-- file: MFMathImpl2.mesa
-- Pascal-to-Mesa translator output, translated at October 31, 1985 4:28:01 pm PST
DIRECTORY
PascalBasic,
PascalWizardFiles,
MFTypes,
MFInteraction,
MFMath;
MFMathImpl2: PROGRAM IMPORTS PascalBasic, MFInteraction, MFMath EXPORTS MFMath = PUBLIC
BEGIN OPEN PascalBasic, PascalWizardFiles, MFTypes, MFInteraction, MFMath;
RoundFraction: PROCEDURE[X: Fraction] RETURNS[RoundFractionResult: Scaled] =
BEGIN BeCareful:PascalInteger;
IF X>=2048 THEN RoundFractionResult←1+( PascalDIVPower2[(X-2048),12]) ELSE IF
X>=-2048 THEN RoundFractionResult←0 ELSE BEGIN BeCareful←X+1;
RoundFractionResult←-(1+( PascalDIVPower2[(-BeCareful-2048),12])); END; END;--:119----121:
SquareRt: PROCEDURE[X: Scaled] RETURNS[SquareRtResult: Scaled] =
BEGIN K:SmallNumber;Y, Q:PascalInteger;
IF X<=0 THEN--122:
BEGIN IF X<0 THEN BEGIN BEGIN IF Interaction=3 THEN NULL;PrintNl[133];
Print[178]; END;PrintScaled[X];Print[179];BEGIN HelpPtr←2;
HelpLine↑[1]←180;HelpLine↑[0]←181; END;Error[]; END;SquareRtResult←0; END--:122
ELSE BEGIN K←23;Q←2;WHILE X<536870912 DO BEGIN K←K-1;X←X+X+X+X; END ENDLOOP ;
IF X<1073741824 THEN Y←0 ELSE BEGIN X←X-1073741824;Y←1; END;
DO--123:--X←X+X;Y←Y+Y;IF X>=1073741824 THEN BEGIN X←X-1073741824;
Y←Y+1; END;X←X+X;Y←Y+Y-Q;Q←Q+Q;
IF X>=1073741824 THEN BEGIN X←X-1073741824;Y←Y+1; END;
IF Y>Q THEN BEGIN Y←Y-Q;Q←Q+2; END ELSE IF Y<=0 THEN BEGIN Q←Q-2;
Y←Y+Q; END;K←K-1--:123--; IF K=0 THEN EXIT; ENDLOOP;SquareRtResult← PascalDIVPower2[(Q),1]; END; END;--:121
--124:-- PythAdd: PROCEDURE[A,B: PascalInteger] RETURNS[PythAddResult: PascalInteger] =
BEGIN R:Fraction;
Big:PascalBoolean; A←ABS[A];B←ABS[B];IF A<B THEN BEGIN R←B;B←A;A←R;
END;
IF A>0 THEN BEGIN
IF A<536870912 THEN Big←FALSE ELSE BEGIN A← PascalDIVPower2[A ,2];
B← PascalDIVPower2[B ,2];Big←TRUE; END;--125:
{WHILE TRUE DO BEGIN R←MakeFraction[B,A];R←TakeFraction[R,R];
IF R=0 THEN GOTO Label30;R←MakeFraction[R,1073741824+R];
A←A+TakeFraction[A+A,R];B←TakeFraction[B,R]; END ENDLOOP ;EXITS Label30 => NULL};--:125--IF Big THEN IF A<536870912 THEN A←A+A+A+A ELSE BEGIN ArithError←TRUE;
A←2147483647; END; END;PythAddResult←A; END;--:124----126:
PythSub: PROCEDURE[A,B: PascalInteger] RETURNS[PythSubResult: PascalInteger] =
BEGIN R:Fraction;
Big:PascalBoolean; A←ABS[A];B←ABS[B];IF A<=B THEN--128:
BEGIN IF A<B THEN BEGIN BEGIN IF Interaction=3 THEN NULL;PrintNl[133];
Print[182]; END;PrintScaled[A];Print[183];PrintScaled[B];Print[179];
BEGIN HelpPtr←2;HelpLine↑[1]←180;HelpLine↑[0]←181; END;Error[]; END;
