/* pgmp -- Module installation SQL script
 *
 * Copyright (C) 2011-2020 Daniele Varrazzo
 *
 * This file is part of the PostgreSQL GMP Module
 *
 * The PostgreSQL GMP Module is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License as
 * published by the Free Software Foundation; either version 3 of the License,
 * or (at your option) any later version.
 *
 * The PostgreSQL GMP Module is distributed in the hope that it will be
 * useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser
 * General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with the PostgreSQL GMP Module.  If not, see
 * https://www.gnu.org/licenses/.
 */

!# This file is made of a mix of Python code and SQL statements.
!# Use the script ``tools/unmix.py`` to convert it into plain SQL.

!! PYON

base_type = 'mpz'

def func(sqlname, argin, argout=None, cname=None, volatile=False, strict=True):
    """Create a SQL function from a C function"""
    if not argout: argout = base_type
    print("CREATE OR REPLACE FUNCTION %s(%s)" \
        % (sqlname, ", ".join(argin.split())))
    print("RETURNS", argout)
    if not cname:
        pre = base_type + '_'
        cname = (sqlname.startswith(pre)
            and "p" + sqlname or 'p' + pre + sqlname)
    # not using MODULE_PATHNAME to make the resulting sql file
    # compatible with both PG pre-9.1 and 9.1
    print("AS '$libdir/pgmp', '%s'" % cname)
    print("LANGUAGE C", end=' ')
    print(volatile and "VOLATILE" or "IMMUTABLE", end=' ')
    print( strict and "STRICT" or "", end=' ')
    print(";")
    print()

def func_tuple(sqlname, args, argout=None, cname=None):
    """Create a SQL function returning many arguments from a C function"""
    if not argout: argout = base_type
    print("CREATE OR REPLACE FUNCTION %s(%s)" \
        % (sqlname, args))
    print("RETURNS RECORD")
    if not cname:
        pre = base_type + '_'
        cname = (sqlname.startswith(pre)
            and "p" + sqlname or 'p' + pre + sqlname)
    print("AS '$libdir/pgmp', '%s'" % cname)
    print("LANGUAGE C IMMUTABLE STRICT;")
    print()


func('gmp_version', '', 'int4', cname='pgmp_gmp_version')

!! PYOFF

--
-- mpz user-defined type
--

!! PYON

func('mpz_in', 'cstring', 'mpz')
func('mpz_out', 'mpz', 'cstring')

!! PYOFF

CREATE TYPE mpz (
      INPUT = mpz_in
    , OUTPUT = mpz_out
    , INTERNALLENGTH = VARIABLE
    , STORAGE = EXTENDED
    , CATEGORY = 'N'
);


-- Other I/O functions

!! PYON

func('mpz', 'text int4', 'mpz', cname='pmpz_in_base')
func('text', 'mpz int4', 'cstring', cname='pmpz_out_base')

!! PYOFF


--
-- mpz cast
--

!! PYON

import re

def castfrom(typname, implicit=False):
    """Create a cast from a different type to `base_type`"""
    func(base_type, typname, cname="p%s_from_%s" % (base_type, typname))

    print("CREATE CAST (%s AS %s)" % (typname, base_type))
    print("WITH FUNCTION %s(%s)" % (base_type, typname))
    print({'I': "AS IMPLICIT;", 'A': "AS ASSIGNMENT;", False: ';'}[implicit])
    print()
    print()

castfrom('int2', implicit='I')
castfrom('int4', implicit='I')
castfrom('int8', implicit='I')
castfrom('float4', implicit='A')
castfrom('float8', implicit='A')
castfrom('numeric', implicit='A')

def castto(typname, implicit=False):
    """Create a cast from `base_type` to a different type"""
    func(typname, base_type, typname, cname="p%s_to_%s" % (base_type, typname))

    print("CREATE CAST (%s AS %s)" % (base_type, typname))
    print("WITH FUNCTION %s(%s)" % (typname, base_type))
    print({'I': "AS IMPLICIT;", 'A': "AS ASSIGNMENT;", False: ';'}[implicit])
    print()
    print()

castto('int8', implicit='A')
castto('int4', implicit='A')
castto('int2', implicit='A')
castto('float4', implicit='A')
castto('float8', implicit='A')

