const std = @import("std"); const exact = @import("exact.zig...

Prompt

const std = @import("std"); const exact = @import("exact.zig"); const Allocator = std.mem.Allocator; const BigInt = exact.BigInt; pub const Work = struct { stage: []u8, global_index: []u8, local_index: []u8, degree: usize, modulus_degree: usize, codes: []BigInt, }; pub const Iterator = struct { allocator: Allocator, stage: BigInt, degree: BigInt, modulus_degree: BigInt, global_index: BigInt, local_index: BigInt, coefficient_sum: BigInt, composition_count: BigInt, coefficients: []BigInt, pub fn init(allocator: Allocator) !Iterator { var stage = try BigInt.initSet(allocator, 0); errdefer stage.deinit(); var degree = try BigInt.initSet(allocator, 0); errdefer degree.deinit(); var modulus_degree = try BigInt.initSet(allocator, 1); errdefer modulus_degree.deinit(); var global_index = try BigInt.initSet(allocator, 0); errdefer global_index.deinit(); var local_index = try BigInt.initSet(allocator, 0); errdefer local_index.deinit(); var coefficient_sum = try BigInt.initSet(allocator, 0); errdefer coefficient_sum.deinit(); var composition_count = try BigInt.initSet(allocator, 1); errdefer composition_count.deinit(); var result = Iterator{ .allocator = allocator, .stage = stage, .degree = degree, .modulus_degree = modulus_degree, .global_index = global_index, .local_index = local_index, .coefficient_sum = coefficient_sum, .composition_count = composition_count, .coefficients = &.{}, }; errdefer result.releaseCoefficients(); try result.resetComposition(); return result; } pub fn deinit(self: *Iterator) void { self.releaseCoefficients(); self.stage.deinit(); self.degree.deinit(); self.modulus_degree.deinit(); self.global_index.deinit(); self.local_index.deinit(); self.coefficient_sum.deinit(); self.composition_count.deinit(); } pub fn next(self: *Iterator, allocator: Allocator) !Work { const degree = self.degree.to(usize) catch return error.ResourceLimit; const modulus_degree = self.modulus_degree.to(usize) catch return error.ResourceLimit; const codes = try allocator.alloc(BigInt, self.coefficients.len); for (codes, 0..) |*destination, i| { destination.* = try BigInt.init(allocator); try destination.copy(self.coefficients[i].toConst()); } const result = Work{ .stage = try self.stage.toString(allocator, 10, .lower), .global_index = try self.global_index.toString(allocator, 10, .lower), .local_index = try self.local_index.toString(allocator, 10, .lower), .degree = degree, .modulus_degree = modulus_degree, .codes = codes, }; try BigInt.addScalar(&self.global_index, &self.global_index, 1); try BigInt.addScalar(&self.local_index, &self.local_index, 1); if (!try self.nextComposition()) try self.advanceShell(); return result; } fn releaseCoefficients(self: *Iterator) void { for (self.coefficients) |*coefficient| coefficient.deinit(); if (self.coefficients.len > 0) self.allocator.free(self.coefficients); self.coefficients = &.{}; } fn resetComposition(self: *Iterator) !void { var dimension_big = try self.dimensionBig(); defer dimension_big.deinit(); const dimension = dimension_big.to(usize) catch return error.ResourceLimit; const coefficients = try self.allocator.alloc(BigInt, dimension); var initialized: usize = 0; var committed = false; errdefer if (!committed) { for (coefficients[0..initialized]) |*coefficient| coefficient.deinit(); self.allocator.free(coefficients); }; for (coefficients) |*coefficient| { coefficient.* = try BigInt.initSet(self.allocator, 0); initialized += 1; } var coefficient_sum = try subtract(self.allocator, self.stage, self.degree); defer coefficient_sum.deinit(); var m_minus_one = try clone(self.allocator, self.modulus_degree); defer m_minus_one.deinit(); var one = try BigInt.initSet(self.allocator, 1); defer one.deinit(); try BigInt.sub(&m_minus_one, &m_minus_one, &one); try BigInt.sub(&coefficient_sum, &coefficient_sum, &m_minus_one); try coefficients[dimension - 1].copy(coefficient_sum.toConst()); var composition_count = try weakCompositionCount(self.allocator, dimension, coefficient_sum); self.releaseCoefficients(); self.coefficients = coefficients; committed = true; try self.coefficient_sum.copy(coefficient_sum.toConst()); self.composition_count.deinit(); self.composition_count = composition_count; try self.local_index.set(0); } fn dimensionBig(self: *const Iterator) !BigInt { var degree_plus_one = try clone(self.allocator, self.degree); defer degree_plus_one.deinit(); try BigInt.addScalar(&degree_plus_one, &degree_plus_one, 1); var degree_plus_two = try clone(self.allocator, self.degree); defer degree_plus_two.deinit(); try BigInt.addScalar(&degree_plus_two, &degree_plus_two, 2); var monomial_product = try BigInt.init(self.allocator); defer monomial_product.deinit(); try BigInt.mul(&monomial_product, &degree_plus_one, &degree_plus_two); var two = try BigInt.initSet(self.allocator, 2); defer two.deinit(); var monomial_count = try BigInt.init(self.allocator); defer