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fix(posit): fix division bugs and complete regression tests (#534) (#537)
* fix(posit): fix division bugs and complete regression tests (#534) Two bugs in posit2's division pipeline: 1. Missing setradix() in normalizeDivision's multi-limb path caused blocksignificand::div() to use wrong radix (bfbits vs divbits), placing quotient bits 2 positions too high (e.g. 10/2=4). 2. Missing sticky bits in convert() — only nbits+4 fraction bits were extracted from the blocktriple, silently discarding remaining quotient bits needed for correct round-to-even decisions (-1 ULP errors). Also completes the posit2 division regression test suite to match posit1: - Random tests at levels 2-4 for posit<16,2> through posit<64,4> - Adversarial worst-case division test functions - Guards posit1-specific functions in posit_test_suite_randoms.hpp so both posit and posit1 can share the same test infrastructure. Verified with both gcc and clang. No regressions in add/sub/mul. * code hygiene --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
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‎docs/bugs/posit-div-port.md‎

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# Posit DIV bug: Issue #534
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## Division Bug RCA
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Two bugs found in posit2's division pipeline:
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Bug 1 — Missing setradix() in normalizeDivision (systematic, the original #534 bug)
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- File: include/sw/universal/number/posit/posit_impl.hpp:1102
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- Cause: The multi-limb path (else branch) of normalizeDivision() did not call tgt.setradix() to set the blocksignificand's radix point. The if constexpr
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fast path used tgt.setbits(raw) which internally calls setradix(), but the else path for wider posits used setblock()/setbit()/bitShift() which do not.
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- Effect: blocksignificand::div() reads lhs.radix() to determine iteration count and quotient bit placement. With the default radixPoint (bfbits=87 instead
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of correct divbits=85 for posit<32,2>), quotient bits were placed 2 positions too high, causing results like 10/2=4.
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- Threshold: Manifested at nbits >= 24 (where divshift >= 64 - fbits, triggering the else branch).
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- Fix: Added tgt.setradix() in the else branch, matching the pattern used in normalizeAddition's else branch at line 1025.
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Bug 2 — Missing sticky bits in convert() (rounding, causing -1 ULP errors)
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- File: include/sw/universal/number/posit/posit_impl.hpp:412
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- Cause: The convert() function extracts only nbits + 4 fraction bits from the blocktriple into a blocksignificand for rounding. For DIV, the blocktriple
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has 3*fbits + 4 fraction bits — far more than extracted. The remaining bits were silently discarded without contributing to the sticky bit in convert_().
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- Effect: Round-to-even decisions were wrong in ~0.1-0.3% of cases, producing results exactly 1 ULP below the correct value.
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- Fix: After the extraction loop, check if any blocktriple bits below the extracted range are set via v.any(), and fold them into the lowest bit of the
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extracted fraction (bit 0) as sticky information.
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## Regression Test Completion
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File: static/tapered/posit/arithmetic/division.cpp
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- Added #include <universal/verification/posit_test_suite_randoms.hpp>
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- Added GenerateWorstCaseDivision, EnumerateToughDivisions, and ToughDivisions2 adversarial test functions (ported from posit1, adapted for posit2's API:
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.get() → to_binary())
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- Added posit<3,2> and posit<3,3> to Level 1 (matching posit1)
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- Level 2: Added VerifyBinaryOperatorThroughRandoms for posit<16,2> and posit<24,2> (1000 randoms)
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- Level 3: Added randoms for posit<20,1>, posit<28,1>, posit<32,1>, posit<32,2>, posit<32,3>
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- Level 4: Added randoms for posit<48,2>, posit<64,2>, posit<64,3>, posit<64,4>
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- Matched posit1's complete test structure exactly
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## Shared Test Suite Compatibility
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File: include/sw/universal/verification/posit_test_suite_randoms.hpp
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- Wrapped Compare() and VerifyConversionThroughRandoms() with #if defined(BITBLOCK_THROW_ARITHMETIC_EXCEPTION) guard, since these functions use
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posit1-specific types (bitblock, .get(), .set(), truncate)
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- VerifyBinaryOperatorThroughRandoms (templated on TestType) works with both posit and posit1 — shared test suite achieved
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## Verification
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- Both bugs fixed, tested with gcc AND clang
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- posit2 division: all exhaustive tests pass (nbits 2-10), all random tests pass through posit<48,2> (matching posit1)
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- posit<64,*> failures are expected in both posit and posit1 (double oracle precision limitation)
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- posit1 division: unaffected by changes, still passes
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- posit2 addition, subtraction, multiplication: no regressions
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‎docs/bugs/posit-division.md‎

