flint.h – global definitions


The file flint.h contains various useful macros.

The macro constant FLINT_BITS is set at compile time to be the number of bits per limb on the machine. FLINT requires it to be either 32 or 64 bits. Other architectures are not currently supported.

The macro constant FLINT_D_BITS is 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 \(53\) or \(31\) on currently supported architectures. Numerous internal functions using precomputed inverses only support operands up to FLINT_D_BITS bits, hence the macro.

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 WORD_MIN.

The macro FLINT_MIN(x, y) returns the minimum of \(x\) and \(y\) for primitive signed or unsigned numerical types. This macro is only safe to use when \(x\) and \(y\) are of the same type, to avoid problems with integer promotion.

Similar to the previous macro, FLINT_MAX(x, y) returns the maximum of \(x\) and \(y\).

The macro FLINT_SWAP(T, x, y) swaps x and y, where x and y are of type 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.


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 \(x > 0\).

mp_limb_t FLINT_BIT_COUNT(mp_limb_t x)

Returns the number of binary bits required to represent an ulong x. If \(x\) is zero, returns \(0\).

Derived from this there are the two macros FLINT_FLOG2(x) and FLINT_CLOG2(x) which, for any \(x \geq 1\), compute \(\lfloor \log_2 x \rfloor\) and \(\lceil \log_2 x \rceil\).

To determine the current FLINT version a number of macros are available. For example, if the current FLINT version is 2.4.0 then __FLINT_VERSION will have the value \(2\), __FLINT_MINOR will have the value \(4\) and __FLINT_PATCHLEVEL will have the value \(0\).

The __FLINT_RELEASE macro gives a single number representing the FLINT version. For example, it will have the value 20400 for version 2.4.0.

The FLINT_VERSION macro is a static text string giving the version number, e.g. “2.4” or “2.4.1”. Note that if the final digit is a zero it is suppressed.

Integer types

The char, short and int types are assumed to be two’s complement types with exactly 8, 16 and 32 bits. This is not technically guaranteed by the C standard, but it is true on mainstream platforms.

Since the C types long and unsigned long do not have a standardized 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. For convenience, the macro FLINT_BITS specifies the word length (32 or 64) of the system.

type slong

The slong type is used for precisions, bit counts, 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().

The constants WORD_MIN and WORD_MAX give the range of this type. This type can be printed with flint_printf using the format string %wd.

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.

The following GMP-defined types are used in methods that manipulate the internal representation of numbers (using limb arrays).

type mp_limb_t

A single limb.

type mp_ptr

Pointer to a writable array of limbs.

type mp_srcptr

Pointer to a read-only array of limbs.

type mp_size_t

A limb count (always nonnegative).

type flint_bitcnt_t

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

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_s

A structure holding the state of a flint pseudo random number generator.

type flint_rand_t

An array of length 1 of flint_rand_s.

flint_rand_s *flint_rand_alloc(void)

Allocates a flint_rand_t object to be used like a heap-allocated flint_rand_t in external libraries. The random state is not initialised.

void flint_rand_free(flint_rand_s *state)

Frees a random state object as allocated using flint_rand_alloc().

void flint_randinit(flint_rand_t state)

Initialize a flint_rand_t.

void flint_randclear(flint_rand_t state)

Free all memory allocated by flint_rand_init().

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.


int flint_printf(const char *format, ...)
int flint_fprintf(FILE *fs, const char *format, ...)
int flint_vprintf(const char *format, va_list vlist)
int flint_vfprintf(FILE *fs, const char *format, va_list vlist)

These functions are extensions of the C standard library functions printf, fprintf, vprintf, and vfprintf.

The first extension is the addition of the length modifier w, used for printing the types ulong, slong and mp_limb_t. 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.

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.

Finally, we currently support printing polynomial of the following types: nmod_poly_t, fmpz_poly_t, fmpq_poly_t, arb_poly_t and acb_poly_t.

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;

/* Initialize and set variables */

    "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",
slong * vslong; slong vslong_len;
mp_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;

/* Initialize and set variables */

    "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"
    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);
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;

/* Initialize and set variables */

    "nmod matrix: %{nmod_mat}\n"
    "fmpz matrix: %{fmpz_mat}\n"
    "fmpz_mod matrix: %{fmpz_mod_mat}\n"
    "fmpq matrix: %{fmpq_mat}\n"
    "arb vector: %{arb_mat}\n"
    "acb vector: %{acb_mat}\n"
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;

/* Initialize and set variables */

    "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"


Printing of FLINT types does not currently support any flags.


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


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_sprintf(char *s, const char *str, ...)

This functions is an extensions of the C standard library functions sprintf. It is currently advised to not use this function as it is currently not coherent with flint_printf().

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 mp_limb_t type.


void flint_abort(void)

FLINT version of the C standard function abort.

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

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

enum flint_err_t

An error code with one of the following values


Describes a generic error.


Describes an overflow.


Describes an impossible inversion.


Describes a domain error.


Describes a division by zero.


Describes a exponent overflow.


Describes an inexact operation.


Describes a test fail.

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

Throws an error of type exc with message msg and aborts via flint_abort(). The printing back-end function is flint_fprintf(), and so it allows for printing of FLINT types as well.