documentation changes for rationals.

This commit is contained in:
Vítor Santos Costa 2010-05-28 12:06:42 +01:00
parent 293dadb003
commit 4a76bde7cb

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