<!DOCTYPE html> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <meta name="generator" content="hevea 2.05"> <meta name="Author" content="Daniel Diaz"> <meta name="Keywords" content="GNU Prolog, manual, Prolog, compiler, constraints, finite domains"> <link rel="icon" type="image/x-icon" href="/gprolog.ico"><link rel="stylesheet" type="text/css" href="gprolog.css"> <title>Arithmetic</title> </head> <body TEXT=black BGCOLOR=white> <a href="gprolog029.html"><img src="previous_motif.gif" alt="Previous"></a> <a href="gprolog024.html"><img src="contents_motif.gif" alt="Up"></a> <a href="gprolog031.html"><img src="next_motif.gif" alt="Next"></a> <hr> <h3 class="subsection" id="sec96">8.6  Arithmetic</h3> <ul> <li><a href="gprolog030.html#sec97">Evaluation of an arithmetic expression</a> </li><li><a href="gprolog030.html#sec98"><span class="c003">(is)/2</span> - evaluate expression</a> </li><li><a href="gprolog030.html#%28%3D%3A%3D%29%2F2"><span class="c003">(=:=)/2</span> - arithmetic equal, <span class="c003">(=</span><span class="c003">\</span><span class="c003">=)/2</span> - arithmetic not equal, <br> <span class="c003">(</span><span class="c003"><</span><span class="c003">)/2</span> - arithmetic less than, <span class="c003">(=</span><span class="c003"><</span><span class="c003">)/2</span> - arithmetic less than or equal to, <br> <span class="c003">(</span><span class="c003">></span><span class="c003">)/2</span> - arithmetic greater than, <span class="c003">(</span><span class="c003">></span><span class="c003">=)/2</span> - arithmetic greater than or equal to</a> </li><li><a href="gprolog030.html#sec100"><span class="c003">succ/2</span></a> </li></ul> <h4 class="subsubsection" id="sec97">8.6.1  Evaluation of an arithmetic expression</h4> <p> <a id="Evaluation-of-an-arithmetic-expression"></a> 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:</p><blockquote class="table"><div class="center"><hr class="c023"></div><table class="c000 cellpadding1" border=1><tr><td class="c020">Expression</td><td class="c016"><div class="flushleft">Result = <span class="c008">eval</span>(Expression)</div></td><td class="c017">Signature</td><td class="c017">ISO </td></tr> <tr><td class="c020">a variable</td><td class="c016"><div class="flushleft">bound to an expression <span class="c003">E</span>, result is <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> an integer number</td><td class="c016"><div class="flushleft">this number</div></td><td class="c017">I</td><td class="c017">Y </td></tr> <tr><td class="c020"> a floating point number</td><td class="c016"><div class="flushleft">this number</div></td><td class="c017">F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">pi</span></td><td class="c016"><div class="flushleft">the value of π = 3.141592...</div></td><td class="c017">F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">e</span></td><td class="c016"><div class="flushleft">the value of <span class="c008">e</span> = 2.718281...</div></td><td class="c017">F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">epsilon</span></td><td class="c016"><div class="flushleft">difference between 1.0 and minimum float > 1.0</div></td><td class="c017">F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">+ E</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">- E</span></td><td class="c016"><div class="flushleft">- <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">inc(E)</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E</span>) + 1</div></td><td class="c017">IF → IF</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">dec(E)</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E</span>) - 1</div></td><td class="c017">IF → IF</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">E1 + E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) + <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 - E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) - <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 * E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) * <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 / E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) / <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 // E2</span></td><td class="c016"><div class="flushleft"><span class="c008">rnd</span>(<span class="c008">eval</span>(<span class="c003">E1</span>) / <span class="c008">eval</span>(<span class="c003">E2</span>))</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 rem E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) - (<span class="c008">rnd</span>(<span class="c008">eval</span>(<span class="c003">E1</span>) / <span class="c008">eval</span>(<span class="c003">E2</span>)) * <span class="c008">eval</span>(<span class="c003">E2</span>))</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 div E2</span></td><td class="c016"><div class="flushleft">⌊(<span class="c008">eval</span>(<span class="c003">E1</span>) - <span class="c008">eval</span>(<span class="c003">E1</span>) <span