861 lines
16 KiB
Plaintext
861 lines
16 KiB
Plaintext
(*
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BSD 2-Clause License
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Copyright (c) 2018, 2019, Anton Krotov
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All rights reserved.
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*)
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MODULE ARITH;
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IMPORT AVLTREES, STRINGS, MACHINE, UTILS;
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CONST
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tINTEGER* = 1; tREAL* = 2; tSET* = 3;
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tBOOLEAN* = 4; tCHAR* = 5; tWCHAR* = 6;
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tSTRING* = 7;
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TYPE
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RELATION* = ARRAY 3 OF CHAR;
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VALUE* = RECORD
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typ*: INTEGER;
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int: INTEGER;
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float: REAL;
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set: SET;
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bool: BOOLEAN;
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string*: AVLTREES.DATA
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END;
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VAR
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digit: ARRAY 256 OF INTEGER;
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PROCEDURE Int* (v: VALUE): INTEGER;
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VAR
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res: INTEGER;
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BEGIN
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IF v.typ = tINTEGER THEN
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res := v.int
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ELSIF v.typ = tCHAR THEN
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res := v.int
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ELSIF v.typ = tWCHAR THEN
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res := v.int
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ELSIF v.typ = tSET THEN
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res := ORD(v.set);
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IF MACHINE._64to32 THEN
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res := MACHINE.Int32To64(res)
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END
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ELSIF v.typ = tBOOLEAN THEN
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res := ORD(v.bool)
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END
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RETURN res
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END Int;
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PROCEDURE getBool* (v: VALUE): BOOLEAN;
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BEGIN
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ASSERT(v.typ = tBOOLEAN);
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RETURN v.bool
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END getBool;
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PROCEDURE Float* (v: VALUE): REAL;
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BEGIN
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ASSERT(v.typ = tREAL);
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RETURN v.float
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END Float;
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PROCEDURE check* (v: VALUE): BOOLEAN;
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VAR
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error: BOOLEAN;
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BEGIN
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error := FALSE;
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IF (v.typ = tINTEGER) & ((v.int < MACHINE.target.minInt) OR (v.int > MACHINE.target.maxInt)) THEN
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error := TRUE
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ELSIF (v.typ = tCHAR) & ((v.int < 0) OR (v.int > 255)) THEN
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error := TRUE
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ELSIF (v.typ = tWCHAR) & ((v.int < 0) OR (v.int > 65535)) THEN
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error := TRUE
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ELSIF (v.typ = tREAL) & ((v.float < -MACHINE.target.maxReal) OR (v.float > MACHINE.target.maxReal)) THEN
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error := TRUE
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END
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RETURN ~error
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END check;
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PROCEDURE isZero* (v: VALUE): BOOLEAN;
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VAR
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res: BOOLEAN;
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BEGIN
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ASSERT(v.typ IN {tINTEGER, tREAL});
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IF v.typ = tINTEGER THEN
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res := v.int = 0
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ELSIF v.typ = tREAL THEN
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res := v.float = 0.0
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END
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RETURN res
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END isZero;
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PROCEDURE iconv* (s: ARRAY OF CHAR; VAR v: VALUE; VAR error: INTEGER);
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VAR
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value: INTEGER;
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i: INTEGER;
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d: INTEGER;
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BEGIN
