This is gmp.info, produced by makeinfo version 4.0 from gmp.texi.

INFO-DIR-SECTION GNU libraries
START-INFO-DIR-ENTRY
* gmp: (gmp).                   GNU Multiple Precision Arithmetic Library.
END-INFO-DIR-ENTRY


File: gmp.info,  Node: Low-level Functions,  Next: Random Number Functions,  Prev: Floating-point Functions,  Up: Top

Low-level Functions
*******************

   This chapter describes low-level GMP functions, used to implement the
high-level GMP functions, but also intended for time-critical user code.

   These functions start with the prefix `mpn_'.

   The `mpn' functions are designed to be as fast as possible, *not* to
provide a coherent calling interface.  The different functions have
somewhat similar interfaces, but there are variations that make them
hard to use.  These functions do as little as possible apart from the
real multiple precision computation, so that no time is spent on things
that not all callers need.

   A source operand is specified by a pointer to the least significant
limb and a limb count.  A destination operand is specified by just a
pointer.  It is the responsibility of the caller to ensure that the
destination has enough space for storing the result.

   With this way of specifying operands, it is possible to perform
computations on subranges of an argument, and store the result into a
subrange of a destination.

   A common requirement for all functions is that each source area
needs at least one limb.  No size argument may be zero.  Unless
otherwise stated, in-place operations are allowed where source and
destination are the same, but not where they only partly overlap.

   The `mpn' functions are the base for the implementation of the
`mpz_', `mpf_', and `mpq_' functions.

   This example adds the number beginning at S1P and the number
beginning at S2P and writes the sum at DESTP.  All areas have N limbs.

     cy = mpn_add_n (destp, s1p, s2p, n)

In the notation used here, a source operand is identified by the
pointer to the least significant limb, and the limb count in braces.
For example, {S1P, S1N}.

 - Function: mp_limb_t mpn_add_n (mp_limb_t *RP, const mp_limb_t *S1P,
          const mp_limb_t *S2P, mp_size_t N)
     Add {S1P, N} and {S2P, N}, and write the N least significant limbs
     of the result to RP.  Return carry, either 0 or 1.

     This is the lowest-level function for addition.  It is the
     preferred function for addition, since it is written in assembly
     for most CPUs.  For addition of a variable to itself (i.e., S1P
     equals S2P, use `mpn_lshift' with a count of 1 for optimal speed.

 - Function: mp_limb_t mpn_add_1 (mp_limb_t *RP, const mp_limb_t *S1P,
          mp_size_t N, mp_limb_t S2LIMB)
     Add {S1P, N} and S2LIMB, and write the N least significant limbs
     of the result to RP.  Return carry, either 0 or 1.

 - Function: mp_limb_t mpn_add (mp_limb_t *RP, const mp_limb_t *S1P,
          mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N)
     Add {S1P, S1N} and {S2P, S2N}, and write the S1N least significant
     limbs of the result to RP.  Return carry, either 0 or 1.

     This function requires that S1N is greater than or equal to S2N.

 - Function: mp_limb_t mpn_sub_n (mp_limb_t *RP, const mp_limb_t *S1P,
          const mp_limb_t *S2P, mp_size_t N)
     Subtract {S2P, N} from {S1P, N}, and write the N least significant
     limbs of the result to RP.  Return borrow, either 0 or 1.

     This is the lowest-level function for subtraction.  It is the
     preferred function for subtraction, since it is written in
     assembly for most CPUs.

 - Function: mp_limb_t mpn_sub_1 (mp_limb_t *RP, const mp_limb_t *S1P,
          mp_size_t N, mp_limb_t S2LIMB)
     Subtract S2LIMB from {S1P, N}, and write the N least significant
     limbs of the result to RP.  Return borrow, either 0 or 1.

 - Function: mp_limb_t mpn_sub (mp_limb_t *RP, const mp_limb_t *S1P,
          mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N)
     Subtract {S2P, S2N} from {S1P, S1N}, and write the S1N least
     significant limbs of the result to RP.  Return borrow, either 0 or
     1.

     This function requires that S1N is greater than or equal to S2N.

 - Function: void mpn_mul_n (mp_limb_t *RP, const mp_limb_t *S1P, const
          mp_limb_t *S2P, mp_size_t N)
     Multiply {S1P, N} and {S2P, N}, and write the 2*N-limb result to
     RP.

     The destination has to have space for 2*N limbs, even if the
     product's most significant limb is zero.

 - Function: mp_limb_t mpn_mul_1 (mp_limb_t *RP, const mp_limb_t *S1P,
          mp_size_t N, mp_limb_t S2LIMB)
     Multiply {S1P, N} by S2LIMB, and write the N least significant
     limbs of the product to RP.  Return the most significant limb of
     the product.  {S1P, N} and {RP, N} are allowed to overlap provided
     RP <= S1P.

     This is a low-level function that is a building block for general
     multiplication as well as other operations in GMP.  It is written
     in assembly for most CPUs.

     Don't call this function if S2LIMB is a power of 2; use
     `mpn_lshift' with a count equal to the logarithm of S2LIMB
     instead, for optimal speed.

 - Function: mp_limb_t mpn_addmul_1 (mp_limb_t *RP, const mp_limb_t
          *S1P, mp_size_t N, mp_limb_t S2LIMB)
     Multiply {S1P, N} and S2LIMB, and add the N least significant
     limbs of the product to {RP, N} and write the result to RP.
     Return the most significant limb of the product, plus carry-out
     from the addition.

     This is a low-level function that is a building block for general
     multiplication as well as other operations in GMP.  It is written
     in assembly for most CPUs.

 - Function: mp_limb_t mpn_submul_1 (mp_limb_t *RP, const mp_limb_t
          *S1P, mp_size_t N, mp_limb_t S2LIMB)
     Multiply {S1P, N} and S2LIMB, and subtract the N least significant
     limbs of the product from {RP, N} and write the result to RP.
     Return the most significant limb of the product, minus borrow-out
     from the subtraction.