class="c003">mod</span> <span class="c008">eval</span>(<span class="c003">E2</span>)) / <span class="c008">eval</span>(<span class="c003">E2</span>)⌋</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 mod E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) - (⌊<span class="c008">eval</span>(<span class="c003">E1</span>) / <span class="c008">eval</span>(<span class="c003">E2</span>)⌋ * <span class="c008">eval</span>(<span class="c003">E2</span>))</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 /\ E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) bitwise_and <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 \/ E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) bitwise_or <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">xor(E1,E2)</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) bitwise_xor <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">\ E</span></td><td class="c016"><div class="flushleft">bitwise_not <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 << E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) integer_shift_left <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 >> E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) integer_shift_right <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">I, I → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">lsb(E)</span></td><td class="c016"><div class="flushleft">least significant bit (from 0) of <span class="c008">eval</span>(<span class="c003">E</span>) or -1</div></td><td class="c017">I → I</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">msb(E)</span></td><td class="c016"><div class="flushleft">most significant bit (from 0) of <span class="c008">eval</span>(<span class="c003">E</span>) or -1</div></td><td class="c017">I → I</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">popcount(E)</span></td><td class="c016"><div class="flushleft">number of 1-bits in <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">I → I</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">abs(E)</span></td><td class="c016"><div class="flushleft">absolute value of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">sign(E)</span></td><td class="c016"><div class="flushleft">sign of <span class="c008">eval</span>(<span class="c003">E</span>) (-1 if < 0, 0 if = 0, +1 if > 0)</div></td><td class="c017">IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">min(E1,E2)</span></td><td class="c016"><div class="flushleft">minimal value between <span class="c008">eval</span>(<span class="c003">E1</span>) and <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → ?</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">max(E1,E2)</span></td><td class="c016"><div class="flushleft">maximal value between <span class="c008">eval</span>(<span class="c003">E1</span>) and <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → ?</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">gcd(E1,E2)</span></td><td class="c016"><div class="flushleft">greatest common divisor of <span class="c008">eval</span>(<span class="c003">E1</span>) and <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">I, I → I</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">E1 ^ E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) raised to the power of <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → IF</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">E1 ** E2</span></td><td class="c016"><div class="flushleft"><span class="c008">eval</span>(<span class="c003">E1</span>) raised to the power of <span class="c008">eval</span>(<span class="c003">E2</span>)</div></td><td class="c017">IF, IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">sqrt(E)</span></td><td class="c016"><div class="flushleft">square root of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">tan(E)</span></td><td class="c016"><div class="flushleft">tangent of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">atan(E)</span></td><td class="c016"><div class="flushleft">arc tangent of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">atan2(Y,X)</span></td><td class="c016"><div class="flushleft">principal value of arc tangent of <span class="c008">eval</span>(<span class="c003">Y</span>) / <span class="c008">eval</span>(<span class="c003">X</span>) using both signs for the quadrant</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">cos(E)</span></td><td class="c016"><div class="flushleft">cosine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">acos(E)</span></td><td class="c016"><div class="flushleft">arc cosine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF, IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">sin(E)</span></td><td class="c016"><div class="flushleft">sine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">asin(E)</span></td><td class="c016"><div class="flushleft">arc sine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">tanh(E)</span></td><td class="c016"><div class="flushleft">hyperbolic