Z3
z3_fpa.h
Go to the documentation of this file.
1 /*++
2 Copyright (c) 2013 Microsoft Corporation
3 
4 Module Name:
5 
6  z3_fpa.h
7 
8 Abstract:
9 
10  Additional APIs for floating-point arithmetic (FP).
11 
12 Author:
13 
14  Christoph M. Wintersteiger (cwinter) 2013-06-05
15 
16 Notes:
17 
18 --*/
19 #pragma once
20 
21 #ifdef __cplusplus
22 extern "C" {
23 #endif // __cplusplus
24 
36  Z3_sort Z3_API Z3_mk_fpa_rounding_mode_sort(Z3_context c);
37 
44  Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_even(Z3_context c);
45 
52  Z3_ast Z3_API Z3_mk_fpa_rne(Z3_context c);
53 
60  Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_away(Z3_context c);
61 
68  Z3_ast Z3_API Z3_mk_fpa_rna(Z3_context c);
69 
76  Z3_ast Z3_API Z3_mk_fpa_round_toward_positive(Z3_context c);
77 
84  Z3_ast Z3_API Z3_mk_fpa_rtp(Z3_context c);
85 
92  Z3_ast Z3_API Z3_mk_fpa_round_toward_negative(Z3_context c);
93 
100  Z3_ast Z3_API Z3_mk_fpa_rtn(Z3_context c);
101 
108  Z3_ast Z3_API Z3_mk_fpa_round_toward_zero(Z3_context c);
109 
116  Z3_ast Z3_API Z3_mk_fpa_rtz(Z3_context c);
117 
128  Z3_sort Z3_API Z3_mk_fpa_sort(Z3_context c, unsigned ebits, unsigned sbits);
129 
136  Z3_sort Z3_API Z3_mk_fpa_sort_half(Z3_context c);
137 
144  Z3_sort Z3_API Z3_mk_fpa_sort_16(Z3_context c);
145 
152  Z3_sort Z3_API Z3_mk_fpa_sort_single(Z3_context c);
153 
160  Z3_sort Z3_API Z3_mk_fpa_sort_32(Z3_context c);
161 
168  Z3_sort Z3_API Z3_mk_fpa_sort_double(Z3_context c);
169 
176  Z3_sort Z3_API Z3_mk_fpa_sort_64(Z3_context c);
177 
184  Z3_sort Z3_API Z3_mk_fpa_sort_quadruple(Z3_context c);
185 
192  Z3_sort Z3_API Z3_mk_fpa_sort_128(Z3_context c);
193 
204  Z3_ast Z3_API Z3_mk_fpa_nan(Z3_context c, Z3_sort s);
205 
219  Z3_ast Z3_API Z3_mk_fpa_inf(Z3_context c, Z3_sort s, bool negative);
220 
234  Z3_ast Z3_API Z3_mk_fpa_zero(Z3_context c, Z3_sort s, bool negative);
235 
258  Z3_ast Z3_API Z3_mk_fpa_fp(Z3_context c, Z3_ast sgn, Z3_ast exp, Z3_ast sig);
259 
280  Z3_ast Z3_API Z3_mk_fpa_numeral_float(Z3_context c, float v, Z3_sort ty);
281 
302  Z3_ast Z3_API Z3_mk_fpa_numeral_double(Z3_context c, double v, Z3_sort ty);
303 
321  Z3_ast Z3_API Z3_mk_fpa_numeral_int(Z3_context c, signed v, Z3_sort ty);
322 
342  Z3_ast Z3_API Z3_mk_fpa_numeral_int_uint(Z3_context c, bool sgn, signed exp, unsigned sig, Z3_sort ty);
343 
363  Z3_ast Z3_API Z3_mk_fpa_numeral_int64_uint64(Z3_context c, bool sgn, int64_t exp, uint64_t sig, Z3_sort ty);
364 
372  Z3_ast Z3_API Z3_mk_fpa_abs(Z3_context c, Z3_ast t);
373 
381  Z3_ast Z3_API Z3_mk_fpa_neg(Z3_context c, Z3_ast t);
382 
394  Z3_ast Z3_API Z3_mk_fpa_add(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2);
395 
407  Z3_ast Z3_API Z3_mk_fpa_sub(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2);
408 
420  Z3_ast Z3_API Z3_mk_fpa_mul(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2);
421 
433  Z3_ast Z3_API Z3_mk_fpa_div(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2);
434 