A←0; END--:128
ELSE BEGIN
IF A<1073741824 THEN Big←FALSE ELSE BEGIN A← PascalDIVPower2[(A),1];
B← PascalDIVPower2[(B),1];Big←TRUE; END;--127:
{WHILE TRUE DO BEGIN R←MakeFraction[B,A];R←TakeFraction[R,R];
IF R=0 THEN GOTO Label30;R←MakeFraction[R,1073741824-R];
A←A-TakeFraction[A+A,R];B←TakeFraction[B,R]; END ENDLOOP ;EXITS Label30 => NULL};--:127--IF Big THEN A←A+A; END;PythSubResult←A; END;--:126----132:
MLog: PROCEDURE[X: Scaled] RETURNS[MLogResult: Scaled] =
BEGIN Y, Z:PascalInteger;K:PascalInteger;
IF X<=0 THEN--134:--BEGIN BEGIN IF Interaction=3 THEN NULL;PrintNl[133];
Print[184]; END;PrintScaled[X];Print[179];BEGIN HelpPtr←2;
HelpLine↑[1]←185;HelpLine↑[0]←181; END;Error[];MLogResult←0; END--:134
ELSE BEGIN Y←1302456860;Z←6581195;WHILE X<1073741824 DO BEGIN X←X+X;
Y←Y-93032639;Z←Z-48782; END ENDLOOP ;Y←Y+( PascalDIVPower2[Z ,16]);K←2;
WHILE X>1073741828 DO--133:--BEGIN Z←( (X-1)/TwoToThe↑[K])+1;
WHILE X<1073741824+Z DO BEGIN Z← PascalDIVPower2[(Z+1),1];K←K+1; END ENDLOOP ;Y←Y+SpecLog↑[K];
X←X-Z; END--:133-- ENDLOOP ;MLogResult← PascalDIVPower2[Y ,3]; END; END;--:132----135:
MExp: PROCEDURE[X: Scaled] RETURNS[MExpResult: Scaled] =
BEGIN K:SmallNumber;Y, Z:PascalInteger;
IF X>174436200 THEN BEGIN ArithError←TRUE;MExpResult←2147483647;
END ELSE IF X<-197694359 THEN MExpResult←0 ELSE BEGIN IF X<=0 THEN BEGIN Z←
-8*X;Y←1048576;
END ELSE BEGIN IF X<=127919879 THEN Z←1023359037-8*X ELSE Z←8*(
174436200-X);Y←2147483647; END;--136:--K←1;
WHILE Z>0 DO BEGIN WHILE Z>=SpecLog↑[K]DO BEGIN Z←Z-SpecLog↑[K];
Y←Y-1-( (Y-TwoToThe↑[K-1])/TwoToThe↑[K]); END ENDLOOP ;K←K+1; END--:136-- ENDLOOP ;
IF X<=127919879 THEN MExpResult← PascalDIVPower2[(Y+8),4] ELSE MExpResult←Y; END; END;--:135
--139:-- NArg: PROCEDURE[X,Y: PascalInteger] RETURNS[NArgResult: Angle] =
BEGIN Z:Angle;T:PascalInteger;
K:SmallNumber;Octant:PascalInteger[1..8];
IF X>=0 THEN Octant←1 ELSE BEGIN X←-X;Octant←2; END;
IF Y<0 THEN BEGIN Y←-Y;Octant←Octant+2; END;IF X<Y THEN BEGIN T←Y;
Y←X;X←T;Octant←Octant+4; END;IF X=0 THEN--140:
BEGIN BEGIN IF Interaction=3 THEN NULL;PrintNl[133];Print[186]; END;
BEGIN HelpPtr←2;HelpLine↑[1]←187;HelpLine↑[0]←181; END;Error[];
NArgResult←0; END--:140-- ELSE BEGIN--142:
WHILE X>=536870912 DO BEGIN X← PascalDIVPower2[(X),1];Y← PascalDIVPower2[(Y),1]; END ENDLOOP ;Z←0;
IF Y>0 THEN BEGIN WHILE X<268435456 DO BEGIN X←X+X;Y←Y+Y; END ENDLOOP ;--143:
K←0;DO Y←Y+Y;K←K+1;IF Y>X THEN BEGIN Z←Z+SpecAtan↑[K];T←X;
X←X+( Y /TwoToThe↑[K+K]);Y←Y-T; END; IF K=15 THEN EXIT; ENDLOOP;DO Y←Y+Y;K←K+1;
