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|
(******************************************************************************)
(* Copyright (c) 1990 by GMD Karlruhe, Germany *)
(* Gesellschaft fuer Mathematik und Datenverarbeitung *)
(* (German National Research Center for Computer Science) *)
(* Forschungsstelle fuer Programmstrukturen an Universitaet Karlsruhe *)
(* All rights reserved. *)
(******************************************************************************)
IMPLEMENTATION MODULE RealConv;
(* (w) 1990 CvR *)
(* 03/93 HH : Endlosschleife bei Infinity beseitigt *)
(* 03/93 HH : korrekte Ueberprufung HIGH(s) bei LongReal2Str *)
(* 03/93 HH : Unterscheidung von Infinity und Nan *)
(* 04/93 HH : Sonderbehandlung bei MIPS *)
FROM LREAL IMPORT LFLOAT, LTRUNC;
(* ++ HH 10.03.93 ++ *)
TYPE LRTRANSLATE = RECORD
CASE : BOOLEAN OF
| TRUE : r : LONGREAL;
| FALSE : c2, c1 : LONGCARD;
END;
END;
RTRANSLATE = RECORD
CASE : BOOLEAN OF
| TRUE : r : REAL;
| FALSE : c : LONGCARD;
END;
END;
PROCEDURE IsLongRealInfinityOrNaN (x: LONGREAL) : BOOLEAN;
VAR tr : LRTRANSLATE;
BEGIN
tr.r := x;
RETURN ((tr.c1 DIV 00100000H) MOD 0800H) = 07FFH
END IsLongRealInfinityOrNaN;
PROCEDURE IsRealInfinityOrNaN (x: REAL) : BOOLEAN;
VAR tr : RTRANSLATE;
BEGIN
tr.r := x;
RETURN ((tr.c DIV 00800000H) MOD 0100H) = 0FFH
END IsRealInfinityOrNaN;
PROCEDURE IsLongRealInfinity (x: LONGREAL) : BOOLEAN;
VAR tr : LRTRANSLATE;
BEGIN
tr.r := x;
RETURN (((tr.c1 DIV 00100000H) MOD 0800H) = 07FFH) AND
((tr.c1 MOD 00100000H) = 0)
END IsLongRealInfinity;
PROCEDURE IsRealInfinity (x: REAL) : BOOLEAN;
VAR tr : RTRANSLATE;
BEGIN
tr.r := x;
RETURN (((tr.c DIV 00800000H) MOD 0100H) = 0FFH) AND
((tr.c MOD 00800000H) = 0)
END IsRealInfinity;
(* ++ HH 10.03.93 ++ *)
PROCEDURE Pow10(e: INTEGER): REAL;
(* Returns 10 to the 'e's. *)
VAR
expNeg: BOOLEAN;
b, x: REAL;
BEGIN
expNeg := e<0;
e := ABS(e);
b := 10.0;
x := 1.0;
WHILE e#0 DO
IF ODD(e) THEN
x := x*b;
END;
b := b*b; e := e DIV 2;
END;
IF expNeg THEN
RETURN 1.0/x;
ELSE
RETURN x;
END;
END Pow10;
PROCEDURE LPow10(e: INTEGER): LONGREAL;
(* Returns 10 to the 'e's. *)
VAR
expNeg: BOOLEAN;
b, x: LONGREAL;
BEGIN
expNeg := e<0;
e := ABS(e);
b := 10.0;
x := 1.0;
WHILE e#0 DO
IF ODD(e) THEN
x := x*b;
END;
b := b*b; e := e DIV 2;
END;
IF expNeg THEN
RETURN 1.0/x;
ELSE
RETURN x;
END;
END LPow10;
PROCEDURE Str2Real(s: ARRAY OF CHAR; VAR done: BOOLEAN): REAL;
(* Converts the string 's' to real 'x'. *)
(* s has to be of the form: *)
(* real = num ['.' {digit}] ['E' num]. *)