449  Z3_ast Z3_API Z3_mk_fpa_fma(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2, Z3_ast t3);
450 
461  Z3_ast Z3_API Z3_mk_fpa_sqrt(Z3_context c, Z3_ast rm, Z3_ast t);
462 
473  Z3_ast Z3_API Z3_mk_fpa_rem(Z3_context c, Z3_ast t1, Z3_ast t2);
474 
486  Z3_ast Z3_API Z3_mk_fpa_round_to_integral(Z3_context c, Z3_ast rm, Z3_ast t);
487 
498  Z3_ast Z3_API Z3_mk_fpa_min(Z3_context c, Z3_ast t1, Z3_ast t2);
499 
510  Z3_ast Z3_API Z3_mk_fpa_max(Z3_context c, Z3_ast t1, Z3_ast t2);
511 
522  Z3_ast Z3_API Z3_mk_fpa_leq(Z3_context c, Z3_ast t1, Z3_ast t2);
523 
534  Z3_ast Z3_API Z3_mk_fpa_lt(Z3_context c, Z3_ast t1, Z3_ast t2);
535 
546  Z3_ast Z3_API Z3_mk_fpa_geq(Z3_context c, Z3_ast t1, Z3_ast t2);
547 
558  Z3_ast Z3_API Z3_mk_fpa_gt(Z3_context c, Z3_ast t1, Z3_ast t2);
559 
572  Z3_ast Z3_API Z3_mk_fpa_eq(Z3_context c, Z3_ast t1, Z3_ast t2);
573 
583  Z3_ast Z3_API Z3_mk_fpa_is_normal(Z3_context c, Z3_ast t);
584 
594  Z3_ast Z3_API Z3_mk_fpa_is_subnormal(Z3_context c, Z3_ast t);
595 
605  Z3_ast Z3_API Z3_mk_fpa_is_zero(Z3_context c, Z3_ast t);
606 
616  Z3_ast Z3_API Z3_mk_fpa_is_infinite(Z3_context c, Z3_ast t);
617 
627  Z3_ast Z3_API Z3_mk_fpa_is_nan(Z3_context c, Z3_ast t);
628 
638  Z3_ast Z3_API Z3_mk_fpa_is_negative(Z3_context c, Z3_ast t);
639 
649  Z3_ast Z3_API Z3_mk_fpa_is_positive(Z3_context c, Z3_ast t);
650 
666  Z3_ast Z3_API Z3_mk_fpa_to_fp_bv(Z3_context c, Z3_ast bv, Z3_sort s);
667 
683  Z3_ast Z3_API Z3_mk_fpa_to_fp_float(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s);
684 
700  Z3_ast Z3_API Z3_mk_fpa_to_fp_real(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s);
701 
718  Z3_ast Z3_API Z3_mk_fpa_to_fp_signed(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s);
719 
736  Z3_ast Z3_API Z3_mk_fpa_to_fp_unsigned(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s);
737 
751  Z3_ast Z3_API Z3_mk_fpa_to_ubv(Z3_context c, Z3_ast rm, Z3_ast t, unsigned sz);
752 
766  Z3_ast Z3_API Z3_mk_fpa_to_sbv(Z3_context c, Z3_ast rm, Z3_ast t, unsigned sz);
767 
779  Z3_ast Z3_API Z3_mk_fpa_to_real(Z3_context c, Z3_ast t);
780 
781 
791  unsigned Z3_API Z3_fpa_get_ebits(Z3_context c, Z3_sort s);
792 
800  unsigned Z3_API Z3_fpa_get_sbits(Z3_context c, Z3_sort s);
801 
809  bool Z3_API Z3_fpa_is_numeral_nan(Z3_context c, Z3_ast t);
810 
818  bool Z3_API Z3_fpa_is_numeral_inf(Z3_context c, Z3_ast t);
819 
827  bool Z3_API Z3_fpa_is_numeral_zero(Z3_context c, Z3_ast t);
828 
836  bool Z3_API Z3_fpa_is_numeral_normal(Z3_context c, Z3_ast t);
837 
845  bool Z3_API Z3_fpa_is_numeral_subnormal(Z3_context c, Z3_ast t);
846 
854  bool Z3_API Z3_fpa_is_numeral_positive(Z3_context c, Z3_ast t);
855 
863  bool Z3_API Z3_fpa_is_numeral_negative(Z3_context c, Z3_ast t);
864 
874  Z3_ast Z3_API Z3_fpa_get_numeral_sign_bv(Z3_context c, Z3_ast t);
875 
885  Z3_ast Z3_API Z3_fpa_get_numeral_significand_bv(Z3_context c, Z3_ast t);
886 
899  bool Z3_API Z3_fpa_get_numeral_sign(Z3_context c, Z3_ast t, int * sgn);
900 
