DOS-History · the-grue · Jun 11, 2026 · Jun 12, 2026 · Jun 12, 2026 · Jun 12, 2026
diff --git a/2_printed_files/bundle_09/ATAN.ASM b/2_printed_files/bundle_09/ATAN.ASM
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+ATAN - Arc tangent                                       Macro-86 %1(12)   0:58:20  13-Nov-81   Page 1-1 
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+    1	 	 	 	 	        TITLE   ATAN - Arc tangent
+    2	 	 	 	 	
+    3	 0000	 	 	 	DATA    SEGMENT WORD PUBLIC 'DATA'
+    4	 	 	 	 	
+    5	 	 	 	 	        EXTRN   $FAC:BYTE, $AC:WORD, $ARG:WORD, $TEMP:WORD
+    6	 	 	 	 	
+    7	 0000	 	 	 	DATA    ENDS
+    8	 	 	 	 	
+    9	 0000	 	 	 	CONST   SEGMENT WORD PUBLIC 'CONST'
+   10	 	 	 	 	
+   11	 	 	 	 	        EXTRN   $ONE:WORD,$HALFPI:WORD,$SIXTHPI:WORD,$SQRT3:WORD
+   12	 	 	 	 	        EXTRN	$TANTWELFTHPI:WORD
+   13	 	 	 	 	
+   14	 	 	 	 	;Coefficients for Hart 4940, relative error 7.69
+   15	 	 	 	 	;ATAN(x) = xP(x^2)
+   16	 	 	 	 	; These constants have been checked with MuMath
+   17	 	 	 	 	
+   18	 0000  0003	 	 	ATANTAB DW      3                       ;Degree
+   19	 0002  62 35 83 7E	 	        DB      062H,035H,083H,07EH     ;-0.12813 3334
+   20	 0006  50 24 4C 7E	 	        DB      050H,024H,04CH,07EH     ;+0.19935 72694
+   21	 000A  79 A9 AA 7F	 	        DB      079H,0A9H,0AAH,07FH     ;-0.33332 42344 5
+   22	 000E  00 00 00 81	 	        DB      000H,000H,000H,081H     ;+0.99999 99797 73
+   23	 	 	 	 	
+   24	 0012	 	 	 	CONST   ENDS
+   25	 	 	 	 	
+   26	 	 	 	 	
+   27	 	 	 	 	DC      GROUP   DATA,CONST
+   28	 	 	 	 	
+   29	 	 	 	 	
+   30	 0000	 	 	 	CODE    SEGMENT BYTE PUBLIC 'CODE'
+   31	 	 	 	 	
+   32	 	 	 	 	        PUBLIC  $ATN
+   33	 	 	 	 	
+   34	 	 	 	 	        EXTRN   $SAVREG:NEAR, $SPOLYX:NEAR
+   35	 	 	 	 	        EXTRN   $SDIV:NEAR, $SMUL:NEAR, $SADD:NEAR, $SSUB:NEAR, $SCMP:NEAR
+   36	 	 	 	 	
+   37	 	 	 	 	        ASSUME  CS:CODE, DS:DC, ES:DC
+   38	 	 	 	 	
+   39	 	 	 	 	
+   40	 	 	 	 	;$ATN - Arc tangent
+   41	 	 	 	 	;
+   42	 	 	 	 	; Inputs:
+   43	 	 	 	 	;       BX = Address of argument
+   44	 	 	 	 	; Outputs:
+   45	 	 	 	 	;       Result in FAC
+   46	 	 	 	 	; Registers:
+   47	 	 	 	 	;       Only F affected.
+   48	 	 	 	 	
+   49	 0000	 	 	 	$ATN:
+   50	 0000  E8 0000 E	 	        CALL    $SAVREG
+   51	 0003  8B F3	 	 	        MOV     SI,BX
+   52	 0005  BF 0000 E	 	        MOV     DI,OFFSET DC:$AC
+   53	 0008  A5	 	 	        MOVSW                   ;Put in FAC
+   54	 0009  AD	 	 	        LODSW
+
+
+ATAN - Arc tangent                                       Macro-86 %1(12)   0:58:20  13-Nov-81   Page 1-2 
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+   55	 000A  AB	 	 	        STOSW
+   56	 000B  0A E4	 	 	        OR      AH,AH           ;Is it zero?
