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Modexp counters done
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@hecmas
hecmas committed Oct 10, 2024
1 parent d32459c commit a705e0d
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4 changes: 2 additions & 2 deletions main/modexp/array_lib/array_add_AGTB.zkasm
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Expand Up @@ -54,8 +54,8 @@ VAR GLOBAL array_add_AGTB_RR
*/

array_add_AGTB:
%MAX_CNT_BINARY - CNT_BINARY - 1 - 2*%ARRAY_MAX_LEN_MINUS_ONE - 2 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 10 - 11*%ARRAY_MAX_LEN_MINUS_ONE - 2 - 8 - 5*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE - 3 :JMPN(outOfCountersStep)
%MAX_CNT_BINARY - CNT_BINARY + 2 - %ARRAY_MAX_LEN_DOUBLED - %ARRAY_MAX_LEN :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 8 - 6*%ARRAY_MAX_LEN_DOUBLED - 4*%ARRAY_MAX_LEN :JMPN(outOfCountersStep)

RR :MSTORE(array_add_AGTB_RR)

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4 changes: 2 additions & 2 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 @@ -45,8 +45,8 @@ VAR GLOBAL array_add_short_RR
*/

array_add_short:
%MAX_CNT_BINARY - CNT_BINARY - 1 - %ARRAY_MAX_LEN_MINUS_ONE :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 10 - 8*%ARRAY_MAX_LEN_MINUS_ONE - 5 :JMPN(outOfCountersStep)
%MAX_CNT_BINARY - CNT_BINARY + 1 - %ARRAY_MAX_LEN :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 8 - 6*%ARRAY_MAX_LEN :JMPN(outOfCountersStep)

RR :MSTORE(array_add_short_RR)

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9 changes: 3 additions & 6 deletions main/modexp/array_lib/array_div_long.zkasm
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Expand Up @@ -93,8 +93,9 @@ VAR GLOBAL array_div_long_RR
array_div_long:
; w.c. until array_mul_long is when inA > inB and len(inA) == len(inB)

%MAX_CNT_BINARY - CNT_BINARY - 2 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 24 - 4*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE - 3*%ARRAY_MAX_LEN - 1 :JMPN(outOfCountersStep) ; till array_mul_long
%MAX_CNT_ARITH - CNT_ARITH - %ARRAY_MAX_LEN + 18*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE - 19*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE*%ARRAY_MAX_LEN :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 2 - 2*%ARRAY_MAX_LEN - 2*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE*%ARRAY_MAX_LEN :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 64 - 7*%ARRAY_MAX_LEN_DOUBLED - 28*%ARRAY_MAX_LEN - 8*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE - 19*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE*%ARRAY_MAX_LEN :JMPN(outOfCountersStep) ; till array_mul_long

RR :MSTORE(array_div_long_RR)

Expand Down Expand Up @@ -255,8 +256,6 @@ array_div_long_mul_quo_inB:
; block (R != 0 and len(R) == len(B)): [steps: 14, bin: 1]

; w.c. is when rem is not zero
%MAX_CNT_BINARY - CNT_BINARY - 1 - 1 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 14 - 5*%ARRAY_MAX_LEN_MINUS_ONE - 2 - 3 - 3*%ARRAY_MAX_LEN_DOUBLED - 1 :JMPN(outOfCountersStep) ; till array_add_AGTB

; Check the remainder
$0{receiveLenRemainder()} => D :JMPZ(array_div_long_rem_is_zero)
Expand Down Expand Up @@ -324,8 +323,6 @@ array_div_long_add_mul_out_rem:
:CALL(array_add_AGTB) ; inputs: [array_add_AGTB_len_inA: C, array_add_AGTB_len_inB: D, array_add_AGTB_inA: array_mul_long_out, array_add_AGTB_inB: array_div_long_rem]
; outputs: [array_add_AGTB_len_out, array_add_AGTB_out]

%MAX_CNT_STEPS - STEP - 3 - 3*%ARRAY_MAX_LEN_DOUBLED - 2 :JMPN(outOfCountersStep)

; The length of q·b + r must be the same as the input of a
$ => C :MLOAD(array_add_AGTB_len_out)
C :MLOAD(array_div_long_len_inA)
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9 changes: 3 additions & 6 deletions main/modexp/array_lib/array_div_short.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -45,8 +45,9 @@ VAR GLOBAL array_div_short_RR
*/

array_div_short:
%MAX_CNT_BINARY - CNT_BINARY - 2 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 20 - 4*%ARRAY_MAX_LEN_MINUS_ONE - 3 :JMPN(outOfCountersStep) ; till array_mul_short
%MAX_CNT_ARITH - CNT_ARITH - %ARRAY_MAX_LEN :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 4 - %ARRAY_MAX_LEN :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 57 - 22*%ARRAY_MAX_LEN :JMPN(outOfCountersStep) ; till array_mul_short

