freepascal.compiler/rtl/i386/math.inc

{
    $Id$
    This file is part of the Free Pascal run time library.
    Copyright (c) 1993-98 by the Free Pascal development team

    Implementation of mathamatical Routines (only for real)

    See the file COPYING.FPC, included in this distribution,
    for details about the copyright.

    This program 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.

 **********************************************************************}

{$ASMMODE DIRECT}

{$ifndef DEFAULT_EXTENDED}

{****************************************************************************
                       Real/Double data type routines
 ****************************************************************************}

    function pi : real;

      begin
         asm
            fldpi
            leave
            ret
         end [];
      end;


    function abs(d : real) : real;

      begin
         asm
            fldl 8(%ebp)
            fabs
            leave
            ret $8
         end [];
      end;

    function sqr(d : real) : real;

      begin
         asm
            fldl 8(%ebp)
            fldl 8(%ebp)
            fmulp
            leave
            ret $8
         end [];
      end;

    function sqrt(d : real) : real;

      begin
         asm
            fldl 8(%ebp)
            fsqrtl
            leave
            ret $8
         end [];
      end;

    function arctan(d : real) : real;

      begin
         asm
            fldl 8(%ebp)
            fld1
            fpatan
            leave
            ret $8
         end [];
      end;

    function cos(d : real) : real;

      begin
         asm
            fldl 8(%ebp)
            fcos
            fstsw
            sahf
            jnp .LCOS1
            fstp %st(0)
            fldl .LCOS0
         .LCOS1:
            leave
            ret $8
         .LCOS0:
            .quad       0xffffffffffffffff
         end ['EAX'];
      end;

    function exp(d : real) : real;

      begin
         asm
            // comes from DJ GPP
            fldl        8(%ebp)
            fldl2e
            fmulp
            fstcw      .LCW1
            fstcw      .LCW2
            fwait
            andw        $0xf3ff,.LCW2
            orw $0x0400,.LCW2
            fldcw      .LCW2
            fldl        %st(0)
            frndint
            fldcw      .LCW1
            fxch        %st(1)
            fsub        %st(1),%st
            f2xm1
            fld1
            faddp
            fscale
            fstp        %st(1)
            leave
            ret $8

            // store some help data in the data segment
            .data
    .LCW1:
            .word       0
    .LCW2:
            .word       0
            .text
         end;
      end;

    function frac(d : real) : real;

      begin
         asm
            subl $16,%esp
            fnstcw -4(%ebp)
            fwait
            movw -4(%ebp),%cx
            orw $0x0c3f,%cx
            movw %cx,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldl 8(%ebp)
            frndint
            fldl 8(%ebp)
            fsub %st(1)
            fstp %st(1)
            fclex
            fldcw -4(%ebp)
            leave
            ret $8
         end ['ECX'];
      end;

    function int(d : real) : real;

      begin
         asm
            subl $16,%esp
            fnstcw -4(%ebp)
            fwait
            movw -4(%ebp),%cx
            orw $0x0c3f,%cx
            movw %cx,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldl 8(%ebp)
            frndint
            fclex
            fldcw -4(%ebp)
            leave
            ret $8
         end ['ECX'];
      end;

    function trunc(d : real) : longint;

      begin
         asm
            subl $16,%esp
            fnstcw -4(%ebp)
            fwait
            movw -4(%ebp),%cx
            orw $0x0c3f,%cx
            movw %cx,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldl 8(%ebp)
            fistpl -8(%ebp)
            movl -8(%ebp),%eax
            fldcw -4(%ebp)
            leave
            ret $8
         end ['EAX','ECX'];
      end;

    function round(d : real) : longint;

      begin
         asm
            subl $8,%esp
            fnstcw -4(%ebp)
            fwait
            movw $0x1372,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldl 8(%ebp)
            fistpl -8(%ebp)
            movl -8(%ebp),%eax
            fldcw -4(%ebp)
            leave
            ret $8
         end ['EAX','ECX'];
      end;

    function ln(d : real) : real;

      begin
         asm
            fldln2
            fldl 8(%ebp)
            fyl2x
            leave
            ret $8
         end [];
      end;

    function sin(d : real) : real;

      begin
         asm
            fldl 8(%ebp)
            fsin
            fstsw
            sahf
            jnp .LSIN1
            fstp %st(0)
            fldl .LSIN0
         .LSIN1:
            leave
            ret $8
         .LSIN0:
            .quad       0xffffffffffffffff
         end ['EAX'];
      end;

   function power(bas,expo : real) : real;
     begin
        power:=exp(ln(bas)*expo);
     end;