!! PYOFF

CREATE CAST (mpz AS numeric) WITH INOUT AS ASSIGNMENT;


--
-- mpz operators
--

!! PYON

func('mpz_uplus', 'mpz')
func('mpz_neg', 'mpz')
func('abs', 'mpz')
func('sgn', 'mpz', 'int4')
func('even', 'mpz', 'bool')
func('odd', 'mpz', 'bool')

!! PYOFF

CREATE OPERATOR - (
    RIGHTARG = mpz,
    PROCEDURE = mpz_neg
);

CREATE OPERATOR + (
    RIGHTARG = mpz,
    PROCEDURE = mpz_uplus
);


!! PYON

def op(sym, fname, rarg=None, comm=None):
    """Create an operator on `base_type`"""
    if rarg == None: rarg = base_type
    func('%s_%s' % (base_type, fname), base_type + " " + rarg)

    print("CREATE OPERATOR %s (" % sym)
    print("    LEFTARG = %s," % base_type)
    print("    RIGHTARG = %s," % rarg)
    if comm: print("    COMMUTATOR = %s," % comm)
    print("    PROCEDURE = %s_%s" % (base_type, fname))
    print(");")
    print()
    print()

op('+', 'add', comm='+')
op('-', 'sub')
op('*', 'mul', comm='*')
op('/', 'tdiv_q')
op('%', 'tdiv_r')
op('+/', 'cdiv_q')
op('+%', 'cdiv_r')
op('-/', 'fdiv_q')
op('-%', 'fdiv_r')
op('/!', 'divexact')
op('<<', 'mul_2exp', rarg='int8')
op('>>', 'tdiv_q_2exp', rarg='int8')
op('%>', 'tdiv_r_2exp', rarg='int8')
op('+>>', 'cdiv_q_2exp', rarg='int8')
op('+%>', 'cdiv_r_2exp', rarg='int8')
op('->>', 'fdiv_q_2exp', rarg='int8')
op('-%>', 'fdiv_r_2exp', rarg='int8')

func_tuple('tdiv_qr', 'mpz, mpz, out q mpz, out r mpz')
func_tuple('cdiv_qr', 'mpz, mpz, out q mpz, out r mpz')
func_tuple('fdiv_qr', 'mpz, mpz, out q mpz, out r mpz')

func('divisible', 'mpz mpz', 'bool')
func('divisible_2exp', 'mpz int8', 'bool')
func('congruent', 'mpz mpz mpz', 'bool')
func('congruent_2exp', 'mpz mpz int8', 'bool')

func('pow', 'mpz int8', cname='pmpz_pow_ui')
func('powm', 'mpz mpz mpz')

op('&', 'and')
op('|', 'ior')
op('#', 'xor')

func('com', 'mpz', 'mpz')
func('popcount', 'mpz', 'mpz')
func('hamdist', 'mpz mpz', 'mpz')
func('scan0', 'mpz mpz', 'mpz')
func('scan1', 'mpz mpz', 'mpz')
func('setbit', 'mpz mpz', 'mpz')
func('clrbit', 'mpz mpz', 'mpz')
func('combit', 'mpz mpz', 'mpz')
func('tstbit', 'mpz mpz', 'int4')
func('gmp_max_bitcnt', '', 'mpz', cname='pgmp_max_bitcnt')

!! PYOFF

CREATE OPERATOR /? (
    LEFTARG = mpz,
    RIGHTARG = mpz,
    PROCEDURE = divisible
);

CREATE OPERATOR >>? (
    LEFTARG = mpz,
    RIGHTARG = int8,
    PROCEDURE = divisible_2exp
);

CREATE OPERATOR ^ (
    LEFTARG = mpz,
    RIGHTARG = int8,
    PROCEDURE = pow
);