RR :MSTORE(array_div_short_RR)

Expand Down Expand Up @@ -163,8 +164,6 @@ array_div_short_mul_quo_inB:
; block (R != 0): [steps: 10, bin: 1]

; w.c. is when rem is not zero
%MAX_CNT_BINARY - CNT_BINARY - 2 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 10 - 3*%ARRAY_MAX_LEN_MINUS_ONE - 1 :JMPN(outOfCountersStep) ; till array_add_short

; Check the remainder
${receiveRemainderChunk_short()} => A
Expand Down Expand Up @@ -193,8 +192,6 @@ array_div_short_add_result_rem:
:CALL(array_add_short) ; inputs: [array_add_short_len_inA: C, array_add_short_inA: array_mul_short_out, array_add_short_inB: array_div_short_inB]
; outputs: [array_add_short_len_out, array_add_short_out]

%MAX_CNT_STEPS - STEP - 3 - 3*%ARRAY_MAX_LEN - 2 :JMPN(outOfCountersStep)

; The length of q·b + r must be the same as the input of a
$ => C :MLOAD(array_add_short_len_out)
C :MLOAD(array_div_short_len_inA)
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10 changes: 2 additions & 8 deletions main/modexp/array_lib/array_div_two.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -42,8 +42,8 @@ VAR GLOBAL array_div_two_RR
*/

array_div_two:
%MAX_CNT_BINARY - CNT_BINARY - 3 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 26 - 4*%ARRAY_MAX_LEN_MINUS_ONE - 1 :JMPN(outOfCountersStep) ; till array_mul_two
%MAX_CNT_BINARY - CNT_BINARY - 2 - 2*%ARRAY_MAX_LEN :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 49 - 25*%ARRAY_MAX_LEN :JMPN(outOfCountersStep) ; till array_mul_two

RR :MSTORE(array_div_two_RR)

Expand Down Expand Up @@ -141,10 +141,6 @@ array_div_two_mul_quo_inB:
:CALL(array_mul_two) ; inputs: [array_mul_two_len_in: C, array_mul_two_in: array_div_two_quo]
; outputs: [array_mul_two_len_out, array_mul_two_out]

; w.c. is when rem is not zero
%MAX_CNT_BINARY - CNT_BINARY - 2 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 9 - 3*%ARRAY_MAX_LEN_MINUS_ONE - 1 :JMPN(outOfCountersStep) ; till array_add_short

; Check the remainder
${receiveRemainderChunk_short()} => A

Expand All @@ -171,8 +167,6 @@ array_div_two_add_result_rem:
:CALL(array_add_short) ; inputs: [array_add_short_len_inA: C, array_add_short_inA: array_mul_two_out, array_add_short_inB: A]
; outputs: [array_add_short_len_out, array_add_short_out]

%MAX_CNT_STEPS - STEP - 3 - 3*%ARRAY_MAX_LEN - 2 :JMPN(outOfCountersStep)

; The length of q·b + r must be the same as the input of a
$ => C :MLOAD(array_add_short_len_out)
C :MLOAD(array_div_two_len_in)
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8 changes: 3 additions & 5 deletions main/modexp/array_lib/array_mul_long.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -55,11 +55,9 @@ VAR GLOBAL array_mul_long_RR
*/

array_mul_long:
; big loop costs (len(inA) - 1)*((len(inB) - 1) * [steps: 21, bin: 2, arith: 1] + [steps: 18, bin: 1, arith: 1])