tangent of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">atanh(E)</span></td><td class="c016"><div class="flushleft">hyperbolic arc tangent of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">cosh(E)</span></td><td class="c016"><div class="flushleft">hyperbolic cosine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">acosh(E)</span></td><td class="c016"><div class="flushleft">hyperbolic arc cosine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF, IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">sinh(E)</span></td><td class="c016"><div class="flushleft">hyperbolic sine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">asinh(E)</span></td><td class="c016"><div class="flushleft">hyperbolic arc sine of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">exp(E)</span></td><td class="c016"><div class="flushleft"><span class="c008">e</span> raised to the power of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">log(E)</span></td><td class="c016"><div class="flushleft">natural logarithm of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">log10(E)</span></td><td class="c016"><div class="flushleft">base 10 logarithm of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">log(R, E)</span></td><td class="c016"><div class="flushleft">base <span class="c008">eval</span>(<span class="c003">R</span>) logarithm of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">F, IF → F</td><td class="c017">N </td></tr> <tr><td class="c020"> <span class="c003">float(E)</span></td><td class="c016"><div class="flushleft">the floating point number equal to <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">IF → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">ceiling(E)</span></td><td class="c016"><div class="flushleft">rounds <span class="c008">eval</span>(<span class="c003">E</span>) upward to the nearest integer</div></td><td class="c017">F → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">floor(E)</span></td><td class="c016"><div class="flushleft">rounds <span class="c008">eval</span>(<span class="c003">E</span>) downward to the nearest integer</div></td><td class="c017">F → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">round(E)</span></td><td class="c016"><div class="flushleft">rounds <span class="c008">eval</span>(<span class="c003">E</span>) to the nearest integer</div></td><td class="c017">F → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">truncate(E)</span></td><td class="c016"><div class="flushleft">the integer value of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">F → I</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">float_fractional_part(E)</span></td><td class="c016"><div class="flushleft">the float equal to the fractional part of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">F → F</td><td class="c017">Y </td></tr> <tr><td class="c020"> <span class="c003">float_integer_part(E)</span></td><td class="c016"><div class="flushleft">the float equal to the integer part of <span class="c008">eval</span>(<span class="c003">E</span>)</div></td><td class="c017">F → F</td><td class="c017">Y </td></tr> </table><div class="center"><hr class="c023"></div></blockquote><p>The meaning of the signature field is as follows:</p><ul class="itemize"><li class="li-itemize">I → I: unary function, the operand must be an integer and the result is an integer.</li><li class="li-itemize">F → F: unary function, the operand must be a floating point number and the result is a floating point number.</li><li class="li-itemize">F → I: unary function, the operand must be a floating point number and the result is an integer.</li><li class="li-itemize">IF → F: unary function, the operand can be an integer or a floating point number and the result is a floating point number.</li><li class="li-itemize">IF → IF: unary function, the operand can be an integer or a floating point number and the result has the same type as the operand.</li><li class="li-itemize">I, I → I: binary function: each operand must be an integer and the result is an integer.</li><li class="li-itemize">IF, IF → IF: binary function: each operand can be an integer or a floating point number and the result is a floating point number if at least one operand is a floating point number, an integer otherwise.</li><li class="li-itemize">IF, IF → ?: binary function: each operand can be an integer or a floating point number and the result has the same type as the selected operand. This is used for <span class="c003">min</span> and <span class="c003">max</span>. Note that in case of equality between an integer and a floating point number the result is an integer.</li></ul><p><span class="c003">is</span>, <span class="c003">+</span>, <span class="c003">-</span>, <span class="c003">*</span>, <span class="c003">/</span>, <span class="c003">//</span>, <span class="c003">div</span>, <span class="c003">rem</span>, <span class="c003">mod</span>, <span class="c003">/\</span>, <span class="c003">\/</span>, <span class="c003"><<</span>, <span class="c003">>></span>, <span class="c003">**</span> and <span class="c003">^</span> are predefined infix operators. <span class="c003">+</span>, <span class="c003">-</span> and <span class="c003">\</span>, are predefined prefix operators (section <a href="gprolog038.html#op%2F3%3A%28Term-input%2Foutput%29">8.14.10</a>).