     This is a low-level function that is a building block for general
     multiplication and division as well as other operations in GMP.
     It is written in assembly for most CPUs.

 - Function: mp_limb_t mpn_mul (mp_limb_t *RP, const mp_limb_t *S1P,
          mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N)
     Multiply {S1P, S1N} and {S2P, S2N}, and write the result to RP.
     Return the most significant limb of the result.

     The destination has to have space for S1N + S2N limbs, even if the
     result might be one limb smaller.

     This function requires that S1N is greater than or equal to S2N.
     The destination must be distinct from both input operands.

 - Function: void mpn_tdiv_qr (mp_limb_t *QP, mp_limb_t *RP, mp_size_t
          QXN, const mp_limb_t *NP, mp_size_t NN, const mp_limb_t *DP,
          mp_size_t DN)
     Divide {NP, NN} by {DP, DN} and put the quotient at {QP, NN-DN+1}
     and the remainder at {RP, DN}.  The quotient is rounded towards 0.

     No overlap is permitted between arguments.  NN must be greater
     than or equal to DN.  The most significant limb of DP must be
     non-zero.  The QXN operand must be zero.

 - Function: mp_limb_t mpn_divrem (mp_limb_t *R1P, mp_size_t QXN,
          mp_limb_t *RS2P, mp_size_t RS2N, const mp_limb_t *S3P,
          mp_size_t S3N)
     [This function is obsolete.  Please call `mpn_tdiv_qr' instead for
     best performance.]

     Divide {RS2P, RS2N} by {S3P, S3N}, and write the quotient at R1P,
     with the exception of the most significant limb, which is
     returned.  The remainder replaces the dividend at RS2P; it will be
     S3N limbs long (i.e., as many limbs as the divisor).

     In addition to an integer quotient, QXN fraction limbs are
     developed, and stored after the integral limbs.  For most usages,
     QXN will be zero.

     It is required that RS2N is greater than or equal to S3N.  It is
     required that the most significant bit of the divisor is set.

     If the quotient is not needed, pass RS2P + S3N as R1P.  Aside from
     that special case, no overlap between arguments is permitted.

     Return the most significant limb of the quotient, either 0 or 1.

     The area at R1P needs to be RS2N - S3N + QXN limbs large.

 - Function: mp_limb_t mpn_divrem_1 (mp_limb_t *R1P, mp_size_t QXN,
          mp_limb_t *S2P, mp_size_t S2N, mp_limb_t S3LIMB)
 - Macro: mp_limb_t mpn_divmod_1 (mp_limb_t *R1P, mp_limb_t *S2P,
          mp_size_t S2N, mp_limb_t S3LIMB)
     Divide {S2P, S2N} by S3LIMB, and write the quotient at R1P.
     Return the remainder.

     The integer quotient is written to {R1P+QXN, S2N} and in addition
     QXN fraction limbs are developed and written to {R1P, QXN}.
     Either or both S2N and QXN can be zero.  For most usages, QXN will
     be zero.

     `mpn_divmod_1' exists for upward source compatibility and is
     simply a macro calling `mpn_divrem_1' with a QXN of 0.

     The areas at R1P and S2P have to be identical or completely
     separate, not partially overlapping.

 - Function: mp_limb_t mpn_divmod (mp_limb_t *R1P, mp_limb_t *RS2P,
          mp_size_t RS2N, const mp_limb_t *S3P, mp_size_t S3N)
     [This function is obsolete.  Please call `mpn_tdiv_qr' instead for
     best performance.]

 - Macro: mp_limb_t mpn_divexact_by3 (mp_limb_t *RP, mp_limb_t *SP,
          mp_size_t N)
 - Function: mp_limb_t mpn_divexact_by3c (mp_limb_t *RP, mp_limb_t *SP,
          mp_size_t N, mp_limb_t CARRY)
     Divide {SP, N} by 3, expecting it to divide exactly, and writing
     the result to {RP, N}.  If 3 divides exactly, the return value is
     zero and the result is the quotient.  If not, the return value is
     non-zero and the result won't be anything useful.

     `mpn_divexact_by3c' takes an initial carry parameter, which can be
     the return value from a previous call, so a large calculation can
     be done piece by piece from low to high.  `mpn_divexact_by3' is
     simply a macro calling `mpn_divexact_by3c' with a 0 carry
     parameter.

     These routines use a multiply-by-inverse and will be faster than
     `mpn_divrem_1' on CPUs with fast multiplication but slow division.

     The source a, result q, size n, initial carry i, and return value
     c satisfy c*b^n + a-i = 3*q, where b=2^mp_bits_per_limb.  The
     return c is always 0, 1 or 2, and the initial carry i must also be
     0, 1 or 2 (these are both borrows really).  When c=0 clearly
     q=(a-i)/3.  When c!=0, the remainder (a-i) mod 3 is given by 3-c,
     because b == 1 mod 3 (when `mp_bits_per_limb' is even, which is
     always so currently).

 - Function: mp_limb_t mpn_mod_1 (mp_limb_t *S1P, mp_size_t S1N,
          mp_limb_t S2LIMB)
     Divide {S1P, S1N} by S2LIMB, and return the remainder.  S1N can be
     zero.

 - Function: mp_limb_t mpn_bdivmod (mp_limb_t *RP, mp_limb_t *S1P,
          mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N, unsigned
          long int D)
     This function puts the low floor(D/mp_bits_per_limb) limbs of Q =
     {S1P, S1N}/{S2P, S2N} mod 2^D at RP, and returns the high D mod
     `mp_bits_per_limb' bits of Q.

