608 lines
15 KiB
C
608 lines
15 KiB
C
/*************************************************************************
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* *
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* YAP Prolog @(#)eval.h 1.2
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* *
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* Yap Prolog was developed at NCCUP - Universidade do Porto *
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* *
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* Copyright L.Damas, V.S.Costa and Universidade do Porto 1985-1997 *
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* *
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**************************************************************************
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* *
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* File: eval.h *
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* Last rev: *
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* mods: *
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* comments: arithmetical functions info *
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* *
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*************************************************************************/
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/**
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@defgroup arithmetic Arithmetic in YAP
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@ingroup YAPBuiltins
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+ See @ref arithmetic_preds for the predicates that implement arithment
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+ See @ref arithmetic_cmps for the arithmetic comparisons supported in YAP
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+ See @ref arithmetic_operators for what arithmetic operations are supported in YAP
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@tableofcontents
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YAP supports several different numeric types:
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<ul>
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<li><b>Tagged integers</b><p>
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YAP supports integers of word size: 32 bits on 32-bit machines, and
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64-bits on 64-bit machines.The engine transprently tags smaller
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integers are tagged so that they fit in a single word. These are the
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so called <em>tagged integers</em>.
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<li><b>Large integers</b><p>
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Larger integers that still fit in a cell
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are represented in the Prolog goal stack. The difference between
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these integers and tagged integers should be transparent to the programmer.
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</li>
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<li><b>Multiple Precision Integers</b><p>
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When YAP is built using the GNU multiple precision arithmetic library
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(GMP), integer arithmetic is unbounded, which means that the size of
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integers is only limited by available memory. The type of integer
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support can be detected using the Prolog flags bounded, min_integer
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and max_integer. As the use of GMP is default, most of the following
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descriptions assume unbounded integer arithmetic.
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</li> <li><b>Rational numbers (Q)</b><p> Rational numbers are
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quotients of two integers. Rational arithmetic is provided if GMP is
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used. Rational numbers that are returned from is/2 are canonical,
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which means the denominator _M_ is positive and that the numerator _N_
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and _M_ have no common divisors. Rational numbers are introduced in
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the computation using the [rational/1][@ref rational_1],
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[rationalize/1][@ref rationalize/1] or the [rdiv/2][@ref rdiv/2]
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(rational division) function.
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</li>
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<li><b>Floating point numbers</b><p>
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Floating point numbers are represented using the C-type double. On
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most today platforms these are 64-bit IEEE-754 floating point
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numbers. YAP now includes the built-in predicates [isinf/1][@ref isinf/1] and to [isnan/1][@ref isnan/1] tests.
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</li>
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</ul>
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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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Evaluation generates the following _Call_
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exceptions:
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@exception "error(instantiation_error, Call )" if not ground
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@exception "type_error(evaluable( V ), Call)" if not evaluable term
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@exception "type_error(integer( V ), Call)" if must be integer
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@exception "type_error(float( V ), Call)" if must be float
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@exception "domain_error(out_of_range( V ), Call)" if argument invalid
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@exception "domain_error(not_less_than_zero( V ), Call)" if argument must be positive or zero
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@exception "evaluation_error(undefined( V ), Call)" result is not defined (nan)
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@exception "evaluation_error(overflow( V ), Call)" result is arithmetic overflow
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@secreflist
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@refitem is/2
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@refitem isnan/1
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@endsecreflist
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**/
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#include <stdlib.h>
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/* C library used to implement floating point functions */
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#if HAVE_MATH_H
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#include <math.h>
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#endif
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#ifdef HAVE_FLOAT_H
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#include <float.h>
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#endif
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#ifdef HAVE_IEEEFP_H
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#include <ieeefp.h>
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#endif
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#ifdef HAVE_LIMITS_H
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#include <limits.h>
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#endif
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#ifdef LONG_MAX
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#define Int_MAX LONG_MAX
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#else
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#define Int_MAX ((Int)((~((CELL)0))>>1))
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#endif
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#ifdef LONG_MIN
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#define Int_MIN LONG_MIN
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#else
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#define Int_MIN (-Int_MAX-(CELL)1)
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#endif
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#define PLMAXTAGGEDINT (MAX_ABS_INT-((CELL)1))
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#define PLMINTAGGEDINT (-MAX_ABS_INT)
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#define PLMAXINT Int_MAX
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#define PLMININT Int_MIN
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/**
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* @addtogroup arithmetic_operators
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* @enum arith0_op constant operators
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* @brief specifies the available unary arithmetic operators
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*/
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typedef enum {
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/** pi [ISO]
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An approximation to the value of <em>pi</em>, that is, the ratio of a circle's circumference to its diameter.