912  Z3_string Z3_API Z3_fpa_get_numeral_significand_string(Z3_context c, Z3_ast t);
913 
926  bool Z3_API Z3_fpa_get_numeral_significand_uint64(Z3_context c, Z3_ast t, uint64_t * n);
927 
940  Z3_string Z3_API Z3_fpa_get_numeral_exponent_string(Z3_context c, Z3_ast t, bool biased);
941 
955  bool Z3_API Z3_fpa_get_numeral_exponent_int64(Z3_context c, Z3_ast t, int64_t * n, bool biased);
956 
968  Z3_ast Z3_API Z3_fpa_get_numeral_exponent_bv(Z3_context c, Z3_ast t, bool biased);
969 
984  Z3_ast Z3_API Z3_mk_fpa_to_ieee_bv(Z3_context c, Z3_ast t);
985 
1002  Z3_ast Z3_API Z3_mk_fpa_to_fp_int_real(Z3_context c, Z3_ast rm, Z3_ast exp, Z3_ast sig, Z3_sort s);
1007 #ifdef __cplusplus
1008 }
1009 #endif // __cplusplus
1010 
Z3_ast Z3_API Z3_mk_fpa_is_infinite(Z3_context c, Z3_ast t)
Predicate indicating whether t is a floating-point number representing +oo or -oo.
Z3_ast Z3_API Z3_mk_fpa_to_fp_int_real(Z3_context c, Z3_ast rm, Z3_ast exp, Z3_ast sig, Z3_sort s)
Conversion of a real-sorted significand and an integer-sorted exponent into a term of FloatingPoint s...
Z3_ast Z3_API Z3_mk_fpa_to_fp_bv(Z3_context c, Z3_ast bv, Z3_sort s)
Conversion of a single IEEE 754-2008 bit-vector into a floating-point number.
Z3_ast Z3_API Z3_mk_fpa_is_subnormal(Z3_context c, Z3_ast t)
Predicate indicating whether t is a subnormal floating-point number.
Z3_ast Z3_API Z3_mk_fpa_to_ieee_bv(Z3_context c, Z3_ast t)
Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
Z3_ast Z3_API Z3_mk_fpa_to_fp_signed(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a 2's complement signed bit-vector term into a term of FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_to_sbv(Z3_context c, Z3_ast rm, Z3_ast t, unsigned sz)
Conversion of a floating-point term into a signed bit-vector.
bool Z3_API Z3_fpa_get_numeral_sign(Z3_context c, Z3_ast t, int *sgn)
Retrieves the sign of a floating-point literal.
Z3_ast Z3_API Z3_mk_fpa_rna(Z3_context c)
Create a numeral of RoundingMode sort which represents the NearestTiesToAway rounding mode.
Z3_ast Z3_API Z3_mk_fpa_sub(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2)
Floating-point subtraction.
Z3_ast Z3_API Z3_mk_fpa_is_normal(Z3_context c, Z3_ast t)
Predicate indicating whether t is a normal floating-point number.
Z3_ast Z3_API Z3_mk_fpa_to_ubv(Z3_context c, Z3_ast rm, Z3_ast t, unsigned sz)
Conversion of a floating-point term into an unsigned bit-vector.
Z3_sort Z3_API Z3_mk_fpa_sort_half(Z3_context c)
Create the half-precision (16-bit) FloatingPoint sort.
unsigned Z3_API Z3_fpa_get_ebits(Z3_context c, Z3_sort s)
Retrieves the number of bits reserved for the exponent in a FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_is_positive(Z3_context c, Z3_ast t)
Predicate indicating whether t is a positive floating-point number.
bool Z3_API Z3_fpa_is_numeral_positive(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is positive.
Z3_ast Z3_API Z3_mk_fpa_rtn(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardNegative rounding mode.
