10.5.16 Arithmetic

Standard arithmetic functions including things like rounding, sign manipulation, and maximum/minimum functions.

roundUp( x )

Rounds a value up to an integer value. Formally, returns the smallest (closest to negative infinity) integer value that is not less than the argument.

• x (floating point): a value.
• return value (integer): x rounded up

roundDown( x )

Rounds a value down to an integer value. Formally, returns the largest (closest to positive infinity) integer value that is not greater than the argument.

• x (floating point): a value
• return value (integer): x rounded down

round( x )

Rounds a value to the nearest integer. Formally, returns the integer that is closest in value to the argument. If two integers are equally close, the result is the even one.

• x (floating point): a floating point value.
• return value (integer): x rounded to the nearest integer

roundDecimal( x, dp )

Rounds a value to a given number of decimal places. The result is a float (32-bit floating point value), so this is only suitable for relatively low-precision values. It's intended for truncating the number of apparent significant figures represented by a value which you know has been obtained by combining other values of limited precision. For more control, see the functions in the Formats class.

• x (floating point): a floating point value
• dp (integer): number of decimal places (digits after the decimal point) to retain
• return value (floating point): floating point value close to x but with a limited apparent precision

abs( x )

Returns the absolute value of an integer value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

• x (integer): the argument whose absolute value is to be determined
• return value (integer): the absolute value of the argument.

abs( x )

Returns the absolute value of a floating point value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

• x (floating point): the argument whose absolute value is to be determined
• return value (floating point): the absolute value of the argument.

max( a, b )

Returns the greater of two integer values. If the arguments have the same value, the result is that same value.

Multiple-argument maximum functions are also provided in the Arrays and Lists packages.

• a (integer): an argument.
• b (integer): another argument.
• return value (integer): the larger of a and b.

maxNaN( a, b )

Returns the greater of two floating point values. If the arguments have the same value, the result is that same value. If either value is blank, then the result is blank.

• a (floating point): an argument.
• b (floating point): another argument.
• return value (floating point): the larger of a and b.

maxReal( a, b )

Returns the greater of two floating point values, ignoring blanks. If the arguments have the same value, the result is that same value. If one argument is blank, the result is the other one. If both arguments are blank, the result is blank.

Multiple-argument maximum functions are also provided in the Arrays and Lists packages.

• a (floating point): an argument
• b (floating point): another argument
• return value (floating point): the larger non-blank value of a and b

min( a, b )

Returns the smaller of two integer values. If the arguments have the same value, the result is that same value.

Multiple-argument minimum functions are also provided in the Arrays and Lists packages.

• a (integer): an argument.
• b (integer): another argument.
• return value (integer): the smaller of a and b.

minNaN( a, b )

Returns the smaller of two floating point values. If the arguments have the same value, the result is that same value. If either value is blank, then the result is blank.

• a (floating point): an argument.
• b (floating point): another argument.
• return value (floating point): the smaller of a and b.

minReal( a, b )

Returns the smaller of two floating point values, ignoring blanks. If the arguments have the same value, the result is that same value. If one argument is blank, the result is the other one. If both arguments are blank, the result is blank.

Multiple-argument minimum functions are also provided in the Arrays and Lists packages.

• a (floating point): an argument
• b (floating point): another argument
• return value (floating point): the larger non-blank value of a and b