mirror of
https://github.com/Z3Prover/z3
synced 2025-04-08 18:31:49 +00:00
566 lines
17 KiB
C
566 lines
17 KiB
C
/*++
|
|
Copyright (c) 2013 Microsoft Corporation
|
|
|
|
Module Name:
|
|
|
|
z3_fpa.h
|
|
|
|
Abstract:
|
|
|
|
Additional APIs for floating-point arithmetic (FPA).
|
|
|
|
Author:
|
|
|
|
Christoph M. Wintersteiger (cwinter) 2013-06-05
|
|
|
|
Notes:
|
|
|
|
--*/
|
|
#ifndef _Z3_FPA_H_
|
|
#define _Z3_FPA_H_
|
|
|
|
#ifdef __cplusplus
|
|
extern "C" {
|
|
#endif // __cplusplus
|
|
|
|
/**
|
|
\defgroup capi C API
|
|
|
|
*/
|
|
|
|
/*@{*/
|
|
|
|
/**
|
|
@name Floating-Point API
|
|
*/
|
|
/*@{*/
|
|
|
|
/**
|
|
\brief Create a rounding mode sort.
|
|
|
|
\param c logical context.
|
|
|
|
def_API('Z3_mk_fpa_rounding_mode_sort', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_rounding_mode_sort(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create a numeral of rounding mode sort which represents the NearestTiesToEven rounding mode.
|
|
|
|
\param c logical context.
|
|
|
|
def_API('Z3_mk_fpa_round_nearest_ties_to_even', AST, (_in(CONTEXT),))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_even(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create a numeral of rounding mode sort which represents the NearestTiesToAway rounding mode.
|
|
|
|
\param c logical context.
|
|
|
|
def_API('Z3_mk_fpa_round_nearest_ties_to_away', AST, (_in(CONTEXT),))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_away(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create a numeral of rounding mode sort which represents the TowardPositive rounding mode.
|
|
|
|
\param c logical context.
|
|
|
|
def_API('Z3_mk_fpa_round_toward_positive', AST, (_in(CONTEXT),))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_round_toward_positive(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create a numeral of rounding mode sort which represents the TowardNegative rounding mode.
|
|
|
|
\param c logical context.
|
|
|
|
def_API('Z3_mk_fpa_round_toward_negative', AST, (_in(CONTEXT),))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_round_toward_negative(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create a numeral of rounding mode sort which represents the TowardZero rounding mode.
|
|
|
|
\param c logical context.
|
|
|
|
def_API('Z3_mk_fpa_round_toward_zero', AST, (_in(CONTEXT),))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_round_toward_zero(__in Z3_context c);
|
|
|
|
|
|
|
|
/**
|
|
\brief Create a floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort', SORT, (_in(CONTEXT), _in(UINT), _in(UINT)))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort(__in Z3_context c, __in unsigned ebits, __in unsigned sbits);
|
|
|
|
/**
|
|
\brief Create the half-precision (16-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_half', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_half(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the half-precision (16-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_16', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_16(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the single-precision (32-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_single', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_single(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the single-precision (32-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_32', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_32(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the double-precision (64-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_double', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_double(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the double-precision (64-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_64', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort__64(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the quadruple-precision (128-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_quadruple', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_quadruple(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create the quadruple-precision (128-bit) floating point sort.
|
|
|
|
\param c logical context.
|
|
\param ebits number of exponent bits
|
|
\param sbits number of significand bits
|
|
|
|
\remark ebits must be larger than 1 and sbits must be larger than 2.
|
|
|
|
def_API('Z3_mk_fpa_sort_128', SORT, (_in(CONTEXT),))
|
|
*/
|
|
Z3_sort Z3_API Z3_mk_fpa_sort_128(__in Z3_context c);
|
|
|
|
/**
|
|
\brief Create a NaN of sort s.
|
|
|
|
\param c logical context.
|
|
\param s target sort
|
|
|
|
def_API('Z3_mk_fpa_nan', AST, (_in(CONTEXT),_in(SORT)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_nan(__in Z3_context c, __in Z3_sort s);
|
|
|
|
/**
|
|
\brief Create a floating point infinity of sort s.
|
|
|
|
\param c logical context.
|
|
\param s target sort
|
|
\param negative indicates whether the result should be negative
|
|
|
|
When \c negative is true, -oo will be generated instead of +oo.
|
|
|
|
def_API('Z3_mk_fpa_inf', AST, (_in(CONTEXT),_in(SORT),_in(BOOL)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_inf(__in Z3_context c, __in Z3_sort s, __in Z3_bool negative);
|
|
|
|
/**
|
|
\brief Create a floating point zero of sort s.
|
|
|
|
\param c logical context.
|
|
\param s target sort
|
|
\param negative indicates whether the result should be negative
|
|
|
|
When \c negative is true, -zero will be generated instead of +zero.
|
|
|
|
def_API('Z3_mk_fpa_zero', AST, (_in(CONTEXT),_in(SORT),_in(BOOL)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_zero(__in Z3_context c, __in Z3_sort s, __in Z3_bool negative);
|
|
|
|
/**
|
|
\brief Create a numeral of floating point sort from a double.