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error := 0;
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value := 0;
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i := 0;
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WHILE STRINGS.digit(s[i]) & (error = 0) DO
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d := digit[ORD(s[i])];
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IF value <= (UTILS.maxint - d) DIV 10 THEN
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value := value * 10 + d;
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INC(i)
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ELSE
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error := 1
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END
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END;
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IF error = 0 THEN
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v.int := value;
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v.typ := tINTEGER;
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IF ~check(v) THEN
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error := 1
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END
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END
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END iconv;
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PROCEDURE hconv* (s: ARRAY OF CHAR; VAR v: VALUE; VAR error: INTEGER);
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VAR
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value: INTEGER;
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i: INTEGER;
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n: INTEGER;
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d: INTEGER;
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BEGIN
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ASSERT(STRINGS.digit(s[0]));
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error := 0;
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value := 0;
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n := -1;
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i := 0;
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WHILE (s[i] # "H") & (s[i] # "X") & (error = 0) DO
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d := digit[ORD(s[i])];
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IF (n = -1) & (d # 0) THEN
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n := i
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END;
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IF (n # -1) & (i - n + 1 > MACHINE.target.maxHex) THEN
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error := 2
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ELSE
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value := value * 16 + d;
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INC(i)
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END
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END;
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IF MACHINE._64to32 THEN
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value := MACHINE.Int32To64(value);
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END;
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IF (s[i] = "X") & (n # -1) & (i - n > 4) THEN
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error := 3
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END;
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IF error = 0 THEN
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v.int := value;
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IF s[i] = "X" THEN
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v.typ := tCHAR;
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IF ~check(v) THEN
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v.typ := tWCHAR;
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IF ~check(v) THEN
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error := 3
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END
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END
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ELSE
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v.typ := tINTEGER;
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IF ~check(v) THEN
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error := 2
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END
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END
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END
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END hconv;
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PROCEDURE opFloat2 (VAR a: REAL; b: REAL; op: CHAR): BOOLEAN;
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VAR
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max: REAL;
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res: BOOLEAN;
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BEGIN
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max := UTILS.maxreal;
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CASE op OF
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|"+":
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IF (a < 0.0) & (b < 0.0) THEN
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res := a > -max - b
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ELSIF (a > 0.0) & (b > 0.0) THEN
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res := a < max - b
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ELSE
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res := TRUE
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END;
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IF res THEN
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a := a + b
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END
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|"-":
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IF (a < 0.0) & (b > 0.0) THEN
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res := a > b - max
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ELSIF (a > 0.0) & (b < 0.0) THEN
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res := a < b + max
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ELSE
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res := TRUE
