui, for example `arb_add_ui()`.

  The constant UWORD_MAX gives the range of this type. This type can be printed with flint_printf using the format string `%wu`.

  This is equivalent to GMP’s mp_limb_t.

type slong

  The slong type is used for precisions, loop indices, array sizes, and the like, even when those values are known to be nonnegative. It is also used for small integer-valued coefficients. In method names, an slong parameter is denoted by si, for example `arb_add_si()`.

  This type can be printed with flint_printf using the format string `%wd` or `%{slong}`.

  This is equivalent to GMP’s mp_limb_signed_t. Furthermore, for UNIX-type systems it is also equivalent to mp_size_t.

UWORD_MIN
UWORD_MAX
WORD_MIN
WORD_MAX

  The minimum and maximum values that a ulong and slong can hold, respectively.

type flint_bitcnt_t

  A bit offset within an array of limbs (always nonnegative).

type nn_ptr

  Pointer to a writable array of limbs.

  This is equivalent to GMP’s mp_ptr.

type nn_srcptr

  Pointer to a read-only array of limbs.

  This is equivalent to GMP’s mp_srcptr.

## Allocation Functions

void *flint_malloc(size_t size)

  Allocate size bytes of memory.

void *flint_realloc(void *ptr, size_t size)

  Reallocate an area of memory previously allocated by `flint_malloc()`, `flint_realloc()`, or `flint_calloc()`.

void *flint_calloc(size_t num, size_t size)

  Allocate num objects of size bytes each, and zero the allocated memory.

void flint_free(void *ptr)

  Free a section of memory allocated by `flint_malloc()`, `flint_realloc()`, or `flint_calloc()`.

## Random Numbers

type flint_rand_struct

  A structure holding the state of the FLINT pseudo random number generator.

type flint_rand_t

  An array of length 1 of `flint_rand_struct`.

void flint_rand_init(flint_rand_t state)
void flint_rand_clear(flint_rand_t state)

  Initialises or clears a `flint_rand_t`:.

## Thread functions

void flint_set_num_threads(int num_threads)

  Set up a thread pool of `num_threads - 1` worker threads (in addition to the master thread) and set the maximum number of worker threads the master thread can start to `num_threads - 1`.

  This function may only be called globally from the master thread. It can also be called at a global level to change the size of the thread pool, but an exception is raised if the thread pool is in use (threads have been woken but not given back). The function cannot be called from inside worker threads.

int flint_get_num_threads(void)

  When called at the global level, this function returns one more than the number of worker threads in the FLINT thread pool, i.e. it returns the number of workers in the thread pool plus one for the master thread.

  In general, this function returns one more than the number of additional worker threads that can be started by the current thread.

  Use `thread_pool_wake()` to set this number for a given worker thread.

  See also: `flint_get_num_available_threads()`.

int flint_set_num_workers(int num_workers)

  Restricts the number of worker threads that can be started by the current thread to `num_workers`. This function can be called from any thread.

  Assumes that the FLINT thread pool is already set up.

  The function returns the old number of worker threads that can be started.

  The function can only be used to reduce the number of workers that can be started from a thread. It cannot be used to increase the number. If a higher number is passed, the function has no effect.

  The number of workers must be restored to the original value by a call to `flint_reset_num_workers()` before the thread is returned to the thread pool.

  The main use of this function and `flint_reset_num_workers()` is to cheaply and temporarily restrict the number of workers that can be started, e.g. by a function that one wishes to call from a thread, and cheaply restore the number of workers to its original value before exiting the current thread.

void flint_reset_num_workers(int num_workers)

  After a call to `flint_set_num_workers()` this function must be called to set the number of workers that may be started by the current thread back to its original value.

## Input/Output

int flint_printf(const char *format, ...)
int flint_fprintf(FILE *fs, const char *format, ...)
int flint_snprintf(char *s, size_t n, const char *str, ...)
int flint_sprintf(char *s, const char *str, ...)
int flint_vprintf(const char *format, va_list vlist)
int flint_vfprintf(FILE *fs, const char *format, va_list vlist)
int flint_vsnprintf(char *s, size_t n, const char *str, va_list vlist)
int flint_vsprintf(char *s, const char *str, va_list vlist)

  These functions are extensions of the C standard library functions `printf`, `fprintf`, `snprintf`, `sprintf`, `vprintf`, `vfprintf`, `vsnprintf`, and `vsprintf`.

