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# ?Result is +Expression

Evaluates the arithmetic expression Expression and unifies the resulting value with Result.

Result
  Output: a number.
Expression
  An arithmetic expression.

## Description

is/2 is used to evaluate arithmetic expressions. An arithmetic expression is a Prolog term that is made up of variables, numbers, atoms and compound terms. If it contains variables, they must be bound to numbers at the time the evaluation takes place.

ECLiPSe distinguishes four types of numbers:

integers e.g. 12345
  Integers can be of arbitrary magnitude. Integers that fit into the word size of the machine are handled more efficiently.
rationals e.g. 3_4
  Rational numbers represent the corresponding mathematical notion (the ratio of two integers). The operations defined on rationals give precise (rational) results.
floats e.g. 3.1415
  Floats are an imprecise approximation of real numbers. They are represented as IEEE double precision floats. Floating point operations are typically subject to rounding errors. Undefined operations produce infinity results if possible, otherwise exceptions (not NaNs).
bounded reals (breal) e.g. 3.1415__3.1416
  Bounded reals are a safe representation of real numbers, characterised by a lower and upper bound in floating point format. Operations on breals are safe in the sense that the resulting bounds always enclose the precise result (interval arithmetic).

Numbers of different types do not unify!

The system performs automatic type conversions in the direction

> integer -> rational -> float -> breal.

These conversions are done (i) to make the types of two input arguments equal and (ii) to lift the type of an input argument to the one expected by the function. The result type is the lifted input type, unless otherwise specified.

A table of predefined arithmetic functions is given below. A predefined function is evaluated by first evaluating its arguments and then calling the corresponding evaluation predicate. The evaluation predicate belonging to a compound term func(a_1,..,a_n) is the predicate func/(n+1). It receives a_1,..,a_n as its first n arguments and returns a numeric result as its last argument. This result is then used in the arithmetic computation.

This evaluation mechanism outlined above is not restricted to the predefined arithmetic functors shown in the table. In fact it works for all atoms and compound terms. It is therefore possible to define a new arithmetic operation by just defining an evaluation predicate. Similarly, many ECLiPSe built-ins return numbers in the last argument and can thus be used as evaluation predicates (e.g. arity/1, cputime/1, random/1, string_length/2, ...). Note that recursive evaluation of arguments is only done for the predefined arithmetic functions, for the others the arguments are simply passed to the evaluation predicate.

Most arithmetic errors will not be reported in is/2, but in the evaluation predicate where it occurred.

       Function       Description                Argument Types       Result Type
      ----------------------------------------------------------------------------
       + E               unary plus                 number              number
       - E               unary minus                number              number
       abs(E)            absolute value             number              number
       sgn(E)            sign value                 number              integer
       floor(E)          round down                 number              number
       ceiling(E)        round up                   number              number
       round(E)          round to nearest           number              number
       truncate(E)       round towards zero         number              number

       E1 + E2           addition                   number x number     number
       E1 - E2           subtraction                number x number     number
       E1 * E2           multiplication             number x number     number
       E1 / E2           division                   number x number     see below
       E1 // E2          integer division truncated integer x integer   integer
       E1 rem E2         integer remainder          integer x integer   integer
       E1 div E2         integer division floored   integer x integer   integer
       E1 mod E2         integer modulus            integer x integer   integer
       gcd(E1,E2)        greatest common divisor    integer x integer   integer
       lcm(E1,E2)        least common multiple      integer x integer   integer
       E1 ^ E2           power operation            number x number     number
       min(E1,E2)        minimum of 2 values        number x number     number
       max(E1,E2)        maximum of 2 values        number x number     number
       copysign(E1,E2)   combine value and sign     number x number     number
       nexttoward(E1,E2) next representable number  number x number     number