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# Posit DIV bug: Issue #534
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## Division Bug RCA
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Two bugs found in posit2's division pipeline:
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Bug 1 — Missing setradix() in normalizeDivision (systematic, the original #534 bug)
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- File: include/sw/universal/number/posit/posit_impl.hpp:1102
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- Cause: The multi-limb path (else branch) of normalizeDivision() did not call tgt.setradix() to set the blocksignificand's radix point. The if constexpr
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fast path used tgt.setbits(raw) which internally calls setradix(), but the else path for wider posits used setblock()/setbit()/bitShift() which do not.
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- Effect: blocksignificand::div() reads lhs.radix() to determine iteration count and quotient bit placement. With the default radixPoint (bfbits=87 instead
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of correct divbits=85 for posit<32,2>), quotient bits were placed 2 positions too high, causing results like 10/2=4.
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- Threshold: Manifested at nbits >= 24 (where divshift >= 64 - fbits, triggering the else branch).
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- Fix: Added tgt.setradix() in the else branch, matching the pattern used in normalizeAddition's else branch at line 1025.
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Bug 2 — Missing sticky bits in convert() (rounding, causing -1 ULP errors)
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- File: include/sw/universal/number/posit/posit_impl.hpp:412
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- Cause: The convert() function extracts only nbits + 4 fraction bits from the blocktriple into a blocksignificand for rounding. For DIV, the blocktriple
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has 3*fbits + 4 fraction bits — far more than extracted. The remaining bits were silently discarded without contributing to the sticky bit in convert_().
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- Effect: Round-to-even decisions were wrong in ~0.1-0.3% of cases, producing results exactly 1 ULP below the correct value.
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- Fix: After the extraction loop, check if any blocktriple bits below the extracted range are set via v.any(), and fold them into the lowest bit of the
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extracted fraction (bit 0) as sticky information.
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## Regression Test Completion
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File: static/tapered/posit/arithmetic/division.cpp
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- Added #include <universal/verification/posit_test_suite_randoms.hpp>
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- Added GenerateWorstCaseDivision, EnumerateToughDivisions, and ToughDivisions2 adversarial test functions (ported from posit1, adapted for posit2's API:
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.get() → to_binary())
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- Added posit<3,2> and posit<3,3> to Level 1 (matching posit1)
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- Level 2: Added VerifyBinaryOperatorThroughRandoms for posit<16,2> and posit<24,2> (1000 randoms)
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- Level 3: Added randoms for posit<20,1>, posit<28,1>, posit<32,1>, posit<32,2>, posit<32,3>
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- Level 4: Added randoms for posit<48,2>, posit<64,2>, posit<64,3>, posit<64,4>
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- Matched posit1's complete test structure exactly
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## Shared Test Suite Compatibility
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File: include/sw/universal/verification/posit_test_suite_randoms.hpp
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- Wrapped Compare() and VerifyConversionThroughRandoms() with #if defined(BITBLOCK_THROW_ARITHMETIC_EXCEPTION) guard, since these functions use
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posit1-specific types (bitblock, .get(), .set(), truncate)
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- VerifyBinaryOperatorThroughRandoms (templated on TestType) works with both posit and posit1 — shared test suite achieved
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## Verification
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- Both bugs fixed, tested with gcc AND clang
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- posit2 division: all exhaustive tests pass (nbits 2-10), all random tests pass through posit<48,2> (matching posit1)
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- posit<64,*> failures are expected in both posit and posit1 (double oracle precision limitation)
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- posit1 division: unaffected by changes, still passes
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- posit2 addition, subtraction, multiplication: no regressions
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## Conclusion
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This port missed key test functionality present in posit1, letting this bug get through.

