Minor improve on division and implement Montgomery reducer - #77
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Mirror the multiplication threshold env-var mechanism for division: when the `tuning` feature is active, `DASHU_THRESHOLD_SIMPLE_DIV` overrides the compile-time schoolbook / divide-and-conquer crossover. Values below 3 are unsupported (the divide-and-conquer split needs at least 2 low words). Co-Authored-By: Claude <noreply@anthropic.com>
Implement an optimized Montgomery modular arithmetic suite under integer/src/monty/, mirroring the structure of integer/src/modular/. Two new public types: MontgomeryRepr (precomputed Montgomery constants for an odd modulus, analogous to ConstDivisor) and Montgomery<'a> (a value in Montgomery form, analogous to Reduced), with multiplication, squaring, addition, subtraction, negation, doubling, exponentiation, and inversion. Single/double-word moduli delegate to num-modular's Montgomery<Word>/<DoubleWord>. The multi-word (Large) path uses word-aligned REDC: the operand product reuses the crate's fast multiply (Karatsuba/Toom-3/NTT), and the reduction is word-by-word with a per-word n0 = -m^-1 mod 2^WORD_BITS (computed by table-free Hensel lifting). Values are kept in the canonical range [0, m). Cross-validated against the Barrett-style modular::Reduced across Single/Double/Large moduli (integer/tests/monty.rs). Co-Authored-By: Claude <noreply@anthropic.com>
Switch the multi-word Montgomery reduction from single-word (one limb/iteration) to double-word (two limbs/iteration via the existing addmul_2 kernel, n0_dword = -m^-1 mod 2^(2*WORD_BITS)), which halves modulus memory traffic. The exit path (residue/inv, sparse input) keeps the single-word REDC, which measures faster there. Microbenchmarks show mul/sqr/pow 10-19% faster than single-word, and inv now faster than either all-single or all-double. Also add integer/benches/modular.rs comparing the Barrett (ConstDivisor) and Montgomery backends across modular mul/sqr/add/sub/pow/inv and modulus sizes (256..16384 bits). Co-Authored-By: Claude <noreply@anthropic.com>
Drop the single-word n0 field (derive it on demand as the low word of n0_dword via n0_word()) and the r_mod_m field (compute the Montgomery form of 1 on demand as REDC(R^2 mod m) in mul::one_large). This leaves the ring storing only modulus, n0_dword, and r2_mod_m — the minimal set needed for REDC and entering Montgomery form. Co-Authored-By: Claude <noreply@anthropic.com>
… use) Add a 'When to use Montgomery vs Barrett' section to the monty module docs and a Performance note on Montgomery::inv, explaining that Montgomery wins for mul/sqr/pow (~256-4096 bits) but Barrett (modular::Reduced) is substantially faster for inverses, since a Montgomery inverse must exit Montgomery form, run ext-GCD, and re-enter. Also corrects the module doc (word-by-word REDC with the addmul_2 kernel, not 'Almost-Montgomery' or fast-multiply correction) and updates the changelog entry to match. Co-Authored-By: Claude <noreply@anthropic.com>
Only 'Efficient Software Implementations of Modular Exponentiation' (Gueron) is relevant to this module; the 'Incomplete Reduction' (Yanik/Savaş/Koç) reference is removed. The Gueron paper now lives as a normal // XXX code comment in pow.rs pointing to AMM as a possible future optimization, rather than as module-level documentation. Co-Authored-By: Claude <noreply@anthropic.com>
…pointer-identity in mul - sqr() and pow_nontrivial: build the squared result directly from scratch memory via sqr_normalized_large instead of cloning raw then overwriting, saving one Box<[Word]> allocation and an s-word copy per squaring. - mul_in_place_large: replace O(n) Box<[Word]> value comparison with O(1) pointer-identity check (lhs.0.as_ptr() == rhs.0.as_ptr()) to detect self-multiplication (a *= a). Distinct-but-equal values are handled correctly by the general mul path. - Extract finish_monty_product helper (REDC + canonicalize) shared by mul_normalized_large and sqr_normalized_large. fix(div): clamp DASHU_THRESHOLD_SIMPLE_DIV to minimum of 3 - The divide-and-conquer algorithm requires n_lo >= 2, which implies a threshold >= 3. The env-var override now enforces this floor instead of relying solely on the compile-time const_assert! on the default. - Added explicit ::<usize> type annotation on parse() to disambiguate the v.max(3) call. Co-Authored-By: Claude <noreply@anthropic.com>