%MAX_CNT_ARITH - CNT_ARITH - 1 - %ARRAY_MAX_LEN_MINUS_ONE - %ARRAY_MAX_LEN_TIMES_DOUBLED - %ARRAY_MAX_LEN_DOUBLED_MINUS_ONE :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 2*%ARRAY_MAX_LEN_TIMES_DOUBLED - %ARRAY_MAX_LEN_DOUBLED_MINUS_ONE - 1 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 12 - 9*%ARRAY_MAX_LEN_MINUS_ONE - 21*%ARRAY_MAX_LEN_TIMES_DOUBLED - 18*%ARRAY_MAX_LEN_DOUBLED_MINUS_ONE - 7 :JMPN(outOfCountersStep)
%MAX_CNT_ARITH - CNT_ARITH - %ARRAY_MAX_LEN_DOUBLED - %ARRAY_MAX_LEN - 19*%ARRAY_MAX_LEN_DOUBLED*%ARRAY_MAX_LEN_MINUS_ONE :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 1 - %ARRAY_MAX_LEN_DOUBLED - 2*%ARRAY_MAX_LEN_DOUBLED*%ARRAY_MAX_LEN_MINUS_ONE :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 15 - 14*%ARRAY_MAX_LEN_DOUBLED - 7*%ARRAY_MAX_LEN - 19*%ARRAY_MAX_LEN_DOUBLED*%ARRAY_MAX_LEN_MINUS_ONE :JMPN(outOfCountersStep)

RR :MSTORE(array_mul_long_RR)

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6 changes: 3 additions & 3 deletions main/modexp/array_lib/array_mul_short.zkasm
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Expand Up @@ -39,9 +39,9 @@ VAR GLOBAL array_mul_short_RR
*/

array_mul_short:
%MAX_CNT_ARITH - CNT_ARITH - 1 - %ARRAY_MAX_LEN_MINUS_ONE :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 1 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 11 - 8*%ARRAY_MAX_LEN_MINUS_ONE - 7 :JMPN(outOfCountersStep)
%MAX_CNT_ARITH - CNT_ARITH - %ARRAY_MAX_LEN :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 1 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 10 - 7*%ARRAY_MAX_LEN :JMPN(outOfCountersStep)

RR :MSTORE(array_mul_short_RR)

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4 changes: 2 additions & 2 deletions main/modexp/array_lib/array_mul_two.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -45,8 +45,8 @@ VAR GLOBAL array_mul_two_RR
*/

array_mul_two:
%MAX_CNT_BINARY - CNT_BINARY - 1 - 2*%ARRAY_MAX_LEN_MINUS_ONE :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 9 - 11*%ARRAY_MAX_LEN_MINUS_ONE - 7 :JMPN(outOfCountersStep)
%MAX_CNT_BINARY - CNT_BINARY + 1 - %ARRAY_MAX_LEN :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 4 - 9*%ARRAY_MAX_LEN :JMPN(outOfCountersStep)

RR :MSTORE(array_mul_two_RR)

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6 changes: 3 additions & 3 deletions main/modexp/array_lib/array_square.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -57,9 +57,9 @@ VAR GLOBAL array_square_RR
*/

array_square:
%MAX_CNT_ARITH - CNT_ARITH - 1 - %ARRAY_MAX_LEN_MINUS_ONE - 2*%ARRAY_MAX_LEN_MINUS_ONE - %ARRAY_MAX_LEN_SQ :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 6*%ARRAY_MAX_LEN_MINUS_ONE - 3*%ARRAY_MAX_LEN_MINUS_ONE - 9*%ARRAY_MAX_LEN_SQ - 1 :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP - 15 - 35*%ARRAY_MAX_LEN_MINUS_ONE - 42*%ARRAY_MAX_LEN_MINUS_ONE - 51*%ARRAY_MAX_LEN_SQ - 8 :JMPN(outOfCountersStep)
%MAX_CNT_ARITH - CNT_ARITH + 1 - %ARRAY_MAX_LEN - %ARRAY_MAX_LEN_SQ :JMPN(outOfCountersArith)
%MAX_CNT_BINARY - CNT_BINARY - 1 + 9*%ARRAY_MAX_LEN - 9*%ARRAY_MAX_LEN_SQ :JMPN(outOfCountersBinary)
%MAX_CNT_STEPS - STEP + 3 + 25*%ARRAY_MAX_LEN - 51*%ARRAY_MAX_LEN_SQ :JMPN(outOfCountersStep)

RR :MSTORE(array_square_RR)