|
|
|
|
This function can be use to create numerals that fit in a double value.
|
|
It is slightly faster than #Z3_mk_numeral since it is not necessary to parse a string.
|
|
|
|
\params c logical context.
|
|
\params v value.
|
|
\params ty sort.
|
|
|
|
ty must be a floating point sort
|
|
|
|
\sa Z3_mk_numeral
|
|
|
|
def_API('Z3_mk_fpa_numeral_double', AST, (_in(CONTEXT), _in(DOUBLE), _in(SORT)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_numeral_double(__in Z3_context c, __in double v, __in Z3_sort ty);
|
|
|
|
/**
|
|
\brief Floating-point absolute value
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_abs', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_abs(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Floating-point negation
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_neg', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_neg(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Floating-point addition
|
|
|
|
\param c logical context.
|
|
\param rm rounding mode
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
rm must be of FPA rounding mode sort, t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_add', AST, (_in(CONTEXT),_in(AST),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_add(__in Z3_context c, __in Z3_ast rm, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point subtraction
|
|
|
|
\param c logical context.
|
|
\param rm rounding mode
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
rm must be of FPA rounding mode sort, t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_sub', AST, (_in(CONTEXT),_in(AST),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_sub(__in Z3_context c, __in Z3_ast rm, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point multiplication
|
|
|
|
\param c logical context.
|
|
\param rm rounding mode
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
rm must be of FPA rounding mode sort, t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_mul', AST, (_in(CONTEXT),_in(AST),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_mul(__in Z3_context c, __in Z3_ast rm, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point division
|
|
|
|
\param c logical context.
|
|
\param rm rounding mode
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
The nodes rm must be of FPA rounding mode sort t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_div', AST, (_in(CONTEXT),_in(AST),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_div(__in Z3_context c, __in Z3_ast rm, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point fused multiply-add.
|
|
|
|
\param c logical context.
|
|
\param rm rounding mode
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
The result is round((t1 * t2) + t3)
|
|
|
|
rm must be of FPA rounding mode sort, t1, t2, and t3 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_fma', AST, (_in(CONTEXT),_in(AST),_in(AST),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_fma(__in Z3_context c, __in Z3_ast rm, __in Z3_ast t1, __in Z3_ast t2, __in Z3_ast t3);
|
|
|
|
/**
|
|
\brief Floating-point square root
|
|
|
|
\param c logical context.
|
|
\param rm rounding mode
|
|
\param t floating-point term.
|
|
|
|
rm must be of FPA rounding mode sort, t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_sqrt', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_sqrt(__in Z3_context c, __in Z3_ast rm, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Floating-point remainder
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_rem', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_rem(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point equality
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
Note that this is IEEE 754 equality (as opposed to SMT-LIB =).
|
|
|
|
t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_eq', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_eq(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point less than or equal
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_le', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_le(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point less-than
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_lt', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_lt(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
|
|
/**
|
|
\brief Floating-point greater than or equal
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_ge', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_ge(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Floating-point greater-than
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1 and t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_gt', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_gt(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Predicate indicating whether t is a normal floating point number
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_is_normal', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_is_normal(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Predicate indicating whether t is a subnormal floating point number
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_is_subnormal', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_is_subnormal(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Predicate indicating whether t is a floating point number with zero value, i.e., +0 or -0.
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_is_zero', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_is_zero(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Predicate indicating whether t is a floating point number representing +Inf or -Inf
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_is_inf', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_is_inf(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Predicate indicating whether t is a NaN
|
|
|
|
\param c logical context.
|
|
\param t floating-point term.
|
|
|
|
t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_is_nan', AST, (_in(CONTEXT),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_is_nan(__in Z3_context c, __in Z3_ast t);
|
|
|
|
/**
|
|
\brief Minimum of floating point numbers
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1, t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_min', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_min(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Maximum of floating point numbers
|
|
|
|
\param c logical context.
|
|
\param t1 floating-point term.
|
|
\param t2 floating-point term.
|
|
|
|
t1, t2 must have the same floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_max', AST, (_in(CONTEXT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_max(__in Z3_context c, __in Z3_ast t1, __in Z3_ast t2);
|
|
|
|
/**
|
|
\brief Conversion of a floating point number to another floating-point sort s.
|
|
|
|
Produces a term that represents the conversion of a floating-point term t to a different
|
|
floating point sort s. If necessary, rounding according to rm is applied.
|
|
|
|
\param c logical context.
|
|
\param s floating-point sort.
|
|
\param rm rounding mode.
|
|
\param t floating-point term.
|
|
|
|
s must be a floating point sort, rm must have rounding mode sort, and t must have floating point sort.
|
|
|
|
def_API('Z3_mk_fpa_convert', AST, (_in(CONTEXT),_in(SORT),_in(AST),_in(AST)))
|
|
*/
|
|
Z3_ast Z3_API Z3_mk_fpa_convert(__in Z3_context c, __in Z3_sort s, __in Z3_ast rm, __in Z3_ast t);
|
|
|
|
/*@}*/
|
|
/*@}*/
|
|
|
|
#ifdef __cplusplus
|
|
};
|
|
#endif // __cplusplus
|
|
|
|
#endif
|