An arithmetic expression is a Prolog term built from numbers, variables, and functors (or operators) that represent arithmetic functions. When an expression is evaluated each variable must be bound to a non-variable expression. An expression evaluates to a number, which may be an integer or a floating point number. The following table details the components of an arithmetic expression, how they are evaluated, the types expected/returned and if they are ISO or an extension:
Expression Result = eval(Expression)Signature ISO a variable bound to an expression E, result is eval(E)IF → IF Y an integer number this numberI Y a floating point number this numberF Y pi the value of π = 3.141592...F Y e the value of e = 2.718281...F N epsilon difference between 1.0 and minimum float > 1.0F N + E eval(E)IF → IF Y - E - eval(E)IF → IF Y inc(E) eval(E) + 1IF → IF N dec(E) eval(E) - 1IF → IF N E1 + E2 eval(E1) + eval(E2)IF, IF → IF Y E1 - E2 eval(E1) - eval(E2)IF, IF → IF Y E1 * E2 eval(E1) * eval(E2)IF, IF → IF Y E1 / E2 eval(E1) / eval(E2)IF, IF → F Y E1 // E2 rnd(eval(E1) / eval(E2))I, I → I Y E1 rem E2 eval(E1) - (rnd(eval(E1) / eval(E2)) * eval(E2))I, I → I Y E1 div E2 ⌊(eval(E1) - eval(E1) mod eval(E2)) / eval(E2)⌋I, I → I Y E1 mod E2 eval(E1) - (⌊eval(E1) / eval(E2)⌋ * eval(E2))I, I → I Y E1 /\ E2 eval(E1) bitwise_and eval(E2)I, I → I Y E1 \/ E2 eval(E1) bitwise_or eval(E2)I, I → I Y xor(E1,E2) eval(E1) bitwise_xor eval(E2)I, I → I Y \ E bitwise_not eval(E)I → I Y E1 << E2 eval(E1) integer_shift_left eval(E2)I, I → I Y E1 >> E2 eval(E1) integer_shift_right eval(E2)I, I → I Y lsb(E) least significant bit (from 0) of eval(E) or -1I → I N msb(E) most significant bit (from 0) of eval(E) or -1I → I N popcount(E) number of 1-bits in eval(E)I → I N abs(E) absolute value of eval(E)IF → IF Y sign(E) sign of eval(E) (-1 if < 0, 0 if = 0, +1 if > 0)IF → IF Y min(E1,E2) minimal value between eval(E1) and eval(E2)IF, IF → ? Y max(E1,E2) maximal value between eval(E1) and eval(E2)IF, IF → ? Y gcd(E1,E2) greatest common divisor of eval(E1) and eval(E2)I, I → I N E1 ^ E2 eval(E1) raised to the power of eval(E2)IF, IF → IF Y E1 ** E2 eval(E1) raised to the power of eval(E2)IF, IF → F Y sqrt(E) square root of eval(E)IF → F Y tan(E) tangent of eval(E)IF → F Y atan(E) arc tangent of eval(E)IF → F Y atan2(Y,X) principal value of arc tangent of eval(Y) / eval(X) using both signs for the quadrantIF → F Y cos(E) cosine of eval(E)IF → F Y acos(E) arc cosine of eval(E)IF, IF → F Y sin(E) sine of eval(E)IF → F Y asin(E) arc sine of eval(E)IF → F Y tanh(E) hyperbolic tangent of eval(E)IF → F N atanh(E) hyperbolic arc tangent of eval(E)IF → F N cosh(E) hyperbolic cosine of eval(E)IF → F N acosh(E) hyperbolic arc cosine of eval(E)IF, IF → F N sinh(E) hyperbolic sine of eval(E)IF → F N asinh(E) hyperbolic arc sine of eval(E)IF → F N exp(E) e raised to the power of eval(E)IF → F Y log(E) natural logarithm of eval(E)IF → F Y log10(E) base 10 logarithm of eval(E)IF → F N log(R, E) base eval(R) logarithm of eval(E)F, IF → F N float(E) the floating point number equal to eval(E)IF → F Y ceiling(E) rounds eval(E) upward to the nearest integerF → I Y floor(E) rounds eval(E) downward to the nearest integerF → I Y round(E) rounds eval(E) to the nearest integerF → I Y truncate(E) the integer value of eval(E)F → I Y float_fractional_part(E) the float equal to the fractional part of eval(E)F → F Y float_integer_part(E) the float equal to the integer part of eval(E)F → F Y
The meaning of the signature field is as follows:
is, +, -, *, /, //, div, rem, mod, /\, \/, <<, >>, ** and ^ are predefined infix operators. +, - and \, are predefined prefix operators (section 8.14.10).