{$else DEFAULT_EXTENDED}

{****************************************************************************
                       EXTENDED data type routines
 ****************************************************************************}

    function pi : extended;{$ifdef MORECONST}[internconst:in_const_pi];{$endif}

      begin
         asm
            fldpi
            leave
            ret
         end [];
      end;

    function abs(d : extended) : extended;[internconst:in_const_abs];

      begin
         asm
            fldt 8(%ebp)
            fabs
            leave
            ret $10
         end [];
      end;

    function sqr(d : extended) : extended;[internconst:in_const_sqr];

      begin
         asm
            fldt 8(%ebp)
            fldt 8(%ebp)
            fmulp
            leave
            ret $10
         end [];
      end;

    function sqrt(d : extended) : extended;{$ifdef MORECONST}[internconst:in_const_sqrt];{$endif}

      begin
         asm
            fldt 8(%ebp)
            fsqrtl
            leave
            ret $10
         end [];
      end;

    function arctan(d : extended) : extended;{$ifdef MORECONST}[internconst:in_const_arctan];{$endif}

      begin
         asm
            fldt 8(%ebp)
            fld1
            fpatan
            leave
            ret $10
         end [];
      end;

    function cos(d : extended) : extended;{$ifdef MORECONST}[internconst:in_const_cos];{$endif}

      begin
         asm
            fldt 8(%ebp)
            fcos
            fstsw
            sahf
            jnp .LCOS1
            fstp %st(0)
            fldt .LCOS0
         .LCOS1:
            leave
            ret $10
         .LCOS0:
            .long       0xffffffff
            .long       0xffffffff
            .word       0xffff
         end ['EAX'];
      end;

    function exp(d : extended) : extended;{$ifdef MORECONST}[internconst:in_const_exp];{$endif}

      begin
         asm
            // comes from DJ GPP
            fldt        8(%ebp)
            fldl2e
            fmulp
            fstcw      .LCW1
            fstcw      .LCW2
            fwait
            andw        $0xf3ff,.LCW2
            orw $0x0400,.LCW2
            fldcw      .LCW2
            fld         %st(0)
            frndint
            fldcw      .LCW1
            fxch        %st(1)
            fsub        %st(1),%st
            f2xm1
            fld1
            faddp
            fscale
            fstp        %st(1)
            leave
            ret $10

            // store some help data in the data segment
            .data
    .LCW1:
            .word       0
    .LCW2:
            .word       0
            .text
         end;
      end;

    function frac(d : extended) : extended;[internconst:in_const_frac];

      begin
         asm
            subl $16,%esp
            fnstcw -4(%ebp)
            fwait
            movw -4(%ebp),%cx
            orw $0x0c3f,%cx
            movw %cx,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldt 8(%ebp)
            frndint
            fldt 8(%ebp)
            fsub %st(1)
            fstp %st(1)
            fclex
            fldcw -4(%ebp)
            leave
            ret $10
         end ['ECX'];
      end;

    function int(d : extended) : extended;[internconst:in_const_int];

      begin
         asm
            subl $16,%esp
            fnstcw -4(%ebp)
            fwait
            movw -4(%ebp),%cx
            orw $0x0c3f,%cx
            movw %cx,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldt 8(%ebp)
            frndint
            fclex
            fldcw -4(%ebp)
            leave
            ret $10
         end ['ECX'];
      end;

    function trunc(d : extended) : longint;[internconst:in_const_trunc];

      begin
         asm
            subl $16,%esp
            fnstcw -4(%ebp)
            fwait
            movw -4(%ebp),%cx
            orw $0x0c3f,%cx
            movw %cx,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldt 8(%ebp)
            fistpl -8(%ebp)
            movl -8(%ebp),%eax
            fldcw -4(%ebp)
            leave
            ret $10
         end ['EAX','ECX'];
      end;

    function round(d : extended) : longint;[internconst:in_const_round];

      begin
         asm
            subl $8,%esp
            fnstcw -4(%ebp)
            fwait
            movw $0x1372,-8(%ebp)
            fldcw -8(%ebp)
            fwait
            fldt 8(%ebp)
            fistpl -8(%ebp)
            movl -8(%ebp),%eax
            fldcw -4(%ebp)
            leave
            ret $10
         end ['EAX','ECX'];
      end;

    function ln(d : extended) : extended;{$ifdef MORECONST}[internconst:in_const_ln];{$endif}

      begin
         asm
            fldln2
            fldt 8(%ebp)
            fyl2x
            leave
            ret $10
         end [];
      end;

    function sin(d : extended) : extended;{$ifdef MORECONST}[internconst:in_const_sin];{$endif}

      begin
         asm
            fldt 8(%ebp)
            fsin
            fstsw
            sahf
            jnp .LSIN1
            fstp %st(0)
            fldt .LSIN0
         .LSIN1:
            leave
            ret $10
         .LSIN0:
            .long       0xffffffff
            .long       0xffffffff
            .word       0xffff
         end ['EAX'];
      end;

   function power(bas,expo : extended) : extended;

     begin
        power:=exp(ln(bas)*expo);
     end;