</p><p><span class="c009">Integer division rounding function</span>: the integer division rounding function <span class="c003"><span class="c008">rnd</span>(X)</span> rounds the floating point number <span class="c003">X</span> to an integer. There are two possible definitions (depending on the target machine) for this function which differ on negative numbers:</p><ul class="itemize"><li class="li-itemize"><span class="c003"><span class="c008">rnd</span>(X)</span> = integer part of <span class="c003">X</span>, e.g. <span class="c003"><span class="c008">rnd</span>(-1.5)</span> = <span class="c003">-1</span> (round toward 0)</li><li class="li-itemize"><span class="c003"><span class="c008">rnd</span>(X)</span> = ⌊<span class="c003">X</span>⌋, e.g. <span class="c003"><span class="c008">rnd</span>(-1.5)</span> = <span class="c003">-2</span> (round toward −∞)</li></ul><p>The definition of this function determines the definition of the integer division and remainder (<span class="c003">(//)/2</span> and <span class="c003">(rem)/2</span>). It is possible to test the value (<span class="c003">toward_zero</span> or <span class="c003">down</span>) of the <a id="hevea_default276"></a><span class="c003">integer_rounding_function</span> <a id="hevea_default277"></a>Prolog flag to determine which function being used (section <a href="gprolog046.html#set-prolog-flag%2F2">8.22.1</a>). Since rounding toward zero is the most common case, two additional evaluable functors (<span class="c003">(div)/2</span> and <span class="c003">(mod)/2</span>) are available which consider rounding toward −∞.</p><p><span class="c009">Fast mathematical mode</span>: in order to speed-up integer computations, the GNU Prolog compiler can generate faster code when invoked with the <a id="hevea_default278"></a><span class="c003">--fast-math</span> option (section <a href="gprolog009.html#Using-the-compiler">4.4.3</a>). 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.</p><p><span class="c009">Errors</span></p><table class="c001 cellpading0"><tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> a sub-expression <span class="c003">E</span> is a variable</td><td class="c013">  </td><td class="c018"><span class="c003">instantiation_error</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> a sub-expression <span class="c003">E</span> is neither a number nor an evaluable functor</td><td class="c013">  </td><td class="c018"><span class="c003">type_error(evaluable, E)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> a sub-expression <span class="c003">E</span> is a floating point number while an integer is expected</td><td class="c013">  </td><td class="c018"><span class="c003">type_error(integer, E)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> a sub-expression <span class="c003">E</span> is an integer while a floating point number is expected</td><td class="c013">  </td><td class="c018"><span class="c003">type_error(float, E)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> a division by zero occurs</td><td class="c013">  </td><td class="c018"><span class="c003">evaluation_error(zero_divisor)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> </table><p><span class="c009">Portability</span></p><p>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: <span class="c003">float_overflow</span>, <span class="c003">int_overflow, int_underflow</span>, and <span class="c003">undefined</span>.</p> <h4 class="subsubsection" id="sec98">8.6.2  <a id="hevea_default279"></a><span class="c003">(is)/2</span> - evaluate expression</h4> <p><span class="c009">Templates</span></p><dl class="list"><dt class="dt-list"> </dt><dd class="dd-list"><span class="c003"> is(?term, +evaluable)</span></dd></dl><p><span class="c009">Description</span></p><p><span class="c003">Result is Expression</span> succeeds if <span class="c003">Result</span> can be unified with <span class="c008">eval</span>(<span class="c003">Expression</span>). Refer to the evaluation of an arithmetic expression for the definition of the <span class="c008">eval</span> function (section <a href="#Evaluation-of-an-arithmetic-expression">8.6.1</a>).</p><p><span class="c003">is</span> is a predefined infix operator (section <a href="gprolog038.html#op%2F3%3A%28Term-input%2Foutput%29">8.14.10</a>).</p><p><span class="c009">Errors</span></p><p>Refer to the evaluation of an arithmetic expression for possible errors (section <a href="#Evaluation-of-an-arithmetic-expression">8.6.1</a>).</p><p><span class="c009">Portability</span></p><p>ISO predicate.