From 077a20a0018c9823c2568eb624122f48ab35c1d5 Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Mon, 17 Oct 2016 18:20:33 -0400 Subject: Add opt versions of add, sub, opp --- src/ModularArithmetic/ModularBaseSystem.v | 21 ++++- src/ModularArithmetic/ModularBaseSystemOpt.v | 107 ++++++++++++++++++++++-- src/ModularArithmetic/ModularBaseSystemProofs.v | 2 +- 3 files changed, 118 insertions(+), 12 deletions(-) (limited to 'src/ModularArithmetic') diff --git a/src/ModularArithmetic/ModularBaseSystem.v b/src/ModularArithmetic/ModularBaseSystem.v index 1769f86c4..ff2c23ab8 100644 --- a/src/ModularArithmetic/ModularBaseSystem.v +++ b/src/ModularArithmetic/ModularBaseSystem.v @@ -60,9 +60,22 @@ Section ModularBaseSystem. (* Placeholder *) Definition div (x y : digits) : digits := encode (F.div (decode x) (decode y)). + Definition carry_ (carry_chain : list nat) (us : digits) : digits := + from_list (carry_sequence carry_chain [[us]]) (length_carry_sequence length_to_list). + + Definition carry_add (carry_chain : list nat) (us vs : digits) : digits := + carry_ carry_chain (add us vs). Definition carry_mul (carry_chain : list nat) (us vs : digits) : digits := - from_list (carry_sequence carry_chain [[mul us vs]]) (length_carry_sequence length_to_list). - + carry_ carry_chain (mul us vs). + Definition carry_sub (carry_chain : list nat) (modulus_multiple: digits) + (modulus_multiple_correct : decode modulus_multiple = 0%F) + (us vs : digits) : digits := + carry_ carry_chain (sub modulus_multiple modulus_multiple_correct us vs). + Definition carry_opp (carry_chain : list nat) (modulus_multiple : digits) + (modulus_multiple_correct : decode modulus_multiple = 0%F) + (x : digits) : digits := + carry_ carry_chain (opp modulus_multiple modulus_multiple_correct x). + Definition rep (us : digits) (x : F modulus) := decode us = x. Local Notation "u ~= x" := (rep u x). Local Hint Unfold rep. @@ -102,8 +115,8 @@ Section ModularBaseSystem. Definition pack (x : digits) : target_digits := from_list (pack target_widths_nonneg bits_eq [[x]]) length_pack. - + Definition unpack (x : target_digits) : digits := from_list (unpack target_widths_nonneg bits_eq [[x]]) length_unpack. -End ModularBaseSystem. \ No newline at end of file +End ModularBaseSystem. diff --git a/src/ModularArithmetic/ModularBaseSystemOpt.v b/src/ModularArithmetic/ModularBaseSystemOpt.v index 3b50662a6..f1b8c601b 100644 --- a/src/ModularArithmetic/ModularBaseSystemOpt.v +++ b/src/ModularArithmetic/ModularBaseSystemOpt.v @@ -410,8 +410,32 @@ Section Carries. End Carries. +Section CarryChain. + Context `{prm : PseudoMersenneBaseParams} {cc : CarryChain limb_widths}. + Local Notation digits := (tuple Z (length limb_widths)). + + Definition carry__opt_sig {T} (f : digits -> T) (us : digits) + : { x | x = f (carry_ carry_chain us) }. + Proof. + eexists. + cbv [carry_]. + rewrite <- from_list_default_eq with (d := 0%Z). + change @from_list_default with @from_list_default_opt. + erewrite <-carry_sequence_opt_cps_correct by eauto using carry_chain_valid, length_to_list. + cbv [carry_sequence_opt_cps]. + reflexivity. + Defined. + + Definition carry__opt_cps {T} (f:digits -> T) (us : digits) : T + := Eval cbv [proj1_sig carry__opt_sig] in proj1_sig (carry__opt_sig f us). + + Definition carry__opt_cps_correct {T} (f:digits -> T) (us : digits) + : carry__opt_cps f us = f (carry_ carry_chain us) + := proj2_sig (carry__opt_sig f us). +End CarryChain. + Section Addition. - Context `{prm : PseudoMersenneBaseParams} {sc : SubtractionCoefficient}. + Context `{prm : PseudoMersenneBaseParams} {sc : SubtractionCoefficient} {cc : CarryChain limb_widths}. Local Notation digits := (tuple Z (length limb_widths)). Definition add_opt_sig (us vs : digits) : { b : digits | b = add us vs }. @@ -426,10 +450,34 @@ Section Addition. Definition add_opt_correct us vs : add_opt us vs = add us vs := proj2_sig (add_opt_sig us vs). + + Definition carry_add_opt_sig {T} (f:digits -> T) + (us vs : digits) : { x | x = f (carry_add carry_chain us vs) }. + Proof. + eexists. + cbv [carry_add]. + rewrite <-carry__opt_cps_correct, <-add_opt_correct. + cbv [carry_sequence_opt_cps carry__opt_cps