     {S1P, S1N} - Q * {S2P, S2N} mod 2^(S1N*mp_bits_per_limb) is placed
     at S1P.  Since the low floor(D/mp_bits_per_limb) limbs of this
     difference are zero, it is possible to overwrite the low limbs at
     S1P with this difference, provided RP <= S1P.

     This function requires that S1N * mp_bits_per_limb >= D, and that
     {S2P, S2N} is odd.

     *This interface is preliminary.  It might change incompatibly in
     future revisions.*

 - Function: mp_limb_t mpn_lshift (mp_limb_t *RP, const mp_limb_t *SP,
          mp_size_t N, unsigned int COUNT)
     Shift {SP, N} left by COUNT bits, and write the result to {RP, N}.
     The bits shifted out at the left are returned in the least
     significant COUNT bits of the return value (the rest of the return
     value is zero).

     COUNT must be in the range 1 to mp_bits_per_limb-1.  The regions
     {SP, N} and {RP, N} may overlap, provided RP >= SP.

     This function is written in assembly for most CPUs.

 - Function: mp_limb_t mpn_rshift (mp_limb_t *RP, const mp_limb_t *SP,
          mp_size_t N, unsigned int COUNT)
     Shift {SP, N} right by COUNT bits, and write the result to {RP,
     N}.  The bits shifted out at the right are returned in the most
     significant COUNT bits of the return value (the rest of the return
     value is zero).

     COUNT must be in the range 1 to mp_bits_per_limb-1.  The regions
     {SP, N} and {RP, N} may overlap, provided RP <= SP.

     This function is written in assembly for most CPUs.

 - Function: int mpn_cmp (const mp_limb_t *S1P, const mp_limb_t *S2P,
          mp_size_t N)
     Compare {S1P, N} and {S2P, N} and return a positive value if S1 >
     S2, 0 if they are equal, or a negative value if S1 < S2.

 - Function: mp_size_t mpn_gcd (mp_limb_t *RP, mp_limb_t *S1P,
          mp_size_t S1N, mp_limb_t *S2P, mp_size_t S2N)
     Set {RP, RETVAL} to the greatest common divisor of {S1P, S1N} and
     {S2P, S2N}.  The result can be up to S2N limbs, the return value
     is the actual number produced.  Both source operands are destroyed.

     {S1P, S1N} must have at least as many bits as {S2P, S2N}.  {S2P,
     S2N} must be odd.  Both operands must have non-zero most
     significant limbs.

 - Function: mp_limb_t mpn_gcd_1 (const mp_limb_t *S1P, mp_size_t S1N,
          mp_limb_t S2LIMB)
     Return the greatest common divisor of {S1P, S1N} and S2LIMB.  Both
     operands must be non-zero.

 - Function: mp_size_t mpn_gcdext (mp_limb_t *R1P, mp_limb_t *R2P,
          mp_size_t *R2N, mp_limb_t *S1P, mp_size_t S1N, mp_limb_t
          *S2P, mp_size_t S2N)
     Calculate the greatest common divisor of {S1P, S1N} and {S2P,
     S2N}.  Store the gcd at {R1P, RETVAL} and the first cofactor at
     {R2P, *R2N}, with *R2N negative if the cofactor is negative.  R1P
     and R2P should each have room for S1N+1 limbs, but the return
     value and value stored through R2N indicate the actual number
     produced.

     {S1P, S1N} >= {S2P, S2N} is required, and both must be non-zero.
     The regions {S1P, S1N+1} and {S2P, S2N+1} are destroyed (i.e. the
     operands plus an extra limb past the end of each).

     The cofactor R1 will satisfy R2*S1 + K*S2 = R1.  The second
     cofactor K is not calculated but can easily be obtained from (R1 -
     R2*S1) / S2.

 - Function: mp_size_t mpn_sqrtrem (mp_limb_t *R1P, mp_limb_t *R2P,
          const mp_limb_t *SP, mp_size_t N)
     Compute the square root of {SP, N} and put the result at {R1P,
     ceil(N/2)} and the remainder at {R2P, RETVAL}.  R2P needs space
     for N limbs, but the return value indicates how many are produced.

     The most significant limb of {SP, N} must be non-zero.  The areas
     {R1P, ceil(N/2)} and {SP, N} must be completely separate.  The
     areas {R2P, N} and {SP, N} must be either identical or completely
     separate.

     If the remainder is not wanted then R2P can be `NULL', and in this
     case the return value is zero or non-zero according to whether the
     remainder would have been zero or non-zero.

     A return value of zero indicates a perfect square.  See also
     `mpz_perfect_square_p'.

 - Function: mp_size_t mpn_get_str (unsigned char *STR, int BASE,
          mp_limb_t *S1P, mp_size_t S1N)
     Convert {S1P, S1N} to a raw unsigned char array at STR in base
     BASE, and return the number of characters produced.  There may be
     leading zeros in the string.  The string is not in ASCII; to
     convert it to printable format, add the ASCII codes for `0' or
     `A', depending on the base and range.

     The most significant limb of the input {S1P, S1N} must be
     non-zero.  The area {S1P, S1N+1} is clobbered.

     The area at STR has to have space for the largest possible number
     represented by a S1N long limb array, plus one extra character.

 - Function: mp_size_t mpn_set_str (mp_limb_t *R1P, const char *STR,
          size_t STRSIZE, int BASE)
     Convert the raw unsigned char array at STR of length STRSIZE to a
     limb array.  The base of STR is BASE.  STRSIZE must be at least 1.

     Return the number of limbs stored in R1P.

 - Function: unsigned long int mpn_scan0 (const mp_limb_t *S1P,
          unsigned long int BIT)
     Scan S1P from bit position BIT for the next clear bit.

     It is required that there be a clear bit within the area at S1P at
     or beyond bit position BIT, so that the function has something to
     return.

 - Function: unsigned long int mpn_scan1 (const mp_limb_t *S1P,
          unsigned long int BIT)
     Scan S1P from bit position BIT for the next set bit.

