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version 1.1.1.2, 2000/09/09 14:12:18 version 1.1.1.3, 2000/12/01 05:44:46
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Line 26  versions, except that this permission notice may be st
 translation approved by the Foundation.  translation approved by the Foundation.
   
   
   File: gmp.info,  Node: Integer Division,  Next: Integer Exponentiation,  Prev: Integer Arithmetic,  Up: Integer Functions
   
   Division Functions
   ==================
   
      Division is undefined if the divisor is zero, and passing a zero
   divisor to the divide or modulo functions, as well passing a zero mod
   argument to the `mpz_powm' and `mpz_powm_ui' functions, will make these
   functions intentionally divide by zero.  This lets the user handle
   arithmetic exceptions in these functions in the same manner as other
   arithmetic exceptions.
   
      There are three main groups of division functions:
      * Functions that truncate the quotient towards 0.  The names of
        these functions start with `mpz_tdiv'.  The `t' in the name is
        short for `truncate'.
   
      * Functions that round the quotient towards -infinity).  The names
        of these routines start with `mpz_fdiv'.  The `f' in the name is
        short for `floor'.
   
      * Functions that round the quotient towards +infinity.  The names of
        these routines start with `mpz_cdiv'.  The `c' in the name is
        short for `ceil'.
   
      For each rounding mode, there are a couple of variants.  Here `q'
   means that the quotient is computed, while `r' means that the remainder
   is computed.  Functions that compute both the quotient and remainder
   have `qr' in the name.
   
    - Function: void mpz_tdiv_q (mpz_t Q, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_tdiv_q_ui (mpz_t Q, mpz_t N,
             unsigned long int D)
        Set Q to [N/D], truncated towards 0.
   
        The function `mpz_tdiv_q_ui' returns the absolute value of the true
        remainder.
   
    - Function: void mpz_tdiv_r (mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_tdiv_r_ui (mpz_t R, mpz_t N,
             unsigned long int D)
        Set R to (N - [N/D] * D), where the quotient is truncated towards
        0.  Unless R becomes zero, it will get the same sign as N.
   
        The function `mpz_tdiv_r_ui' returns the absolute value of the
        remainder.
   
    - Function: void mpz_tdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_tdiv_qr_ui (mpz_t Q, mpz_t R, mpz_t
             N, unsigned long int D)
        Set Q to [N/D], truncated towards 0.  Set R to (N - [N/D] * D).
        Unless R becomes zero, it will get the same sign as N.  If Q and R
        are the same variable, the results are undefined.
   
        The function `mpz_tdiv_qr_ui' returns the absolute value of the
        remainder.
   
    - Function: unsigned long int mpz_tdiv_ui (mpz_t N, unsigned long int
             D)
        Like `mpz_tdiv_r_ui', but the remainder is not stored anywhere; its
        absolute value is just returned.
   
    - Function: void mpz_fdiv_q (mpz_t Q, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_fdiv_q_ui (mpz_t Q, mpz_t N,
             unsigned long int D)
        Set Q to N/D, rounded towards -infinity.
   
        The function `mpz_fdiv_q_ui' returns the remainder.
   
    - Function: void mpz_fdiv_r (mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_fdiv_r_ui (mpz_t R, mpz_t N,
             unsigned long int D)
        Set R to (N - N/D * D), where the quotient is rounded towards
        -infinity.  Unless R becomes zero, it will get the same sign as D.
   
        The function `mpz_fdiv_r_ui' returns the remainder.
   
    - Function: void mpz_fdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_fdiv_qr_ui (mpz_t Q, mpz_t R, mpz_t
             N, unsigned long int D)
        Set Q to N/D, rounded towards -infinity.  Set R to (N - N/D * D).
        Unless R becomes zero, it will get the same sign as D.  If Q and R
        are the same variable, the results are undefined.
   
        The function `mpz_fdiv_qr_ui' returns the remainder.
   
    - Function: unsigned long int mpz_fdiv_ui (mpz_t N, unsigned long int
             D)
        Like `mpz_fdiv_r_ui', but the remainder is not stored anywhere; it
        is just returned.
   
