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6.6.6 Required functions

6.6.6.1 General

The required functions shall be arithmetic functions, transfer functions, ordinal functions, and Boolean functions.

6.6.6.2 Arithmetic functions

For the following arithmetic functions, the expression x shall be either of real-type or integer-type. For the functions abs and sqr, the type of the result shall be the same as the type of the parameter, x. For the remaining arithmetic functions, the result shall always be of real-type. The result shall be as shown in table 2.

Table 2 --- Arithmetic function results

Function Result

abs(x) absolute value of x

sqr(x) square of x

It shall be an error if such a value does not exist.

sin(x) sine of x, where x is in radians

cos(x) cosine of x, where x is in radians

exp(x) base of natural logarithms raised to the power x

ln(x) natural logarithm of x, if x is greater than zero

It shall be an error if x is not greater than zero.

sqrt(x) non-negative square root of x, if x is not negative

It shall be an error if x is negative.

`arctan(x) principal value, in radians, of the arctangent of x

6.6.6.3 Transfer functions

trunc(x)

From the expression x that shall be of real-type, this function shall return a result of integer-type. The value of trunc(x) shall be such that if x is positive or zero, then 0£x-trunc(x)<1; otherwise, -1<x-trunc(x)£0. It shall be an error if such a value does not exist.

Examples:

trunc(3.5) {yields 3}

trunc(-3.5) {yields -3}

round(x)

From the expression x that shall be of real-type, this function shall return a result of integer-type. If x is positive or zero, round(x) shall be equivalent to trunc(x+0.5); otherwise, round(x) shall be equivalent to trunc(x-0.5). It shall be error if such a value does not exist.

Examples:

round(3.5) {yields 4}

round(-3.5) {yields -4}

6.6.6.4 Ordinal functions

ord(x)

From the expression x that shall be of an ordinal-type, this function shall return a result of integer-type that shall be the ordinal number (see 6.4.2.2 and 6.4.2.3) of the value of the expression x.

chr(x)

From the expression x that shall be of integer-type, this function shall return a result of char-type that shall be the value whose ordinal number is equal to the value of the expression x, if such a character value exists. It shall be an error if such a character value does not exist. For any value, ch, of char-type, it shall be true that

chr(ord(ch)) = ch

succ(x)

From the expression x that shall be of an ordinal-type, this function shall return a result that shall be of the same type as that of the expression (see 6.7.1). The function shall yield a value whose ordinal number is one greater than that of the expression x, if such a value exists. It shall be an error if such a value does not exist.

pred(x)

From the expression x that shall be of an ordinal-type, this function shall return a result that shall be of the same type as that of the expression (see 6.7.1). The function shall yield a value whose ordinal number is one less than that of the expression x, if such a value exists. It shall be an error if such a value does not exist.

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