Z3_ast Z3_API Z3_mk_fpa_numeral_int(Z3_context c, signed v, Z3_sort ty)
Create a numeral of FloatingPoint sort from a signed integer.
bool Z3_API Z3_fpa_get_numeral_exponent_int64(Z3_context c, Z3_ast t, int64_t *n, bool biased)
Return the exponent value of a floating-point numeral as a signed 64-bit integer.
Z3_ast Z3_API Z3_mk_fpa_rtp(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardPositive rounding mode.
bool Z3_API Z3_fpa_is_numeral_nan(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is a NaN.
unsigned Z3_API Z3_fpa_get_sbits(Z3_context c, Z3_sort s)
Retrieves the number of bits reserved for the significand in a FloatingPoint sort.
const char * Z3_string
Z3 string type. It is just an alias for const char *.
Definition: z3_api.h:84
Z3_ast Z3_API Z3_mk_fpa_round_toward_negative(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardNegative rounding mode.
Z3_ast Z3_API Z3_mk_fpa_max(Z3_context c, Z3_ast t1, Z3_ast t2)
Maximum of floating-point numbers.
Z3_ast Z3_API Z3_mk_fpa_to_fp_real(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a term of real sort into a term of FloatingPoint sort.
bool Z3_API Z3_fpa_get_numeral_significand_uint64(Z3_context c, Z3_ast t, uint64_t *n)
Return the significand value of a floating-point numeral as a uint64.
Z3_string Z3_API Z3_fpa_get_numeral_exponent_string(Z3_context c, Z3_ast t, bool biased)
Return the exponent value of a floating-point numeral as a string.
Z3_ast Z3_API Z3_mk_fpa_inf(Z3_context c, Z3_sort s, bool negative)
Create a floating-point infinity of sort s.
Z3_ast Z3_API Z3_mk_fpa_nan(Z3_context c, Z3_sort s)
Create a floating-point NaN of sort s.
bool Z3_API Z3_fpa_is_numeral_subnormal(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is subnormal.
Z3_ast Z3_API Z3_mk_fpa_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Floating-point greater than.
Z3_ast Z3_API Z3_mk_fpa_is_zero(Z3_context c, Z3_ast t)
Predicate indicating whether t is a floating-point number with zero value, i.e., +zero or -zero.
Z3_ast Z3_API Z3_mk_fpa_round_toward_positive(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardPositive rounding mode.
Z3_ast Z3_API Z3_mk_fpa_eq(Z3_context c, Z3_ast t1, Z3_ast t2)
Floating-point equality.
Z3_sort Z3_API Z3_mk_fpa_sort_16(Z3_context c)
Create the half-precision (16-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_geq(Z3_context c, Z3_ast t1, Z3_ast t2)
Floating-point greater than or equal.
Z3_ast Z3_API Z3_mk_fpa_numeral_float(Z3_context c, float v, Z3_sort ty)
Create a numeral of FloatingPoint sort from a float.
Z3_ast Z3_API Z3_mk_fpa_rtz(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardZero rounding mode.
bool Z3_API Z3_fpa_is_numeral_negative(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is negative.
Z3_ast Z3_API Z3_fpa_get_numeral_significand_bv(Z3_context c, Z3_ast t)
Retrieves the significand of a floating-point literal as a bit-vector expression.
Z3_sort Z3_API Z3_mk_fpa_sort_quadruple(Z3_context c)
Create the quadruple-precision (128-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_numeral_int64_uint64(Z3_context c, bool sgn, int64_t exp, uint64_t sig, Z3_sort ty)
Create a numeral of FloatingPoint sort from a sign bit and two 64-bit integers.
Z3_ast Z3_API Z3_mk_fpa_rem(Z3_context c, Z3_ast t1, Z3_ast t2)
Floating-point remainder.
Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_away(Z3_context c)
Create a numeral of RoundingMode sort which represents the NearestTiesToAway rounding mode.
Z3_ast Z3_API Z3_mk_fpa_min(Z3_context c, Z3_ast t1, Z3_ast t2)
Minimum of floating-point numbers.
Z3_ast Z3_API Z3_mk_fpa_round_to_integral(Z3_context c, Z3_ast rm, Z3_ast t)
Floating-point roundToIntegral. Rounds a floating-point number to the closest integer,...
Z3_ast Z3_API Z3_mk_fpa_to_real(Z3_context c, Z3_ast t)
Conversion of a floating-point term into a real-numbered term.
