Removed MIT licensed Mathpaqs packages in favour of bindings to GMP

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-------------------------------------------------------------------------------

---  File:            multi_precision_integers.ads

---

---  Description:     Multiple precision integers package

---

---  Date/version:       Aug-2007: - No more generics (Long_Block_type,

---                                  Block_type,... always the largest possible

---                                  idea: J.C.)

---                                - Fixed Basic(...) (based on J.C.'s remarks)

---                      Nov-2006: - unsigned types for blocks

---                                - a block uses 2 bits more

---                                - Ada95+ only

---                      Mar-2002: Bugs fixed related to zero field, division

---                      Nov-1999: - procedures (no stack, less copies !)

---                                - new data structure

---                      Dec-1996: First version (operators only)

---

---  Author:          G. de Montmollin, Univ. Neuchatel

---

---  Thanks to:       Duncan Sands, Univ. Paris-Sud, CNRS

---                   Jeffrey R. Carter

---

---  Tested on:       Intel 586 (32 bit) - Windows 98, NT4+ - GNAT 3.13p+

---                   Intel 586 (32 bit) - Windows 98, NT4+ - ObjectAda 7.2.1+

---                   Alpha-AXP (64 bit) - OpenVMS 7.1      - Compaq Ada

---

---  Division algorithm adaptated from BigInt 1.0 library,

---  by Stephen Adams, that refers to

---  D. E. Knuth, the Art of computer programming

---  volume 2, "Seminumerical Algorithms"

---  section 4.3.1, "Multiple-Precision Arithmetic"

---

-------------------------------------------------------------------------------

-

-

-

-

-------------------------------------------------------------------------------

---

---  Copyright (c) 2007 G. de Montmollin, Univ. Neuchatel

---

---  Permission is hereby granted, free of charge, to any person obtaining a copy

---  of this software and associated documentation files (the "Software"), to deal

---  in the Software without restriction, including without limitation the rights

---  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell

---  copies of the Software, and to permit persons to whom the Software is

---  furnished to do so, subject to the following conditions:

---

---  The above copyright notice and this permission notice shall be included in all

---  copies or substantial portions of the Software.

---

---  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

---  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

---  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

---  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

---  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

---  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

---  SOFTWARE.

---

-------------------------------------------------------------------------------

-

-

-

-

-with System;

-

-package Multi_precision_integers is

-

-  -- Integers for array indexing --

-

-  subtype Index_int is Integer;

-

-  -- THE multi-precision integer type --

-

-  type Multi_int (n: Index_int) is private;

-

-  -- Integer type for small values --

-

-  subtype Basic_int is Integer; -- the "normal" signed integer

-

-  ----------------------------------------------------------------

-  -- Debug mode: checks results of arithmetic operations and    --

-  -- Multi_int variables' integrity.                            --

-  -- CAUTION: Debug = True reduces monstruously the performance --

-  ----------------------------------------------------------------

-

-  Debug : constant Boolean:= False;

-

-  ---------------------------------------------

-  ----- Informations, conversions, filling ----

-  ---------------------------------------------

-

-  -- Convert Basic_int to Multi_int

-  function Multi (small: Basic_int) return Multi_int;

-

-  -- Convert Multi_int to Basic_int (when possible, else: Cannot_fit raised)

-  function Basic (large: Multi_int) return Basic_int;

-

-  -- Fill an Multi_int of greater array dimension with a smaller one

-  procedure Fill (what: out Multi_int; with_smaller: Multi_int);

-  procedure Fill (what: out Multi_int; with_basic: Basic_int);

-

-  -- Comparisons

-  function Equal (i1, i2: Multi_int) return Boolean;

-  function Equal (i1 : Multi_int; i2:Basic_int) return Boolean;

-  function ">" (i1, i2: Multi_int) return Boolean;

-  function ">" (i1 : Multi_int; i2:Basic_int) return Boolean;

-  function "<" (i1, i2: Multi_int) return Boolean;

-  function "<" (i1 : Multi_int; i2:Basic_int) return Boolean;

-  function ">=" (i1, i2: Multi_int) return Boolean;

-  function ">=" (i1 : Multi_int; i2:Basic_int) return Boolean;

-  function "<=" (i1, i2: Multi_int) return Boolean;

-  function "<=" (i1 : Multi_int; i2:Basic_int) return Boolean;

-

-  -- Other informations

-  function Bits_per_block return Positive;

-

-  ---------------------------------------------------------------------------

-  -------- Arithmetic operators.                                   ----------

-  -------- For speed, the "procedure" variants should be preferred ----------

-  ---------------------------------------------------------------------------

-

-  ---------------------------

-  ----- Unary operators -----

-  ---------------------------

-

-  procedure Opp (i: in out Multi_int);

-  function "+" (i : Multi_int) return Multi_int;

-  function "-" (i : Multi_int) return Multi_int;

-

-  procedure Abso (i: in out Multi_int);

-  function "ABS" (i : Multi_int) return Multi_int;

-

-  function Sign (i: Multi_int) return Basic_int;

-  function Even (i: Multi_int) return Boolean;

-  function Odd (i : Multi_int) return Boolean;

-

-  ----------------------------

-  ----- Binary operators -----

-  ----------------------------

-

-  ---------------------------

-  -- Addition, subtraction --

-  ---------------------------

-

-  procedure Add (i1,i2: in Multi_int; i3: in out Multi_int);

-

-  function "+" (i1, i2: Multi_int) return Multi_int;

