-- 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.