+   57	 000D  74 11	 	 	        JZ      DONE            ;If so, result is too
+   58	 000F  A8 80	 	 	        TEST    AL,80H          ;Check sign
+   59	 0011  79 0E	 	 	        JNS     POSATAN
+   60	 0013  24 7F	 	 	        AND     AL,7FH
+   61	 0015  A2 FFFF E	 	        MOV     [$FAC-1],AL     ;Make it positive
+   62	 0018  E8 0021 R	 	        CALL    POSATAN         ;Take arctan of positive number
+   63	 001B  80 36 FFFF E 80	 	        XOR     [$FAC-1],80H    ;Invert sign back
+   64	 0020  C3	 	 	DONE:   RET
+   65	 	 	 	 	
+   66	 0021	 	 	 	POSATAN:
+   67	 0021  80 FC 81	 	 	        CMP     AH,81H          ;Is it >= 1?
+   68	 0024  72 15	 	 	        JB      LESSTHAN1
+   69	 0026  BE 0000 E	 	        MOV     SI,OFFSET DC:$ONE
+   70	 0029  BF 0000 E	 	        MOV     DI,OFFSET DC:$AC
+   71	 002C  E8 0000 E	 	        CALL    $SDIV           ;It's reciprocal is < 1
+   72	 002F  E8 003B R	 	        CALL    LESSTHAN1       ;Compute arc-cotan on number < 1
+   73	 0032  BE 0000 E	 	        MOV     SI,OFFSET DC:$HALFPI
+   74	 0035  BF 0000 E	 	        MOV     DI,OFFSET DC:$AC
+   75	 0038  E9 0000 E	 	        JMP     $SSUB           ;Correct by subtracting from PI/2
+   76	 	 	 	 	
+   77	 003B	 	 	 	LESSTHAN1:
+   78	 003B  BE 0000 E	 	        MOV     SI,OFFSET DC:$TANTWELFTHPI
+   79	 003E  BF 0000 E	 	        MOV     DI,OFFSET DC:$AC
+   80	 0041  E8 0000 E	 	        CALL    $SCMP           ;Compare argument to PI/12
+   81	 0044  73 40	 	 	        JAE     DOATAN          ;Range reduction complete if <= PI/12
+   82	 0046  BE 0000 E	 	        MOV     SI,OFFSET DC:$AC
+   83	 0049  BF 0000 E	 	        MOV     DI,OFFSET DC:$ARG
+   84	 004C  A5	 	 	        MOVSW                   ;Save X in ARG
+   85	 004D  A5	 	 	        MOVSW
+   86	 004E  BE 0000 E	 	        MOV     SI,OFFSET DC:$SQRT3  ;Point to TAN(PI/6) (PI/6 = 30 degrees)
+   87	 0051  BF 0000 E	 	        MOV     DI,OFFSET DC:$AC
+   88	 0054  E8 0000 E	 	        CALL    $SADD           ;FAC = X + TAN(PI/6)
+   89	 0057  BE 0000 E	 	        MOV     SI,OFFSET DC:$AC
+   90	 005A  BF 0000 E	 	        MOV     DI,OFFSET DC:$TEMP
+   91	 005D  A5	 	 	        MOVSW                   ;Save in TEMP
+   92	 005E  A5	 	 	        MOVSW
+   93	 005F  BE 0000 E	 	        MOV     SI,OFFSET DC:$SQRT3
+   94	 0062  BF 0000 E	 	        MOV     DI,OFFSET DC:$ARG
+   95	 0065  E8 0000 E	 	        CALL    $SMUL           ;FAC = X * TAN(PI/6)
+   96	 0068  BE 0000 E	 	        MOV     SI,OFFSET DC:$AC
+   97	 006B  BF 0000 E	 	        MOV     DI,OFFSET DC:$ONE
+   98	 006E  E8 0000 E	 	        CALL    $SSUB           ;FAC = X * TAN(PI/6) - 1
+   99	 0071  BE 0000 E	 	        MOV     SI,OFFSET DC:$AC
+  100	 0074  BF 0000 E	 	        MOV     DI,OFFSET DC:$TEMP