{$endif DEFAULT_EXTENDED}


{****************************************************************************
                       Longint data type routines
 ****************************************************************************}

   function power(bas,expo : longint) : longint;
     begin
        power:=round(exp(ln(bas)*expo));
     end;


{****************************************************************************
                         Fixed data type routines
 ****************************************************************************}

{$ifdef _SUPPORT_FIXED} { Not yet allowed }

    function sqrt(d : fixed) : fixed;

      begin
         asm
            movl d,%eax
            movl %eax,%ebx
            movl %eax,%ecx
            jecxz .L_kl
            xorl %esi,%esi
         .L_it:
            xorl %edx,%edx
            idivl %ebx
            addl %ebx,%eax
            shrl $1,%eax
            subl %eax,%esi
            cmpl $1,%esi
            jbe .L_kl
            movl %eax,%esi
            movl %eax,%ebx
            movl %ecx,%eax
            jmp .L_it
         .L_kl:
            shl $8,%eax
            leave
            ret $4
         end;
      end;


    function int(d : fixed) : fixed;
    {*****************************************************************}
    { Returns the integral part of d                                  }
    {*****************************************************************}
    begin
      int:=d and $ffff0000;       { keep only upper bits      }
    end;


    function trunc(d : fixed) : longint;
    {*****************************************************************}
    { Returns the Truncated integral part of d                        }
    {*****************************************************************}
    begin
      trunc:=longint(integer(d shr 16));   { keep only upper 16 bits  }
    end;

    function frac(d : fixed) : fixed;
    {*****************************************************************}
    { Returns the Fractional part of d                                }
    {*****************************************************************}
    begin
      frac:=d AND $ffff;         { keep only decimal parts - lower 16 bits }
    end;

    function abs(d : fixed) : fixed;
    {*****************************************************************}
    { Returns the Absolute value of d                                 }
    {*****************************************************************}
    begin
       asm
           movl d,%eax
           rol $16,%eax             { Swap high & low word.}
           {Absolute value: Invert all bits and increment when <0 .}
           cwd                      { When ax<0, dx contains $ffff}
           xorw %dx,%ax             { Inverts all bits when dx=$ffff.}
           subw %dx,%ax             { Increments when dx=$ffff.}
           rol $16,%eax             { Swap high & low word.}
           leave
           ret $4
       end;
    end;


    function sqr(d : fixed) : fixed;
    {*****************************************************************}
    { Returns the Absolute squared value of d                         }
    {*****************************************************************}
    begin
            {16-bit precision needed, not 32 =)}
       sqr := d*d;
{       sqr := (d SHR 8 * d) SHR 8; }
    end;


    function Round(x: fixed): longint;
    {*****************************************************************}
    { Returns the Rounded value of d as a longint                     }
    {*****************************************************************}
    var
     lowf:integer;
     highf:integer;
    begin
      lowf:=x and $ffff;       { keep decimal part ... }
      highf :=integer(x shr 16);
      if lowf > 5 then
        highf:=highf+1
      else
      if lowf = 5 then
      begin
        { here we must check the sign ...       }
        { if greater or equal to zero, then     }
        { greater value will be found by adding }
        { one...                                }
         if highf >= 0 then
           Highf:=Highf+1;
      end;
      Round:= longint(highf);
    end;

{$endif SUPPORT_FIXED}

{$ASMMODE ATT}

{
  $Log$
  Revision 1.10  1998-10-02 09:25:29  peter
    * more constant expression evals

  Revision 1.9  1998/09/11 17:38:49  pierre
     merge for fixes branch

  Revision 1.8.2.1  1998/09/11 17:37:25  pierre
    * correction respective to stricter as v2.9.1 syntax

  Revision 1.8  1998/09/01 17:36:18  peter
    + internconst

  Revision 1.7  1998/08/25 08:49:05  florian
    * corrected exp() function

  Revision 1.6  1998/08/11 21:39:04  peter
    * splitted default_extended from support_extended

  Revision 1.5  1998/08/11 00:04:50  peter
    * $ifdef ver0_99_5 updates

  Revision 1.4  1998/08/10 15:54:50  peter
    * removed dup power(longint)

  Revision 1.3  1998/08/08 12:28:09  florian
    * a lot small fixes to the extended data type work

  Revision 1.2  1998/05/31 14:15:49  peter
    * force to use ATT or direct parsing

}