Integer division rounding function: the integer division rounding function rnd(X) rounds the floating point number X to an integer. There are two possible definitions (depending on the target machine) for this function which differ on negative numbers:
The definition of this function determines the definition of the integer division and remainder ((//)/2 and (rem)/2). It is possible to test the value (toward_zero or down) of the integer_rounding_function Prolog flag to determine which function being used (section 8.22.1). Since rounding toward zero is the most common case, two additional evaluable functors ((div)/2 and (mod)/2) are available which consider rounding toward −∞.
Fast mathematical mode: in order to speed-up integer computations, the GNU Prolog compiler can generate faster code when invoked with the --fast-math option (section 4.4.3). In this mode only integer operations are allowed and a variable in an expression must be bound at evaluation time to an integer. No type checking is done.
Errors
a sub-expression E is a variable | instantiation_error | |
a sub-expression E is neither a number nor an evaluable functor | type_error(evaluable, E) | |
a sub-expression E is a floating point number while an integer is expected | type_error(integer, E) | |
a sub-expression E is an integer while a floating point number is expected | type_error(float, E) | |
a division by zero occurs | evaluation_error(zero_divisor) | |
Portability
Refer to the above table to determine which evaluable functors are ISO and which are GNU Prolog extensions. For efficiency reasons, GNU Prolog does not detect the following ISO arithmetic errors: float_overflow, int_overflow, int_underflow, and undefined.
Templates
Description
Result is Expression succeeds if Result can be unified with eval(Expression). Refer to the evaluation of an arithmetic expression for the definition of the eval function (section 8.6.1).
is is a predefined infix operator (section 8.14.10).
Errors
Refer to the evaluation of an arithmetic expression for possible errors (section 8.6.1).
Portability
ISO predicate.
Templates
Description
Expr1 =:= Expr2 succeeds if eval(Expr1) = eval(Expr2).
Expr1 =\= Expr2 succeeds if eval(Expr1) ≠ eval(Expr2).
Expr1 < Expr2 succeeds if eval(Expr1) < eval(Expr2).
Expr1 =< Expr2 succeeds if eval(Expr1) ≤ eval(Expr2).
Expr1 > Expr2 succeeds if eval(Expr1) > eval(Expr2).
Expr1 >= Expr2 succeeds if eval(Expr1) ≥ eval(Expr2).
Refer to the evaluation of an arithmetic expression for the definition of the eval function (section 8.6.1).
=:=, =\=, <, =<, > and >= are predefined infix operators (section 8.14.10).
Errors
Refer to the evaluation of an arithmetic expression for possible errors (section 8.6.1).
Portability
ISO predicates.
Templates
Description
succ(X, Y) is true iff Y is the successor of the non-negative integer X.
Errors
X and Y are both variables | instantiation_error | |
X is neither a variable nor an integer | type_error(integer, X) | |
Y is neither a variable nor an integer | type_error(integer, Y) | |
X is an integer < 0 | domain_error(not_less_than_zero, X) | |
Y is an integer < 0 | domain_error(not_less_than_zero, Y) | |
Portability
GNU Prolog predicate.