       \ E               bitwise complement         integer             integer
       E1 /\ E2          bitwise conjunction        integer x integer   integer
       E1 \/ E2          bitwise disjunction        integer x integer   integer
       xor(E1,E2)        bitwise exclusive or       integer x integer   integer
       E1 >> E2          shift E1 right by E2 bits  integer x integer   integer
       E1 << E2          shift E1 left by E2 bits   integer x integer   integer
       setbit(E1,E2)     set bit E2 in E1           integer x integer   integer
       clrbit(E1,E2)     clear bit E2 in E1         integer x integer   integer
       getbit(E1,E2)     get of bit E2 in E1        integer x integer   integer

       sin(E)            trigonometric function     number              float or breal
       cos(E)            trigonometric function     number              float or breal
       tan(E)            trigonometric function     number              float or breal
       asin(E)           trigonometric function     number              float
       acos(E)           trigonometric function     number              float
       atan(E)           trigonometric function     number              float or breal
       atan(E1,E2)       trigonometric function     number x number     float or breal
       exp(E)            exponential function ex    number              float or breal
       ln(E)             natural logarithm          number              float or breal
       sqrt(E)           square root                number              float or breal
       pi                the constant pi            ---                 float
       e                 the constant e             ---                 float

       fix(E)            truncate to integer        number              integer
       integer(E)        convert to integer         number              integer
       float(E)          convert to float           number              float
       rational(E)       convert to rational        number              rational
       rationalize(E)    convert to rational        number              rational
       numerator(E)      numerator of rational      integer or rational integer
       denominator(E)    denominator of rational    integer or rational integer
       breal(E)          convert to bounded real    number              breal
       breal_min(E)      lower bound of bounded real    number          float
       breal_max(E)      upper bound of bounded real    number          float
       breal_from_bounds(Lo, Hi)
                         make bounded real from bounds  number x number breal

       sum(Es)           sum of elements            vector              number
       sum(Es*Es)        scalar product             vector*vector       number
       min(Es)           minimum of elements        vector              number
       max(Es)           maximum of elements        vector              number
       eval(E)           eval runtime expression    term                number

The division operator / yields either a rational or a float result, depending on the value of the global flag prefer_rationals. The same is true for the result of ^ if an integer is raised to a negative integral power.

The relation between integer divisions // and div, and remainder and modulus operations rem and mod is as follows:

        X =:= (X rem Y) + (X  // Y) * Y.
        X =:= (X mod Y) + (X div Y) * Y.

### Modes and Determinism

- is(-, +) is det

### Modules

This predicate is sensitive to its module context (tool predicate, see @/2).

### Fail Conditions

Fails if a user-defined evaluation predicate fails

### Exceptions

(4) instantiation fault
  Expression is uninstantiated
(21) undefined arithmetic expression
  An evaluation predicate in the expression is not defined.
(24) number expected
  Expression is not a valid arithmetic expression.

## Examples

       Success:
         103 is 3 + 4 * 5 ^ 2.
         X is asin(sin(pi/4)).            % gives X = 0.785398.
         Y is 2 * 3, X is 4 + Y.          % gives X = 10, Y = 6.
         X is string_length("four") + 1.  % gives X = 5.

         [eclipse]: [user].
          myconst(4.56).
          user compiled 40 bytes in 0.02 seconds
         yes.
         [eclipse]: 5.56 is myconst + 1.
         yes.
    Fail:
         3.14 is pi.                    % different values
         atom is 4.
         1 is 1.0.
    Error:
         X is _.                        (Error 4)
         X is "s".                      (Error 24)

         [eclipse]: X is undef(1).
         calling an undefined procedure undef(1, _g63) in ...

         [eclipse]: X is 3 + Y.
         instantiation fault in +(3, _g45, _g53)

## See Also

+ / 2, + / 3, - / 2, - / 3, * / 3, / / 3, // / 3, \ / 2, /\ / 3, \/ / 3, >> / 3, << / 3, ^ / 3, abs / 2, acos / 2, asin / 2, atan / 2, atan / 3, breal / 1, breal / 2, breal_from_bounds / 3, breal_min / 2, breal_max / 2, ceiling / 2, clrbit / 3, copysign / 3, cos / 2, denominator / 2, div / 3, eval / 2, exp / 2, fix / 2, float / 1, float / 2, floor / 2, gcd / 3, getbit / 3, integer / 1, integer / 2, lcm / 3, ln / 2, max / 2, max / 3, min / 2, min / 3, mod / 3, nexttoward / 3, numerator / 2, number / 1, rational / 1, rational / 2, rationalize / 2, rem / 3, round / 2, sgn / 2, setbit / 3, sin / 2, sqrt / 2, sum / 2, tan / 2, truncate / 2, xor / 3, get_flag / 2, set_flag / 3