SIN,COS倍角式

SIN(X+Y)=SIN(X)*COS(Y)+COS(X)*SIN(Y)
COS(X+Y)=COS(X)*COS(Y)-SIN(X)*SIN(Y)
を使っています

PUBLIC NUMERIC MAXLEVEL
OPTION BASE 0
LET MAXLEVEL=20
DIM COSA(MAXLEVEL),COSB(MAXLEVEL),SINA(MAXLEVEL,MAXLEVEL),SINB(MAXLEVEL,MAXLEVEL)
DIM COSINE(MAXLEVEL),SINE(MAXLEVEL,MAXLEVEL)
LET COSA(1)=1
LET SINA(1,0)=1
LET COSB(1)=1
LET SINB(1,0)=1
FOR F=2 TO MAXLEVEL
CALL COSINEX(MIN(F*2,MAXLEVEL),COSA,SINA,COSB,SINB,COSINE)
PRINT "COS(";STR$(F);"X)=";
CALL DISPLAYCOS(F,COSINE)
PRINT
CALL SINEX(MIN(F*2,MAXLEVEL),COSA,SINA,COSB,SINB,SINE)
PRINT "SIN(";STR$(F);"X)=";
CALL DISPLAYSIN(F,SINE)
PRINT
FOR I=0 TO F
LET COSB(I)=COSINE(I)
LET COSINE(I)=0
FOR J=0 TO F
LET SINB(I,J)=SINE(I,J)
LET SINE(I,J)=0
NEXT J
NEXT I
NEXT F
END

EXTERNAL SUB DISPLAYSIN(F,SINE(,))
FOR I=F TO 0 STEP -1
FOR J=F TO 0 STEP -1
IF SINE(I,J)<>0 THEN
IF FL=1 THEN
IF SINE(I,J)<0 THEN PRINT "-"; ELSE PRINT "+";
END IF
IF FL=0 THEN
IF SINE(I,J)<0 THEN PRINT "-";
LET FL=1
END IF
IF I>1 THEN
PRINT STR$(ABS(SINE(I,J)));"*SIN(X)^";STR$(I);
ELSEIF I=1 THEN
PRINT STR$(ABS(SINE(I,J)));"*SIN(X)";
END IF
IF J>1 THEN
PRINT "*COS(X)^";STR$(J);
ELSEIF J=1 THEN
PRINT "*COS(X)";
END IF
END IF
NEXT J
NEXT I
END SUB

EXTERNAL SUB DISPLAYCOS(K,COSINE())
PRINT STR$(COSINE(K));"*COS(X)^";STR$(K);
FOR I=K-1 TO 1 STEP -1
IF COSINE(I)<>0 THEN
IF COSINE(I)<0 THEN PRINT "-"; ELSE PRINT "+";
IF I>1 THEN
PRINT STR$(ABS(COSINE(I)));"*COS(X)^";STR$(I);
ELSE
PRINT STR$(ABS(COSINE(I)));"*COS(X)";
END IF
END IF
NEXT I
IF COSINE(0)<>0 THEN
IF COSINE(0)<0 THEN PRINT "-"; ELSE PRINT "+";
PRINT STR$(ABS(COSINE(0)));
END IF
END SUB

EXTERNAL SUB COSINEX(F,COSA(),SINA(,),COSB(),SINB(,),COSINE())
OPTION BASE 0
DIM SINE(MAXLEVEL,MAXLEVEL),C(2)
LET C(2)=-1
LET C(0)=1
FOR I=0 TO F
FOR J=0 TO F-I
LET COSINE(I+J)=COSINE(I+J)+COSA(I)*COSB(J)
NEXT J
NEXT I
FOR M=0 TO F
FOR N=0 TO F-M
FOR I=0 TO F
FOR J=0 TO F-I
LET SINE(M+N,I+J)=SINE(M+N,I+J)+SINA(M,I)*SINB(N,J)
NEXT J
NEXT I
NEXT N
NEXT M
FOR L=F TO 2 STEP -2
FOR I=0 TO F-2
FOR J=0 TO 2
LET SINE(L-2,I+J)=SINE(L-2,I+J)+SINE(L,I)*C(J)
NEXT J
NEXT I
NEXT L
FOR K=0 TO F
LET COSINE(K)=COSINE(K)-SINE(0,K)
NEXT K
END SUB

