439 lines
17 KiB
Plaintext
439 lines
17 KiB
Plaintext
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010 William Hart
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******************************************************************************/
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*******************************************************************************
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Memory management
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*******************************************************************************
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fmpz * _fmpz_vec_init(slong len)
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Returns an initialised vector of \code{fmpz}'s of given length.
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void _fmpz_vec_clear(fmpz * vec, slong len)
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Clears the entries of \code{(vec, len)} and frees the space allocated
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for \code{vec}.
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*******************************************************************************
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Randomisation
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*******************************************************************************
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void _fmpz_vec_randtest(fmpz * f, flint_rand_t state,
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slong len, mp_bitcnt_t bits)
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Sets the entries of a vector of the given length to random integers with
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up to the given number of bits per entry.
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void _fmpz_vec_randtest_unsigned(fmpz * f, flint_rand_t state,
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slong len, mp_bitcnt_t bits)
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Sets the entries of a vector of the given length to random unsigned
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integers with up to the given number of bits per entry.
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*******************************************************************************
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Bit sizes and norms
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*******************************************************************************
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slong _fmpz_vec_max_bits(const fmpz * vec, slong len)
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If $b$ is the maximum number of bits of the absolute value of any
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coefficient of \code{vec}, then if any coefficient of \code{vec} is
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negative, $-b$ is returned, else $b$ is returned.
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slong _fmpz_vec_max_bits_ref(const fmpz * vec, slong len)
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If $b$ is the maximum number of bits of the absolute value of any
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coefficient of \code{vec}, then if any coefficient of \code{vec} is
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negative, $-b$ is returned, else $b$ is returned.
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This is a slower reference implementation of \code{_fmpz_vec_max_bits}.
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ulong _fmpz_vec_max_limbs(const fmpz * vec, slong len)
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Returns the maximum number of limbs needed to store the absolute value
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of any entry in \code{(vec, len)}. If all entries are zero, returns
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zero.
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void _fmpz_vec_height(fmpz_t height, const fmpz * vec, slong len)
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Computes the height of \code{(vec, len)}, defined as the largest of the
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absolute values the coefficients. Equivalently, this gives the infinity
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norm of the vector. If \code{len} is zero, the height is $0$.
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slong _fmpz_vec_height_index(const fmpz * vec, slong len)
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Returns the index of an entry of maximum absolute value in the vector.
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The the length must be at least 1.
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*******************************************************************************
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Input and output
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*******************************************************************************
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int _fmpz_vec_fread(FILE * file, fmpz ** vec, slong * len)
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Reads a vector from the stream \code{file} and stores it at
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\code{*vec}. The format is the same as the output format of
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\code{_fmpz_vec_fprint()}, followed by either any character
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or the end of the file.
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The interpretation of the various input arguments depends on whether
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or not \code{*vec} is \code{NULL}:
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If \code{*vec == NULL}, the value of \code{*len} on input is ignored.
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Once the length has been read from \code{file}, \code{*len} is set
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to that value and a vector of this length is allocated at \code{*vec}.
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Finally, \code{*len} coefficients are read from the input stream. In
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case of a file or parsing error, clears the vector and sets \code{*vec}
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and \code{*len} to \code{NULL} and \code{0}, respectively.
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Otherwise, if \code{*vec != NULL}, it is assumed that \code{(*vec, *len)}
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is a properly initialised vector. If the length on the input stream
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does not match \code{*len}, a parsing error is raised. Attempts to read
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the right number of coefficients from the input stream. In case of a
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file or parsing error, leaves the vector \code{(*vec, *len)} in its
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current state.
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In case of success, returns a positive value. In case of failure,
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returns a non-positive value.
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int _fmpz_vec_read(fmpz ** vec, slong * len)
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Reads a vector from \code{stdin} and stores it at \code{*vec}.
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For further details, see \code{_fmpz_vec_fread()}.
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int _fmpz_vec_fprint(FILE * file, const fmpz * vec, slong len)
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Prints the vector of given length to the stream \code{file}. The
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format is the length followed by two spaces, then a space separated
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list of coefficients. If the length is zero, only $0$ is printed.
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In case of success, returns a positive value. In case of failure,
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returns a non-positive value.
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int _fmpz_vec_print(const fmpz * vec, slong len)
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Prints the vector of given length to \code{stdout}.
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For further details, see \code{_fmpz_vec_fprint()}.
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*******************************************************************************
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Conversions
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*******************************************************************************
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void _fmpz_vec_get_nmod_vec(mp_ptr res,
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const fmpz * poly, slong len, nmod_t mod)
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Reduce the coefficients of \code{(poly, len)} modulo the given
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modulus and set \code{(res, len)} to the result.