+  101	 0077  E8 0000 E	 	        CALL    $SDIV           ;FAC = (X*TAN(PI/6) - 1)/(X + TAN(PI/6)
+  102	 007A  E8 0086 R	 	        CALL    DOATAN          ;Comput e arctan on argument < PI/12
+  103	 007D  BE 0000 E	 	        MOV     SI,OFFSET DC:$SIXTHPI
+  104	 0080  BF 0000 E	 	        MOV     DI,OFFSET DC:$AC
+  105	 0083  E9 0000 E	 	        JMP     $SADD           ;Correct for range reduction by adding PI/6
+  106	 	 	 	 	
+  107	 0086	 	 	 	DOATAN:
+  108	 0086  BB 0000 R	 	        MOV     BX,OFFSET DC:ATANTAB
+
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+ATAN - Arc tangent                                       Macro-86 %1(12)   0:58:20  13-Nov-81   Page 1-3 
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+  109	 0089  E9 0000 E	 	        JMP     $SPOLYX
+  110	 	 	 	 	
+  111	 008C	 	 	 	CODE    ENDS
+  112	 	 	 	 	        END
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+ATAN - Arc tangent                                       Macro-86 %1(12)   0:58:20  13-Nov-81   Symbols-1
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+Segments and groups:
+
+	 	N a m e	 	 	Size	align	combine	class
+
+CODE . . . . . . . . . . . . . .	008C	BYTE  	PUBLIC	'CODE'
+DC . . . . . . . . . . . . . . .	GROUP
+  DATA . . . . . . . . . . . . . .	0000	WORD  	PUBLIC	'DATA'
+  CONST. . . . . . . . . . . . . .	0012	WORD  	PUBLIC	'CONST'
+
+Symbols:            
+
+	 	N a m e	 	 	Type	Value	Attr         
+
+ATANTAB. . . . . . . . . . . . .	L WORD 	0000	CONST
+DOATAN . . . . . . . . . . . . .	L NEAR 	0086	CODE
+DONE . . . . . . . . . . . . . .	L NEAR 	0020	CODE
+LESSTHAN1. . . . . . . . . . . .	L NEAR 	003B	CODE
+POSATAN. . . . . . . . . . . . .	L NEAR 	0021	CODE
+$AC. . . . . . . . . . . . . . .	V WORD 	0000	DATA	External
+$ARG . . . . . . . . . . . . . .	V WORD 	0000	DATA	External
+$ATN . . . . . . . . . . . . . .	L NEAR 	0000	CODE	Global
+$FAC . . . . . . . . . . . . . .	V BYTE 	0000	DATA	External
+$HALFPI. . . . . . . . . . . . .	V WORD 	0000	CONST	External
+$ONE . . . . . . . . . . . . . .	V WORD 	0000	CONST	External
+$SADD. . . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$SAVREG. . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$SCMP. . . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$SDIV. . . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$SIXTHPI . . . . . . . . . . . .	V WORD 	0000	CONST	External
+$SMUL. . . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$SPOLYX. . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$SQRT3 . . . . . . . . . . . . .	V WORD 	0000	CONST	External
+$SSUB. . . . . . . . . . . . . .	L NEAR 	0000	CODE	External
+$TANTWELFTHPI. . . . . . . . . .	V WORD 	0000	CONST	External
+$TEMP. . . . . . . . . . . . . .	V WORD 	0000	DATA	External
+
+Warning Severe
+Errors	Errors 
+0	0
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