‎include/sw/universal/number/posit/posit_impl.hpp‎

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@@ -409,6 +409,15 @@ inline posit<nbits, es, bt>& convert(const blocktriple<fbits, op, bt>& v, posit<
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frac.setbit(extractBits - 1 - i, v.at(static_cast<unsigned>(srcPos)));
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}
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}
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// Capture sticky information from blocktriple bits below the extracted range.
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// Without this, division (and other ops with wide significands) can lose
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// rounding-critical bits, causing systematic -1 ULP errors.
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int lowestExtracted = msbPos - static_cast<int>(extractBits);
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if (lowestExtracted > 0) {
417+
if (v.any(static_cast<unsigned>(lowestExtracted))) {
418+
frac.setbit(0, true); // fold remaining bits into sticky position
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}
420+
}
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return convert_<nbits, es, bt, extractBits>(v.sign(), realScale, frac, p);
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}
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@@ -1099,6 +1108,7 @@ class posit {
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for (unsigned i = 0; i < fracBlocks; ++i) {
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tgt.setblock(i, frac[i]);
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}
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tgt.setradix();
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tgt.setbit(fbits); // add the hidden bit
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tgt.bitShift(divshift); // alignment shift for division
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}

‎include/sw/universal/verification/posit_test_suite_randoms.hpp‎

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@@ -384,6 +384,10 @@ namespace sw { namespace universal {
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return nrOfFailedTests;
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}
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// The following functions depend on posit1's bitblock internal type.
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// They are only compiled when the bitblock-based posit1 headers are included.
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#if defined(BITBLOCK_THROW_ARITHMETIC_EXCEPTION) || defined(BITBLOCK_ROUND_TIES_TO_ZERO)
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387391
template<size_t nbits, size_t es>
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int Compare(long double input, const posit<nbits, es>& testresult, const posit<nbits, es>& ptarget, const posit<nbits+1,es>& pref, bool reportTestCases) {
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int fail = 0;
@@ -482,4 +486,6 @@ namespace sw { namespace universal {
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return nrOfFailedTests;
483487
}
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#endif // BITBLOCK_THROW_ARITHMETIC_EXCEPTION || BITBLOCK_ROUND_TIES_TO_ZERO
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485491
}} // namespace sw::universal

