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Modexp feijoa #377

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Modexp feijoa #377

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f81876c
Loop in array_add_AGTB missing
hecmas Apr 9, 2024
4d5a85d
Now failing if add short is not used for division
hecmas Apr 9, 2024
6816234
Merge pull request #375 from 0xPolygonHermez/fix/array-add-AGTB
hecmas Apr 9, 2024
d63f429
Merge pull request #376 from 0xPolygonHermez/fix/array-short
hecmas Apr 9, 2024
29000fa
First batch of mini-optimizations to array_lib
hecmas Apr 9, 2024
5bdcb8c
Improving overall comments and minor optimizations
hecmas Apr 11, 2024
af9fa00
Merge pull request #378 from 0xPolygonHermez/feature/modexp-nf-feijoa
hecmas Oct 3, 2024
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85 changes: 35 additions & 50 deletions main/modexp/array_lib/array_add_AGTB.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -13,31 +13,27 @@
;; · out = inA + inB, with len(out) <= C + 1
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

; function array_add_AGTB(a: bigint[], b: bigint[], base: bigint): bigint[] {
; const alen = a.length;
; const blen = b.length;
; let result = new Array<bigint>(alen);
; let sum = 0n;
; let carry = 0n;
; for (let i = 0; i < blen; i++) {
; sum = a[i] + b[i] + carry;
; carry = sum >= base ? 1n : 0n;
; out[i] = sum - carry * base;
; }
; for (let i = blen; i < alen; i++) {
; sum = a[i] + carry;
; carry = sum == base ? 1n : 0n; // the past carry is at most 1n
; out[i] = sum - carry * base;
; }

; if (carry === 1n) {
; result.push(carry);
; }
; return result;
; }
;; WARNING: This function is tailored for checking that a = q·b + r in the array_div_long function.
;; In can be used for other purposes except for the worst case, i.e. when len(inA) == %ARRAY_MAX_LEN_DOUBLED.
;; Specifically, there is an implicit assumption that the output len of this function cannot be
;; greater than %ARRAY_MAX_LEN_DOUBLED, and do not allow to generate the proof in such case.

; NOTE: It's unoptimized for the case where len(inB) = 1. Use array_add_short instead.

; code
; --------------------------
; first_iteration <-- Compute a[0] + b[0]
; while(inB_index_check) { <-- While 0 < i < len(b)
; loop2inB <-- Compute a[i] + b[i] + carry
; }
; while (inA_index_check) { <-- While 0 < i < len(a)
; loop2inA <-- Compute a[i] + carry
; }
; 1] check_carry <-- If there is a carry, append it to the result
; 2] trim <-- Otherwise, trim the result
; end
; --------------------------

VAR GLOBAL array_add_AGTB_inA[%ARRAY_MAX_LEN_DOUBLED]
VAR GLOBAL array_add_AGTB_inB[%ARRAY_MAX_LEN]
VAR GLOBAL array_add_AGTB_out[%ARRAY_MAX_LEN_DOUBLED] ; This cannot be bigger because we use it for division checking
Expand Down Expand Up @@ -71,10 +67,11 @@ array_add_AGTB_first_iteration:
;-----------------

1 => E
$ => B :MLOAD(array_add_AGTB_len_inB)
B - E :JMPZ(array_add_AGTB_loop_index_check)

array_add_AGTB_loopZero2inB:
array_add_AGTB_inB_index_check:
$ - E :F_MLOAD(array_add_AGTB_len_inB), JMPZ(array_add_AGTB_inA_index_check)

array_add_AGTB_loop2inB:
; a[i] + b[i], where a[i],b[i] ∈ [0,base-1]: This number cannot be GT base + (base - 2), two chunks
$ => A :MLOAD(array_add_AGTB_inA + E)
$ => B :MLOAD(array_add_AGTB_inB + E)
Expand All @@ -98,39 +95,28 @@ array_add_AGTB_loopZero2inB:

D :MSTORE(array_add_AGTB_carry)

E + 1 => E
$ => B :MLOAD(array_add_AGTB_len_inB)
B - E :JMPZ(array_add_AGTB_loop_index_check, array_add_AGTB_loopZero2inB)
E + 1 => E :JMP(array_add_AGTB_inB_index_check)

array_add_AGTB_loop_index_check:
$ => C :MLOAD(array_add_AGTB_len_inA)
C - E :JMPZ(array_add_AGTB_check_carry)
array_add_AGTB_inA_index_check:
$ - E :F_MLOAD(array_add_AGTB_len_inA), JMPZ(array_add_AGTB_check_carry)

array_add_AGTB_last_two_additions:
array_add_AGTB_loop2inA:
; sum = a[i] + carry: This number cannot be GT base, two chunks
; This sum can produce, at most, one additional carry
$ => A :MLOAD(array_add_AGTB_inA + E)
D => B
$ :ADD, MSTORE(array_add_AGTB_out + E), JMPNC(array_add_AGTB_set)

E + 1 => E
C - E :JMPZ(array_add_AGTB_is_carry)