    - Function: void mpz_cdiv_q (mpz_t Q, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_cdiv_q_ui (mpz_t Q, mpz_t N,
             unsigned long int D)
        Set Q to N/D, rounded towards +infinity.
   
        The function `mpz_cdiv_q_ui' returns the negated remainder.
   
    - Function: void mpz_cdiv_r (mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_cdiv_r_ui (mpz_t R, mpz_t N,
             unsigned long int D)
        Set R to (N - N/D * D), where the quotient is rounded towards
        +infinity.  Unless R becomes zero, it will get the opposite sign
        as D.
   
        The function `mpz_cdiv_r_ui' returns the negated remainder.
   
    - Function: void mpz_cdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_cdiv_qr_ui (mpz_t Q, mpz_t R, mpz_t
             N, unsigned long int D)
        Set Q to N/D, rounded towards +infinity.  Set R to (N - N/D * D).
        Unless R becomes zero, it will get the opposite sign as D.  If Q
        and R are the same variable, the results are undefined.
   
        The function `mpz_cdiv_qr_ui' returns the negated remainder.
   
    - Function: unsigned long int mpz_cdiv_ui (mpz_t N, unsigned long int
             D)
        Like `mpz_tdiv_r_ui', but the remainder is not stored anywhere; its
        negated value is just returned.
   
    - Function: void mpz_mod (mpz_t R, mpz_t N, mpz_t D)
    - Function: unsigned long int mpz_mod_ui (mpz_t R, mpz_t N, unsigned
             long int D)
        Set R to N `mod' D.  The sign of the divisor is ignored; the
        result is always non-negative.
   
        The function `mpz_mod_ui' returns the remainder.
   
    - Function: void mpz_divexact (mpz_t Q, mpz_t N, mpz_t D)
        Set Q to N/D.  This function produces correct results only when it
        is known in advance that D divides N.
   
        Since mpz_divexact is much faster than any of the other routines
        that produce the quotient (*note References:: Jebelean), it is the
        best choice for instances in which exact division is known to
        occur, such as reducing a rational to lowest terms.
   
    - Function: void mpz_tdiv_q_2exp (mpz_t Q, mpz_t N, unsigned long int
             D)
        Set Q to N divided by 2 raised to D.  The quotient is truncated
        towards 0.
   
    - Function: void mpz_tdiv_r_2exp (mpz_t R, mpz_t N, unsigned long int
             D)
        Divide N by (2 raised to D), rounding the quotient towards 0, and
        put the remainder in R.  Unless it is zero, R will have the same
        sign as N.
   
    - Function: void mpz_fdiv_q_2exp (mpz_t Q, mpz_t N, unsigned long int
             D)
        Set Q to N divided by 2 raised to D, rounded towards -infinity.
        This operation can also be defined as arithmetic right shift D bit
        positions.
   
    - Function: void mpz_fdiv_r_2exp (mpz_t R, mpz_t N, unsigned long int
             D)
        Divide N by (2 raised to D), rounding the quotient towards
        -infinity, and put the remainder in R.  The sign of R will always
        be positive.  This operation can also be defined as masking of the
        D least significant bits.
   
   
 File: gmp.info,  Node: Integer Exponentiation,  Next: Integer Roots,  Prev: Integer Division,  Up: Integer Functions  File: gmp.info,  Node: Integer Exponentiation,  Next: Integer Roots,  Prev: Integer Division,  Up: Integer Functions
   
 Exponentiation Functions  Exponentiation Functions
Line 577  Miscellaneous Functions
Line 740  Miscellaneous Functions
  - Function: double mpq_get_d (mpq_t OP)   - Function: double mpq_get_d (mpq_t OP)
      Convert OP to a double.       Convert OP to a double.
   
  - Function: double mpq_set_d (mpq_t ROP, double D)   - Function: void mpq_set_d (mpq_t ROP, double D)
      Set ROP to the value of d, without rounding.       Set ROP to the value of d, without rounding.
   
    These functions assign between either the numerator or denominator     These functions assign between either the numerator or denominator
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