  The first extension is the addition of the length modifier `w`, used for printing the types `ulong`, `slong` and `ulong`. As these types are either defined as signed and unsigned `long int` or `long long int`, this comes in handy. Just like `long int` and `long long int`, the conversion format specifier are allowed to be `d`, `i`, `o`, `x`, `X` and `u`.

  The second and final extension is printing of FLINT types. Currently supported types are the base types `ulong`, `slong`, `fmpz_t`, `fmpq_t`, `mag_t`, `arf_t`, `arb_t` and `acb_t` as well as the context structures for modulo arithmetic `nmod_t` and `fmpz_mod_ctx_t`. We also support the GMP types `mpz_t` and `mpq_t`.

  We currently support printing vectors of pointers to the following base types: `slong`, `ulong`, `fmpz`, `fmpq`, `mag_struct`, `arf_struct`, `arb_struct` and `acb_struct`. In this case the nonnegative length of the vector must be passed as a second parameter following the pointer. Warning: the length parameter must be passed as a `slong`, not `int`.

  We also support printing matrices of the following types: `nmod_mat_t`, `fmpz_mat_t`, `fmpq_mat_t`, `arb_mat_t` and `acb_mat_t`.

  We also support printing polynomial of the following types: `nmod_poly_t`, `fmpz_poly_t`, `fmpq_poly_t`, `arb_poly_t` and `acb_poly_t`.

  Triple-valued booleans of type `truth_t` can also be printed.

  Finally, we support printing generic elements of type `gr_ptr` as well as `gr_poly_t` and `gr_mat_t`. For each of these types, the object to be printed must be followed by the corresponding `gr_ctx_t`. The context object itself can also printed as a standalone object.

    ulong bulong;
    slong bslong;
    fmpz_t bfmpz;
    fmpq_t bfmpq;
    mag_t bmag;
    arf_t barf;
    arb_t barb;
    acb_t bacb;
    nmod_t bnmod;
    fmpz_mod_ctx_t bfmpz_mod_ctx;
    mpz_t bmpz;
    mpq_t bmpq;
    truth_t btruth;
    gr_ctx_t bgr_ctx;
    gr_ptr bgr;

    /* Initialize and set variables */

    flint_printf(
        "ulong: %{ulong}\n"
        "slong: %{slong}\n"
        "fmpz: %{fmpz}\n"
        "fmpq: %{fmpq}\n"
        "mag: %{mag}\n"
        "arf: %{arf}\n"
        "arb: %{arb}\n"
        "acb: %{acb}\n"
        "nmod: %{nmod}\n"
        "fmpz_mod_ctx: %{fmpz_mod_ctx}\n"
        "mpz: %{mpz}\n"
        "mpq: %{mpq}\n"
        "truth: %{truth}\n"
        "gr: %{gr}\n"
        "gr: %{gr_ctx}\n",
        bulong,
        bslong,
        bfmpz,
        bfmpq,
        bmag,
        barf,
        barb,
        bacb,
        bnmod,
        bfmpz_mod_ctx,
        bmpz,
        bmpq,
        btruth,
        bgr, bgr_ctx,
        bgr_ctx);

    slong * vslong; slong vslong_len;
    nn_ptr vnmod; slong vnmod_len; /* The base type for nmod is ulong */
    fmpz * vfmpz; slong vfmpz_len;
    /* fmpz_mod vectors are given by the type `fmpz *' */
    fmpq * vfmpq; slong vfmpq_len;
    mag_ptr vmag; slong vmag_len;
    arf_ptr varf; slong varf_len;
    arb_ptr varb; slong varb_len;
    acb_ptr vacb; slong vacb_len;
    gr_ptr vgr; slong vgr_len; gr_ctx_t vgr_ctx;

    /* Initialize and set variables */

    flint_printf(
        "slong vector: %{slong*}\n"
        "nmod vector: %{ulong*}\n"
        "fmpz vector: %{fmpz*}\n"
        "fmpq vector: %{fmpq*}\n"
        "mag vector: %{mag*}\n"
        "arf vector: %{arf*}\n"
        "arb vector: %{arb*}\n"
        "acb vector: %{acb*}\n"
        "gr vector: %{gr*}\n"
        vslong, vslong_len, /* They require a vector length specifier */
        vnmod, vnmod_len,
        vfmpz, vfmpz_len,
        vfmpq, vfmpq_len,
        vmag, vmag_len,
        varf, varf_len,
        varb, varb_len,
        vacb, vacb_len,
        vgr, vgr_len, vgr_ctx);

    nmod_mat_t mnmod;
    fmpz_mat_t mfmpz;
    fmpz_mod_mat_t mfmpz_mod;
    fmpq_mat_t mfmpq;
    arb_mat_t marb;
    acb_mat_t macb;
    gr_mat_t mgr; gr_ctx_t mgr_ctx;