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void _fmpz_vec_set_nmod_vec(fmpz * res,
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mp_srcptr poly, slong len, nmod_t mod)
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Set the coefficients of \code{(res, len)} to the symmetric modulus
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of the coefficients of \code{(poly, len)}, i.e. convert the given
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coefficients modulo the given modulus $n$ to their signed integer
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representatives in the range $[-n/2, n/2)$.
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slong _fmpz_vec_get_fft(mp_limb_t ** coeffs_f,
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const fmpz * coeffs_m, slong l, slong length)
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Convert the vector of coeffs \code{coeffs_m} to an fft vector
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\code{coeffs_f} of the given \code{length} with \code{l} limbs per
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coefficient with an additional limb for overflow.
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void _fmpz_vec_set_fft(fmpz * coeffs_m, slong length,
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const mp_ptr * coeffs_f, slong limbs, slong sign)
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Convert an fft vector \code{coeffs_f} of the given \code{length}
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to a vector of \code{fmpz}'s. Each is assumed to be the given
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number of limbs in length with an additional limb for overflow. If the
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output coefficients are to be signed then set \code{sign},
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otherwise clear it.
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*******************************************************************************
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Assignment and basic manipulation
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*******************************************************************************
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void _fmpz_vec_set(fmpz * vec1, const fmpz * vec2, slong len2)
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Makes a copy of \code{(vec2, len2)} into \code{vec1}.
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void _fmpz_vec_swap(fmpz * vec1, fmpz * vec2, slong len2)
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Swaps the integers in \code{(vec1, len2)} and \code{(vec2, len2)}.
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void _fmpz_vec_zero(fmpz * vec, slong len)
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Zeros the entries of \code{(vec, len)}.
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void _fmpz_vec_neg(fmpz * vec1, const fmpz * vec2, slong len2)
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Negates \code{(vec2, len2)} and places it into \code{vec1}.
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*******************************************************************************
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Comparison
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*******************************************************************************
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int _fmpz_vec_equal(const fmpz * vec1, const fmpz * vec2, slong len)
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Compares two vectors of the given length and returns $1$ if they are
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equal, otherwise returns $0$.
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int _fmpz_vec_is_zero(const fmpz * vec, slong len)
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Returns $1$ if \code{(vec, len)} is zero, and $0$ otherwise.
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*******************************************************************************
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Sorting
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*******************************************************************************
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void _fmpz_vec_sort(fmpz * vec, slong len)
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Sorts the coefficients of \code{vec} in ascending order.
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*******************************************************************************
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Addition and subtraction
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*******************************************************************************
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void _fmpz_vec_add(fmpz * res, const fmpz * vec1,
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const fmpz * vec2, slong len2)
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Sets \code{(res, len2)} to the sum of \code{(vec1, len2)}
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and \code{(vec2, len2)}.
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void _fmpz_vec_sub(fmpz * res, const fmpz * vec1,
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const fmpz * vec2, slong len2)
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Sets \code{(res, len2)} to \code{(vec1, len2)} minus \code{(vec2, len2)}.
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*******************************************************************************
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Scalar multiplication and division
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*******************************************************************************
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void _fmpz_vec_scalar_mul_fmpz(fmpz * vec1,
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const fmpz * vec2, slong len2, const fmpz_t x)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} multiplied by $c$,
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where $c$ is an \code{fmpz_t}.
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id _fmpz_vec_scalar_mul_si(fmpz * vec1, const fmpz * vec2, slong len2, slong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} multiplied by $c$,
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where $c$ is a \code{slong}.
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void _fmpz_vec_scalar_mul_ui(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} multiplied by $c$,
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where $c$ is an \code{ulong}.
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void _fmpz_vec_scalar_mul_2exp(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong exp)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} multiplied by \code{2^exp}.
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void _fmpz_vec_scalar_divexact_fmpz(fmpz * vec1,
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const fmpz * vec2, slong len2, const fmpz_t x)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $x$, where the
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division is assumed to be exact for every entry in \code{vec2}.
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void _fmpz_vec_scalar_divexact_si(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $x$, where the
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division is assumed to be exact for every entry in \code{vec2}.
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void _fmpz_vec_scalar_divexact_ui(fmpz * vec1,
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const fmpz * vec2, ulong len2, ulong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $x$, where the
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division is assumed to be exact for every entry in \code{vec2}.
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void _fmpz_vec_scalar_fdiv_q_fmpz(fmpz * vec1,
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const fmpz * vec2, slong len2, const fmpz_t c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $c$, rounding
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down towards minus infinity whenever the division is not exact.
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void _fmpz_vec_scalar_fdiv_q_si(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $c$, rounding
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down towards minus infinity whenever the division is not exact.