(* num = ['+'|'-'] digit {digit}. *)
CONST
HighM = 0;
(* HighM+1 Cardinals will be used to store the Mantissa. *)
VAR
i: CARDINAL;
e, fractionDigits, truncatedDigits: INTEGER;
phase: (Integral,Fractional);
M: ARRAY[0..HighM] OF CARDINAL;
(* Will hold the DezimalMantissa. *)
N: ARRAY[0..HighM] OF INTEGER;
(* N[i]= Number of decimal digits stored in M[i]. *)
m: CARDINAL;
(* The actual Index for M and N. *)
x: REAL;
mantNeg, expNeg: BOOLEAN;
BEGIN
done:=FALSE; mantNeg:=FALSE;
i:=0;
fractionDigits:=0; truncatedDigits:=0;
FOR m:=0 TO HighM DO M[m]:=0; N[m]:=0; END;
m:=0;
phase := Integral;
IF s[i]='-' THEN
INC(i);
mantNeg := TRUE;
ELSIF s[i]='+' THEN
INC(i);
END;
IF (i<=HIGH(s)) & (s[i]#0C) THEN
REPEAT
IF ('0'<=s[i]) & (s[i]<='9') THEN
IF phase=Fractional THEN
INC(fractionDigits);
END;
IF (m<HighM) & (M[m]>=MAX(INTEGER) DIV 10) THEN
(* MUST be MAX(INTEGER) since we're *)
(* calling LFLOAT(x:INTEGER) with it. *)
INC(m);
END;
IF M[m]<MAX(INTEGER) DIV 10 THEN
M[m] := M[m]*10 + (ORD(s[i]) - ORD('0')); INC(N[m]);
ELSE
INC(truncatedDigits);
END;
ELSIF (phase=Integral) & (s[i]='.') THEN
phase := Fractional;
ELSE
RETURN 0.0;
END;
INC(i);
UNTIL (i>HIGH(s)) OR (s[i]=0C) OR (s[i]='E');
END;
e:=0; expNeg:=FALSE;
IF (i<=HIGH(s)) & (s[i]#0C) & (s[i]='E') THEN
INC(i);
IF (i>HIGH(s)) OR (s[i]=0C) THEN RETURN 0.0; END;
IF s[i]='-' THEN
INC(i);
expNeg := TRUE;
ELSIF s[i]='+' THEN
INC(i);
END;
IF (i>HIGH(s)) OR (s[i]=0C) THEN RETURN 0.0; END;
REPEAT
IF ('0'<=s[i]) & (s[i]<='9') THEN
e:=e*10+INTEGER(ORD(s[i])-ORD('0'));
(* ToDo: Overflowchecks !!! *)
ELSE
RETURN 0.0;
END;
INC(i);
UNTIL (i>HIGH(s)) OR (s[i]=0C);
IF expNeg THEN e:=-e END;
END;
e:=e-fractionDigits+truncatedDigits;
(* ToDo: Overflowchecks !!! *)
x:=0.0;
LOOP
x:=x+FLOAT(M[m])*Pow10(e);
IF m=0 THEN EXIT; END;
e:=e+N[m];
DEC(m);
END;
done := TRUE;
IF mantNeg THEN
RETURN -x;
ELSE
RETURN x;
END;
END Str2Real;
PROCEDURE Str2LongReal(s: ARRAY OF CHAR; VAR done: BOOLEAN): LONGREAL;
(* Converts the string 's' to real 'x'. *)
(* s has to be of the form: *)
(* real = num ['.' {digit}] ['E' num]. *)
(* num = ['+'|'-'] digit {digit}. *)
CONST
HighM = 1;
(* HighM+1 Cardinals will be used to store the Mantissa. *)
VAR
i: CARDINAL;
e, fractionDigits, truncatedDigits: INTEGER;
phase: (Integral,Fractional);
M: ARRAY[0..HighM] OF CARDINAL;
(* Will hold the DezimalMantissa. *)
N: ARRAY[0..HighM] OF INTEGER;
(* N[i]= Number of decimal digits stored in M[i]. *)
m: CARDINAL;
(* The actual Index for M and N. *)