Z3_sort Z3_API Z3_mk_fpa_sort_128(Z3_context c)
Create the quadruple-precision (128-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_add(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2)
Floating-point addition.
Z3_ast Z3_API Z3_mk_fpa_is_negative(Z3_context c, Z3_ast t)
Predicate indicating whether t is a negative floating-point number.
Z3_ast Z3_API Z3_mk_fpa_to_fp_unsigned(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a 2's complement unsigned bit-vector term into a term of FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_abs(Z3_context c, Z3_ast t)
Floating-point absolute value.
Z3_ast Z3_API Z3_mk_fpa_numeral_int_uint(Z3_context c, bool sgn, signed exp, unsigned sig, Z3_sort ty)
Create a numeral of FloatingPoint sort from a sign bit and two integers.
Z3_ast Z3_API Z3_mk_fpa_is_nan(Z3_context c, Z3_ast t)
Predicate indicating whether t is a NaN.
Z3_ast Z3_API Z3_mk_fpa_fp(Z3_context c, Z3_ast sgn, Z3_ast exp, Z3_ast sig)
Create an expression of FloatingPoint sort from three bit-vector expressions.
Z3_ast Z3_API Z3_fpa_get_numeral_exponent_bv(Z3_context c, Z3_ast t, bool biased)
Retrieves the exponent of a floating-point literal as a bit-vector expression.
Z3_sort Z3_API Z3_mk_fpa_sort_single(Z3_context c)
Create the single-precision (32-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_neg(Z3_context c, Z3_ast t)
Floating-point negation.
Z3_ast Z3_API Z3_mk_fpa_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Floating-point less than.
Z3_sort Z3_API Z3_mk_fpa_sort_32(Z3_context c)
Create the single-precision (32-bit) FloatingPoint sort.
Z3_sort Z3_API Z3_mk_fpa_sort_64(Z3_context c)
Create the double-precision (64-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_to_fp_float(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a FloatingPoint term into another term of different FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_even(Z3_context c)
Create a numeral of RoundingMode sort which represents the NearestTiesToEven rounding mode.
Z3_ast Z3_API Z3_mk_fpa_leq(Z3_context c, Z3_ast t1, Z3_ast t2)
Floating-point less than or equal.
Z3_ast Z3_API Z3_mk_fpa_numeral_double(Z3_context c, double v, Z3_sort ty)
Create a numeral of FloatingPoint sort from a double.
Z3_ast Z3_API Z3_mk_fpa_mul(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2)
Floating-point multiplication.
Z3_ast Z3_API Z3_mk_fpa_div(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2)
Floating-point division.
Z3_sort Z3_API Z3_mk_fpa_sort(Z3_context c, unsigned ebits, unsigned sbits)
Create a FloatingPoint sort.
Z3_ast Z3_API Z3_mk_fpa_sqrt(Z3_context c, Z3_ast rm, Z3_ast t)
Floating-point square root.
Z3_string Z3_API Z3_fpa_get_numeral_significand_string(Z3_context c, Z3_ast t)
Return the significand value of a floating-point numeral as a string.
Z3_ast Z3_API Z3_fpa_get_numeral_sign_bv(Z3_context c, Z3_ast t)
Retrieves the sign of a floating-point literal as a bit-vector expression.
bool Z3_API Z3_fpa_is_numeral_normal(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is normal.
Z3_ast Z3_API Z3_mk_fpa_fma(Z3_context c, Z3_ast rm, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Floating-point fused multiply-add.
Z3_ast Z3_API Z3_mk_fpa_round_toward_zero(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardZero rounding mode.
Z3_ast Z3_API Z3_mk_fpa_zero(Z3_context c, Z3_sort s, bool negative)
Create a floating-point zero of sort s.
Z3_sort Z3_API Z3_mk_fpa_rounding_mode_sort(Z3_context c)
Create the RoundingMode sort.
Z3_ast Z3_API Z3_mk_fpa_rne(Z3_context c)
Create a numeral of RoundingMode sort which represents the NearestTiesToEven rounding mode.
Z3_sort Z3_API Z3_mk_fpa_sort_double(Z3_context c)
Create the double-precision (64-bit) FloatingPoint sort.
bool Z3_API Z3_fpa_is_numeral_inf(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is a +oo or -oo.
bool Z3_API Z3_fpa_is_numeral_zero(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is +zero or -zero.