     It is required that there be a set bit within the area at S1P at or
     beyond bit position BIT, so that the function has something to
     return.

 - Function: void mpn_random (mp_limb_t *R1P, mp_size_t R1N)
 - Function: void mpn_random2 (mp_limb_t *R1P, mp_size_t R1N)
     Generate a random number of length R1N and store it at R1P.  The
     most significant limb is always non-zero.  `mpn_random' generates
     uniformly distributed limb data, `mpn_random2' generates long
     strings of zeros and ones in the binary representation.

     `mpn_random2' is intended for testing the correctness of the `mpn'
     routines.

 - Function: unsigned long int mpn_popcount (const mp_limb_t *S1P,
          mp_size_t N)
     Count the number of set bits in {S1P, N}.

 - Function: unsigned long int mpn_hamdist (const mp_limb_t *S1P, const
          mp_limb_t *S2P, mp_size_t N)
     Compute the hamming distance between {S1P, N} and {S2P, N}.

 - Function: int mpn_perfect_square_p (const mp_limb_t *S1P, mp_size_t
          N)
     Return non-zero iff {S1P, N} is a perfect square.


File: gmp.info,  Node: Random Number Functions,  Next: Formatted Output,  Prev: Low-level Functions,  Up: Top

Random Number Functions
***********************

   Sequences of pseudo-random numbers in GMP are generated using a
variable of type `gmp_randstate_t', which holds an algorithm selection
and a current state.  Such a variable must be initialized by a call to
one of the `gmp_randinit' functions, and can be seeded with one of the
`gmp_randseed' functions.

   The functions actually generating random numbers are described in
*Note Integer Random Numbers::, and *Note Miscellaneous Float
Functions::.

   The older style random number functions don't accept a
`gmp_randstate_t' parameter but instead share a global variable of that
type.  They use a default algorithm and are currently not seeded
(though perhaps that will change in the future).  The new functions
accepting a `gmp_randstate_t' are recommended for applications that
care about randomness.

* Menu:

* Random State Initialization::
* Random State Seeding::


File: gmp.info,  Node: Random State Initialization,  Next: Random State Seeding,  Prev: Random Number Functions,  Up: Random Number Functions

Random State Initialization
===========================

 - Function: void gmp_randinit_default (gmp_randstate_t STATE)
     Initialize STATE with a default algorithm.  This will be a
     compromise between speed and randomness, and is recommended for
     applications with no special requirements.

 - Function: void gmp_randinit_lc_2exp (gmp_randstate_t STATE, mpz_t A,
          unsigned long C, unsigned long M2EXP)
     Initialize STATE with a linear congruential algorithm X = (A*X +
     C) mod 2^M2EXP.

     The low bits of X in this algorithm are not very random.  The least
     significant bit will have a period no more than 2, and the second
     bit no more than 4, etc.  For this reason only the high half of
     each X is actually used.

     When a random number of more than M2EXP/2 bits is to be generated,
     multiple iterations of the recurrence are used and the results
     concatenated.

 - Function: int gmp_randinit_lc_2exp_size (gmp_randstate_t STATE,
          unsigned long SIZE)
     Initialize STATE for a linear congruential algorithm as per
     `gmp_randinit_lc_2exp'.  A, C and M2EXP are selected from a table,
     chosen so that SIZE bits (or more) of each X will be used, ie.
     M2EXP >= SIZE/2.

     If successful the return value is non-zero.  If SIZE is bigger
     than the table data provides then the return value is zero.  The
     maximum SIZE currently supported is 128.

 - Function: void gmp_randinit (gmp_randstate_t STATE,
          gmp_randalg_t ALG, ...)
     *This function is obsolete.*

     Initialize STATE with an algorithm selected by ALG.  The only
     choice is `GMP_RAND_ALG_LC', which is `gmp_randinit_lc_2exp_size'.
     A third parameter of type `unsigned long' is required, this is the
     SIZE for that function.  `GMP_RAND_ALG_DEFAULT' or 0 are the same
     as `GMP_RAND_ALG_LC'.

     `gmp_randinit' sets bits in `gmp_errno' to indicate an error.
     `GMP_ERROR_UNSUPPORTED_ARGUMENT' if ALG is unsupported, or
     `GMP_ERROR_INVALID_ARGUMENT' if the SIZE parameter is too big.

 - Function: void gmp_randclear (gmp_randstate_t STATE)
     Free all memory occupied by STATE.


File: gmp.info,  Node: Random State Seeding,  Prev: Random State Initialization,  Up: Random Number Functions

Random State Seeding
====================

 - Function: void gmp_randseed (gmp_randstate_t STATE, mpz_t SEED)
 - Function: void gmp_randseed_ui (gmp_randstate_t STATE,
          unsigned long int SEED)
     Set an initial seed value into STATE.

     The size of a seed determines how many different sequences of
     random numbers that it's possible to generate.  The "quality" of
     the seed is the randomness of a given seed compared to the
     previous seed used, and this affects the randomness of separate
     number sequences.  The method for choosing a seed is critical if
     the generated numbers are to be used for important applications,
     such as generating cryptographic keys.

     Traditionally the system time has been used to seed, but care
     needs to be taken with this.  If an application seeds often and
     the resolution of the system clock is low, then the same sequence
     of numbers might be repeated.  Also, the system time is quite easy
     to guess, so if unpredictability is required then it should
     definitely not be the only source for the seed value.  On some
     systems there's a special device `/dev/random' which provides
     random data better suited for use as a seed.