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END;
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IF res THEN
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a := a - b
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END
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|"*":
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IF (ABS(a) > 1.0) & (ABS(b) > 1.0) THEN
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res := ABS(a) < max / ABS(b)
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ELSE
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res := TRUE
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END;
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IF res THEN
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a := a * b
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END
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|"/":
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IF ABS(b) < 1.0 THEN
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res := ABS(a) < max * ABS(b)
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ELSE
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res := TRUE
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END;
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IF res THEN
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a := a / b
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END
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END
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RETURN res
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END opFloat2;
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PROCEDURE fconv* (s: ARRAY OF CHAR; VAR v: VALUE; VAR error: INTEGER);
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VAR
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value: REAL;
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exp10: REAL;
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i, n, d: INTEGER;
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minus: BOOLEAN;
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BEGIN
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error := 0;
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value := 0.0;
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exp10 := 10.0;
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minus := FALSE;
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n := 0;
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i := 0;
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WHILE (error = 0) & STRINGS.digit(s[i]) DO
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IF opFloat2(value, 10.0, "*") & opFloat2(value, FLT(digit[ORD(s[i])]), "+") THEN
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INC(i)
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ELSE
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error := 4
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END
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END;
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INC(i);
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WHILE (error = 0) & STRINGS.digit(s[i]) DO
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IF opFloat2(value, FLT(digit[ORD(s[i])]) / exp10, "+") & opFloat2(exp10, 10.0, "*") THEN
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INC(i)
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ELSE
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error := 4
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END
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END;
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IF s[i] = "E" THEN
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INC(i)
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END;
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IF (s[i] = "-") OR (s[i] = "+") THEN
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minus := s[i] = "-";
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INC(i)
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END;
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WHILE (error = 0) & STRINGS.digit(s[i]) DO
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d := digit[ORD(s[i])];
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IF n <= (UTILS.maxint - d) DIV 10 THEN
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n := n * 10 + d;
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INC(i)
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ELSE
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error := 5
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END
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END;
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exp10 := 1.0;
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WHILE (error = 0) & (n > 0) DO
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IF opFloat2(exp10, 10.0, "*") THEN
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DEC(n)
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ELSE
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error := 4
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END
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END;
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IF error = 0 THEN
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IF minus THEN
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IF ~opFloat2(value, exp10, "/") THEN
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error := 4
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END
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ELSE
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IF ~opFloat2(value, exp10, "*") THEN
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error := 4
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END
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END
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END;
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IF error = 0 THEN
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v.float := value;
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v.typ := tREAL;
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IF ~check(v) THEN
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error := 4