x: LONGREAL;
mantNeg, expNeg: BOOLEAN;
BEGIN
done:=FALSE; mantNeg:=FALSE;
i:=0;
fractionDigits:=0; truncatedDigits:=0;
FOR m:=0 TO HighM DO M[m]:=0; N[m]:=0; END;
m:=0;
phase := Integral;
IF s[i]='-' THEN
INC(i);
mantNeg := TRUE;
ELSIF s[i]='+' THEN
INC(i);
END;
IF (i<=HIGH(s)) & (s[i]#0C) THEN
REPEAT
IF ('0'<=s[i]) & (s[i]<='9') THEN
IF phase=Fractional THEN
INC(fractionDigits);
END;
IF (m<HighM) & (M[m]>=MAX(INTEGER) DIV 10) THEN
INC(m);
END;
IF M[m]<MAX(INTEGER) DIV 10 THEN
M[m] := M[m]*10 + (ORD(s[i]) - ORD('0')); INC(N[m]);
ELSE
INC(truncatedDigits);
END;
ELSIF (phase=Integral) & (s[i]='.') THEN
phase := Fractional;
ELSE
RETURN 0.0;
END;
INC(i);
UNTIL (i>HIGH(s)) OR (s[i]=0C) OR (s[i]='E');
END;
e:=0; expNeg:=FALSE;
IF (i<=HIGH(s)) & (s[i]='E') THEN
INC(i);
IF (i>HIGH(s)) OR (s[i]=0C) THEN RETURN 0.0; END;
IF s[i]='-' THEN
INC(i);
expNeg := TRUE;
ELSIF s[i]='+' THEN
INC(i);
END;
IF (i>HIGH(s)) OR (s[i]=0C) THEN RETURN 0.0; END;
REPEAT
IF ('0'<=s[i]) & (s[i]<='9') THEN
e:=e*10+INTEGER(ORD(s[i])-ORD('0'));
(* ToDo: Overflowchecks !!! *)
ELSE
RETURN 0.0;
END;
INC(i);
UNTIL (i>HIGH(s)) OR (s[i]=0C);
IF expNeg THEN e:=-e END;
END;
e:=e-fractionDigits+truncatedDigits;
(* ToDo: Overflowchecks !!! *)
x:=0.0;
LOOP
x:=x+LFLOAT(M[m])*LPow10(e);
IF m=0 THEN EXIT; END;
e:=e+N[m];
DEC(m);
END;
done := TRUE;
IF mantNeg THEN
RETURN -x;
ELSE
RETURN x;
END;
END Str2LongReal;
PROCEDURE Real2Str (x : REAL; n : CARDINAL; k : INTEGER;
VAR S: ARRAY OF CHAR; VAR done: BOOLEAN);
(* Convert real 'x' into external representation. *)
(* If k > 0 use k decimal places. *)
(* If k = 0 write x as integer. *)
(* If k < 0 use scientific notation. *)
BEGIN
LongReal2Str(x,n,k,S,done);
END Real2Str;
PROCEDURE LongReal2Str (x : LONGREAL; n : CARDINAL; k : INTEGER;
VAR S: ARRAY OF CHAR; VAR done: BOOLEAN);
(* Convert long real 'x' into external representation.*)
(* If k > 0 use k decimal places. *)
(* If k = 0 write x as integer. *)
(* If k < 0 use scientific notation. *)
VAR
xl : LONGREAL;
c : CARDINAL;
neg : BOOLEAN;
exp, i, p, rexp : INTEGER;
blanks, ExpLength,
n0, i0, k0, exp0 : INTEGER;
BEGIN
done:=FALSE; S[0]:=0C;
IF HIGH(S)+1<n THEN RETURN END; (* Result won't fit into given String *)
(* ++ HH 10.03.93 ++ *)
IF IsLongRealInfinityOrNaN (x)
THEN
IF HIGH(S) >= 8
THEN
IF IsLongRealInfinity (x)
THEN
IF n > 9 THEN p := n-1 ELSE p := 8 END;
FOR i := 0 TO p-9 DO S[i] := ' ' END;
IF x > 0.0 THEN S[p-8] := ' ' ELSE S[p-8] := '-' END;
S[p-7] := 'I';
S[p-6] := 'n';
S[p-5] := 'f';
S[p-4] := 'i';