File: gmp.info,  Node: Formatted Output,  Next: Formatted Input,  Prev: Random Number Functions,  Up: Top

Formatted Output
****************

* Menu:

* Formatted Output Strings::
* Formatted Output Functions::
* C++ Formatted Output::


File: gmp.info,  Node: Formatted Output Strings,  Next: Formatted Output Functions,  Prev: Formatted Output,  Up: Formatted Output

Format Strings
==============

   `gmp_printf' and friends accept format strings similar to the
standard C `printf' (*note Formatted Output: (libc)Formatted Output.).
A format specification is of the form

     % [flags] [width] [.[precision]] [type] conv

   GMP adds types `Z', `Q' and `F' for `mpz_t', `mpq_t' and `mpf_t'
respectively.  `Z' and `Q' behave like integers.  `Q' will print a `/'
and a denominator, if needed.  `F' behaves like a float.  For example,

     mpz_t z;
     gmp_printf ("%s is an mpz %Zd\n", "here", z);
     
     mpq_t q;
     gmp_printf ("a hex rational: %#40Qx\n", q);
     
     mpf_t f;
     int   n;
     gmp_printf ("fixed point mpf %.*Ff with %d digits\n", n, f, n);

   All the standard C `printf' types behave the same as the C library
`printf', and can be freely intermixed with the GMP extensions.  In the
current implementation the standard parts of the format string are
simply handed to `printf' and only the GMP extensions handled directly.

   The flags accepted are as follows.  GLIBC style ' (*note Locales and
Internationalization: (libc)Locales.) is only for the standard C types
(not the GMP types), and only if the C library supports it.

     0         pad with zeros (rather than spaces)
     #         show the base with `0x', `0X' or `0'
     +         always show a sign
     (space)   show a space or a `-' sign
     '         group digits, GLIBC style (not GMP types)

   The standard types accepted are as follows.  `h' and `l' are
portable, the rest will depend on the compiler (or include files) for
the type and the C library for the output.

     h         short
     hh        char
     j         intmax_t or uintmax_t
     l         long or wchar_t
     ll        same as L
     L         long long or long double
     q         quad_t or u_quad_t
     t         ptrdiff_t
     z         size_t

The GMP types are

     F         mpf_t, float conversions
     Q         mpq_t, integer conversions
     Z         mpz_t, integer conversions

   The conversions accepted are as follows.  `a' and `A' are always
supported for `mpf_t' but depend on the C library for standard C float
types.  `m' and `p' depend on the C library.

     a A       hex floats, GLIBC style
     c         character
     d         decimal integer
     e E       scientific format float
     f         fixed point float
     i         same as d
     g G       fixed or scientific float
     m         `strerror' string, GLIBC style
     n         characters written so far
     o         octal integer
     p         pointer
     s         string
     u         unsigned integer
     x X       hex integer

   `o', `x' and `X' are unsigned for the standard C types, but for `Z'
and `Q' a sign is included.  `u' is not meaningful for `Z' and `Q'.

   `n' can be used with any of the types, even the GMP types.

   Other types or conversions that might be accepted by the C library
`printf' cannot be used through `gmp_printf', this includes for
instance extensions registered with GLIBC `register_printf_function'.
Also currently there's no support for POSIX `$' style numbered arguments
(perhaps this will be added in the future).

   The precision field has it's usual meaning for integer `Z' and float
`F' types, but is currently undefined for `Q' and should not be used
with that.

   `mpf_t' conversions only ever generate as many digits as can be
accurately represented by the operand, the same as `mpf_get_str' does.
Zeros will be used if necessary to pad to the requested precision.  This
happens even for an `f' conversion of an `mpf_t' which is an integer,
for instance 2^1024 in an `mpf_t' of 128 bits precision will only
produce about 20 digits, then pad with zeros to the decimal point.  An
empty precision field like `%.Fe' or `%.Ff' can be used to specifically
request all significant digits.

   The decimal point character (or string) is taken from the current
locale settings on systems which provide `localeconv' (*note Locales
and Internationalization: (libc)Locales.).  The C library will normally
do the same for standard float output.


File: gmp.info,  Node: Formatted Output Functions,  Next: C++ Formatted Output,  Prev: Formatted Output Strings,  Up: Formatted Output

Functions
=========

   Each of the following functions is similar to the corresponding C
library function.  The basic `printf' forms take a variable argument
list.  The `vprintf' forms take an argument pointer, see *Note Variadic
Functions: (libc)Variadic Functions, or `man 3 va_start'.

   It should be emphasised that if a format string is invalid, or the
arguments don't match what the format specifies, then the behaviour of
any of these functions will be unpredictable.  GCC format string
checking is not available, since it doesn't recognise the GMP
extensions.

   The file based functions `gmp_printf' and `gmp_fprintf' will return
-1 to indicate a write error.  All the functions can return -1 if the C
library `printf' variant in use returns -1, but this shouldn't normally
occur.

 - Function: int gmp_printf (const char *FMT, ...)
 - Function: int gmp_vprintf (const char *FMT, va_list AP)
     Print to the standard output `stdout'.  Return the number of
     characters written, or -1 if an error occurred.

 - Function: int gmp_fprintf (FILE *FP, const char *FMT, ...)
 - Function: int gmp_vfprintf (FILE *FP, const char *FMT, va_list AP)
     Print to the stream FP.  Return the number of characters written,
     or -1 if an error occurred.

 - Function: int gmp_sprintf (char *BUF, const char *FMT, ...)
 - Function: int gmp_vsprintf (char *BUF, const char *FMT, va_list AP)
     Form a null-terminated string in BUF.  Return the number of
     characters written, excluding the terminating null.

     No overlap is permitted between the space at BUF and the string
     FMT.

     These functions are not recommended, since there's no protection
     against exceeding the space available at BUF.

 - Function: int gmp_snprintf (char *BUF, size_t SIZE, const char *FMT,
          ...)
 - Function: int gmp_vsnprintf (char *BUF, size_t SIZE, const char
          *FMT, va_list AP)
     Form a null-terminated string in BUF.  No more than SIZE bytes
     will be written.  To get the full output, SIZE must be enough for
     the string and null-terminator.