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*
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*/
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op_pi,
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/** e
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Euler's number, the base of the natural logarithms (approximately 2.718281828).
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*
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*/
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op_e,
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/** epsilon
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The difference between the float `1.0` and the next largest floating point number.
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*
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*/
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op_epsilon,
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/** inf
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Infinity according to the IEEE Floating-Point standard. Note that evaluating this term will generate a domain error in the `iso` language mode. Also note that
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* ?- +inf =:= -inf.
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* false.
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*
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*/
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op_inf,
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op_nan,
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op_random,
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op_cputime,
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op_heapused,
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op_localsp,
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op_globalsp,
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op_b,
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op_env,
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op_tr,
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op_stackfree
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} arith0_op;
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/**
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* @addtogroup arithmetic_operators
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* @enum arith1_op unary operators
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* @brief specifies the available unary arithmetic operators
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*/
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typedef enum {
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/** \+ _X_: the value of _X_ .
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*
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* X =:= +X.
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*/
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op_uplus,
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/** \- _X_: the complement of _X_ .
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*
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* 0-X =:= -X.
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*/
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op_uminus,
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/** \\ _X_, The bitwise negation of _X_ .
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*
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* \X /\ X =:= 0.
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*
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* Note that the number of bits of an integer is at least the size in bits of a Prolog term cell.
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*/
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op_unot,
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/** exp( _X_ ), natural exponentiation of _X_ .
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*
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* X = 0.0, abs(1.0 - exp( _X_ )) < 0.0001
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*
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*/
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op_exp,
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/** log( _X_ ), natural logarithm of _X_ .
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*
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* X = 1.0, abs( log( exp( _X_ )) -1.0) < 0.0001
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*
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*/
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op_log,
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/** log10( _X_ ) [ISO]
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*
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* Decimal logarithm.
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*
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.prolog}
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* ?- between(1, 10, I), Delta is log10(I*10) + log10(1/(I*10)), format('0 == ~3g~n',[Delta]), fail.
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* 0 == 0
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* 0 == 0
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* 0 == 0
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* 0 == 0
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* 0 == 0
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* 0 == 0
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* 0 == 0
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* 0 == 0
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* 0 == 2.22e-16
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* 0 == 0
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* false.