…perands The &Montgomery * &Montgomery impl previously cloned self then used mul_assign, which completely overwrites the cloned buffer via copy_from_slice from scratch memory. For Large (multi-word) operands this wasted one Box<[Word]> allocation and an s-word copy. Now the Large case builds the result directly from scratch via mul_normalized_large (or sqr_normalized_large when lhs and rhs share the same allocation), saving one allocation and copy per multiply. Single/Double (Copy types) keep the existing clone path — it is zero-cost for them. Add, sub, and neg on references are intentionally unchanged: their in-place operations read-then-write lhs.0, so the clone correctly seeds the output buffer with the operand value. Co-Authored-By: Claude <noreply@anthropic.com>
- Add forward_modular_binop_to_assign!, impl_modular_commutative_op_for_ref!, impl_modular_binop_ref_ref_by_clone!, forward_modular_binop_to_ref_ref! macros in helper_macros.rs, parameterized by target type. Apply them to both Montgomery and Reduced Add/Sub/Mul/Div, eliminating the by-value/by-ref/assign boilerplate per operator. - Move add_mul_word_same_len_in_place, add_mul_word_in_place, sub_mul_word_same_len_in_place from mul/mod.rs to mul/simple.rs (alongside the other schoolbook kernels), and widen add_mul_dword_same_len_in_place from pub(crate) to pub. Old mul::* paths still work via re-exports. - Extract simple::MIN_LEN = 3 in div/simple.rs (mirroring mul::karatsuba::MIN_LEN); the threshold tuning override now clamps against this named constant. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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* Add DASHU_THRESHOLD_SIMPLE_DIV runtime override for division threshold Mirror the multiplication threshold env-var mechanism for division: when the `tuning` feature is active, `DASHU_THRESHOLD_SIMPLE_DIV` overrides the compile-time schoolbook / divide-and-conquer crossover. Values below 3 are unsupported (the divide-and-conquer split needs at least 2 low words). Co-Authored-By: Claude <noreply@anthropic.com> * Add Montgomery modular arithmetic (monty module) Implement an optimized Montgomery modular arithmetic suite under integer/src/monty/, mirroring the structure of integer/src/modular/. Two new public types: MontgomeryRepr (precomputed Montgomery constants for an odd modulus, analogous to ConstDivisor) and Montgomery<'a> (a value in Montgomery form, analogous to Reduced), with multiplication, squaring, addition, subtraction, negation, doubling, exponentiation, and inversion. Single/double-word moduli delegate to num-modular's Montgomery<Word>/<DoubleWord>. The multi-word (Large) path uses word-aligned REDC: the operand product reuses the crate's fast multiply (Karatsuba/Toom-3/NTT), and the reduction is word-by-word with a per-word n0 = -m^-1 mod 2^WORD_BITS (computed by table-free Hensel lifting). Values are kept in the canonical range [0, m). Cross-validated against the Barrett-style modular::Reduced across Single/Double/Large moduli (integer/tests/monty.rs). Co-Authored-By: Claude <noreply@anthropic.com> * Use double-word Montgomery REDC and add modular benchmark Switch the multi-word Montgomery reduction from single-word (one limb/iteration) to double-word (two limbs/iteration via the existing addmul_2 kernel, n0_dword = -m^-1 mod 2^(2*WORD_BITS)), which halves modulus memory traffic. The exit path (residue/inv, sparse input) keeps the single-word REDC, which measures faster there. Microbenchmarks show mul/sqr/pow 10-19% faster than single-word, and inv now faster than either all-single or all-double. Also add integer/benches/modular.rs comparing the Barrett (ConstDivisor) and Montgomery backends across modular mul/sqr/add/sub/pow/inv and modulus sizes (256..16384 bits). Co-Authored-By: Claude <noreply@anthropic.com> * Eliminate redundant n0 and r_mod_m fields from MontgomeryLargeRepr Drop the single-word n0 field (derive it on demand as the low word of n0_dword via n0_word()) and the r_mod_m field (compute the Montgomery form of 1 on demand as REDC(R^2 mod m) in