$ => A :MLOAD(array_add_AGTB_inA + E)
1 => B
$ :ADD, MSTORE(array_add_AGTB_out + E)
$ :ADD, MSTORE(array_add_AGTB_out + E), JMPNC(__array_add_AGTB_continue_6)
;-----------------
1 => D :JMP(__array_add_AGTB_continue_7)
__array_add_AGTB_continue_6:
0 => D
__array_add_AGTB_continue_7:
;-----------------

array_add_AGTB_set:
E + 1 => E
$ => A :MLOAD(array_add_AGTB_len_inA)
A - E :JMPZ(array_add_AGTB_trim)
$ => A :MLOAD(array_add_AGTB_inA + E)
A :MSTORE(array_add_AGTB_out + E), JMP(array_add_AGTB_set)
E + 1 => E :JMP(array_add_AGTB_inA_index_check)

array_add_AGTB_check_carry:
D :JMPZ(array_add_AGTB_trim)

array_add_AGTB_is_carry:
; Carry path
E - %ARRAY_MAX_LEN_DOUBLED :JMPZ(failAssert)

Expand All @@ -142,5 +128,4 @@ array_add_AGTB_trim:
E :MSTORE(array_add_AGTB_len_out)

array_add_AGTB_end:
$ => RR :MLOAD(array_add_AGTB_RR)
:RETURN
$ => RR :MLOAD(array_add_AGTB_RR), RETURN
64 changes: 27 additions & 37 deletions main/modexp/array_lib/array_add_short.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -11,26 +11,25 @@
;; · out = inA + inB, with len(out) <= C + 1
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

; function array_add_short(a: bigint[], b: bigint, base: bigint): bigint[] {
; const alen = a.length;
; let result = new Array<bigint>(alen);
; let sum = 0n;
; let carry = b;
; for (let i = 0; i < alen; i++) {
; sum = a[i] + carry;
; carry = sum >= base ? 1n : 0n;
; out[i] = sum - carry * base;
; }

; if (carry === 1n) {
; result.push(carry);
; }
; return result;
;; WARNING: This function is tailored for checking that a = q·b + r in the array_div_short function.
;; In can be used for other purposes except for the worst case, i.e. when len(inA) == %ARRAY_MAX_LEN.
;; Specifically, there is an implicit assumption that the output len of this function cannot be
;; greater than %ARRAY_MAX_LEN, and do not allow to generate the proof in such case.

; code
; --------------------------
; first_iteration <-- Compute a[0] + b
; while(loop_index_check) { <-- While 0 < i < len(a)
; loop2inA <-- Compute a[i] + carry
; }
; 1] check_carry <-- If there is a carry, append it to the result
; 2] trim <-- Otherwise, trim the result
; end
; --------------------------

VAR GLOBAL array_add_short_inA[%ARRAY_MAX_LEN]
VAR GLOBAL array_add_short_inB
VAR GLOBAL array_add_short_out[%ARRAY_MAX_LEN_PLUS_ONE]
VAR GLOBAL array_add_short_out[%ARRAY_MAX_LEN] ; This cannot be bigger because we use it for division checking
VAR GLOBAL array_add_short_len_inA
VAR GLOBAL array_add_short_len_out

Expand All @@ -44,51 +43,43 @@ array_add_short:

C :MSTORE(array_add_short_len_inA)

; Load b
$ => B :MLOAD(array_add_short_inB)

array_add_short_first_iteration:
; The result will be stored as D·base + C

; a[0] + b, where a[i] ∈ [0,base-1]: the number cannot be GT base + (base - 2), two chunks
; a[0] + b, where a[0] ∈ [0,base-1]: the number cannot be GT base + (base - 2), two chunks
$ => A :MLOAD(array_add_short_inA)
$ => C :ADD, JMPC(__array_add_short_continue_1)
$ => B :MLOAD(array_add_short_inB)
$ :ADD, MSTORE(array_add_short_out), JMPC(__array_add_short_continue_1)
; ---------------------
0 => D :JMP(__array_add_short_continue_2)
__array_add_short_continue_1:
1 => D
__array_add_short_continue_2:
; ---------------------

C :MSTORE(array_add_short_out)

1 => E
$ => A :MLOAD(array_add_short_len_inA)
A - E :JMPZ(array_add_short_check_carry)

array_add_short_loopZero2inA:
; The result will be stored as D·base + C
array_add_short_loop_index_check:
; C = len_inA
C - E :JMPZ(array_add_short_check_carry)

array_add_short_loop2inA:
; a[i] + carry, where a[i] ∈ [0,base-1]: the number cannot be GT base, two chunks
$ => A :MLOAD(array_add_short_inA + E)
D => B
$ => C :ADD, JMPC(__array_add_short_continue_3)
$ :ADD, MSTORE(array_add_short_out + E), JMPC(__array_add_short_continue_3)
; ---------------------
0 => D :JMP(__array_add_short_continue_4)
__array_add_short_continue_3:
1 => D
__array_add_short_continue_4:
; ---------------------

C :MSTORE(array_add_short_out + E)

E + 1 => E
$ => A :MLOAD(array_add_short_len_inA)
A - E :JMPZ(array_add_short_check_carry, array_add_short_loopZero2inA)
E + 1 => E :JMP(array_add_short_loop_index_check)

array_add_short_check_carry:
D :JMPZ(array_add_short_trim)

; Carry path
E - %ARRAY_MAX_LEN :JMPZ(failAssert)

; In this case, the carry = 1 and we should append it to the result
1 :MSTORE(array_add_short_out + E)
Expand All @@ -98,5 +89,4 @@ array_add_short_trim:
E :MSTORE(array_add_short_len_out)

array_add_short_end:
$ => RR :MLOAD(array_add_short_RR)
:RETURN
$ => RR :MLOAD(array_add_short_RR), RETURN
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