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* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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*/
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op_log10,
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op_sqrt,
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op_sin,
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op_cos,
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op_tan,
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op_sinh,
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op_cosh,
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op_tanh,
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op_asin,
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op_acos,
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op_atan,
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op_asinh,
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op_acosh,
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op_atanh,
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op_floor,
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op_ceiling,
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op_round,
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op_truncate,
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op_integer,
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op_float,
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op_abs,
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op_lsb,
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op_msb,
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op_popcount,
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op_ffracp,
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op_fintp,
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op_sign,
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op_lgamma,
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op_erf,
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op_erfc,
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op_rational,
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op_rationalize,
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op_random1
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} arith1_op;
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/**
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* @addtogroup arithmetic_operators
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* @enum arith2_op binary operators
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* @brief specifies the available unary arithmetic operators
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*/
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typedef enum {
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op_plus,
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op_minus,
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op_times,
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op_fdiv,
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op_mod,
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op_rem,
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op_div,
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op_idiv,
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op_sll,
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op_slr,
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op_and,
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op_or,
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op_xor,
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op_atan2,
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/* C-Prolog exponentiation */
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op_power,
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/* ISO-Prolog exponentiation */
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/* op_power, */
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op_power2,
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/* Quintus exponentiation */
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/* op_power, */
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op_gcd,
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op_min,
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op_max,
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op_rdiv
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} arith2_op;
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Functor EvalArg(Term);
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/* Needed to handle numbers:
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these two macros are fundamental in the integer/float conversions */
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#ifdef C_PROLOG
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#define FlIsInt(X) ( (X) == (Int)(X) && IntInBnd((X)) )
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#else
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#define FlIsInt(X) ( FALSE )
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#endif
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#ifdef M_WILLIAMS
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#define MkEvalFl(X) MkFloatTerm(X)
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#else
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#define MkEvalFl(X) ( FlIsInt(X) ? MkIntTerm((Int)(X)) : MkFloatTerm(X) )
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#endif
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/* Macros used by some of the eval functions */
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#define REvalInt(I) { eval_int = (I); return(FInt); }
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#define REvalFl(F) { eval_flt = (F); return(FFloat); }
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#define REvalError() { return(FError); }
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/* this macro, dependent on the particular implementation
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is used to interface the arguments into the C libraries */
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#ifdef MPW
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#define FL(X) ((extended)(X))
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#else
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#define FL(X) ((double)(X))
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#endif
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void Yap_InitConstExps(void);
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void Yap_InitUnaryExps(void);
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void Yap_InitBinaryExps(void);
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int Yap_ReInitConstExps(void);
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int Yap_ReInitUnaryExps(void);
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int Yap_ReInitBinaryExps(void);
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Term Yap_eval_atom(Int);
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Term Yap_eval_unary(Int,Term);
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Term Yap_eval_binary(Int,Term,Term);
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Term Yap_InnerEval(Term);
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Int Yap_ArithError(yap_error_number,Term,char *msg, ...);
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#include "inline-only.h"
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INLINE_ONLY inline EXTERN Term
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Yap_Eval(Term t);
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INLINE_ONLY inline EXTERN Term
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Yap_Eval(Term t)
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{
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if (t == 0L || ( !IsVarTerm(t) && IsNumTerm(t) ))
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return t;
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return Yap_InnerEval(t);
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}
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#ifdef P
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inline static Term
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Yap_FoundArithError(Term t, Term inp)
