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Fixedpoint unit tests and transcribed bv puzzle (#5291)
* simple fixed point arithmetic tests * transcribe puzzle
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alexandernutz
GitHub
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49e9782238
1 changed files with 217 additions and 3 deletions
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@ -347,12 +347,14 @@ namespace polysat {
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/**
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* Monotonicity example from certora
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*
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* We do overflow checks by doubling the base bitwidth here.
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*/
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static void test_monot() {
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scoped_solver s(__func__);
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auto baseBw = 5;
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auto max_int_const = 31; // (2^5 - 1) -- change this if you change baseBw
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auto max_int_const = 31; // (2^5 - 1) -- change this when you change baseBw
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auto bw = 2 * baseBw;
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auto max_int = s.var(s.add_var(bw));
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@ -377,8 +379,6 @@ namespace polysat {
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auto err = s.var(s.add_var(bw));
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s.add_ule(err, max_int);
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auto zero = a - a;
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auto rem1 = s.var(s.add_var(bw));
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auto quot2 = s.var(s.add_var(bw));
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s.add_ule(quot2, max_int);
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@ -429,6 +429,220 @@ namespace polysat {
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s.pop();
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}
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/*
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* Mul-then-div in fixed point arithmetic is (roughly) neutral.
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*
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* I.e. we prove "(((a * b) / sf) * sf) / b" to be equal to a, up to some error margin.
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*
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* sf is the scaling factor (we could leave this unconstrained, but non-zero, to make the benchmark a bit harder)
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* em is the error margin
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*
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* We do overflow checks by doubling the base bitwidth here.
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*/
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static void test_fixed_point_arith_mul_div_inverse() {
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scoped_solver s(__func__);
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auto baseBw = 5;
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auto max_int_const = 31; // (2^5 - 1) -- change this when you change baseBw
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auto bw = 2 * baseBw;
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auto max_int = s.var(s.add_var(bw));
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s.add_eq(max_int - max_int_const);
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auto zero = max_int - max_int;
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// "input" variables
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auto a = s.var(s.add_var(bw));
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s.add_ule(a, max_int);
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auto b = s.var(s.add_var(bw));
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s.add_ule(b, max_int);
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s.add_ult(zero, b); // b > 0
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// scaling factor (setting it, somewhat arbitrarily, to max_int/3)
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auto sf = s.var(s.add_var(bw));
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s.add_eq(sf - (max_int_const/3));
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// (a * b) / sf = quot1 <=> quot1 * sf + rem1 - (a * b) = 0
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auto quot1 = s.var(s.add_var(bw));
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auto rem1 = s.var(s.add_var(bw));
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s.add_eq((quot1 * sf) + rem1 - (a * b));
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s.add_ult(rem1, sf);
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s.add_ule(quot1 * sf, max_int);
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// (((a * b) / sf) * sf) / b <=> quot2 * b + rem2 - (((a * b) / sf) * sf) = 0
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auto quot2 = s.var(s.add_var(bw));
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auto rem2 = s.var(s.add_var(bw));
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s.add_eq((quot2 * b) + rem2 - (quot1 * sf));
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s.add_ult(rem2, b);
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s.add_ule(quot2 * b, max_int);
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// sf / b = quot3 <=> quot3 * b + rem3 = sf
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auto quot3 = s.var(s.add_var(bw));
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auto rem3 = s.var(s.add_var(bw));
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s.add_eq((quot3 * b) + rem3 - sf);
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s.add_ult(rem3, b);
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s.add_ule(quot3 * b, max_int);
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// em = sf / b + 1
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auto em = s.var(s.add_var(bw));
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s.add_eq(quot3 + 1 - em);
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// we prove quot3 <= a and quot3 + em >= a
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s.push();
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s.add_ult(a, quot3);
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s.check_sat();
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s.expect_unsat();
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s.pop();
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s.push();
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s.add_ult(quot3 + em, a);
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s.check_sat();
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s.expect_unsat();
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s.pop();
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}
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/*
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* Div-then-mul in fixed point arithmetic is (roughly) neutral.
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*
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* I.e. we prove "(b * ((a * sf) / b)) / sf" to be equal to a, up to some error margin.
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*
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* sf is the scaling factor (we could leave this unconstrained, but non-zero, to make the benchmark a bit harder)
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* em is the error margin
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*
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* We do overflow checks by doubling the base bitwidth here.