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11 changes: 7 additions & 4 deletions main/modexp/modexp.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -88,14 +88,17 @@ VAR GLOBAL modexp_RR
; num_times_E_is_odd = HammingWeight(E) (i.e., number of 1s in the binary representation of E)
; num_times_E_is_even = nIterations - num_times_E_is_odd
; -------------------------------------------
; cost(w.c): cost(first_part) + ⌊log₂(E)⌋*odd_iteration + cost(last_part)
; · cost(first_part) = [steps: 74 + 10*len(B) + 26*len(M) + 8*len(Q(B,M)) + 8*len(R(B,M)) + 19*len(Q(B,M))*len(M),
; bin: 2 + 2*len(M) + 2*len(Q(B,M))*len(M),
; arith: len(M) - 18*len(Q(B,M)) + 19*len(Q(B,M))*len(M)]
; · cost(odd_iteration) = [steps: 229 - 2*len(O) - 24*len(B) + 51*len(B)² + 10*len(B²) + 6*len(E) + 25*len(Q(E,2)) + 19*len(O)*len(B) + 10*len(O·B) + 52*len(M) + 8*len(Q(O·B,M)) + 8*len(R(O·B,M)) + 19*len(Q(O·B,M))*len(M) + 8*len(Q(B²,M)) + 8*len(R(B²,M)) + 19*len(Q(B²,M))*len(M),
; bin: 11 + 4*len(M) - 9*len(B) + 9*len(B)² - len(O) + 2*len(O)*len(B) + 2*len(Q(O·B,M))*len(M) + 2*len(Q(E,2)) + 2*len(Q(B²,M))*len(M),
; arith: -1 + 2*len(M) - 18*len(O) + 2*len(B) + len(B)² + 19*len(O)*len(B) - 18*len(Q(O·B,M)) + 19*len(Q(O·B,M))*len(M) - 18*len(Q(B²,M)) + 19*len(Q(B²,M))*len(M)]
; · cost(odd_iteration) = [steps: 229 + 14*len(B) + 6*len(E) + 68*len(M) + 51*len(B)² + 38*len(B)*len(M) + 25*len(Q(E,2)) + 19*len(Q(B²,M))*len(M) + 8*len(Q(B²,M)) + 8*len(R(B²,M)),
; bin: 11 - 9*len(B) + 3*len(M) + 9*len(B)² + 4*len(B)*len(M) + 2*len(Q(E,2)) + 2*len(Q(B²,M))*len(M),
; arith: -1 - 16*len(B) - 16*len(M) + len(B)² + 38*len(B)*len(M) + 19*len(Q(B²,M))*len(M) - 18*len(Q(B²,M))]
; · cost(last_part) = [steps: 2]
; -------------------------------------------
; cost(w.c): cost(first_part) + ⌊log₂(E)⌋*odd_iteration + cost(last_part)
; -------------------------------------------
; Note: For the total count, we have used that O <= M, len(B²) <= 2*len(B), len(O·B) <= len(M·B) <= len(M) + len(B), Q(O·B,M) <= Q(M·B,M) = B and R(O·B,M) < M

modexp:
%MAX_CNT_STEPS - STEP - 7 - 3*%ARRAY_MAX_LEN - 3*%ARRAY_MAX_LEN - 1 :JMPN(outOfCountersStep) ; init and array div long
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23 changes: 22 additions & 1 deletion test/testArrayArith.zkasm
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Original file line number Diff line number Diff line change
Expand Up @@ -120,7 +120,28 @@ start:
1n :MLOAD(array_add_AGTB_out + E)
5 :MLOAD(array_add_AGTB_len_out)

; 4] [2**256-2]*%ARRAY_MAX_LEN_DOUBLED + [1]*%ARRAY_MAX_LEN
; 4] [2**256-2,2**256-2,2**256-1,2**256-1] + [1]
4 => C
1 => D
%ARRAY_BASE_MINUS_ONE :MSTORE(array_add_AGTB_inA)
1 => E
%ARRAY_BASE_MINUS_ONE :MSTORE(array_add_AGTB_inA + E)
2 => E
%ARRAY_BASE_MINUS_TWO :MSTORE(array_add_AGTB_inA + E)
3 => E
%ARRAY_BASE_MINUS_TWO :MSTORE(array_add_AGTB_inA + E)
1n :MSTORE(array_add_AGTB_inB)
:CALL(array_add_AGTB)
0n :MLOAD(array_add_AGTB_out)
1 => E
0n :MLOAD(array_add_AGTB_out + E)
2 => E
115792089237316195423570985008687907853269984665640564039457584007913129639935n :MLOAD(array_add_AGTB_out + E)
3 => E
115792089237316195423570985008687907853269984665640564039457584007913129639934n :MLOAD(array_add_AGTB_out + E)
4 :MLOAD(array_add_AGTB_len_out)

; 5] [2**256-2]*%ARRAY_MAX_LEN_DOUBLED + [1]*%ARRAY_MAX_LEN
%ARRAY_MAX_LEN_DOUBLED => C
%ARRAY_MAX_LEN => D
C - 1 => E
Expand Down
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