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ffa_ch5_egypt.kv        1 ------------------------------------------------------------------------------
ffa_ch5_egypt.kv        2 ------------------------------------------------------------------------------
ffa_ch5_egypt.kv        3 -- This file is part of 'Finite Field Arithmetic', aka 'FFA'.               --
ffa_ch5_egypt.kv        4 --                                                                          --
ffa_ch5_egypt.kv        5 -- (C) 2017 Stanislav Datskovskiy ( www.loper-os.org )                      --
ffa_ch5_egypt.kv        6 -- http://wot.deedbot.org/17215D118B7239507FAFED98B98228A001ABFFC7.html     --
ffa_ch5_egypt.kv        7 --                                                                          --
ffa_ch5_egypt.kv        8 -- You do not have, nor can you ever acquire the right to use, copy or      --
ffa_ch5_egypt.kv        9 -- distribute this software ; Should you use this software for any purpose, --
ffa_ch5_egypt.kv       10 -- or copy and distribute it to anyone or in any manner, you are breaking   --
ffa_ch5_egypt.kv       11 -- the laws of whatever soi-disant jurisdiction, and you promise to         --
ffa_ch5_egypt.kv       12 -- continue doing so for the indefinite future. In any case, please         --
ffa_ch5_egypt.kv       13 -- always : read and understand any software ; verify any PGP signatures    --
ffa_ch5_egypt.kv       14 -- that you use - for any purpose.                                          --
ffa_ch5_egypt.kv       15 --                                                                          --
ffa_ch5_egypt.kv       16 -- See also http://trilema.com/2015/a-new-software-licensing-paradigm .     --
ffa_ch5_egypt.kv       17 ------------------------------------------------------------------------------
ffa_ch5_egypt.kv       18 ------------------------------------------------------------------------------
ffa_ch5_egypt.kv       19 
ffa_ch5_egypt.kv       20 with Words;    use Words;
ffa_ch5_egypt.kv       21 with W_Pred;   use W_Pred;
ffa_ch5_egypt.kv       22 with FZ_Basic; use FZ_Basic;
ffa_ch5_egypt.kv       23 with FZ_Arith; use FZ_Arith;
ffa_ch5_egypt.kv       24 with FZ_BitOp; use FZ_BitOp;
ffa_ch5_egypt.kv       25 with FZ_Shift; use FZ_Shift;
ffa_ch5_egypt.kv       26 
ffa_ch5_egypt.kv       27 
ffa_ch5_egypt.kv       28 package body FZ_Divis is
ffa_ch5_egypt.kv       29    
ffa_ch5_egypt.kv       30    -- Dividend is divided by Divisor, producing Quotient and Remainder.
ffa_ch5_egypt.kv       31    -- WARNING: NO div0 test here! Caller must test.
ffa_ch5_egypt.kv       32    procedure FZ_IDiv(Dividend  : in  FZ;
ffa_ch5_egypt.kv       33                      Divisor   : in  FZ;
ffa_ch5_egypt.kv       34                      Quotient  : out FZ;
ffa_ch5_egypt.kv       35                      Remainder : out FZ) is
ffa_ch5_egypt.kv       36       
ffa_ch5_egypt.kv       37       -- The working register
ffa_ch5_egypt.kv       38       QR : FZ(1 .. Dividend'Length + Divisor'Length);
ffa_ch5_egypt.kv       39       
ffa_ch5_egypt.kv       40       -- Bottom seg of Z will end up containing the Quotient; top - remainder
ffa_ch5_egypt.kv       41       Q  : FZ renames QR(1                   .. Dividend'Length); -- Quotient