add_opt add]. + rewrite to_list_from_list. + reflexivity. + Defined. + + Definition carry_add_opt_cps {T} (f:digits -> T) (us vs : digits) : T + := Eval cbv [proj1_sig carry_add_opt_sig] in proj1_sig (carry_add_opt_sig f us vs). + + Definition carry_add_opt_cps_correct {T} (f:digits -> T) (us vs : digits) + : carry_add_opt_cps f us vs = f (carry_add carry_chain us vs) + := proj2_sig (carry_add_opt_sig f us vs). + + Definition carry_add_opt := carry_add_opt_cps id. + + Definition carry_add_opt_correct (us vs : digits) + : carry_add_opt us vs = carry_add carry_chain us vs := + carry_add_opt_cps_correct id us vs. End Addition. Section Subtraction. - Context `{prm : PseudoMersenneBaseParams} {sc : SubtractionCoefficient}. + Context `{prm : PseudoMersenneBaseParams} {sc : SubtractionCoefficient} {cc : CarryChain limb_widths}. Local Notation digits := (tuple Z (length limb_widths)). Definition sub_opt_sig (us vs : digits) : { b : digits | b = sub coeff coeff_mod us vs }. @@ -446,6 +494,30 @@ Section Subtraction. : sub_opt us vs = sub coeff coeff_mod us vs := proj2_sig (sub_opt_sig us vs). + Definition carry_sub_opt_sig {T} (f:digits -> T) + (us vs : digits) : { x | x = f (carry_sub carry_chain coeff coeff_mod us vs) }. + Proof. + eexists. + cbv [carry_sub]. + rewrite <-carry__opt_cps_correct, <-sub_opt_correct. + cbv [carry_sequence_opt_cps carry__opt_cps sub_opt]. + rewrite to_list_from_list. + reflexivity. + Defined. + + Definition carry_sub_opt_cps {T} (f:digits -> T) (us vs : digits) : T + := Eval cbv [proj1_sig carry_sub_opt_sig] in proj1_sig (carry_sub_opt_sig f us vs). + + Definition carry_sub_opt_cps_correct {T} (f:digits -> T) (us vs : digits) + : carry_sub_opt_cps f us vs = f (carry_sub carry_chain coeff coeff_mod us vs) + := proj2_sig (carry_sub_opt_sig f us vs). + + Definition carry_sub_opt := carry_sub_opt_cps id. + + Definition carry_sub_opt_correct (us vs : digits) + : carry_sub_opt us vs = carry_sub carry_chain coeff coeff_mod us vs := + carry_sub_opt_cps_correct id us vs. + Definition opp_opt_sig (us : digits) : { b : digits | b = opp coeff coeff_mod us }. Proof. eexists. @@ -461,6 +533,30 @@ Section Subtraction. : opp_opt us = opp coeff coeff_mod us := proj2_sig (opp_opt_sig us). + Definition carry_opp_opt_sig {T} (f:digits -> T) + (us : digits) : { x | x = f (carry_opp carry_chain coeff coeff_mod us) }. + Proof. + eexists. + cbv [carry_opp]. + rewrite <-carry__opt_cps_correct, <-opp_opt_correct. + cbv [carry_sequence_opt_cps carry__opt_cps opp_opt opp sub_opt]. + rewrite to_list_from_list. + reflexivity. + Defined. + + Definition carry_opp_opt_cps {T} (f:digits -> T) (us : digits) : T + := Eval cbv [proj1_sig carry_opp_opt_sig] in proj1_sig (carry_opp_opt_sig f us). + + Definition carry_opp_opt_cps_correct {T} (f:digits -> T) (us : digits) + : carry_opp_opt_cps f us = f (carry_opp carry_chain coeff coeff_mod us) + := proj2_sig (carry_opp_opt_sig f us). + + Definition carry_opp_opt := carry_opp_opt_cps id. + + Definition carry_opp_opt_correct (us : digits) + : carry_opp_opt us = carry_opp carry_chain coeff coeff_mod us := + carry_opp_opt_cps_correct id us. + End Subtraction. Section Multiplication. @@ -616,11 +712,8 @@ Section Multiplication. Proof. eexists. cbv [carry_mul]. - rewrite <- from_list_default_eq with (d := 0%Z). - change @from_list_default with @from_list_default_opt. - erewrite <-carry_sequence_opt_cps_correct by eauto using carry_chain_valid, length_to_list. - erewrite <-mul_opt_correct. - cbv [carry_sequence_opt_cps mul_opt]. + rewrite <-carry__opt_cps_correct, <-mul_opt_correct. + cbv [carry_sequence_opt_cps carry__opt_cps mul_opt]. erewrite from_list_default_eq. rewrite to_list_from_list. reflexivity. diff --git a/src/ModularArithmetic/ModularBaseSystemProofs.v b/src/ModularArithmetic/ModularBaseSystemProofs.v index c160eca7f..9cef5710d 100644 --- a/src/ModularArithmetic/ModularBaseSystemProofs.v +++ b/src/ModularArithmetic/ModularBaseSystemProofs.v @@ -360,7 +360,7 @@ Section FieldOperationProofs. + eapply _zero_neq_one. + trivial. Qed. - End FieldProofs. +End FieldProofs. End FieldOperationProofs. Opaque encode add mul sub inv pow. -- cgit v1.2.3