     The return value is the total number of characters which ought to
     have been produced, excluding the terminating null.  If RETVAL >=
     SIZE then the actual output has been truncated to the first SIZE-1
     characters, and a null appended.

     No overlap is permitted between the region {BUF,SIZE} and the FMT
     string.

     Notice the return value is in ISO C99 `snprintf' style.  This is
     so even if the C library `vsnprintf' is the older GLIBC 2.0.x
     style.

 - Function: int gmp_asprintf (char **PP, const char *FMT, ...)
 - Function: int gmp_vasprintf (char *PP, const char *FMT, va_list AP)
     Form a null-terminated string in a block of memory obtained from
     the current memory allocation function (*note Custom
     Allocation::).  The block will be the size of the string and
     null-terminator.  Put the address of the block in *PP.  Return the
     number of characters produced, excluding the null-terminator.

     Unlike the C library `asprintf', `gmp_asprintf' doesn't return -1
     if there's no more memory available, it lets the current allocation
     function handle that.

 - Function: int gmp_obstack_printf (struct obstack *OB, const char
          *FMT, ...)
 - Function: int gmp_obstack_vprintf (struct obstack *OB, const char
          *FMT, va_list AP)
     Append to the current obstack object, in the same style as
     `obstack_printf'.  Return the number of characters written.  A
     null-terminator is not written.

     FMT cannot be within the current obstack object, since the object
     might move as it grows.

     These functions are available only when the C library provides the
     obstack feature, which probably means only on GNU systems, see
     *Note Obstacks: (libc)Obstacks.


File: gmp.info,  Node: C++ Formatted Output,  Prev: Formatted Output Functions,  Up: Formatted Output

C++ Formatted Output
====================

   The following functions are provided in `libgmpxx', which is built
if C++ support is enabled (*note Build Options::).  Prototypes are
available from `<gmp.h>'.

 - Function: ostream& operator<< (ostream& STREAM, mpz_t OP)
     Print OP to STREAM, using its `ios' formatting settings.
     `ios::width' is reset to 0 after output, the same as the standard
     `ostream operator<<' routines do.

     In hex or octal, OP is printed as a signed number, the same as for
     decimal.  This is unlike the standard `operator<<' routines on
     `int' etc, which instead give twos complement.

 - Function: ostream& operator<< (ostream& STREAM, mpq_t OP)
     Print OP to STREAM, using its `ios' formatting settings.
     `ios::width' is reset to 0 after output, the same as the standard
     `ostream operator<<' routines do.

     Output will be a fraction like `5/9', or if the denominator is 1
     then just a plain integer like `123'.

     In hex or octal, OP is printed as a signed value, the same as for
     decimal.  If `ios::showbase' is set then a base indicator is shown
     on both the numerator and denominator (if the denominator is
     required).

 - Function: ostream& operator<< (ostream& STREAM, mpf_t OP)
     Print OP to STREAM, using its `ios' formatting settings.
     `ios::width' is reset to 0 after output, the same as the standard
     `ostream operator<<' routines do.  The decimal point follows the
     current locale, on systems providing `localeconv'.

     Hex and octal are supported, unlike the standard `operator<<'
     routines on `double' etc.  The mantissa will be in hex or octal,
     the exponent will be in decimal.  For hex the exponent delimiter
     is an `@'.  This is as per `mpf_out_str'.  `ios::showbase' is
     supported, and will put a base on the mantissa.

   These operators mean that GMP types can be printed in the usual C++
way, for example,

     mpz_t  z;
     int    n;
     ...
     cout << "iteration " << n << " value " << z << "\n";

   But note that `ostream' output (and `istream' input, *note C++
Formatted Input::) is the only overloading available and using for
instance `+' with an `mpz_t' will have unpredictable results.


File: gmp.info,  Node: Formatted Input,  Next: C++ Class Interface,  Prev: Formatted Output,  Up: Top

Formatted Input
***************

* Menu:

* Formatted Input Strings::
* Formatted Input Functions::
* C++ Formatted Input::


File: gmp.info,  Node: Formatted Input Strings,  Next: Formatted Input Functions,  Prev: Formatted Input,  Up: Formatted Input

Formatted Input Strings
=======================

   `gmp_scanf' and friends accept format strings similar to the
standard C `scanf' (*note Formatted Input: (libc)Formatted Input.).  A
format specification is of the form

     % [flags] [width] [type] conv

   GMP adds types `Z', `Q' and `F' for `mpz_t', `mpq_t' and `mpf_t'
respectively.  `Z' and `Q' behave like integers.  `Q' will read a `/'
and a denominator, if present.  `F' behaves like a float.

   GMP variables don't require an `&' when passed to `gmp_scanf', since
they're already "call-by-reference".  For example,

     /* to read say "a(5) = 1234" */
     int   n;
     mpz_t z;
     gmp_scanf ("a(%d) = %Zd\n", &n, z);
     
     mpq_t q1, q2;
     gmp_sscanf ("0377 + 0x10/0x11", "%Qi + %Qi", q1, q2);
     
     /* to read say "topleft (1.55,-2.66)" */
     mpf_t x, y;
     char  buf[32];
     gmp_scanf ("%31s (%Ff,%Ff)", buf, x, y);

   All the standard C `scanf' types behave the same as in the C library
`scanf', and can be freely intermixed with the GMP extensions.  In the
current implementation the standard parts of the format string are
simply handed to `scanf' and only the GMP extensions handled directly.

   The flags accepted are as follows.  `a' and `'' will depend on
support from the C library, and `'' cannot be used with GMP types.

