documentation changes for rationals.
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Vítor Santos Costa
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docs/yap.tex
110
docs/yap.tex
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@ -3174,6 +3174,12 @@ Checks whether @var{T} is a database reference.
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@cnindex float/1
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Checks whether @var{T} is a floating point number.
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@item rational(@var{T}) [ISO]
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@findex rational/1
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@syindex rational/1
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@cyindex rational/1
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Checks whether @code{T} is a rational number.
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@item integer(@var{T}) [ISO]
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@findex integer/1
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@syindex integer/1
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@ -3190,7 +3196,7 @@ The opposite of @code{var(@var{T})}.
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@findex number/1
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@syindex number/1
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@cyindex number/1
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Checks whether @code{T} is an integer or a float.
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Checks whether @code{T} is an integer, rational or a float.
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@item primitive(@var{T})
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@findex primitive/1
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@ -3640,16 +3646,18 @@ variables come before numbers, numbers come before atoms which in turn
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come before compound terms, i.e.: variables @@< numbers @@< atoms @@<
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compound terms.
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@item
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variables are roughly ordered by "age" (the "oldest" variable is put
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Variables are roughly ordered by "age" (the "oldest" variable is put
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first);
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@item
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floating point numbers are sorted in increasing order;
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Floating point numbers are sorted in increasing order;
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@item
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Rational numbers are sorted in increasing order;
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@item
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Integers are sorted in increasing order;
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@item
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atoms are sorted in lexicographic order;
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Atoms are sorted in lexicographic order;
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@item
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compound terms are ordered first by arity of the main functor, then by
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Compound terms are ordered first by arity of the main functor, then by
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the name of the main functor, and finally by their arguments in
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left-to-right order.
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@end itemize
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@ -3779,8 +3787,50 @@ of length @var{S}.
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@node Arithmetic, I/O, Comparing Terms, Top
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@section Arithmetic
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Arithmetic expressions in YAP may use the following operators
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or @i{evaluable predicates}:
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YAP now supposets several different numeric types:
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@table @code
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@item integers
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When YAP is built using the GNU multiple precision arithmetic
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library (GMP), integer arithmetic is unbounded, which means that
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the size of integers is limited by available memory only. Without
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GMP, SWI-Prolog integers have the same size as an address. The
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type of integer support can be detected using the Prolog flags
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bounded, min_integer and max_integer. As the use of GMP is
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default, most of the following descriptions assume unbounded
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integer arithmetic.
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Internally, SWI-Prolog has three integer representations. Small
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integers (defined by the Prolog flag max_tagged_integer) are
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encoded directly. Larger integers are represented as cell values
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on the global stack. Integers that do not fit in 64-bit are
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represented as serialised GNU MPZ structures on the global stack.
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@item number
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Rational numbers (Q) are quotients of two integers. Rational
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arithmetic is only provided if GMP is used (see above). Rational
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numbers that are returned from is/2 are canonical, which means M
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is positive and N and M have no common divisors. Rational numbers
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are introduced in the computation using the rational/1,
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rationalize/1 or the rdiv/2 (rational division) function.
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@item float
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Floating point numbers are represented using the C-type double. On most today platforms these are 64-bit IEEE floating point numbers.
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@end table
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Arithmetic functions that require integer arguments accept, in addition
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to integers, rational numbers with denominator `1' and floating point
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numbers that can be accurately converted to integers. If the required
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argument is a float the argument is converted to float. Note that
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conversion of integers to floating point numbers may raise an overflow
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exception. In all other cases, arguments are converted to the same type
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using the order integer to rational number to floating point number.
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Arithmetic expressions in YAP may use the following operators or
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@i{evaluable predicates}:
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@table @code
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@ -3866,13 +3916,13 @@ Hyperbolic arc cosine.
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Hyperbolic arc tangent.
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@item lgamma(@var{X})
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gamma function.
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Logarithm of gamma function.
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@item erf(@var{X})
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gaussian error function.
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Gaussian error function.
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@item erfc(@var{X})
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complementary gaussian error function.
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Complementary gaussian error function.
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@item random(@var{X}) [ISO]
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An integer random number between 0 and @var{X}.
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@ -3904,13 +3954,13 @@ or @var{X} if @var{X} is an integer. In the @code{iso} language mode,
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The absolute value of @var{X}.
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@item ceiling(@var{X}) [ISO]
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The float that is the smallest integral value not smaller than @var{X}.
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The integer that is the smallest integral value not smaller than @var{X}.
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In @code{iso} language mode the argument must be a floating
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point-number and the result is an integer.
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@item floor(@var{X}) [ISO]
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The float that is the greatest integral value not greater than @var{X}.
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The integer that is the greatest integral value not greater than @var{X}.
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In @code{iso} language mode the argument must be a floating
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point-number and the result is an integer.
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@ -3931,9 +3981,43 @@ evaluates to a floating-point number return 1.0 for a positive @var{X},
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0.0 for 0.0, and -1.0 otherwise.
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@item truncate(@var{X}) [ISO]
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The float that is the integral value between @var{X} and 0 closest to
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The integral value between @var{X} and 0 closest to
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@var{X}.
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@item rational(@var{X})
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Convert the expression @var{X} to a rational number or integer. The
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function returns the input on integers and rational numbers. For
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floating point numbers, the returned rational number exactly represents
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the float. As floats cannot exactly represent all decimal numbers the
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results may be surprising. In the examples below, doubles can represent
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@code{0.25} and the result is as expected, in contrast to the result of
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@code{rational(0.1)}. The function @code{rationalize/1} gives a more
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intuitive result.
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@example
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?- A is rational(0.25).
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A is 1 rdiv 4
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?- A is rational(0.1).
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A = 3602879701896397 rdiv 36028797018963968
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@end example
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@item rationalize(@var{X})
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Convert the Expr to a rational number or integer. The function is
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similar to @code{rational/1}, but the result is only accurate within the
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rounding error of floating point numbers, generally producing a much
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smaller denominator.
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@example
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?- A is rationalize(0.25).
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A = 1 rdiv 4
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?- A is rationalize(0.1).
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A = 1 rdiv 10
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@end example
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@item max(@var{X},@var{Y})
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The greater value of @var{X} and @var{Y}.
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