IF Y>X THEN BEGIN Z←Z+SpecAtan↑[K];Y←Y-X; END; IF K=26--:143-- THEN EXIT; ENDLOOP;
END--:142--;--141:--SELECT Octant FROM 1 =>NArgResult←Z;5 =>NArgResult←94371840-Z;
6 =>NArgResult←94371840+Z;2 =>NArgResult←188743680-Z;4 =>NArgResult←Z-188743680;
8 =>NArgResult←-Z-94371840;7 =>NArgResult←Z-94371840;3 =>NArgResult←-Z; ENDCASE--:141--; END; END;
--:139----145:-- NSinCos: PROCEDURE[Z: Angle] =
BEGIN K:SmallNumber;Q:PascalInteger[0..7];
R:Fraction;X, Y, T:PascalInteger; WHILE Z<0 DO Z←Z+377487360 ENDLOOP ;
Z← Z MOD 377487360;Q← Z /47185920;Z← Z MOD 47185920;X←268435456;
Y←X;IF NOT PascalODD[Q] THEN Z←47185920-Z;--147:--K←1;
WHILE Z>0 DO BEGIN IF Z>=SpecAtan↑[K] THEN BEGIN Z←Z-SpecAtan↑[K];T←X;
X← T+Y /TwoToThe↑[K];Y← Y-T /TwoToThe↑[K]; END;K←K+1; END ENDLOOP ;
IF Y<0 THEN Y←0--:147--;--146:--SELECT Q FROM 0 => NULL;1 =>BEGIN T←X;X←Y;Y←T; END;
2 =>BEGIN T←X;X←-Y;Y←T; END;3 =>X←-X;4 =>BEGIN X←-X;Y←-Y; END;
5 =>BEGIN T←X;X←-Y;Y←-T; END;6 =>BEGIN T←X;X←Y;Y←-T; END;7 =>Y←-Y;
ENDCASE--:146--;R←PythAdd[X,Y];NCos←MakeFraction[X,R];
NSin←MakeFraction[Y,R]; END;--:145----149:-- NewRandoms: PROCEDURE
=
BEGIN K:PascalInteger[0..54];X:Fraction;
FOR i:INT IN [ INT[0 ].. INT[23 ]] DO K ← i; X←Randoms↑[K]-Randoms↑[K+31];
IF X<0 THEN X←X+268435456;Randoms↑[K]←X; ENDLOOP;
FOR i:INT IN [ INT[24 ].. INT[54 ]] DO K ← i; X←Randoms↑[K]-Randoms↑[K-24];
IF X<0 THEN X←X+268435456;Randoms↑[K]←X; ENDLOOP;JRandom←54; END;--:149
--150:-- InitRandoms: PROCEDURE[Seed: Scaled] =
BEGIN J, Jj, K:Fraction;I:PascalInteger[0..54];
J←ABS[Seed];WHILE J>=268435456 DO J← PascalDIVPower2[(J),1] ENDLOOP ;K←1;
FOR i:INT IN [ INT[0 ].. INT[54 ]] DO I ← i; Jj←K;K←J-K;J←Jj;IF K<0 THEN K←K+268435456;
Randoms↑[ (I*21)MOD 55]←J; ENDLOOP;NewRandoms[];NewRandoms[];NewRandoms[]; END;
--:150----151:-- UnifRand: PROCEDURE[X: Scaled] RETURNS[UnifRandResult: Scaled] =
BEGIN Y:Scaled;
IF JRandom=0 THEN NewRandoms [] ELSE JRandom←JRandom-1;
Y←TakeFraction[ABS[X],Randoms↑[JRandom]];
IF Y=ABS[X] THEN UnifRandResult←0 ELSE IF X>0 THEN UnifRandResult←Y ELSE
UnifRandResult←-Y; END;--:151----152:-- NormRand: PROCEDURE RETURNS[NormRandResult: Scaled]
=
BEGIN X, U, L:PascalInteger;
DO DO IF JRandom=0 THEN NewRandoms [] ELSE JRandom←
JRandom-1;X←TakeFraction[112429,Randoms↑[JRandom]-134217728];
IF JRandom=0 THEN NewRandoms [] ELSE JRandom←JRandom-1;
U←Randoms↑[JRandom]; IF ABS[X]<U THEN EXIT; ENDLOOP;X←MakeFraction[X,U];
L←139548960-MLog[U]; IF AbVsCd[1024,L,X,X]>=0 THEN EXIT; ENDLOOP;NormRandResult←X; END;
END.