    /* Initialize and set variables */

    flint_printf(
        "nmod matrix: %{nmod_mat}\n"
        "fmpz matrix: %{fmpz_mat}\n"
        "fmpz_mod matrix: %{fmpz_mod_mat}\n"
        "fmpq matrix: %{fmpq_mat}\n"
        "arb matrix: %{arb_mat}\n"
        "acb matrix: %{acb_mat}\n"
        "gr matrix: %{gr_mat}\n"
        mnmod,
        mfmpz,
        mfmpz_mod,
        mfmpq,
        marb,
        macb,
        mgr, mgr_ctx);

    nmod_poly_t pnmod;
    fmpz_poly_t pfmpz;
    fmpz_mod_poly_t pfmpz_mod;
    fmpq_poly_t pfmpq;
    arb_poly_t parb;
    acb_poly_t pacb;
    gr_poly_t pgr; gr_ctx_t pgr_ctx;

    /* Initialize and set variables */

    flint_printf(
        "nmod polynomial: %{nmod_poly}\n"
        "fmpz polynomial: %{fmpz_poly}\n"
        "fmpz_mod polynomial: %{fmpz_mod_poly}\n"
        "fmpq polynomial: %{fmpq_poly}\n"
        "arb polynomial: %{arb_poly}\n"
        "acb polynomial: %{acb_poly}\n"
        pnmod,
        pfmpz,
        pfmpz_mod,
        pfmpq,
        parb,
        pacb,
        pgr, pgr_ctx);

Note

Printing of FLINT types does not currently support any flags.

Note

Any use of `%n` flags will be invalid, but will not generate any error.

Note

Invalid formats using variable minimum field width and/or precision such as `"%* p"` may be wrongly parsed, and may result in a different result compared to the C standard library functions.

int flint_scanf(const char *str, ...)
int flint_fscanf(FILE *f, const char *str, ...)
int flint_sscanf(const char *s, const char *str, ...)

  These are equivalent to the standard library functions `scanf`, `fscanf`, and `sscanf` with an additional length modifier “w” for reading an `ulong` type.

## Exceptions

enum flint_err_t

  An error code with one of the following values

  FLINT_ERROR

    Describes a generic error.

  FLINT_OVERFLOW

    Describes an overflow.

  FLINT_IMPINV

    Describes an impossible inversion.

  FLINT_DOMERR

    Describes a domain error.

  FLINT_DIVZERO

    Describes a division by zero.

  FLINT_EXPOF

    Describes a exponent overflow.

  FLINT_INEXACT

    Describes an inexact operation.

  FLINT_TEST_FAIL

    Describes a test fail.

void flint_abort(void)

  FLINT’s function for aborting, which defaults to the C standard function `abort`. To redirect what function should be used for the abort, use `flint_set_abort()`.

void flint_throw(flint_err_t exc, const char *msg, ...)

  FLINT’s function for throwing, which is throwing an error of type `exc` with message `msg`. This defaults to printing `exc` followed by printing the message `msg`, to then abort via `flint_abort()`, where the back-end printing function is `flint_fprintf()` that allows printing of FLINT types.

  To redirect what function should be used for throwing, use `flint_set_throw()`.

void flint_set_abort(void (*func)(void))

  Sets the `flint_abort()` function to call `func` instead of `abort`.

void flint_set_throw(void (*func)(flint_err_t, const char*, va_list))

  Sets the `flint_throw()` function use `func` instead of a private throw function. `func` is expected to call `va_end`, and to not alter \(const char *\) in any way.

## Sorting and searching

void flint_merge_sort(void *buf, slong len, slong size, int (*cmp)(const void*, const void*, void*), void *data)
void flint_sort(void *buf, slong len, slong size, int (*cmp)(const void*, const void*, void*), void *data)

  Sorts an array buf with len elements of size size according to the comparison function cmp. The comparison function takes as arguments pointers to the two elements being compared and a pointer to arbitrary data passed to the sorting function. It must return an \(int\) less than, equal to or greater than zero according to whether the first element is strictly smaller than, equal to, or strictly larger than the second.

  The `merge_sort` version uses a simple implementation of the merge sort algorithm. The generic version uses the system’s `qsort_r` (or equivalent) function when detected and falls back to `flint_merge_sort` otherwise.