‎static/tapered/posit/arithmetic/division.cpp‎

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@@ -16,6 +16,7 @@
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//#define ALGORITHM_TRACE_DIV
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#include <universal/number/posit/posit.hpp>
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#include <universal/verification/posit_test_suite.hpp>
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#include <universal/verification/posit_test_suite_randoms.hpp>
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// generate specific test case that you can trace with the trace conditions in posit.h
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// for most bugs they are traceable with _trace_conversion and _trace_div
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pdiv = pa / pb;
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std::cout << std::setprecision(nbits - 2);
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std::cout << std::setw(nbits) << a << " / " << std::setw(nbits) << b << " = " << std::setw(nbits) << ref << std::endl;
33-
std::cout << pa.get() << " / " << pb.get() << " = " << pdiv.get() << " (reference: " << pref.get() << ") ";
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std::cout << to_binary(pa) << " / " << to_binary(pb) << " = " << to_binary(pdiv) << " (reference: " << to_binary(pref) << ") ";
3435
std::cout << (pref == pdiv ? "PASS" : "FAIL") << std::endl << std::endl;
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std::cout << std::setprecision(5);
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}
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template<size_t nbits, size_t es>
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void GenerateWorstCaseDivision() {
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std::stringstream posit_descriptor;
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posit_descriptor << "posit<" << nbits << ", " << es << ">";
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sw::universal::posit<nbits, es> p_plus_eps(1), p_minus_eps(1), p_result;
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p_plus_eps++;
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p_minus_eps--;
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p_result = p_plus_eps / p_minus_eps;
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if constexpr (es < 2) {
48+
std::cout << posit_descriptor.str() << " minpos = " << std::fixed << std::setprecision(nbits) << sw::universal::posit<nbits, es>(sw::universal::SpecificValue::minpos) << std::dec << std::endl;
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}
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else {
51+
std::cout << posit_descriptor.str() << " minpos = " << std::setprecision(nbits) << sw::universal::posit<nbits, es>(sw::universal::SpecificValue::minpos) << std::endl;
52+
}
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std::cout << to_binary(p_plus_eps) << " / " << to_binary(p_minus_eps) << " = " << to_binary(p_result) << std::endl;
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std::cout << std::setprecision(nbits - 2) << std::setw(nbits) << p_plus_eps << " / " << std::setw(nbits) << p_minus_eps << " = " << std::setw(nbits) << p_result << std::endl;
55+
std::cout << std::endl;
56+
}
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void EnumerateToughDivisions() {
59+
GenerateWorstCaseDivision<8, 0>();
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GenerateWorstCaseDivision<12, 0>();
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GenerateWorstCaseDivision<16, 1>();
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GenerateWorstCaseDivision<20, 1>();
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GenerateWorstCaseDivision<24, 1>();
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GenerateWorstCaseDivision<28, 1>();
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GenerateWorstCaseDivision<32, 1>();
66+
GenerateWorstCaseDivision<32, 2>();
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GenerateWorstCaseDivision<40, 2>();
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GenerateWorstCaseDivision<48, 2>();
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GenerateWorstCaseDivision<56, 2>();
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GenerateWorstCaseDivision<60, 3>();
71+
}
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/*
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Tricky division cases from posit1 test suite.
75+
All are in the <16,1> environment.
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Let
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A = posit represented by integer 20479 (value is 8191/4096 = 1.999755859375)
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B = posit represented by integer 2 (value is 1/67108864 = 0.00000001490116119384765625)
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C = posit represented by integer 16383 (value is 8191/8192 = 0.9998779296875)
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D = posit represented by integer 16385 (value is 4097/4096 = 1.000244140625)
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Then the divide routine should return the following:
84+
B / A = posit represented by integer 2 (that is, the division leaves B unchanged)
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A / B = posit represented by integer 32766 (value is 67108864)
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C / D = posit represented by integer 16381 (value is 0.996337890625)
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D / C = posit represented by integer 16386 (value is 1.00048828125)
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*/
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void ToughDivisions2() {
90+
sw::universal::posit<16, 1> a, b, c, d;
91+
a.setbits(20479);
92+
b.setbits(2);
93+
c.setbits(16383);
94+
d.setbits(16385);
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96+
GenerateTestCase<16, 1>(b, a);
97+
GenerateTestCase<16, 1>(a, b);
98+
GenerateTestCase<16, 1>(c, d);
99+
GenerateTestCase<16, 1>(d, c);
100+
}
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38102
// Regression testing guards: typically set by the cmake configuration, but MANUAL_TESTING is an override
39103
#define MANUAL_TESTING 0
40104
// REGRESSION_LEVEL_OVERRIDE is set by the cmake file to drive a specific regression intensity
@@ -65,6 +129,11 @@ try {
65129
#if MANUAL_TESTING
66130