S[p-3] := 'n';
S[p-2] := 'i';
S[p-1] := 't';
S[p ] := 'y';
ELSE
IF n > 3 THEN p := n-1 ELSE p := 3 END;
FOR i := 0 TO p-3 DO S[i] := ' ' END;
S[p-2] := 'N';
S[p-1] := 'a';
S[p ] := 'N';
END;
IF p+1 <= VAL (INTEGER,HIGH(S)) THEN S[p+1] := 0C END;
done := TRUE;
ELSE
S[0] := 0C;
done := FALSE;
END;
RETURN
END;
(* ++ HH 10.03.93 ++ *)
p:=0;
n0 := n;
k0 := k;
neg := x < 0.0;
IF neg THEN x := -x; END;
IF k>=0 THEN
x:=x+0.5*LPow10(-k);
END;
(* get exponent *)
exp := 0;
IF x >= 10.0 THEN
REPEAT
INC (exp); x := x / 10.0;
UNTIL x < 10.0;
ELSIF (x < 1.0) & (x # 0.0) THEN
REPEAT
DEC (exp); x := x * 10.0;
UNTIL x >= 1.0;
END;
IF k<0 THEN
x:=x+0.5*LPow10(k);
END;
IF x>=10.0 THEN
INC(exp); x:=x/10.0;
END;
(* calculate leading blanks *)
exp0 := exp;
ExpLength := 0;
REPEAT
INC (ExpLength); exp0 := exp0 DIV 10;
UNTIL exp0 = 0;
IF k < 0 THEN
blanks := n0 - (-k0 + 3 + ExpLength);
IF exp < 0 THEN DEC (blanks); END;
ELSE
IF k > 0 THEN
IF exp < 0 THEN
blanks := n0 - (k0 + 2);
ELSE
blanks := n0 - (exp + 2 + k0); (* HH 16.03.93 war: exp0 *)
END;
ELSE
IF exp < 0 THEN
(* will be zero *)
neg := FALSE;
blanks := n0 - 1;
ELSE
blanks := n0 - (exp + 1); (* HH 16.03.93 war: exp0 *)
END;
END;
END;
IF neg THEN DEC (blanks); END;
IF (blanks<0) & (VAL(INTEGER,n)-VAL(INTEGER,HIGH(S))>blanks) THEN
RETURN (* Result won't fit into given string. *)
END;
done:=TRUE;
(* fill in leading blanks *)
WHILE blanks > 0 DO
S[p]:=' '; INC(p);
DEC(blanks);
END;
(* sign *)
IF neg THEN
S[p]:='-'; INC(p);
END;
(* absolute value *)
IF k >= 0 THEN
IF exp < 0 THEN
S[p]:='0'; INC(p);
ELSE
FOR i := 0 TO exp DO
c := LTRUNC (x);
S[p]:=VAL (CHAR, ORD ('0') + c); INC(p);
xl := LFLOAT (c);
x := (x - xl) * 10.0;
END;
END;
ELSE (* k < 0 *)
c := LTRUNC (x);
S[p]:=VAL (CHAR, ORD ('0') + c); INC(p);
xl := LFLOAT (c);
x := (x - xl) * 10.0;
END;
IF k # 0 THEN
S[p]:='.'; INC(p);
IF (k > 0) & (exp < 0) THEN
IF k < ABS (exp) THEN
FOR i := 1 TO k DO
S[p]:='0'; INC(p);
END;
IF p<=VAL(INTEGER,HIGH(S)) THEN S[p]:=0C; END;
RETURN
ELSE
FOR i := 1 TO ABS (exp) - 1 DO
S[p]:='0'; INC(p);
END;
k := k + exp + 1;
END;
END;
FOR i := 1 TO ABS (k) DO
c := LTRUNC (x);
S[p]:=VAL (CHAR, ORD ('0') + c); INC(p);
xl := LFLOAT (c);
x := (x - xl) * 10.0;
END;
IF k < 0 THEN
S[p]:='E'; INC(p);
IF exp<0 THEN exp:=-exp;
S[p]:='-'; INC(p);
END;
i:=ExpLength-1;
WHILE i>=0 DO
S[p+i]:=VAL(CHAR, ORD('0')+exp MOD 10); exp:=exp DIV 10;
DEC(i);
END;
INC(p,ExpLength);
END;
END;
IF p<=VAL(INTEGER,HIGH(S)) THEN S[p]:=0C; END;
END LongReal2Str;
END RealConv.
|