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END
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END
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END fconv;
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PROCEDURE setChar* (VAR v: VALUE; ord: INTEGER);
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BEGIN
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v.typ := tCHAR;
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v.int := ord
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END setChar;
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PROCEDURE setWChar* (VAR v: VALUE; ord: INTEGER);
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BEGIN
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v.typ := tWCHAR;
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v.int := ord
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END setWChar;
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PROCEDURE addInt (VAR a: INTEGER; b: INTEGER): BOOLEAN;
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VAR
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error: BOOLEAN;
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BEGIN
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IF (a > 0) & (b > 0) THEN
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error := a > UTILS.maxint - b
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ELSIF (a < 0) & (b < 0) THEN
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error := a < UTILS.minint - b
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ELSE
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error := FALSE
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END;
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IF ~error THEN
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a := a + b
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ELSE
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a := 0
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END
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RETURN ~error
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END addInt;
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PROCEDURE subInt (VAR a: INTEGER; b: INTEGER): BOOLEAN;
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VAR
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error: BOOLEAN;
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BEGIN
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IF (a > 0) & (b < 0) THEN
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error := a > UTILS.maxint + b
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ELSIF (a < 0) & (b > 0) THEN
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error := a < UTILS.minint + b
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ELSIF (a = 0) & (b < 0) THEN
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error := b = UTILS.minint
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ELSE
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error := FALSE
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END;
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IF ~error THEN
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a := a - b
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ELSE
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a := 0
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END
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RETURN ~error
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END subInt;
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PROCEDURE lg2 (x: INTEGER): INTEGER;
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VAR
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n: INTEGER;
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BEGIN
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ASSERT(x > 0);
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n := 0;
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WHILE ~ODD(x) DO
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x := x DIV 2;
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INC(n)
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END;
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IF x # 1 THEN
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n := 255
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END
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RETURN n
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END lg2;
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PROCEDURE mulInt* (VAR a: INTEGER; b: INTEGER): BOOLEAN;
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VAR
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error: BOOLEAN;
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min, max: INTEGER;
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BEGIN
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min := UTILS.minint;
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max := UTILS.maxint;
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IF ((a > 1) & (b > 1)) OR ((a < 0) & (b < 0)) THEN
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error := (a = min) OR (b = min) OR (ABS(a) > max DIV ABS(b))
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ELSIF ((a > 1) & (b < 0)) OR ((a < 0) & (b > 1)) THEN
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error := (a = min) OR (b = min);
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IF ~error THEN
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IF lg2(ABS(a)) + lg2(ABS(b)) >= UTILS.bit_depth THEN
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error := ABS(a) > max DIV ABS(b)
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END
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END
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ELSE
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error := FALSE
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END;
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IF ~error THEN
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a := a * b
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ELSE
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a := 0
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END
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RETURN ~error
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END mulInt;