--
-- mpz comparisons
--

CREATE OR REPLACE FUNCTION mpz_eq(mpz, mpz)
RETURNS boolean
AS '$libdir/pgmp', 'pmpz_eq'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR = (
    LEFTARG = mpz
    , RIGHTARG = mpz
    , PROCEDURE = mpz_eq
    , COMMUTATOR = =
    , NEGATOR = <>
    , RESTRICT = eqsel
    , JOIN = eqjoinsel
    , HASHES
    , MERGES
);

CREATE OR REPLACE FUNCTION mpz_ne(mpz, mpz)
RETURNS boolean
AS '$libdir/pgmp', 'pmpz_ne'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR <> (
    LEFTARG = mpz
    , RIGHTARG = mpz
    , PROCEDURE = mpz_ne
    , COMMUTATOR = <>
    , NEGATOR = =
    , RESTRICT = neqsel
    , JOIN = neqjoinsel
);

!! PYON

def bop(sym, fname, comm, neg):
    """Create an operator on `base_type` returning a bool"""
    func('%s_%s' % (base_type, fname), 
        base_type + " " + base_type, argout='boolean')
    fname1 = fname[0] + 't'

    print("CREATE OPERATOR %s (" % sym)
    print("    LEFTARG =", base_type)
    print("    , RIGHTARG =", base_type)
    print("    , PROCEDURE = %s_%s" % (base_type, fname))
    print("    , COMMUTATOR = %s" % comm)
    print("    , NEGATOR = %s" % neg)
    print("    , RESTRICT = scalar%ssel" % fname1)
    print("    , JOIN = scalar%sjoinsel" % fname1)
    print(");")
    print()
    print()

bop('>', 'gt', comm='<', neg='<=')
bop('>=', 'ge', comm='<=', neg='<')
bop('<', 'lt', comm='>', neg='>=')
bop('<=', 'le', comm='>=', neg='>')

!! PYOFF


--
-- mpz indexes
--

CREATE OR REPLACE FUNCTION mpz_cmp(mpz, mpz)
RETURNS integer
AS '$libdir/pgmp', 'pmpz_cmp'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR CLASS mpz_ops
DEFAULT FOR TYPE mpz USING btree AS
    OPERATOR    1   <   ,
    OPERATOR    2   <=  ,
    OPERATOR    3   =   ,
    OPERATOR    4   >=  ,
    OPERATOR    5   >   ,
    FUNCTION    1   mpz_cmp(mpz, mpz)
    ;

CREATE OR REPLACE FUNCTION mpz_hash(mpz)
RETURNS integer
AS '$libdir/pgmp', 'pmpz_hash'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR CLASS mpz_ops
DEFAULT FOR TYPE mpz USING hash AS
    OPERATOR    1   =   ,
    FUNCTION    1   mpz_hash(mpz)
    ;

-- TODO: OPERATOR FAMILY?

-- mpz functions

!! PYON

func('sqrt', 'mpz', 'mpz')
func('root', 'mpz int8', 'mpz')
func('perfect_power', 'mpz', 'bool', cname='pmpz_perfect_power')
func('perfect_square', 'mpz', 'bool', cname='pmpz_perfect_square')

func_tuple('rootrem', 'mpz, int8, out root mpz, out rem mpz')
func_tuple('sqrtrem', 'mpz, out root mpz, out rem mpz')

!! PYOFF


--
-- Number Theoretic Functions
--

!! PYON

func('probab_prime', 'mpz int4', 'int4', cname='pmpz_probab_prime_p')
func('nextprime', 'mpz')
func('gcd', 'mpz mpz', 'mpz')
func('lcm', 'mpz mpz', 'mpz')
func('invert', 'mpz mpz', 'mpz')
func('jacobi', 'mpz mpz', 'int4')
func('legendre', 'mpz mpz', 'int4')
func('kronecker', 'mpz mpz', 'int4')
func('remove', 'mpz mpz', 'mpz')
func('fac', 'int8', 'mpz', cname='pmpz_fac_ui')
func('bin', 'mpz int8', 'mpz', cname='pmpz_bin_ui')
func('fib', 'int8', 'mpz', cname='pmpz_fib_ui')
func('lucnum', 'int8', 'mpz', cname='pmpz_lucnum_ui')

func_tuple('gcdext', 'mpz, mpz, out g mpz, out s mpz, out t mpz')
func_tuple('fib2', 'int8, out fn mpz, out fnsub1 mpz', cname='pmpz_fib2_ui')
func_tuple('lucnum2', 'int8, out ln mpz, out lnsub1 mpz', cname='pmpz_lucnum2_ui')