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{
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CACHE_REGS
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if (LOCAL_Error_TYPE) {
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Yap_Error(LOCAL_Error_TYPE, (inp ? inp : LOCAL_Error_Term), LOCAL_ErrorMessage);
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P = FAILCODE;
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return 0L;
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}
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return t;
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}
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#endif
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#define RINT(v) return(MkIntegerTerm(v))
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#define RFLOAT(v) return(MkFloatTerm(v))
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#define RBIG(v) return(Yap_MkBigIntTerm(v))
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#define RERROR() return(0L)
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static inline blob_type
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ETypeOfTerm(Term t)
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{
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if (IsIntTerm(t))
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return long_int_e;
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if (IsApplTerm(t)) {
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Functor f = FunctorOfTerm(t);
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if (f == FunctorDouble)
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return double_e;
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if (f == FunctorLongInt)
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return long_int_e;
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if (f == FunctorBigInt) {
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return big_int_e;
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}
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}
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return db_ref_e;
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}
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#if USE_GMP
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char *Yap_mpz_to_string(MP_INT *b, char *s, size_t sz, int base);
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Term Yap_gmq_rdiv_int_int(Int, Int);
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Term Yap_gmq_rdiv_int_big(Int, Term);
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Term Yap_gmq_rdiv_big_int(Term, Int);
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Term Yap_gmq_rdiv_big_big(Term, Term);
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Term Yap_gmp_add_ints(Int, Int);
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Term Yap_gmp_sub_ints(Int, Int);
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Term Yap_gmp_mul_ints(Int, Int);
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Term Yap_gmp_sll_ints(Int, Int);
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Term Yap_gmp_add_int_big(Int, Term);
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Term Yap_gmp_sub_int_big(Int, Term);
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Term Yap_gmp_sub_big_int(Term, Int);
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Term Yap_gmp_mul_int_big(Int, Term);
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Term Yap_gmp_div_int_big(Int, Term);
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Term Yap_gmp_div_big_int(Term, Int);
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Term Yap_gmp_div2_big_int(Term, Int);
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Term Yap_gmp_fdiv_int_big(Int, Term);
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Term Yap_gmp_fdiv_big_int(Term, Int);
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Term Yap_gmp_and_int_big(Int, Term);
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Term Yap_gmp_ior_int_big(Int, Term);
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Term Yap_gmp_xor_int_big(Int, Term);
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Term Yap_gmp_sll_big_int(Term, Int);
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Term Yap_gmp_add_big_big(Term, Term);
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Term Yap_gmp_sub_big_big(Term, Term);
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Term Yap_gmp_mul_big_big(Term, Term);
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Term Yap_gmp_div_big_big(Term, Term);
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Term Yap_gmp_div2_big_big(Term, Term);
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Term Yap_gmp_fdiv_big_big(Term, Term);
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Term Yap_gmp_and_big_big(Term, Term);
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Term Yap_gmp_ior_big_big(Term, Term);
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Term Yap_gmp_xor_big_big(Term, Term);
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Term Yap_gmp_mod_big_big(Term, Term);
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Term Yap_gmp_mod_big_int(Term, Int);
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Term Yap_gmp_mod_int_big(Int, Term);
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Term Yap_gmp_rem_big_big(Term, Term);
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Term Yap_gmp_rem_big_int(Term, Int);
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Term Yap_gmp_rem_int_big(Int, Term);
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Term Yap_gmp_exp_int_int(Int,Int);
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Term Yap_gmp_exp_int_big(Int,Term);
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Term Yap_gmp_exp_big_int(Term,Int);
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Term Yap_gmp_exp_big_big(Term,Term);
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Term Yap_gmp_gcd_int_big(Int,Term);
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Term Yap_gmp_gcd_big_big(Term,Term);
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Term Yap_gmp_big_from_64bits(YAP_LONG_LONG);
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Term Yap_gmp_float_to_big(Float);
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Term Yap_gmp_float_to_rational(Float);
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Term Yap_gmp_float_rationalize(Float);
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Float Yap_gmp_to_float(Term);
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Term Yap_gmp_add_float_big(Float, Term);
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Term Yap_gmp_sub_float_big(Float, Term);
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Term Yap_gmp_sub_big_float(Term, Float);
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Term Yap_gmp_mul_float_big(Float, Term);
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Term Yap_gmp_fdiv_float_big(Float, Term);
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Term Yap_gmp_fdiv_big_float(Term, Float);
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int Yap_gmp_cmp_big_int(Term, Int);
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#define Yap_gmp_cmp_int_big(I, T) (-Yap_gmp_cmp_big_int(T, I))
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int Yap_gmp_cmp_big_float(Term, Float);
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#define Yap_gmp_cmp_float_big(D, T) (-Yap_gmp_cmp_big_float(T, D))
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int Yap_gmp_cmp_big_big(Term, Term);
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int Yap_gmp_tcmp_big_int(Term, Int);
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#define Yap_gmp_tcmp_int_big(I, T) (-Yap_gmp_tcmp_big_int(T, I))
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int Yap_gmp_tcmp_big_float(Term, Float);
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#define Yap_gmp_tcmp_float_big(D, T) (-Yap_gmp_tcmp_big_float(T, D))
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int Yap_gmp_tcmp_big_big(Term, Term);
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Term Yap_gmp_neg_int(Int);
