From 7db40334d4b6a4afb3ee9bde90d80458a5512df6 Mon Sep 17 00:00:00 2001 From: feltroid Prime Date: Mon, 5 Jun 2023 13:28:55 +0200 Subject: [PATCH] =?UTF-8?q?=F0=9F=94=92=EF=B8=8F=20update=20hints=20docume?= =?UTF-8?q?nt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/hints_whitelist.md | 272 +++++++++++++++++++++++++++++++++++----- 1 file changed, 243 insertions(+), 29 deletions(-) diff --git a/docs/hints_whitelist.md b/docs/hints_whitelist.md index ce4fe66d..16ebb359 100644 --- a/docs/hints_whitelist.md +++ b/docs/hints_whitelist.md @@ -5,11 +5,10 @@ BASE = ids.BASE assert 1 < ids.N_LIMBS <= 12 - p, sub_limbs = 0, [] + p, sum_limbs = 0, [] for i in range(ids.N_LIMBS): p+=getattr(ids, 'P'+str(i)) * BASE**i - sum_limbs=[] p_limbs = [getattr(ids, 'P'+str(i)) for i in range(ids.N_LIMBS)] sum_limbs = [getattr(getattr(ids, 'a'), 'd'+str(i)) + getattr(getattr(ids, 'b'), 'd'+str(i)) for i in range(ids.N_LIMBS)] sum_unreduced = sum([sum_limbs[i] * BASE**i for i in range(ids.N_LIMBS)]) @@ -80,14 +79,13 @@ ``` ### fq_bigint3.mul() -#L524-L536 ```python %{ from starkware.cairo.common.math_utils import as_int assert 1 < ids.N_LIMBS <= 12 assert ids.DEGREE == ids.N_LIMBS-1 a,b,p=0,0,0 - + a_limbs, b_limbs, p_limbs = ids.N_LIMBS*[0], ids.N_LIMBS*[0], ids.N_LIMBS*[0] def split(x, degree=ids.DEGREE, base=ids.BASE): coeffs = [] for n in range(degree, 0, -1): @@ -97,27 +95,79 @@ coeffs.append(x) return coeffs[::-1] + def poly_mul(a:list, b:list,n=ids.N_LIMBS) -> list: + assert len(a) == len(b) == n + result = [0] * ids.N_LIMBS_UNREDUCED + for i in range(n): + for j in range(n): + result[i+j] += a[i]*b[j] + return result + def poly_mul_plus_c(a:list, b:list, c:list, n=ids.N_LIMBS) -> list: + assert len(a) == len(b) == n + result = [0] * ids.N_LIMBS_UNREDUCED + for i in range(n): + for j in range(n): + result[i+j] += a[i]*b[j] + for i in range(n): + result[i] += c[i] + return result + def poly_sub(a:list, b:list, n=ids.N_LIMBS_UNREDUCED) -> list: + assert len(a) == len(b) == n + result = [0] * n + for i in range(n): + result[i] = a[i] - b[i] + return result + + def abs_poly(x:list): + result = [0] * len(x) + for i in range(len(x)): + result[i] = abs(x[i]) + return result + + def reduce_zero_poly(x:list): + x = x.copy() + carries = [0] * (len(x)-1) + for i in range(0, len(x)-1): + carries[i] = x[i] // ids.BASE + x[i] = x[i] % ids.BASE + assert x[i] == 0 + x[i+1] += carries[i] + assert x[-1] == 0 + return x, carries + for i in range(ids.N_LIMBS): a+=as_int(getattr(ids.a, 'd'+str(i)),PRIME) * ids.BASE**i b+=as_int(getattr(ids.b, 'd'+str(i)),PRIME) * ids.BASE**i p+=getattr(ids, 'P'+str(i)) * ids.BASE**i + a_limbs[i]=as_int(getattr(ids.a, 'd'+str(i)),PRIME) + b_limbs[i]=as_int(getattr(ids.b, 'd'+str(i)),PRIME) + p_limbs[i]=getattr(ids, 