     *         read but don't store
     a         allocate a buffer (string conversions)
     '         group digits, GLIBC style (not GMP types)

   The standard types accepted are as follows.  `h' and `l' are
portable, the rest will depend on the compiler (or include files) for
the type and the C library for the input.

     h         short
     hh        char
     j         intmax_t or uintmax_t
     l         long or wchar_t
     ll        same as L
     L         long long or long double
     q         quad_t or u_quad_t
     t         ptrdiff_t
     z         size_t

The GMP types are

     F         mpf_t, float conversions
     Q         mpq_t, integer conversions
     Z         mpz_t, integer conversions

   The conversions accepted are as follows.  `p' and `[' will depend on
support from the C library, the rest are standard.

     c         character or characters
     d         decimal integer
     e E f g G float
     i         integer with base indicator
     n         characters written so far
     o         octal integer
     p         pointer
     s         string of non-whitespace characters
     u         decimal integer
     x X       hex integer
     [         string of characters in a set

   `e', `E', `f', `g' and `G' are identical, they all read either fixed
point or scientific format, and either `e' or `E' for the exponent in
scientific format.

   `x' and `X' are identical, both accept both upper and lower case
hexadecimal.

   `o', `u', `x' and `X' all read positive or negative values.  For the
standard C types these are described as "unsigned" conversions, but
that merely affects certain overflow handling, negatives are still
allowed (see `strtoul', *Note Parsing of Integers: (libc)Parsing of
Integers).  For GMP types there are no overflows, and `d' and `u' are
identical.

   `Q' type reads the numerator and (optional) denominator as given.
If the value might not be in canonical form then `mpq_canonicalize'
must be called before using it in any calculations (*note Rational
Number Functions::).

   `Qi' will read a base specification separately for the numerator and
denominator.  For example `0x10/11' would be 16/11, whereas `0x10/0x11'
would be 16/17.

   `n' can be used with any of the types above, even the GMP types.
`*' to suppress assignment is allowed, though the field would then do
nothing at all.

   Other conversions or types that might be accepted by the C library
`scanf' cannot be used through `gmp_scanf'.

   Whitespace is read and discarded before a field, except for `c' and
`[' conversions.

   For float conversions, the decimal point character (or string)
expected is taken from the current locale settings on systems which
provide `localeconv' (*note Locales and Internationalization:
(libc)Locales.).  The C library will normally do the same for standard
float input.


File: gmp.info,  Node: Formatted Input Functions,  Next: C++ Formatted Input,  Prev: Formatted Input Strings,  Up: Formatted Input

Formatted Input Functions
=========================

   Each of the following functions is similar to the corresponding C
library function.  The plain `scanf' forms take a variable argument
list.  The `vscanf' forms take an argument pointer, see *Note Variadic
Functions: (libc)Variadic Functions, or `man 3 va_start'.

   It should be emphasised that if a format string is invalid, or the
arguments don't match what the format specifies, then the behaviour of
any of these functions will be unpredictable.  GCC format string
checking is not available, since it doesn't recognise the GMP
extensions.

   No overlap is permitted between the FMT string and any of the results
produced.

 - Function: int gmp_scanf (const char *FMT, ...)
 - Function: int gmp_vscanf (const char *FMT, va_list AP)
     Read from the standard input `stdin'.

 - Function: int gmp_fscanf (FILE *FP, const char *FMT, ...)
 - Function: int gmp_vfscanf (FILE *FP, const char *FMT, va_list AP)
     Read from the stream FP.

 - Function: int gmp_sscanf (const char *S, const char *FMT, ...)
 - Function: int gmp_vsscanf (const char *S, const char *FMT, va_list
          AP)
     Read from a null-terminated string S.

   The return value from each of these functions is the same as the
standard C99 `scanf', namely the number of fields successfully parsed
and stored.  `%n' fields and fields read but suppressed by `*' don't
count towards the return value.

   If end of file or file error, or end of string, is reached when a
match is required, and when no previous non-suppressed fields have
matched, then the return value is EOF instead of 0.  A match is
required for a literal character in the format string or a field other
than `%n'.  Whitespace in the format string is only an optional match
and won't induce an EOF in this fashion.  Leading whitespace read and
discarded for a field doesn't count as a match.


File: gmp.info,  Node: C++ Formatted Input,  Prev: Formatted Input Functions,  Up: Formatted Input

C++ Formatted Input
===================

   The following functions are provided in `libgmpxx', which is built
only if C++ support is enabled (*note Build Options::).  Prototypes are
available from `<gmp.h>'.

 - Function: istream& operator>> (istream& STREAM, mpz_t ROP)
     Read ROP from STREAM, using its `ios' formatting settings.

 - Function: istream& operator>> (istream& STREAM, mpq_t ROP)
     Read ROP from STREAM, using its `ios' formatting settings.

     An integer like `123' will be read, or a fraction like `5/9'.  If
     the fraction is not in canonical form then `mpq_canonicalize' must
     be called (*note Rational Number Functions::).

 - Function: istream& operator>> (istream& STREAM, mpf_t ROP)
     Read ROP from STREAM, using its `ios' formatting settings.

     Hex or octal floats are not supported, but might be in the future.

   These operators mean that GMP types can be read in the usual C++
way, for example,

     mpz_t  z;
     ...
     cin >> z;

   But note that `istream' input (and `ostream' output, *note C++
Formatted Output::) is the only overloading available and using for
instance `+' with an `mpz_t' will have unpredictable results.


File: gmp.info,  Node: C++ Class Interface,  Next: BSD Compatible Functions,  Prev: Formatted Input,  Up: Top

C++ Class Interface
*******************

   This chapter describes the C++ class based interface to GMP.

   All GMP C language types and functions can be used in C++ programs,
since `gmp.h' has `extern "C"' qualifiers, but the class interface
offers overloaded functions and operators which may be more convenient.

   Due to the implementation of this interface, a reasonably recent C++
compiler is required, one supporting namespaces, partial specialization
of templates and member templates.  For GCC this means version 2.91 or
later.

