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Arithmetic functions are terms which are evaluated by the arithmetic predicates described in section 4.27.2. There are four types of arguments to functions:
|Expr||Arbitrary expression, returning either a floating point value or an integer.|
|IntExpr||Arbitrary expression that must evaluate to an integer.|
|RatExpr||Arbitrary expression that must evaluate to a rational number.|
|FloatExpr||Arbitrary expression that must evaluate to a floating point.|
For systems using bounded integer arithmetic (default is unbounded, see section 126.96.36.199 for details), integer operations that would cause overflow automatically convert to floating point arithmetic.
SWI-Prolog provides many extensions to the set of floating point functions defined by the ISO standard. The current policy is to provide such functions on `as-needed' basis if the function is widely supported elsewhere and notably if it is part of the C99 mathematical library. In addition, we try to maintain compatibility with YAP.
is followed by a number, the parser discards the
true, both arguments are converted to float and the return value is a float. Otherwise (default), if both arguments are integers the operation returns an integer if the division is exact. If at least one of the arguments is rational and the other argument is integer, the operation returns a rational number. In all other cases the return value is a float. See also ///2 and rdiv/2.
divis floored division.
towards_zero.111Future versions might guarantee rounding towards zero.
Y =\= 0.
Q is div(X, Y), M is mod(X, Y), X =:= Y*Q+M.
"a"evaluates to the character code of the letter `a' (97) using the traditional mapping of double quoted string to a list of character codes. Arithmetic evaluation also translates a string object (see section 5.2) of one character length into the character code for that character. This implies that expression
"a"also works of the Prolog flag double_quotes is set to
string. The recommended way to specify the character code of the letter `a' is
/dev/random.112On Windows the state is initialised from CryptGenRandom(). Otherwise it is set from the system clock. If unbounded arithmetic is not supported, random numbers are shared between threads and the seed is initialised from the clock when SWI-Prolog was started. The predicate set_random/1 can be used to control the random number generator.
Warning! Although properly seeded (if supported on the OS),
the Mersenne Twister algorithm does not produce
cryptographically secure random numbers. To generate cryptographically
secure random numbers, use crypto_n_random_bytes/2
library(crypto) provided by the
floor(Expr+1/2), i.e., rounding down. This is an unconventional choice and under which the relation
round(Expr) == -round(-Expr)does not hold. SWI-Prolog rounds outward, e.g.,
round(1.5) =:= 2and round
round(-1.5) =:= -2.
rational(0.1). The function rationalize/1 remedies this. See section 188.8.131.52 for more information on rational number support.
?- A is rational(0.25). A is 1 rdiv 4 ?- A is rational(0.1). A = 3602879701896397 rdiv 36028797018963968
?- A is rationalize(0.25). A = 1 rdiv 4 ?- A is rationalize(0.1). A = 1 rdiv 10
floor(Expr). For Expr < 0 this is the same as
ceil(Expr). That is, truncate/1 rounds towards zero.
Note that the ISO Prolog standard demands
to raise an evaluation error, whereas the C99 and POSIX standards demand
this to evaluate to 0.0. SWI-Prolog follows C99 and POSIX.
resourceerror if the result does not fit in memory.
The ISO standard demands a float result for all inputs and introduces ^/2 for integer exponentiation. The function float/1 can be used on one or both arguments to force a floating point result. Note that casting the input result in a floating point computation, while casting the output performs integer exponentiation followed by a conversion to float.
|Int||Int||**/2||Int or Float||Float|
|Int||Int||^/2||Int or Float||Int or error|
The functions below are not covered by the standard. The
msb/1 function also
appears in hProlog and SICStus Prolog. The getbit/2
function also appears in ECLiPSe, which also provides
clrbit(Vector,Index). The others are SWI-Prolog
extensions that improve handling of ---unbounded--- integers as
(IntExpr >> N) /\ 1 =:= 1. This is the (zero-origin) index of the most significant 1 bit in the value of IntExpr, which must evaluate to a positive integer. Errors for 0, negative integers, and non-integers.
(IntExpr >> N) /\ 1 =:= 1. This is the (zero-origin) index of the least significant 1 bit in the value of IntExpr, which must evaluate to a positive integer. Errors for 0, negative integers, and non-integers.
(IntExprV >> IntExprI)/\1, but more efficient because materialization of the shifted value is avoided. Future versions will optimise
(IntExprV >> IntExprI)/\1to a call to getbit/2, providing both portability and performance.118This issue was fiercely debated at the ISO standard mailinglist. The name getbit was selected for compatibility with ECLiPSe, the only system providing this support. Richard O'Keefe disliked the name and argued that efficient handling of the above implementation is the best choice for this functionality.