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*/
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static void test_fixed_point_arith_div_mul_inverse() {
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scoped_solver s(__func__);
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auto baseBw = 5;
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auto max_int_const = 31; // (2^5 - 1) -- change this when you change baseBw
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auto bw = 2 * baseBw;
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auto max_int = s.var(s.add_var(bw));
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s.add_eq(max_int - max_int_const);
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auto zero = max_int - max_int;
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// "input" variables
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auto a = s.var(s.add_var(bw));
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s.add_ule(a, max_int);
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auto b = s.var(s.add_var(bw));
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s.add_ule(b, max_int);
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s.add_ult(zero, b); // b > 0
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// scaling factor (setting it, somewhat arbitrarily, to max_int/3)
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auto sf = s.var(s.add_var(bw));
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s.add_eq(sf - (max_int_const/3));
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// (a * sf) / b = quot1 <=> quot1 * b + rem1 - (a * sf) = 0
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auto quot1 = s.var(s.add_var(bw));
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auto rem1 = s.var(s.add_var(bw));
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s.add_eq((quot1 * b) + rem1 - (a * sf));
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s.add_ult(rem1, b);
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s.add_ule(quot1 * b, max_int);
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// (b * ((a * sf) / b)) / sf = quot2 <=> quot2 * sf + rem2 - (b * ((a * sf) / b)) = 0
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auto quot2 = s.var(s.add_var(bw));
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auto rem2 = s.var(s.add_var(bw));
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s.add_eq((quot2 * sf) + rem2 - (b * quot1));
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s.add_ult(rem2, sf);
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s.add_ule(quot2 * sf, max_int);
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// b / sf = quot3 <=> quot3 * sf + rem3 - b = 0
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auto quot3 = s.var(s.add_var(bw));
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auto rem3 = s.var(s.add_var(bw));
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s.add_eq((quot3 * sf) + rem3 - b);
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s.add_ult(rem3, sf);
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s.add_ule(quot3 * sf, max_int);
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// em = b / sf + 1
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auto em = s.var(s.add_var(bw));
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s.add_eq(quot3 + 1 - em);
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// we prove quot3 <= a and quot3 + em >= a
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s.push();
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s.add_ult(a, quot3);
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s.check_sat();
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s.expect_unsat();
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s.pop();
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s.push();
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s.add_ult(quot3 + em, a);
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s.check_sat();
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s.expect_unsat();
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s.pop();
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}
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/*
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* Transcribed from https://github.com/NikolajBjorner/polysat/blob/main/puzzles/bv.smt2 .
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* We do overflow checks by doubling the base bitwidth here.
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*/
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static void test_fixed_point_arith_div_mul_inverse() {
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scoped_solver s(__func__);
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auto baseBw = 5;
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auto max_int_const = 31; // (2^5 - 1) -- change this when you change baseBw
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auto bw = 2 * baseBw;
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auto max_int = s.var(s.add_var(bw));
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s.add_eq(max_int - max_int_const);
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auto zero = max_int - max_int;
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auto first = s.var(s.add_var(bw));
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s.add_ule(first, max_int);
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auto second = s.var(s.add_var(bw));
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s.add_ule(second, max_int);
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auto idx = s.var(s.add_var(bw));
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s.add_ule(idx, max_int);
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auto r = s.var(s.add_var(bw));
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s.add_ule(r, max_int);
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// q = max_int / idx <=> q * idx + r - max_int = 0
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auto q = s.var(s.add_var(bw));
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auto r = s.var(s.add_var(bw));
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s.add_eq((q * idx) + r - max_int);
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s.add_ult(r, idx);
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s.add_ule(q * idx, max_int);
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/* last assertion:
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(not
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(=> (bvugt second first)
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(=>
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(=> (not (= idx #x00000000))
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(bvule (bvsub second first) q))
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(bvumul_noovfl (bvsub second first) idx))))
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transforming negated boolean skeleton:
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(not (=> a (=> (or b c) d))) <=> (and a (not d) (or b c))
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*/
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// (bvugt second first)
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s.add_ult(first, second);
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// (bvumul_noovfl (bvsub second first) idx)
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s.add_ule((second - first) * idx, max_int);
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// resolving disjunction via push/pop
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// first disjunct: (= idx #x00000000)
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s.push();
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s.add_eq(idx);
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s.check_sat();
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s.expect_unsat();
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s.pop();
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// second disjunct: (bvule (bvsub second first) q)
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s.push();
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s.add_ule(second - first, q);
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s.check_sat();
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s.expect_unsat();
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s.pop();
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}
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// Goal: we probably mix up polysat variables and PDD variables at several points; try to uncover such cases
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// NOTE: actually, add_var seems to keep them in sync, so this is not an issue at the moment (but we should still test it later)
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// static void test_mixed_vars() {
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