!! PYOFF


--
-- Random numbers
--

!! PYON

func('randinit', '', 'void', cname='pgmp_randinit_default', volatile=True)
func('randinit_mt', '', 'void', cname='pgmp_randinit_mt', volatile=True)
func('randinit_lc_2exp', 'mpz int8 int8', 'void',
    cname='pgmp_randinit_lc_2exp', volatile=True)
func('randinit_lc_2exp_size', 'int8', 'void',
    cname='pgmp_randinit_lc_2exp_size', volatile=True)
func('randseed', 'mpz', 'void', cname='pgmp_randseed', volatile=True)
func('urandomb', 'int8', 'mpz', volatile=True)
func('urandomm', 'mpz', 'mpz', volatile=True)
func('rrandomb', 'int8', 'mpz', volatile=True)

!! PYOFF


--
-- Aggregation functions
--

!! PYON

def agg(sqlname, argin, sfunc, argout=None, ffunc=None, sortop=None):
    assert sfunc.startswith('_' + base_type)
    cname = '_p' + sfunc[1:]
    func(sfunc, 'internal ' + argin, 'internal', cname=cname, strict=False)
    if not argout: argout = base_type
    print("CREATE AGGREGATE %s(%s)\n(" \
        % (sqlname, ", ".join(argin.split())))
    print("      SFUNC =", sfunc)
    print("    , STYPE = internal")
    print("    , FINALFUNC =", ffunc or "_%s_from_agg" % base_type)
    if sortop: print("    , SORTOP =", sortop)
    print(");")
    print()

func('_mpz_from_agg', 'internal', 'mpz', cname='_pmpz_from_agg')
agg('sum', 'mpz', '_mpz_agg_add')
agg('prod', 'mpz', '_mpz_agg_mul')
agg('max', 'mpz', '_mpz_agg_max', sortop='>')
agg('min', 'mpz', '_mpz_agg_min', sortop='<')
agg('bit_and', 'mpz', '_mpz_agg_and')
agg('bit_or', 'mpz', '_mpz_agg_ior')
agg('bit_xor', 'mpz', '_mpz_agg_xor')

!! PYOFF


--
-- mpq user-defined type
--

!! PYON

base_type = 'mpq'

func('mpq_in', 'cstring', 'mpq')
func('mpq_out', 'mpq', 'cstring')

!! PYOFF

CREATE TYPE mpq (
      INPUT = mpq_in
    , OUTPUT = mpq_out
    , INTERNALLENGTH = VARIABLE
    , STORAGE = EXTENDED
    , CATEGORY = 'N'
);

!! PYON

func('mpq', 'text int4', 'mpq', cname='pmpq_in_base')
func('text', 'mpq int4', 'cstring', cname='pmpq_out_base')


func('mpq', 'mpz mpz', 'mpq', cname='pmpq_mpz_mpz')
# Currently not exposing these versions as they have surprising limits
# E.g. calling mpq(n, d) with two numeric literal of which one fits
# into an int and one doesn't fails to find a best candidate.
# So we currently only accept mpq(n, d) if both fit into a type smaller
# than numeric (because of the implicit casts int? -> mpz) and require
# explicit mpz for bigger numbers.
# func('mpq', 'int4 int4', 'mpq', cname='pmpq_int4_int4')
# func('mpq', 'numeric numeric', 'mpq', cname='pmpq_numeric_numeric')
func('num', 'mpq', 'mpz')
func('den', 'mpq', 'mpz')

castfrom('int2', implicit='I')
castfrom('int4', implicit='I')
castfrom('int8', implicit='I')
castfrom('float4', implicit='I')
castfrom('float8', implicit='I')
castfrom('numeric', implicit='I')
castfrom('mpz', implicit='I')

castto('int2', implicit='A')
castto('int4', implicit='A')
castto('int8', implicit='A')
castto('float4', implicit='A')
castto('float8', implicit='A')
castto('mpz', implicit='A')