'P'+str(i)) + mul = a*b q, r = divmod(mul, p) qs, rs = split(q), split(r) for i in range(ids.N_LIMBS): setattr(ids.r, 'd'+str(i), rs[i]) setattr(ids.q, 'd'+str(i), qs[i]) + + val_limbs = poly_mul(a_limbs, b_limbs) + q_P_plus_r_limbs = poly_mul_plus_c(qs, p_limbs, rs) + diff_limbs = poly_sub(q_P_plus_r_limbs, val_limbs) + _, carries = reduce_zero_poly(diff_limbs) + carries = abs_poly(carries) + for i in range(ids.N_LIMBS_UNREDUCED-1): + setattr(ids, 'flag'+str(i), 1 if diff_limbs[i] >= 0 else 0) + setattr(ids, 'q'+str(i), carries[i]) %} ``` ### fq_bigint3.mul_by_9() -#L587-L595 ```python %{ - from starkware.cairo.common.math_utils import as_int + from starkware.cairo.common.math_utils import as_int assert 1 < ids.N_LIMBS <= 12 assert ids.DEGREE == ids.N_LIMBS-1 a,p=0,0 - + a_limbs, p_limbs = ids.N_LIMBS*[0], ids.N_LIMBS*[0] def split(x, degree=ids.DEGREE, base=ids.BASE): coeffs = [] for n in range(degree, 0, -1): @@ -127,27 +177,63 @@ coeffs.append(x) return coeffs[::-1] + def poly_sub(a:list, b:list, n=ids.N_LIMBS_UNREDUCED) -> list: + assert len(a) == len(b) == n + result = [0] * n + for i in range(n): + result[i] = a[i] - b[i] + return result + + def abs_poly(x:list): + result = [0] * len(x) + for i in range(len(x)): + result[i] = abs(x[i]) + return result + + def reduce_zero_poly(x:list): + x = x.copy() + carries = [0] * (len(x)-1) + for i in range(0, len(x)-1): + carries[i] = x[i] // ids.BASE + x[i] = x[i] % ids.BASE + assert x[i] == 0 + x[i+1] += carries[i] + assert x[-1] == 0 + return x, carries + for i in range(ids.N_LIMBS): - a+=as_int(getattr(ids.a, 'd'+str(i)), PRIME) * ids.BASE**i + a+=as_int(getattr(ids.a, 'd'+str(i)),PRIME) * ids.BASE**i p+=getattr(ids, 'P'+str(i)) * ids.BASE**i + a_limbs[i]=as_int(getattr(ids.a, 'd'+str(i)),PRIME) + p_limbs[i]=getattr(ids, 'P'+str(i)) mul = a*9 q, r = divmod(mul, p) - ids.q=q%PRIME rs = split(r) for i in range(ids.N_LIMBS): setattr(ids.r, 'd'+str(i), rs[i]) + ids.q=q + + val_limbs = [a_limbs[i] * 9 for i in range(ids.N_LIMBS)] + q_P_plus_r_limbs = [q * p_limbs[i] + rs[i] for i in range(ids.N_LIMBS)] + + diff_limbs = poly_sub(q_P_plus_r_limbs, val_limbs, ids.N_LIMBS) + _, carries = reduce_zero_poly(diff_limbs) + carries = abs_poly(carries) + for i in range(ids.N_LIMBS-1): + setattr(ids, 'flag'+str(i), 1 if diff_limbs[i] >= 0 else 0) + setattr(ids, 'q'+str(i), carries[i]) %} ``` ### fq_bigint3.mul_by_10() #L621-L629 ```python %{ - from starkware.cairo.common.math_utils import as_int + from starkware.cairo.common.math_utils import as_int assert 1 < ids.N_LIMBS <= 12 assert ids.DEGREE == ids.N_LIMBS-1 a,p=0,0 - + a_limbs, p_limbs = ids.N_LIMBS*[0], ids.N_LIMBS*[0] def split(x, degree=ids.DEGREE, base=ids.BASE): coeffs = [] for n in range(degree, 0, -1): @@ -157,16 +243,52 @@ coeffs.append(x) return coeffs[::-1] + def poly_sub(a:list, b:list, n=ids.N_LIMBS_UNREDUCED) -> list: + assert len(a) == len(b) == n + result = [0] * n + for i in range(n): + result[i] = a[i] - b[i] + return result + + def abs_poly(x:list): + result = [0] * len(x) + for i in range(len(x)): + result[i] = abs(x[i]) + return result + + def reduce_zero_poly(x:list): + x = x.copy() + carries = [0] * (len(x)-1) + for i in range(0, len(x)-1): + carries[i] = x[i] // ids.BASE + x[i] = x[i] % ids.BASE + assert x[i] == 0 + x[i+1] += carries[i] + assert x[-1] == 0 + return x, carries + for i in range(ids.N_LIMBS): - a+=as_int(getattr(ids.a, 'd'+str(i)), PRIME) * ids.BASE**i + a+=as_int(getattr(ids.a, 'd'+str(i)),PRIME) * ids.BASE**i p+=getattr(ids, 'P'+str(i)) * ids.BASE**i + a_limbs[i]=as_int(getattr(ids.a, 'd'+str(i)),PRIME) + p_limbs[i]=getattr(ids, 'P'+str(i)) mul = a*10 q, r = divmod(mul, p) - ids.q=q%PRIME rs = split(r) for i in range(ids.N_LIMBS): setattr(ids.r, 'd'+str(i), rs[i]) + ids.q=q + + val_limbs = [a_limbs[i] * 10 for i in range(ids.N_LIMBS)] + q_P_plus_r_limbs = [q * p_limbs[i] + rs[i] for i in range(ids.N_LIMBS)] + + diff_limbs = poly_sub(q_P_plus_r_limbs, val_limbs, ids.N_LIMBS) + _, carries = reduce_zero_poly(diff_limbs) + carries = abs_poly(carries) + for i in range(ids.N_LIMBS-1): + setattr(ids, 'flag'+str(i), 1 if diff_limbs[i] >= 0 else 0) + setattr(ids, 'q'+str(i), carries[i]) %} ``` @@ -202,33 +324,79 @@ ### verify_zero3() -#L726-L736 ```python %{ from starkware.cairo.common.math_utils import as_int assert 1 < ids.N_LIMBS <= 12 - a,p=0,0 + assert ids.DEGREE == ids.N_LIMBS-1 + val, p=0,0 + val_limbs, p_limbs = ids.N_LIMBS_UNREDUCED*[0], ids.N_LIMBS*[0] + def split(x, degree=ids.DEGREE, base=ids.BASE): + coeffs = [] + for n in range(degree, 0, -1): + q, r = divmod(x, base ** n) + coeffs.append(q) + x = r + coeffs.append(x) + return coeffs[::-1] + + def poly_sub(a:list, b:list, n=ids.N_LIMBS_UNREDUCED) -> list: + assert len(a) == len(b) == n + result = [0] * n + for i in range(n): + result[i] = a[i] - b[i] + return result + + def abs_poly(x:list): + result = [0] * len(x) + for i in range(len(x)): + result[i] = abs(x[i]) + return result + + def reduce_zero_poly(x:list): + x = x.copy() + carries = [0] * (len(x)-1) + for i in range(0, len(x)-1): + carries[i] = x[i] // ids.BASE + x[i] = x[i] % ids.BASE + assert x[i] == 0 + x[i+1] += carries[i] + assert x[-1] == 0 + return x, carries for i in range(ids.N_LIMBS): - a+=as_int(getattr(ids.val, 'd'+str(i)), PRIME) * ids.BASE**i p+=getattr(ids, 'P'+str(i)) * ids.BASE**i + p_limbs[i]=getattr(ids, 'P'+str(i)) + val_limbs[i]+=as_int(getattr(ids.val, 'd'+str(i)), PRIME) + val+=as_int(getattr(ids.val, 'd'+str(i)), PRIME) * ids.BASE**i + + mul = val + q, r = divmod(mul, p) - q, r = divmod(a, p) assert r == 0, f"verify_zero: Invalid input." - ids.q=q%PRIME + qs = split(q) + for i in range(ids.N_LIMBS): + setattr(ids.q, 'd'+str(i), qs[i]) + + q_P_limbs = [q*P for P in p_limbs] + diff_limbs = poly_sub(q_P_limbs, val_limbs) + _, carries = reduce_zero_poly(diff_limbs) + carries = abs_poly(carries) + for i in range(ids.N_LIMBS-1): + setattr(ids, 'flag'+str(i), 1 if diff_limbs[i] >= 0 else 0) + setattr(ids, 'q'+str(i), carries[i]) %} ``` ### verify_zero5() -#L756-L768 ```python %{ - from starkware.cairo.common.math_utils import as_int + from starkware.cairo.common.math_utils import as_int assert 1 < ids.N_LIMBS <= 12 - assert ids.DEGREE == ids.N_LIMBS - 1 - N_LIMBS_UNREDUCED=ids.DEGREE*2+1 - a,p=0,0 + assert ids.DEGREE == ids.N_LIMBS-1 + val, p=0,0 + val_limbs, p_limbs = ids.N_LIMBS_UNREDUCED*[0], ids.N_LIMBS*[0] def split(x, degree=ids.DEGREE, base=ids.BASE): coeffs = [] for n in range(degree, 0, -1): @@ -237,16 +405,62 @@ x = r coeffs.append(x) return coeffs[::-1] + + def poly_mul(a:list, b:list,n=ids.N_LIMBS) -> list: + assert len(a) == len(b) == n + result = [0] * ids.N_LIMBS_UNREDUCED + for i in range(n): + for j in range(n): + result[i+j] += a[i]*b[j] + return result + def poly_sub(a:list, b:list, n=ids.N_LIMBS_UNREDUCED) -> list: + assert len(a) == len(b) == n + result = [0] * n + for i in range(n): + result[i] = a[i] - b[i] + return result + + def abs_poly(x:list): + result = [0] * len(x) + for i in range(len(x)): + result[i] = abs(x[i]) + return result + + def reduce_zero_poly(x:list): + x = x.copy() + carries = [0] * (len(x)-1) + for i in range(0, len(x)-1): + carries[i] = x[i] // ids.BASE + x[i] = x[i] % ids.BASE + assert x[i] == 0 + x[i+1] += carries[i] + assert x[-1] == 0 + return x, carries + + for i in range(ids.N_LIMBS_UNREDUCED): + val_limbs[i]+=as_int(getattr(ids.val, 'd'+str(i)), PRIME) + val+=as_int(getattr(ids.val, 'd'+str(i)), PRIME) * ids.BASE**i + + for i in range(ids.N_LIMBS): p+=getattr(ids, 'P'+str(i)) * ids.BASE**i - for i in range(N_LIMBS_UNREDUCED): - a+=as_int(getattr(ids.val, 'd'+str(i)), PRIME) * ids.BASE**i + p_limbs[i]=getattr(ids, 'P'+str(i)) + + mul = val + q, r = divmod(mul, p) - q, r = divmod(a, p) - assert r == 0, f"verify_zero: Invalid input {a}, {a.bit_length()}." - q_split = split(q) + assert r == 0, f"verify_zero: Invalid input." + qs = split(q) for i in range(ids.N_LIMBS): - setattr(ids.q, 'd'+str(i), q_split[i]) + setattr(ids.q, 'd'+str(i), qs[i]) + + q_P_limbs = poly_mul(qs, p_limbs) + diff_limbs = poly_sub(q_P_limbs, val_limbs) + _, carries = reduce_zero_poly(diff_limbs) + carries = abs_poly(carries) + for i in range(ids.N_LIMBS_UNREDUCED-1): + setattr(ids, 'flag'+str(i), 1 if diff_limbs[i] >= 0 else 0) + setattr(ids, 'q'+str(i), carries[i]) %} ```