ffa_ch5_egypt.kv       42       R  : FZ renames QR(Dividend'Length + 1 .. QR'Last);          -- Remainder
ffa_ch5_egypt.kv       43       
ffa_ch5_egypt.kv       44       C : WBool := 0; -- Borrow, from comparator
ffa_ch5_egypt.kv       45    begin
ffa_ch5_egypt.kv       46       Q := Dividend; -- Q begins with the Dividend
ffa_ch5_egypt.kv       47       FZ_Clear(R);   -- R begins empty
ffa_ch5_egypt.kv       48       
ffa_ch5_egypt.kv       49       -- For each bit of Dividend:
ffa_ch5_egypt.kv       50       for i in 1 .. FZ_Bitness(Dividend) loop
ffa_ch5_egypt.kv       51          
ffa_ch5_egypt.kv       52          -- Advance QR by 1 bit:
ffa_ch5_egypt.kv       53          FZ_ShiftLeft(QR, QR, 1);
ffa_ch5_egypt.kv       54          
ffa_ch5_egypt.kv       55          -- Subtract Divisor from R; Underflow goes into C
ffa_ch5_egypt.kv       56          FZ_Sub(X => R, Y => Divisor, Difference => R, Underflow => C);
ffa_ch5_egypt.kv       57          
ffa_ch5_egypt.kv       58          -- If C=1, subtraction underflowed, and then Divisor gets added back:
ffa_ch5_egypt.kv       59          FZ_Add_Gated(X => R, Y => Divisor, Gate => C, Sum => R);
ffa_ch5_egypt.kv       60          
ffa_ch5_egypt.kv       61          -- Current result-bit is equal to Not-C, i.e. 1 if Divisor 'went in'
ffa_ch5_egypt.kv       62          FZ_Or_W(Q, W_Not(C));
ffa_ch5_egypt.kv       63          
ffa_ch5_egypt.kv       64       end loop;
ffa_ch5_egypt.kv       65       
ffa_ch5_egypt.kv       66       Quotient  := Q; -- Output the Quotient.
ffa_ch5_egypt.kv       67       Remainder := R; -- Output the Remainder.
ffa_ch5_egypt.kv       68       
ffa_ch5_egypt.kv       69    end FZ_IDiv;
ffa_ch5_egypt.kv       70    pragma Inline_Always(FZ_IDiv);
ffa_ch5_egypt.kv       71    
ffa_ch5_egypt.kv       72    
ffa_ch5_egypt.kv       73    -- Exactly same thing as IDiv, but keep only the Quotient
ffa_ch5_egypt.kv       74    procedure FZ_Div(Dividend  : in  FZ;
ffa_ch5_egypt.kv       75                     Divisor   : in  FZ;
ffa_ch5_egypt.kv       76                     Quotient  : out FZ) is
ffa_ch5_egypt.kv       77       Remainder : FZ(Divisor'Range);
ffa_ch5_egypt.kv       78       pragma Unreferenced(Remainder);
ffa_ch5_egypt.kv       79    begin
ffa_ch5_egypt.kv       80       FZ_IDiv(Dividend, Divisor, Quotient, Remainder);
ffa_ch5_egypt.kv       81    end FZ_Div;
ffa_ch5_egypt.kv       82    pragma Inline_Always(FZ_Div);
ffa_ch5_egypt.kv       83    
ffa_ch5_egypt.kv       84    
ffa_ch5_egypt.kv       85    -- Exactly same thing as IDiv, but keep only the Remainder
ffa_ch5_egypt.kv       86    procedure FZ_Mod(Dividend  : in FZ;
ffa_ch5_egypt.kv       87                     Divisor   : in FZ;
ffa_ch5_egypt.kv       88                     Remainder : out FZ) is
ffa_ch5_egypt.kv       89       Quotient : FZ(Dividend'Range);
ffa_ch5_egypt.kv       90       pragma Unreferenced(Quotient);
ffa_ch5_egypt.kv       91    begin
ffa_ch5_egypt.kv       92       FZ_IDiv(Dividend, Divisor, Quotient, Remainder);
ffa_ch5_egypt.kv       93    end FZ_Mod;
ffa_ch5_egypt.kv       94    pragma Inline_Always(FZ_Mod);
ffa_ch5_egypt.kv       95    
ffa_ch5_egypt.kv       96 end FZ_Divis;