</p> <h4 class="subsubsection" id="(=:=)/2">8.6.3  <a id="hevea_default280"></a><span class="c003">(=:=)/2</span> - arithmetic equal, <a id="hevea_default281"></a><span class="c003">(=\=)/2</span> - arithmetic not equal, <br> <a id="hevea_default282"></a><span class="c003">(<)/2</span> - arithmetic less than, <a id="hevea_default283"></a><span class="c003">(=<)/2</span> - arithmetic less than or equal to, <br> <a id="hevea_default284"></a><span class="c003">(>)/2</span> - arithmetic greater than, <a id="hevea_default285"></a><span class="c003">(>=)/2</span> - arithmetic greater than or equal to</h4> <p><span class="c009">Templates</span></p><dl class="list"><dt class="dt-list"> </dt><dd class="dd-list"><span class="c003"> =:=(+evaluable, +evaluable)<br> =\=(+evaluable, +evaluable)<br> <(+evaluable, +evaluable)<br> =<(+evaluable, +evaluable)<br> >(+evaluable, +evaluable)<br> >=(+evaluable, +evaluable)</span></dd></dl><p><span class="c009">Description</span></p><p><span class="c003">Expr1 =:= Expr2</span> succeeds if <span class="c008">eval</span>(<span class="c003">Expr1</span>) = <span class="c008">eval</span>(<span class="c003">Expr2</span>).</p><p><span class="c003">Expr1 =\= Expr2</span> succeeds if <span class="c008">eval</span>(<span class="c003">Expr1</span>) ≠ <span class="c008">eval</span>(<span class="c003">Expr2</span>).</p><p><span class="c003">Expr1 < Expr2</span> succeeds if <span class="c008">eval</span>(<span class="c003">Expr1</span>) < <span class="c008">eval</span>(<span class="c003">Expr2</span>).</p><p><span class="c003">Expr1 =< Expr2</span> succeeds if <span class="c008">eval</span>(<span class="c003">Expr1</span>) ≤ <span class="c008">eval</span>(<span class="c003">Expr2</span>).</p><p><span class="c003">Expr1 > Expr2</span> succeeds if <span class="c008">eval</span>(<span class="c003">Expr1</span>) > <span class="c008">eval</span>(<span class="c003">Expr2</span>).</p><p><span class="c003">Expr1 >= Expr2</span> succeeds if <span class="c008">eval</span>(<span class="c003">Expr1</span>) ≥ <span class="c008">eval</span>(<span class="c003">Expr2</span>).</p><p>Refer to the evaluation of an arithmetic expression for the definition of the <span class="c008">eval</span> function (section <a href="#Evaluation-of-an-arithmetic-expression">8.6.1</a>).</p><p><span class="c003">=:=</span>, <span class="c003">=\=</span>, <span class="c003"><</span>, <span class="c003">=<</span>, <span class="c003">></span> and <span class="c003">>=</span> are predefined infix operators (section <a href="gprolog038.html#op%2F3%3A%28Term-input%2Foutput%29">8.14.10</a>).</p><p><span class="c009">Errors</span></p><p>Refer to the evaluation of an arithmetic expression for possible errors (section <a href="#Evaluation-of-an-arithmetic-expression">8.6.1</a>).</p><p><span class="c009">Portability</span></p><p>ISO predicates.</p> <h4 class="subsubsection" id="sec100">8.6.4  <a id="hevea_default286"></a><span class="c003">succ/2</span></h4> <p><span class="c009">Templates</span></p><dl class="list"><dt class="dt-list"> </dt><dd class="dd-list"><span class="c003"> succ(+integer, ?integer) <br> succ(-integer, +integer) </span></dd></dl><p><span class="c009">Description</span></p><p><span class="c003">succ(X, Y)</span> is true iff <span class="c003">Y</span> is the successor of the non-negative integer <span class="c003">X</span>. </p><p><span class="c009">Errors</span></p><table class="c001 cellpading0"><tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> <span class="c003">X</span> and <span class="c003">Y</span> are both variables</td><td class="c013">  </td><td class="c018"><span class="c003">instantiation_error</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> <span class="c003">X</span> is neither a variable nor an integer</td><td class="c013">  </td><td class="c018"><span class="c003">type_error(integer, X)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> <span class="c003">Y</span> is neither a variable nor an integer</td><td class="c013">  </td><td class="c018"><span class="c003">type_error(integer, Y)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> <span class="c003">X</span> is an integer < 0</td><td class="c013">  </td><td class="c018"><span class="c003">domain_error(not_less_than_zero, X)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> <tr><td class="c018"> <span class="c003">Y</span> is an integer < 0</td><td class="c013">  </td><td class="c018"><span class="c003">domain_error(not_less_than_zero, Y)</span> </td></tr> <tr><td class="hbar" colspan=3></td></tr> </table><p><span class="c009">Portability</span></p><p>GNU Prolog predicate.</p> <hr class="c011"> Copyright (C) 1999-2013 Daniel Diaz Verbatim copying and distribution of this entire article is permitted in any medium, provided this notice is preserved. <a href="index.html#copyright">More about the copyright</a> <hr> <a href="gprolog029.html"><img src="previous_motif.gif" alt="Previous"></a> <a href="gprolog024.html"><img src="contents_motif.gif" alt="Up"></a> <a href="gprolog031.html"><img src="next_motif.gif" alt="Next"></a> </body> </html>