mul::one_large). This leaves the ring storing only modulus, n0_dword, and r2_mod_m — the minimal set needed for REDC and entering Montgomery form. Co-Authored-By: Claude <noreply@anthropic.com> * Document Montgomery vs Barrett tradeoff (prefer Barrett for inv-heavy use) Add a 'When to use Montgomery vs Barrett' section to the monty module docs and a Performance note on Montgomery::inv, explaining that Montgomery wins for mul/sqr/pow (~256-4096 bits) but Barrett (modular::Reduced) is substantially faster for inverses, since a Montgomery inverse must exit Montgomery form, run ext-GCD, and re-enter. Also corrects the module doc (word-by-word REDC with the addmul_2 kernel, not 'Almost-Montgomery' or fast-multiply correction) and updates the changelog entry to match. Co-Authored-By: Claude <noreply@anthropic.com> * Drop the j56 reference; move the Gueron paper to a code comment Only 'Efficient Software Implementations of Modular Exponentiation' (Gueron) is relevant to this module; the 'Incomplete Reduction' (Yanik/Savaş/Koç) reference is removed. The Gueron paper now lives as a normal // XXX code comment in pow.rs pointing to AMM as a possible future optimization, rather than as module-level documentation. Co-Authored-By: Claude <noreply@anthropic.com> * perf(monty): eliminate redundant clone+overwrite in sqr and pow, use pointer-identity in mul - sqr() and pow_nontrivial: build the squared result directly from scratch memory via sqr_normalized_large instead of cloning raw then overwriting, saving one Box<[Word]> allocation and an s-word copy per squaring. - mul_in_place_large: replace O(n) Box<[Word]> value comparison with O(1) pointer-identity check (lhs.0.as_ptr() == rhs.0.as_ptr()) to detect self-multiplication (a *= a). Distinct-but-equal values are handled correctly by the general mul path. - Extract finish_monty_product helper (REDC + canonicalize) shared by mul_normalized_large and sqr_normalized_large. fix(div): clamp DASHU_THRESHOLD_SIMPLE_DIV to minimum of 3 - The divide-and-conquer algorithm requires n_lo >= 2, which implies a threshold >= 3. The env-var override now enforces this floor instead of relying solely on the compile-time const_assert! on the default. - Added explicit ::<usize> type annotation on parse() to disambiguate the v.max(3) call. Co-Authored-By: Claude <noreply@anthropic.com> * perf(monty): eliminate clone in &Montgomery * &Montgomery for Large operands The &Montgomery * &Montgomery impl previously cloned self then used mul_assign, which completely overwrites the cloned buffer via copy_from_slice from scratch memory. For Large (multi-word) operands this wasted one Box<[Word]> allocation and an s-word copy. Now the Large case builds the result directly from scratch via mul_normalized_large (or sqr_normalized_large when lhs and rhs share the same allocation), saving one allocation and copy per multiply. Single/Double (Copy types) keep the existing clone path — it is zero-cost for them. Add, sub, and neg on references are intentionally unchanged: their in-place operations read-then-write lhs.0, so the clone correctly seeds the output buffer with the operand value. Co-Authored-By: Claude <noreply@anthropic.com> * refactor(int): dedup modular binop impls and reorganize mul/div helpers - Add forward_modular_binop_to_assign!, impl_modular_commutative_op_for_ref!, impl_modular_binop_ref_ref_by_clone!, forward_modular_binop_to_ref_ref! macros in helper_macros.rs, parameterized by target type. Apply them to both Montgomery and Reduced Add/Sub/Mul/Div, eliminating the by-value/by-ref/assign boilerplate per operator. - Move add_mul_word_same_len_in_place, add_mul_word_in_place, sub_mul_word_same_len_in_place from mul/mod.rs to mul/simple.rs (alongside the other schoolbook kernels), and widen add_mul_dword_same_len_in_place from pub(crate) to pub. Old mul::* paths still work via re-exports. - Extract simple::MIN_LEN = 3 in div/simple.rs (mirroring mul::karatsuba::MIN_LEN); the threshold tuning override now clamps against this named constant. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> --------- Co-authored-by: Jacob Zhong <jacob@rimbot.com> Co-authored-by: Claude <noreply@anthropic.com>
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