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PROCEDURE _ASR (x, n: INTEGER): INTEGER;
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BEGIN
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IF MACHINE._64to32 THEN
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x := MACHINE.Int32To64(x)
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END
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RETURN ASR(x, n)
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END _ASR;
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PROCEDURE _LSR (x, n: INTEGER): INTEGER;
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BEGIN
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IF MACHINE._64to32 THEN
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x := MACHINE.Int64To32(x);
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x := LSR(x, n);
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x := MACHINE.Int32To64(x)
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ELSE
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x := LSR(x, n)
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END
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RETURN x
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END _LSR;
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PROCEDURE _LSL (x, n: INTEGER): INTEGER;
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BEGIN
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x := LSL(x, n);
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IF MACHINE._64to32 THEN
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x := MACHINE.Int32To64(x)
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END
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RETURN x
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END _LSL;
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PROCEDURE _ROR1_32 (x: INTEGER): INTEGER;
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BEGIN
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x := MACHINE.Int64To32(x);
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x := ORD(BITS(LSR(x, 1)) + BITS(LSL(x, 31)))
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RETURN MACHINE.Int32To64(x)
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END _ROR1_32;
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PROCEDURE _ROR (x, n: INTEGER): INTEGER;
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BEGIN
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IF MACHINE._64to32 THEN
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n := n MOD 32;
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WHILE n > 0 DO
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x := _ROR1_32(x);
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DEC(n)
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END
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ELSE
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x := ROR(x, n)
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END
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RETURN x
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END _ROR;
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PROCEDURE opInt* (VAR a: VALUE; b: VALUE; op: CHAR): BOOLEAN;
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VAR
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success: BOOLEAN;
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BEGIN
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success := TRUE;
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CASE op OF
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|"+": success := addInt(a.int, b.int)
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|"-": success := subInt(a.int, b.int)
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|"*": success := mulInt(a.int, b.int)
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|"/": success := FALSE
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|"D": IF (b.int # -1) OR (a.int # UTILS.minint) THEN a.int := a.int DIV b.int ELSE success := FALSE END
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|"M": a.int := a.int MOD b.int
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|"L": a.int := _LSL(a.int, b.int)
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|"A": a.int := _ASR(a.int, b.int)
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|"O": a.int := _ROR(a.int, b.int)
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|"R": a.int := _LSR(a.int, b.int)
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|"m": a.int := MIN(a.int, b.int)
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|"x": a.int := MAX(a.int, b.int)
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END;
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a.typ := tINTEGER
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RETURN success & check(a)
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END opInt;
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PROCEDURE charToStr* (c: VALUE; VAR s: ARRAY OF CHAR);
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BEGIN
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s[0] := CHR(c.int);
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s[1] := 0X
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END charToStr;
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PROCEDURE opSet* (VAR a: VALUE; b: VALUE; op: CHAR);
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BEGIN
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CASE op OF
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|"+": a.set := a.set + b.set
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|"-": a.set := a.set - b.set
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|"*": a.set := a.set * b.set
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|"/": a.set := a.set / b.set
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END;
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a.typ := tSET
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END opSet;
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PROCEDURE opFloat* (VAR a: VALUE; b: VALUE; op: CHAR): BOOLEAN;
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BEGIN
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a.typ := tREAL
