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(*******************************************************************
*
* TTCalc.Pas 1.2
*
* Arithmetic and Vectorial Computations (specification)
*
* Copyright 1996 David Turner, Robert Wilhelm and Werner Lemberg
*
* This file is part of the FreeType project, and may only be used
* modified and distributed under the terms of the FreeType project
* license, LICENSE.TXT. By continuing to use, modify or distribute
* this file you indicate that you have read the license and
* understand and accept it fully.
*
* NOTES : All vector operations were moved to the interpreter
*
******************************************************************)
unit TTCalc;
interface
{$I TTCONFIG.INC}
type
(* IntN types : *)
(* *)
(* These types are used as a way to guarantee the size of some *)
(* specific integers. *)
(* *)
(* Of course, they are equivalent to Short, UShort, Long, etc .. *)
(* but parts of this unit could be used by different programs. *)
(* *)
(* Define the 16-bit type *)
{$IFDEF BORLANDPASCAL}
Int16 = Integer;
Word16 = Word; (* 16-bits unsigned *)
{$ENDIF}
{$IFDEF DELPHI16}
Int16 = Integer;
Word16 = Word; (* 16-bits unsigned *)
{$ENDIF}
{$IFDEF DELPHI32}
Int16 = SmallInt;
Word16 = Word; (* 16-bits unsigned *)
{$ENDIF}
{$IFDEF FPC}
Int16 = SmallInt;
Word16 = Word; (* 16-bits unsigned *)
{$ENDIF}
Int32 = Longint; (* 32 bits integer *)
Word32 = Cardinal; (* 32 bits 'unsigned'. Note that there's *)
(* no unsigned long in Pascal.. *)
(* As cardinals are only 31 bits !! *)
// No need to define our own type, just use the build-in one
{ Int64 = record (* 64 "" *)
Lo,
Hi : LongInt;
end;}
function MulDiv( A, B, C : Int32 ): Int32;
function MulDiv_Round( A, B, C : Int32 ): Int32;
procedure MulTo64( X, Y : Int32; out Z : Int64 );
function Div64by32( X : Int64; Y : Int32 ) : Int32;
function Order64( Z : Int64 ) : integer;
function Order32( Z : Int32 ) : integer;
function Sqrt32( L : Int32 ): LongInt;
function Sqrt64( L : Int64 ): LongInt;
{$IFDEF TEST}
procedure Neg64( var x : Int64 );
procedure DivMod64by32( X : Int64; Y : Int32; out Q, R : Int32 );
{$ENDIF}
implementation
(* add support for Virtual Pascal inline assembly *)
{$IFDEF VIRTUALPASCAL}
{$I TTCALC2.INC}
{$ENDIF}
(* add support for Delphi 2 and 3 inline assembly *)
{$IFDEF DELPHI32}
{$I TTCALC3.INC}
{$ENDIF}
(* add support for Borland Pascal and Turbo Pascal inline assembly *)
{$IFDEF BORLANDPASCAL}
{$I TTCALC1.INC}
{$ENDIF}
(* Delphi 16 uses the same inline assembly than Borland Pascal *)
{$IFDEF DELPHI16}
{$I TTCALC1.INC}
{$ENDIF}
(* add support for Free Pascal inline assembly *)
{$IFDEF FPC}
{$I TTCALC4.INC}
{$ENDIF}
(*****************************************************************)
(* *)
(* MulDiv : computes A*B/C with an intermediate 64 bits *)
(* precision. *)
(* *)
(*****************************************************************)
function MulDiv( a, b, c : Int32 ) : Int32; {$IFDEF INLINE} inline; {$ENDIF}
begin
{$ifdef CPUI386}
{$asmmode intel}
asm
mov eax, a
imul b
idiv c
mov result, eax
end;
{$else}
MulDiv := int64(a)*int64(b) div c;
{$endif}
end;
(*****************************************************************)
(* *)
(* MulDiv : computes A*B/C with an intermediate 64 bits *)
(* _Round precision and rounding. *)
(* *)
(*****************************************************************)
function MulDiv_Round( a, b, c : Int32 ) : Int32;
var
temp: Int64;
begin
temp := int64(a)*int64(b);
if temp >= 0 then temp += c shr 1
else temp -= c shr 1;
result := temp div c;
end;
(**********************************************************)
(* MSB index ( return -1 for 0 ) *)
function Order64( Z : Int64 ) : integer;
var b : integer;
begin
b := 0;
while Z <> 0 do begin Z := Z shr 1; inc( b ); end;
Result := b-1;
end;
(**********************************************************)
(* MSB index ( return -1 for 0 ) *)
function Order32( Z : Int32 ) : integer;
var b : integer;
begin
b := 0;
while Z <> 0 do begin Z := Z shr 1; inc( b ); end;
Order32 := b-1;
end;
const
Roots : array[0..62] of LongInt
= (
1, 1, 2, 3, 4, 5, 8, 11,
16, 22, 32, 45, 64, 90, 128, 181,
256, 362, 512, 724, 1024, 1448, 2048, 2896,
4096, 5892, 8192, 11585, 16384, 23170, 32768, 46340,
65536, 92681, 131072, 185363, 262144, 370727,
524288, 741455, 1048576, 1482910, 2097152, 2965820,
4194304, 5931641, 8388608, 11863283, 16777216, 23726566,
33554432, 47453132, 67108864, 94906265,
134217728, 189812531, 268435456, 379625062,
536870912, 759250125, 1073741824, 1518500250,
2147483647
);
(**************************************************)
(* Integer Square Root *)
function Sqrt32( L : Int32 ): LongInt;
var
R, S : LongInt;
begin
if L<=0 then result:=0 else
if L=1 then result:=1 else
begin
R:=Roots[ Order32(L) ];
Repeat
S:=R;
R:=( R+ L div R ) shr 1;
until ( R <= S ) and ( R*R <= L );
result:=R;
end;
end;
(**************************************************)
(* Integer Square Root *)
function Sqrt64( L : Int64 ): LongInt;
begin
Result := Round(sqrt(L));
end;
{var
L2 : Int64;
R, S : LongInt;
begin
if L.Hi < 0 then Sqrt64:=0 else
begin
S := Order64(L);
if S = 0 then Sqrt64:=1 else
begin
R := Roots[S];
Repeat
S := R;
R := ( R+Div64by32(L,R) ) shr 1;
if ( R > S ) then continue;
MulTo64( R, R, L2 );
Sub64 ( L, L2, L2 );
until ( L2.Hi >= 0 );
Sqrt64 := R;
end
end
end;}
end.
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