-  function "+" (i1 : Multi_int; i2: Basic_int) return Multi_int;

-  function "+" (i1 : Basic_int; i2: Multi_int) return Multi_int;

-

-  procedure Sub      (i1, i2: in Multi_int; i3: in out Multi_int);

-  procedure Subtract (i1,i2: in Multi_int; i3: in out Multi_int)

-    renames Sub;

-

-  function "-" (i1, i2: Multi_int) return Multi_int;

-  function "-" (i1 : Multi_int; i2: Basic_int) return Multi_int;

-  function "-" (i1 : Basic_int; i2: Multi_int) return Multi_int;

-

-  --------------------

-  -- Multiplication --

-  --------------------

-

-  procedure Multiply (i1,i2: in Multi_int; i3: in out Multi_int);

-  procedure Mult     (i1, i2: in Multi_int; i3: in out Multi_int)

-    renames Multiply;

-

-  procedure Multiply (i1: in Multi_int; i2: Basic_int; i3: in out Multi_int);

-  procedure Mult     (i1 : in Multi_int; i2: Basic_int; i3: in out Multi_int)

-    renames Multiply;

-

-  function "*" (i1, i2: Multi_int) return Multi_int;

-  function "*" (i1 : Multi_int; i2: Basic_int) return Multi_int;

-  function "*" (i1 : Basic_int; i2: Multi_int) return Multi_int;

-

-  -------------------------

-  -- Division, Remainder --

-  -------------------------

-

-  procedure Div_Rem (i1 : in     Multi_int; i2: in     Basic_int;

-                     q  :    out Multi_int; r :    out Basic_int);

-  procedure Div_Rem (i1, i2: in Multi_int;  q,r:   out Multi_int);

-

-  procedure Divide (i1, i2: in Multi_int; q: out Multi_int);

-

-  function "/" (i1, i2: Multi_int) return Multi_int;

-  function "/" (i1 : Multi_int; i2: Basic_int) return Multi_int;

-  function "Rem" (i1, i2: Multi_int) return Multi_int;

-  function "Rem" (i1 : Multi_int; i2: Basic_int) return Multi_int;

-  function "Rem" (i1 : Multi_int; i2: Basic_int) return Basic_int;

-  function "Mod" (i1, i2: Multi_int) return Multi_int;

-  function "Mod" (i1 : Multi_int; i2: Basic_int) return Multi_int;

-  function "Mod" (i1 : Multi_int; i2: Basic_int) return Basic_int;

-

-  -----------

-  -- Power --

-  -----------

-

-  procedure Power (i : Multi_int; n: Natural; ipn: out Multi_int);

-  function "**" (i : Multi_int; n: Natural) return Multi_int;

-  -- + 26-Mar-2002 :

-  procedure Power (i : Multi_int; n: Multi_int; ipn: out Multi_int;

-                   modulo : Multi_int);

-

-  Cannot_fit, Empty_multi_int : exception;

-

-  Array_too_small : exception;

-

-  Result_undersized,

-  Quotient_undersized,

-  Remainder_undersized : exception;

-

-  Division_by_zero : exception;

-

-  Zero_power_zero, Power_negative : exception;

-  Power_modulo_non_positive : exception;

-

-private

-

-  --> Long_Block_type is used for + and * of blocks.

-  -- It is by design

-  --   a/ the largest possible modular integer, and

-  --   b/ twice the size of Block_type defined below.

-  -- With the double of bits (2n) one can store m**2 + 2m without overflow

-  --   where m = 2**n - 1 is the largest value possible on n bits.

-  type Long_Block_type is mod System.Max_Binary_Modulus;

-

-  --> Same size as Long_Block_type, but signed:

-  type Long_Block_type_signed is

-    range -2**(Long_Block_type'Size-1)..2**(Long_Block_type'Size-1)-1;

-

-  --> Block_type: unsigned integer used to store a chunk of a Multi_int.

-  type Block_type is mod 2 ** (Long_Block_type'Size / 2);

-

-  Block_type_bits: constant:= Block_type'Size;

-

-  cardblock: constant:= 2 ** Block_type_bits;

-  -- Number of possible values

-  maxblock: constant:= Block_type'Last;

-  -- NB: GNAT (2006) optimizes out correctly the Block_type(l and maxblock_long)

-  --     to Block_type(l), the latter form being caught when range checks are on.

-

-  type Block_array is array( Index_int range <> ) of Block_type;

-  -- 2006: was "of Basic_int" for obscure reasons...

-

-  type Multi_int(n: Index_int) is record

-    blk:       Block_array( 0..n ); -- the n blocks with ABSOLUTE value

-    neg:       Boolean;             -- negative flag

-    zero:      Boolean:=True;       -- zero flag (supercedes the other fields)

-    last_used: Index_int;           -- the others blocks are supposed 0

-  end record;

-

-  -- NB the `zero' field supercedes EVERY other information (last_used, neg)

-

-  ----------------------------------------------------------------------------

-  --   Format of type Multi_int.blk: ( i_0, i_1, ..., i_k, *, ..., * )      --

-  --   i_0..i_k are >=0 ; others (*) are treated as 0                       --

-  ----------------------------------------------------------------------------

-

-  -- Some internal procedures use by check:

-

-  procedure Multiply_internal_copy_export(i1,i2: in Multi_int; i3: in out Multi_int);

-

-  procedure Div_Rem_internal_both_export(i1,i2: in Multi_int; q,r: in out Multi_int);

-

-end Multi_precision_integers;