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Term Yap_gmp_abs_big(Term);
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Term Yap_gmp_neg_big(Term);
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Term Yap_gmp_unot_big(Term);
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Term Yap_gmp_floor(Term);
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Term Yap_gmp_ceiling(Term);
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Term Yap_gmp_round(Term);
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Term Yap_gmp_trunc(Term);
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Term Yap_gmp_float_fractional_part(Term);
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Term Yap_gmp_float_integer_part(Term);
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Term Yap_gmp_sign(Term);
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Term Yap_gmp_lsb(Term);
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Term Yap_gmp_msb(Term);
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Term Yap_gmp_popcount(Term);
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char * Yap_gmp_to_string(Term, char *, size_t, int);
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size_t Yap_gmp_to_size(Term, int);
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int Yap_term_to_existing_big(Term, MP_INT *);
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int Yap_term_to_existing_rat(Term, MP_RAT *);
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void Yap_gmp_set_bit(Int i, Term t);
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#endif
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#define Yap_Mk64IntegerTerm(i) __Yap_Mk64IntegerTerm((i) PASS_REGS)
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INLINE_ONLY inline EXTERN Term __Yap_Mk64IntegerTerm(YAP_LONG_LONG USES_REGS);
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INLINE_ONLY inline EXTERN Term
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__Yap_Mk64IntegerTerm(YAP_LONG_LONG i USES_REGS)
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{
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if (i <= Int_MAX && i >= Int_MIN) {
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return MkIntegerTerm((Int)i);
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} else {
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#if USE_GMP
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return Yap_gmp_big_from_64bits(i);
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#else
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return MkIntTerm(-1);
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#endif
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}
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}
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#if __clang__ && FALSE /* not in OSX yet */
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#define DO_ADD() if (__builtin_sadd_overflow( i1, i2, & z ) ) { goto overflow; }
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#endif
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inline static Term
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add_int(Int i, Int j USES_REGS)
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{
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#if USE_GMP
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UInt w = (UInt)i+(UInt)j;
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if (i > 0) {
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if (j > 0 && (Int)w < 0) goto overflow;
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} else {
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if (j < 0 && (Int)w > 0) goto overflow;
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}
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RINT( (Int)w);
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/* Integer overflow, we need to use big integers */
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overflow:
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return Yap_gmp_add_ints(i, j);
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#else
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RINT(i+j);
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#endif
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}
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static inline Term
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p_plus(Term t1, Term t2 USES_REGS) {
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switch (ETypeOfTerm(t1)) {
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case long_int_e:
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switch (ETypeOfTerm(t2)) {
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case long_int_e:
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/* two integers */
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return add_int(IntegerOfTerm(t1),IntegerOfTerm(t2) PASS_REGS);
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case double_e:
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{
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/* integer, double */
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Float fl1 = (Float)IntegerOfTerm(t1);
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Float fl2 = FloatOfTerm(t2);
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RFLOAT(fl1+fl2);
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}
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case big_int_e:
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#ifdef USE_GMP
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return(Yap_gmp_add_int_big(IntegerOfTerm(t1), t2));
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#endif
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default:
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RERROR();
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}
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case double_e:
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switch (ETypeOfTerm(t2)) {
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case long_int_e:
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/* float * integer */
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RFLOAT(FloatOfTerm(t1)+IntegerOfTerm(t2));
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case double_e:
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RFLOAT(FloatOfTerm(t1)+FloatOfTerm(t2));
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case big_int_e:
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#ifdef USE_GMP
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return Yap_gmp_add_float_big(FloatOfTerm(t1),t2);
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#endif
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default:
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RERROR();
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}
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case big_int_e:
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#ifdef USE_GMP
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switch (ETypeOfTerm(t2)) {
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case long_int_e:
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return Yap_gmp_add_int_big(IntegerOfTerm(t2), t1);
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case big_int_e:
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/* two bignums */
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return Yap_gmp_add_big_big(t1, t2);
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case double_e:
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return Yap_gmp_add_float_big(FloatOfTerm(t2),t1);
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default:
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RERROR();
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}
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#endif
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default:
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RERROR();
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}
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RERROR();
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}
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