By Dominique Hervé

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**Extra resources for Parures de rêve: Perles de cristal et perles de rocaille**

**Sample text**

Occur.. The fact that negative values are strictly excluded ft'om the set of cardinals requires care. , for example, is likely to succumb to the following plttall: Assume that a statement S is to be executed repeatedly with variable I having values N-I, N-2, ... , I, O. The statements 1:= N-I; WInLEi)=ODO S; 1:= i-I END will perform correctly, if I is of type INTEGER.. However, if I is CARDINAL, the computation will fan, because it generates the value -1. The expression i ) 0 is, in fact, vacuous, because cardinals are always non-negative.

0; i:= i-1 UNTILi = 0; WriteReal(s2, 16); WriteLn; WriteString(tln = tI); ReadCard(n) END; WriteLn END Harmonic. The major reason for strictly distinguishing between real numbers and integers lies in the different representation used internally. Hence, also the arithmetic operations are implemented by instructions which are distinct for each type. Modula therefore disallows expressions with mixed operands. However, integers can be transformed into real numbers (more exactly: internal representations as integers can be transformed into their corresponding floating-point representation) by explicit transfer functions, namely FLOAT(c) TRUNC(x) FLOAT(c) is of type REAL and represents the value of the cardinal c; TRUNC(x) represents the truncated real value x and is of type CARDINAL.

WriteString. WriteCard; CONST Base = 10; N = 32; VAR i. j. m: CARDINAL; rem: CARDINAL; d: ARRAY [1 .. N] OF CARDINAL; (*digits*) x: ARRAY [0 .. N] OF CARDINAL; (*index*) BEGIN FORi:= 2TONDO FOR j : = 0 TO i-I DO xU] : = 0 END ; 44 m:=O;rem:=l; REPEAT m:= m+l; x[rem]:= m; rem : = Base. "); FOR j : = 1 TO x[rem]-l 00 Write(CHR(d[f]+ORD("O"») END ; Write(""'); FORj : = x[rem] TO m 00 Wrfte(CHR(d[f]+ORD("O"») END ; WriteLn END END Fractions. 6'0 o. 1'6 O. 126'0 O. 1'0 o. 08'3 O. 05'0 O. 03125'0 4S Our last example of a program computes a list of prime numbers.