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void _fmpz_vec_scalar_fdiv_q_ui(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $c$, rounding
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down towards minus infinity whenever the division is not exact.
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void _fmpz_vec_scalar_fdiv_q_2exp(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong exp)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by \code{2^exp},
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rounding down towards minus infinity whenever the division is not exact.
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void _fmpz_vec_scalar_fdiv_r_2exp(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong exp)
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Sets \code{(vec1, len2)} to the remainder of \code{(vec2, len2)}
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divided by \code{2^exp}, rounding down the quotient towards minus
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infinity whenever the division is not exact.
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void _fmpz_vec_scalar_tdiv_q_fmpz(fmpz * vec1,
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const fmpz * vec2, slong len2, const fmpz_t c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $c$, rounding
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towards zero whenever the division is not exact.
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void _fmpz_vec_scalar_tdiv_q_si(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $c$, rounding
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towards zero whenever the division is not exact.
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void _fmpz_vec_scalar_tdiv_q_ui(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong c)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by $c$, rounding
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towards zero whenever the division is not exact.
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void _fmpz_vec_scalar_tdiv_q_2exp(fmpz * vec1,
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const fmpz * vec2, slong len2, ulong exp)
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Sets \code{(vec1, len2)} to \code{(vec2, len2)} divided by \code{2^exp},
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rounding down towards zero whenever the division is not exact.
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void _fmpz_vec_scalar_addmul_fmpz(fmpz * vec1,
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const fmpz * vec2, slong len2, const fmpz_t c)
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Adds \code{(vec2, len2)} times $c$ to \code{(vec1, len2)}, where $c$ is a
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\code{fmpz_t}.
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void _fmpz_vec_scalar_addmul_si(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c)
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Adds \code{(vec2, len2)} times $c$ to \code{(vec1, len2)}, where $c$ is a
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\code{slong}.
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void _fmpz_vec_scalar_addmul_si_2exp(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c, ulong exp)
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Adds \code{(vec2, len2)} times \code{c * 2^exp} to \code{(vec1, len2)},
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where $c$ is a \code{slong}.
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void _fmpz_vec_scalar_submul_fmpz(fmpz * vec1,
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const fmpz * vec2, slong len2, const fmpz_t x)
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Subtracts \code{(vec2, len2)} times $c$ from \code{(vec1, len2)},
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where $c$ is a \code{fmpz_t}.
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void _fmpz_vec_scalar_submul_si(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c)
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Subtracts \code{(vec2, len2)} times $c$ from \code{(vec1, len2)},
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where $c$ is a \code{slong}.
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void _fmpz_vec_scalar_submul_si_2exp(fmpz * vec1,
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const fmpz * vec2, slong len2, slong c, ulong e)
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Subtracts \code{(vec2, len2)} times $c \times 2^e$
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from \code{(vec1, len2)}, where $c$ is a \code{slong}.
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*******************************************************************************
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Sums and products
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*******************************************************************************
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void _fmpz_vec_sum(fmpz_t res, const fmpz * vec, slong len)
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Sets \code{res} to the sum of the entries in \code{(vec, len)}.
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Aliasing of \code{res} with the entries in \code{vec} is not permitted.
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void _fmpz_vec_prod(fmpz_t res, const fmpz * vec, slong len)
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Sets \code{res} to the product of the entries in \code{(vec, len)}.
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Aliasing of \code{res} with the entries in \code{vec} is not permitted.
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Uses binary splitting.
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*******************************************************************************
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Reduction mod $p$
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*******************************************************************************
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void _fmpz_vec_scalar_mod_fmpz(fmpz *res,
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const fmpz *vec, slong len, const fmpz_t p)
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Reduces all entries in \code{(vec, len)} modulo $p > 0$.
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void _fmpz_vec_scalar_smod_fmpz(fmpz *res,
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const fmpz *vec, slong len, const fmpz_t p)
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Reduces all entries in \code{(vec, len)} modulo $p > 0$, choosing
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the unique representative in $(-p/2, p/2]$.
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*******************************************************************************
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Gaussian content
|
||
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*******************************************************************************
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void _fmpz_vec_content(fmpz_t res, const fmpz * vec, slong len)
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Sets \code{res} to the non-negative content of the entries in \code{vec}.
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The content of a zero vector, including the case when the length is zero,
|
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is defined to be zero.
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void _fmpz_vec_lcm(fmpz_t res, const fmpz * vec, slong len)
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Sets \code{res} to the nonnegative least common multiple of the entries
|
||
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in \code{vec}. The least common multiple is zero if any entry in
|
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the vector is zero. The least common multiple of a length zero vector is
|
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|
|
defined to be one.
|
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