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RETURN opFloat2(a.float, b.float, op) & check(a)
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END opFloat;
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PROCEDURE ord* (VAR v: VALUE);
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BEGIN
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CASE v.typ OF
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|tCHAR, tWCHAR:
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|tBOOLEAN: v.int := ORD(v.bool)
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|tSET:
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v.int := ORD(v.set);
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IF MACHINE._64to32 THEN
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v.int := MACHINE.Int32To64(v.int)
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END
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END;
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v.typ := tINTEGER
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END ord;
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PROCEDURE odd* (VAR v: VALUE);
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BEGIN
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v.typ := tBOOLEAN;
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v.bool := ODD(v.int)
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END odd;
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PROCEDURE bits* (VAR v: VALUE);
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BEGIN
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v.typ := tSET;
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v.set := BITS(v.int)
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END bits;
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PROCEDURE abs* (VAR v: VALUE): BOOLEAN;
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VAR
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res: BOOLEAN;
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BEGIN
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res := FALSE;
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|
|
CASE v.typ OF
|
|
|tREAL:
|
|
v.float := ABS(v.float);
|
|
res := TRUE
|
|
|tINTEGER:
|
|
IF v.int # UTILS.minint THEN
|
|
v.int := ABS(v.int);
|
|
res := TRUE
|
|
END
|
|
END
|
|
|
|
RETURN res
|
|
END abs;
|
|
|
|
|
|
PROCEDURE floor* (VAR v: VALUE): BOOLEAN;
|
|
VAR
|
|
res: BOOLEAN;
|
|
|
|
BEGIN
|
|
v.typ := tINTEGER;
|
|
res := (FLT(UTILS.minint) <= v.float) & (v.float <= FLT(UTILS.maxint));
|
|
IF res THEN
|
|
v.int := FLOOR(v.float)
|
|
END
|
|
|
|
RETURN res
|
|
END floor;
|
|
|
|
|
|
PROCEDURE flt* (VAR v: VALUE);
|
|
BEGIN
|
|
v.typ := tREAL;
|
|
v.float := FLT(v.int)
|
|
END flt;
|
|
|
|
|
|
PROCEDURE neg* (VAR v: VALUE): BOOLEAN;
|
|
VAR
|
|
z: VALUE;
|
|
res: BOOLEAN;
|
|
|
|
BEGIN
|
|
res := TRUE;
|
|
|
|
z.typ := tINTEGER;
|
|
z.int := 0;
|
|
|
|
CASE v.typ OF
|
|
|tREAL: v.float := -v.float
|
|
|tSET: v.set := -v.set
|
|
|tINTEGER: res := opInt(z, v, "-"); v := z
|
|
|tBOOLEAN: v.bool := ~v.bool
|
|
END
|
|
|
|
RETURN res
|
|
END neg;
|
|
|
|
|
|
PROCEDURE setbool* (VAR v: VALUE; b: BOOLEAN);
|
|
BEGIN
|
|
v.bool := b;
|
|
v.typ := tBOOLEAN
|
|
END setbool;
|
|
|
|
|
|
PROCEDURE opBoolean* (VAR a: VALUE; b: VALUE; op: CHAR);
|
|
BEGIN
|
|
CASE op OF
|
|
|"&": a.bool := a.bool & b.bool
|
|
|"|": a.bool := a.bool OR b.bool
|
|
END;
|
|
a.typ := tBOOLEAN
|
|
END opBoolean;
|
|
|
|
|
|
PROCEDURE range* (i: VALUE; a, b: INTEGER): BOOLEAN;
|
|
RETURN (a <= i.int) & (i.int <= b)
|
|
END range;
|
|
|
|
|
|
PROCEDURE less (v, v2: VALUE; VAR error: INTEGER): BOOLEAN;
|
|
VAR
|
|
res: BOOLEAN;
|
|
|
|
BEGIN
|
|
res := FALSE;
|
|
|
|
IF (v.typ = v2.typ) OR (v.typ IN {tCHAR, tWCHAR}) & (v2.typ IN {tCHAR, tWCHAR}) THEN
|
|
CASE v.typ OF
|
|
|tINTEGER,
|
|
tWCHAR,
|
|
tCHAR: res := v.int < v2.int
|
|
|tREAL: res := v.float < v2.float
|
|
|tBOOLEAN,
|
|
tSET: error := 1
|
|
END
|
|
ELSE
|
|
error := 1
|
|
END
|
|
|
|
RETURN res
|
|
END less;
|
|
|
|
|
|
PROCEDURE equal (v, v2: VALUE; VAR error: INTEGER): BOOLEAN;
|
|
VAR
|
|
res: BOOLEAN;
|
|
|
|
BEGIN
|
|
res := FALSE;
|
|
|
|
IF (v.typ = v2.typ) OR (v.typ IN {tCHAR, tWCHAR}) & (v2.typ IN {tCHAR, tWCHAR}) THEN
|
|
CASE v.typ OF
|
|
|tINTEGER,
|
|
tWCHAR,
|
|
tCHAR: res := v.int = v2.int
|
|
|tREAL: res := v.float = v2.float
|
|
|tBOOLEAN: res := v.bool = v2.bool
|
|
|tSET: res := v.set = v2.set
|
|
END
|
|
ELSE
|
|
error := 1
|
|
END
|
|
|
|
RETURN res
|
|
END equal;
|
|
|
|
|
|
PROCEDURE relation* (VAR v: VALUE; v2: VALUE; operator: RELATION; VAR error: INTEGER);
|
|
VAR
|
|
res: BOOLEAN;
|
|
|
|
BEGIN
|
|
error := 0;
|
|
|
|
res := FALSE;
|
|
|
|
CASE operator[0] OF
|
|
|
|
|"=":
|
|
res := equal(v, v2, error)
|
|
|
|
|"#":
|
|
res := ~equal(v, v2, error)
|
|
|
|
|"<":
|
|
IF operator[1] = "=" THEN
|
|
res := less(v, v2, error);
|
|
IF error = 0 THEN
|
|
res := equal(v, v2, error) OR res
|
|
END
|
|
ELSE
|
|
res := less(v, v2, error)
|
|
END
|
|
|
|
|">":
|
|
IF operator[1] = "=" THEN
|
|
res := ~less(v, v2, error)
|
|
ELSE
|
|
res := less(v, v2, error);
|
|
IF error = 0 THEN
|
|
res := equal(v, v2, error) OR res
|
|
END;
|
|
res := ~res
|
|
END
|
|
|
|
|"I":
|
|
IF (v.typ = tINTEGER) & (v2.typ = tSET) THEN
|
|
IF range(v, 0, MACHINE.target.maxSet) THEN
|
|
res := v.int IN v2.set
|
|
ELSE
|
|
error := 2
|
|
END
|
|
ELSE
|
|
error := 1
|
|
END
|
|
|
|
END;
|
|
|
|
IF error = 0 THEN
|
|
v.bool := res;
|
|
v.typ := tBOOLEAN
|
|
END
|
|
|
|
END relation;
|
|
|
|
|
|
PROCEDURE emptySet* (VAR v: VALUE);
|
|
BEGIN
|
|
v.typ := tSET;
|
|
v.set := {}
|
|
END emptySet;
|
|
|
|
|
|
PROCEDURE constrSet* (VAR v: VALUE; a, b: VALUE);
|
|
BEGIN
|
|
v.typ := tSET;
|
|
v.set := {a.int .. b.int}
|
|
END constrSet;
|
|
|
|
|
|
PROCEDURE getInt* (v: VALUE): INTEGER;
|
|
BEGIN
|
|
ASSERT(check(v))
|
|
|
|
RETURN v.int
|
|
END getInt;
|
|
|
|
|
|
PROCEDURE setInt* (VAR v: VALUE; i: INTEGER): BOOLEAN;
|
|
BEGIN
|
|
v.int := i;
|
|
v.typ := tINTEGER
|
|
|
|
RETURN check(v)
|
|
END setInt;
|
|
|
|
|
|
PROCEDURE init;
|
|
VAR
|
|
i: INTEGER;
|
|
|
|
BEGIN
|
|
FOR i := 0 TO LEN(digit) - 1 DO
|
|
digit[i] := -1
|
|
END;
|
|
|
|
FOR i := ORD("0") TO ORD("9") DO
|
|
digit[i] := i - ORD("0")
|
|
END;
|
|
|
|
FOR i := ORD("A") TO ORD("F") DO
|
|
digit[i] := i - ORD("A") + 10
|
|
END
|
|
END init;
|
|
|
|
|
|
BEGIN
|
|
init
|
|
END ARITH. |