67131
// generate individual testcases to hand trace/debug
132+
ToughDivisions2();
133+
134+
// Generate the worst fraction pressure for different posit configurations
135+
EnumerateToughDivisions();
136+
68137
GenerateTestCase<4, 0, double>(0.5, 1.0);
69138
GenerateTestCase<4, 0, double>(0.5, -1.0);
70139
GenerateTestCase<8, 0, double>(1.0, 0.5);
@@ -81,6 +150,8 @@ try {
81150

82151
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<3, 0>>(reportTestCases), "posit< 3,0>", "division");
83152
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<3, 1>>(reportTestCases), "posit< 3,1>", "division");
153+
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<3, 2>>(reportTestCases), "posit< 3,2>", "division");
154+
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<3, 3>>(reportTestCases), "posit< 3,3>", "division");
84155

85156
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<4, 0>>(reportTestCases), "posit< 4,0>", "division");
86157
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<4, 1>>(reportTestCases), "posit< 4,1>", "division");
@@ -112,17 +183,41 @@ try {
112183
#endif
113184

114185
#if REGRESSION_LEVEL_2
115-
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 0>>(reportTestCases), "posit<10,0>", "division");
116-
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 1>>(reportTestCases), "posit<10,1>", "division");
186+
// nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 0>>(reportTestCases), "posit<10,0>", "division");
187+
// nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 1>>(reportTestCases), "posit<10,1>", "division");
117188
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 2>>(reportTestCases), "posit<10,2>", "division");
118-
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 3>>(reportTestCases), "posit<10,3>", "division");
189+
// nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<10, 3>>(reportTestCases), "posit<10,3>", "division");
190+
191+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<16, 2>>(reportTestCases, OPCODE_DIV, 1000), "posit<16,2>", "division");
192+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<24, 2>>(reportTestCases, OPCODE_DIV, 1000), "posit<24,2>", "division");
119193
#endif
120194

121195
#if REGRESSION_LEVEL_3
196+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<20, 1>>(reportTestCases, OPCODE_DIV, 1000), "posit<20,1>", "division");
197+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<28, 1>>(reportTestCases, OPCODE_DIV, 1000), "posit<28,1>", "division");
198+
199+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<32, 1>>(reportTestCases, OPCODE_DIV, 1000), "posit<32,1>", "division");
200+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<32, 2>>(reportTestCases, OPCODE_DIV, 1000), "posit<32,2>", "division");
201+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<32, 3>>(reportTestCases, OPCODE_DIV, 1000), "posit<32,3>", "division");
122202
#endif
123203

124204
#if REGRESSION_LEVEL_4
125-
#endif
205+
// nbits = 48 also shows failures
206+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<48, 2>>(reportTestCases, OPCODE_DIV, 1000), "posit<48,2>", "division");
207+
208+
// nbits=64 requires long double compiler support
209+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<64, 2>>(reportTestCases, OPCODE_DIV, 1000), "posit<64,2>", "division");
210+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<64, 3>>(reportTestCases, OPCODE_DIV, 1000), "posit<64,3>", "division");
211+
// posit<64,4> is hitting subnormal numbers
212+
nrOfFailedTestCases += ReportTestResult(VerifyBinaryOperatorThroughRandoms<posit<64, 4>>(reportTestCases, OPCODE_DIV, 1000), "posit<64,4>", "division");
213+
214+
#ifdef HARDWARE_ACCELERATION
215+
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<12, 1>>(reportTestCases), "posit<12,1>", "division");
216+
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<14, 1>>(reportTestCases), "posit<14,1>", "division");
217+
nrOfFailedTestCases += ReportTestResult(VerifyDivision<posit<16, 1>>(reportTestCases), "posit<16,1>", "division");
218+
#endif // HARDWARE_ACCELERATION
219+
220+
#endif // REGRESSION_LEVEL_4
126221

127222
ReportTestSuiteResults(test_suite, nrOfFailedTestCases);
128223
return (nrOfFailedTestCases > 0 ? EXIT_FAILURE : EXIT_SUCCESS);

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