SIN,COS倍角式	返事を書くノートメニュー
しばっち <dihjvcfsyu> 2008/02/08 20:45:02
SIN(X+Y)=SIN(X)COS(Y)+COS(X)SIN(Y) COS(X+Y)=COS(X)COS(Y)-SIN(X)SIN(Y) を使っています PUBLIC NUMERIC MAXLEVEL OPTION BASE 0 LET MAXLEVEL=20 DIM COSA(MAXLEVEL),COSB(MAXLEVEL),SINA(MAXLEVEL,MAXLEVEL),SINB(MAXLEVEL,MAXLEVEL) DIM COSINE(MAXLEVEL),SINE(MAXLEVEL,MAXLEVEL) LET COSA(1)=1 LET SINA(1,0)=1 LET COSB(1)=1 LET SINB(1,0)=1 FOR F=2 TO MAXLEVEL CALL COSINEX(MIN(F2,MAXLEVEL),COSA,SINA,COSB,SINB,COSINE) PRINT "COS(";STR$(F);"X)="; CALL DISPLAYCOS(F,COSINE) PRINT CALL SINEX(MIN(F2,MAXLEVEL),COSA,SINA,COSB,SINB,SINE) PRINT "SIN(";STR$(F);"X)="; CALL DISPLAYSIN(F,SINE) PRINT FOR I=0 TO F LET COSB(I)=COSINE(I) LET COSINE(I)=0 FOR J=0 TO F LET SINB(I,J)=SINE(I,J) LET SINE(I,J)=0 NEXT J NEXT I NEXT F END EXTERNAL SUB DISPLAYSIN(F,SINE(,)) FOR I=F TO 0 STEP -1 FOR J=F TO 0 STEP -1 IF SINE(I,J)<>0 THEN IF FL=1 THEN IF SINE(I,J)<0 THEN PRINT "-"; ELSE PRINT "+"; END IF IF FL=0 THEN IF SINE(I,J)<0 THEN PRINT "-"; LET FL=1 END IF IF I>1 THEN PRINT STR$(ABS(SINE(I,J)));"SIN(X)^";STR$(I); ELSEIF I=1 THEN PRINT STR$(ABS(SINE(I,J)));"SIN(X)"; END IF IF J>1 THEN PRINT "COS(X)^";STR$(J); ELSEIF J=1 THEN PRINT "COS(X)"; END IF END IF NEXT J NEXT I END SUB EXTERNAL SUB DISPLAYCOS(K,COSINE()) PRINT STR$(COSINE(K));"COS(X)^";STR$(K); FOR I=K-1 TO 1 STEP -1 IF COSINE(I)<>0 THEN IF COSINE(I)<0 THEN PRINT "-"; ELSE PRINT "+"; IF I>1 THEN PRINT STR$(ABS(COSINE(I)));"COS(X)^";STR$(I); ELSE PRINT STR$(ABS(COSINE(I)));"COS(X)"; END IF END IF NEXT I IF COSINE(0)<>0 THEN IF COSINE(0)<0 THEN PRINT "-"; ELSE PRINT "+"; PRINT STR$(ABS(COSINE(0))); END IF END SUB EXTERNAL SUB COSINEX(F,COSA(),SINA(,),COSB(),SINB(,),COSINE()) OPTION BASE 0 DIM SINE(MAXLEVEL,MAXLEVEL),C(2) LET C(2)=-1 LET C(0)=1 FOR I=0 TO F FOR J=0 TO F-I LET COSINE(I+J)=COSINE(I+J)+COSA(I)COSB(J) NEXT J NEXT I FOR M=0 TO F FOR N=0 TO F-M FOR I=0 TO F FOR J=0 TO F-I LET SINE(M+N,I+J)=SINE(M+N,I+J)+SINA(M,I)SINB(N,J) NEXT J NEXT I NEXT N NEXT M FOR L=F TO 2 STEP -2 FOR I=0 TO F-2 FOR J=0 TO 2 LET SINE(L-2,I+J)=SINE(L-2,I+J)+SINE(L,I)C(J) NEXT J NEXT I NEXT L FOR K=0 TO F LET COSINE(K)=COSINE(K)-SINE(0,K) NEXT K END SUB