   *Everything described in this chapter is to be considered preliminary
and might be subject to incompatible changes if some unforeseen
difficulty reveals itself.*

* Menu:

* C++ Interface General::
* C++ Interface Integers::
* C++ Interface Rationals::
* C++ Interface Floats::
* C++ Interface MPFR::
* C++ Interface Random Numbers::
* C++ Interface Limitations::


File: gmp.info,  Node: C++ Interface General,  Next: C++ Interface Integers,  Prev: C++ Class Interface,  Up: C++ Class Interface

C++ Interface General
=====================

All the C++ classes and functions are available with

     #include <gmpxx.h>

The classes defined are

 - Class: mpz_class
 - Class: mpq_class
 - Class: mpf_class

   The standard operators and various standard functions are overloaded
to allow arithmetic with these classes.  For example,

     int
     main (void)
     {
       mpz_class a, b, c;
     
       a = 1234;
       b = "-5678";
       c = a+b;
       cout << "sum is " << c << "\n";
       cout << "absolute value is " << abs(c) << "\n";
     
       return 0;
     }

   An important feature of the implementation is that an expression like
`a=b+c' results in a single call to the corresponding `mpz_add',
without using a temporary for the `b+c' part.  Expressions which by
their nature imply intermediate values, like `a=b*c+d*e', still use
temporaries though.

   The classes can be freely intermixed in expressions, as can the
classes and the standard C++ types.

   Conversions back from the classes to standard C++ types aren't done
automatically, instead member functions like `get_si' are provided (see
the following sections for details).

   Also there are no automatic conversions from the classes to the
corresponding GMP C types, instead a reference to the underlying C
object can be obtained with the following functions,

 - Function: mpz_t mpz_class::get_mpz_t ()
 - Function: mpq_t mpq_class::get_mpq_t ()
 - Function: mpf_t mpf_class::get_mpf_t ()

   These can be used to call a C function which doesn't have a C++ class
interface.  For example to set `a' to the GCD of `b' and `c',

     mpz_class a, b, c;
     ...
     mpz_gcd (a.get_mpz_t(), b.get_mpz_t(), c.get_mpz_t());

   In the other direction, a class can be initialized from the
corresponding GMP C type, or assigned to if an explicit constructor is
used.  In both cases this makes a copy of the value, it doesn't create
any sort of association.  For example,

     mpz_t z;
     // ... init and calculate z ...
     mpz_class x(z);
     mpz_class y;
     y = mpz_class (z);

   There are no namespace setups in `gmpxx.h', all types and functions
are simply put into the global namespace.  This is what `gmp.h' has
done in the past, and continues to do for compatibility.  The extras
provided by `gmpxx.h' follow GMP naming conventions and are unlikely to
clash with anything.


File: gmp.info,  Node: C++ Interface Integers,  Next: C++ Interface Rationals,  Prev: C++ Interface General,  Up: C++ Class Interface

C++ Interface Integers
======================

 - Function: void mpz_class::mpz_class (type N)
     Construct an `mpz_class'.  All the standard C++ types may be used,
     except `long long' and `long double', and all the GMP C++ classes
     can be used.  Any necessary conversion follows the corresponding C
     function, for example `double' follows `mpz_set_d' (*note
     Assigning Integers::).

 - Function: void mpz_class::mpz_class (mpz_t Z)
     Construct an `mpz_class' from an `mpz_t'.  The value in Z is
     copied into the new `mpz_class', there won't be any permanent
     association between it and Z.

 - Function: void mpz_class::mpz_class (const char *S)
 - Function: void mpz_class::mpz_class (const char *S, int base)
 - Function: void mpz_class::mpz_class (const string& S)
 - Function: void mpz_class::mpz_class (const string& S, int base)
     Construct an `mpz_class' converted from a string using
     `mpz_set_str', (*note Assigning Integers::).  If the BASE is not
     given then 0 is used.

 - Function: mpz_class operator/ (mpz_class A, mpz_class D)
 - Function: mpz_class operator% (mpz_class A, mpz_class D)
     Divisions involving `mpz_class' round towards zero, as per the
     `mpz_tdiv_q' and `mpz_tdiv_r' functions (*note Integer Division::).
     This corresponds to the rounding used for plain `int' calculations
     on most machines.

     The `mpz_fdiv...' or `mpz_cdiv...' functions can always be called
     directly if desired.  For example,

          mpz_class q, a, d;
          ...
          mpz_fdiv_q (q.get_mpz_t(), a.get_mpz_t(), d.get_mpz_t());

 - Function: mpz_class abs (mpz_class OP1)
 - Function: int cmp (mpz_class OP1, type OP2)
 - Function: int cmp (type OP1, mpz_class OP2)
 - Function: double mpz_class::get_d (void)
 - Function: long mpz_class::get_si (void)
 - Function: unsigned long mpz_class::get_ui (void)
 - Function: bool mpz_class::fits_sint_p (void)
 - Function: bool mpz_class::fits_slong_p (void)
 - Function: bool mpz_class::fits_sshort_p (void)
 - Function: bool mpz_class::fits_uint_p (void)
 - Function: bool mpz_class::fits_ulong_p (void)
 - Function: bool mpz_class::fits_ushort_p (void)
 - Function: int sgn (mpz_class OP)
 - Function: mpz_class sqrt (mpz_class OP)
     These functions provide a C++ class interface to the corresponding
     GMP C routines.

     `cmp' can be used with any of the classes or the standard C++
     types, except `long long' and `long double'.


   Overloaded operators for combinations of `mpz_class' and `double'
are provided for completeness, but it should be noted that if the given
`double' is not an integer then the way any rounding is done is
currently unspecified.  The rounding might take place at the start, in
the middle, or at the end of the operation, and it might change in the
future.

   Conversions between `mpz_class' and `double', however, are defined
to follow the corresponding C functions `mpz_get_d' and `mpz_set_d'.
And comparisons are always made exactly, as per `mpz_cmp_d'.