!! PYOFF

CREATE OR REPLACE FUNCTION mpq_to_numeric(mpq, int4)
RETURNS numeric
AS '$libdir/pgmp', 'pmpq_to_numeric'
LANGUAGE C IMMUTABLE STRICT ;

CREATE CAST (mpq AS numeric)
WITH FUNCTION mpq_to_numeric(mpq, int4)
AS ASSIGNMENT;


--
-- mpq operators
--

!! PYON

func('mpq_uplus', 'mpq')
func('mpq_neg', 'mpq')
func('abs', 'mpq')
func('inv', 'mpq')

!! PYOFF

CREATE OPERATOR - (
    RIGHTARG = mpq,
    PROCEDURE = mpq_neg
);

CREATE OPERATOR + (
    RIGHTARG = mpq,
    PROCEDURE = mpq_uplus
);


!! PYON

op('+', 'add', comm='+')
op('-', 'sub')
op('*', 'mul', comm='*')
op('/', 'div')
op('<<', 'mul_2exp', rarg='int8')
op('>>', 'div_2exp', rarg='int8')

func('limit_den', 'mpq')
func('limit_den', 'mpq mpz')

!! PYOFF


--
-- mpq comparisons
--

CREATE OR REPLACE FUNCTION mpq_eq(mpq, mpq)
RETURNS boolean
AS '$libdir/pgmp', 'pmpq_eq'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR = (
    LEFTARG = mpq
    , RIGHTARG = mpq
    , PROCEDURE = mpq_eq
    , COMMUTATOR = =
    , NEGATOR = <>
    , RESTRICT = eqsel
    , JOIN = eqjoinsel
    , HASHES
    , MERGES
);

CREATE OR REPLACE FUNCTION mpq_ne(mpq, mpq)
RETURNS boolean
AS '$libdir/pgmp', 'pmpq_ne'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR <> (
    LEFTARG = mpq
    , RIGHTARG = mpq
    , PROCEDURE = mpq_ne
    , COMMUTATOR = <>
    , NEGATOR = =
    , RESTRICT = neqsel
    , JOIN = neqjoinsel
);

!! PYON

bop('>', 'gt', comm='<', neg='<=')
bop('>=', 'ge', comm='<=', neg='<')
bop('<', 'lt', comm='>', neg='>=')
bop('<=', 'le', comm='>=', neg='>')

!! PYOFF


--
-- mpq indexes
--

CREATE OR REPLACE FUNCTION mpq_cmp(mpq, mpq)
RETURNS integer
AS '$libdir/pgmp', 'pmpq_cmp'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR CLASS mpq_ops
DEFAULT FOR TYPE mpq USING btree AS
    OPERATOR    1   <   ,
    OPERATOR    2   <=  ,
    OPERATOR    3   =   ,
    OPERATOR    4   >=  ,
    OPERATOR    5   >   ,
    FUNCTION    1   mpq_cmp(mpq, mpq)
    ;


CREATE OR REPLACE FUNCTION mpq_hash(mpq)
RETURNS integer
AS '$libdir/pgmp', 'pmpq_hash'
LANGUAGE C IMMUTABLE STRICT;

CREATE OPERATOR CLASS mpq_ops
DEFAULT FOR TYPE mpq USING hash AS
    OPERATOR    1   =   ,
    FUNCTION    1   mpq_hash(mpq)
    ;

-- TODO: OPERATOR FAMILY?


--
-- Aggregation functions
--

!! PYON

func('_mpq_from_agg', 'internal', 'mpq', cname='_pmpq_from_agg')
agg('sum', 'mpq', '_mpq_agg_add')
agg('prod', 'mpq', '_mpq_agg_mul')
agg('max', 'mpq', '_mpq_agg_max', sortop='>')
agg('min', 'mpq', '_mpq_agg_min', sortop='<')

!! PYOFF