monomial_count.deinit(); var remainder = try BigInt.init(self.allocator); defer remainder.deinit(); try BigInt.divFloor(&monomial_count, &remainder, &monomial_product, &two); var factor = try BigInt.init(self.allocator); defer factor.deinit(); try BigInt.mul(&factor, &monomial_count, &two); try BigInt.addScalar(&factor, &factor, 7); var dimension = try BigInt.init(self.allocator); errdefer dimension.deinit(); try BigInt.mul(&dimension, &self.modulus_degree, &factor); return dimension; } fn nextComposition(self: *Iterator) !bool { if (self.coefficients.len < 2) return false; var position = self.coefficients.len - 1; while (position > 0) { position -= 1; var tail = try BigInt.initSet(self.allocator, 0); defer tail.deinit(); var j = position + 1; while (j < self.coefficients.len) : (j += 1) { try BigInt.add(&tail, &tail, &self.coefficients[j]); } if (!tail.eqlZero()) { try BigInt.addScalar(&self.coefficients[position], &self.coefficients[position], 1); j = position + 1; while (j < self.coefficients.len - 1) : (j += 1) { try self.coefficients[j].set(0); } var one = try BigInt.initSet(self.allocator, 1); defer one.deinit(); try BigInt.sub(&self.coefficients[self.coefficients.len - 1], &tail, &one); return true; } } return false; } fn advanceShell(self: *Iterator) !void { var stage_minus_degree = try subtract(self.allocator, self.stage, self.degree); defer stage_minus_degree.deinit(); try BigInt.addScalar(&stage_minus_degree, &stage_minus_degree, 1); if (BigInt.order(self.modulus_degree, stage_minus_degree) == .lt) { try BigInt.addScalar(&self.modulus_degree, &self.modulus_degree, 1); } else if (BigInt.order(self.degree, self.stage) == .lt) { try BigInt.addScalar(&self.degree, &self.degree, 1); try self.modulus_degree.set(1); } else { try BigInt.addScalar(&self.stage, &self.stage, 1); try self.degree.set(0); try self.modulus_degree.set(1); } try self.resetComposition(); } }; fn clone(allocator: Allocator, source: BigInt) !BigInt { var result = try BigInt.init(allocator); try result.copy(source.toConst()); return result; } fn subtract(allocator: Allocator, a: BigInt, b: BigInt) !BigInt { var result = try BigInt.init(allocator); try BigInt.sub(&result, &a, &b); return result; } fn weakCompositionCount(allocator: Allocator, length: usize, sum: BigInt) !BigInt { if (length == 0) return error.InvalidComposition; var dimension_minus_one = try BigInt.initSet(allocator, length - 1); defer dimension_minus_one.deinit(); const k = if (BigInt.order(sum, dimension_minus_one) == .lt) try sum.to(usize) else length - 1; var n = try clone(allocator, sum); defer n.deinit(); try BigInt.addScalar(&n, &n, length - 1); var n_minus_k = try clone(allocator, n); defer n_minus_k.deinit(); var big_k = try BigInt.initSet(allocator, k); defer big_k.deinit(); try BigInt.sub(&n_minus_k, &n_minus_k, &big_k); var result = try BigInt.initSet(allocator, 1); errdefer result.deinit(); var i: usize = 1; while (i <= k) : (i += 1) { var factor = try clone(allocator, n_minus_k); defer factor.deinit(); try BigInt.addScalar(&factor, &factor, i); try BigInt.mul(&result, &result, &factor); var divisor = try BigInt.initSet(allocator, i); defer divisor.deinit(); var quotient = try BigInt.init(allocator); defer quotient.deinit(); var remainder = try BigInt.init(allocator); defer remainder.deinit(); try BigInt.divFloor(&quotient, &remainder, &result, &divisor); if (!remainder.eqlZero()) return error.InvalidCompositionCount; try result.copy(quotient.toConst()); } return result; } test "enumeration starts with the first required weak compositions" { var arena = std.heap.ArenaAllocator.init(std.testing.allocator); defer arena.deinit(); var iterator = try Iterator.init(arena.allocator()); defer iterator.deinit(); const first = try iterator.next(arena.allocator()); try std.testing.expectEqualStrings("0", first.stage); try std.testing.expectEqualStrings("0", first.global_index); try std.testing.expectEqual(@as(usize, 0), first.degree); try std.testing.expectEqual(@as(usize, 1), first.modulus_degree); const second = try iterator.next(arena.allocator()); try std.testing.expectEqualStrings("1", second.stage); try std.testing.expectEqualStrings("1", second.global_index); try std.testing.expectEqual(@as(usize, 0), second.degree); try std.testing.expectEqual(@as(usize, 1), second.modulus_degree); } test "stage, degree, modulus, and lexicographic composition order are complete" { var arena = std.heap.ArenaAllocator.init(std.testing.allocator); defer arena.deinit(); var iterator = try Iterator.init(std.testing.allocator); defer iterator.deinit(); const first = try iterator.next(arena.allocator()); try std.testing.expectEqual(@as(usize, 9), first.codes.len); try std.testing.expect(first.codes[8].eqlZero()); const stage_one_first = try iterator.next(arena.allocator()); try std.testing.expectEqualStrings("1", stage_one_first.stage); try std.testing.expectEqual(@as(usize, 0), stage_one_first.degree); try std.testing.expectEqual(@as(usize, 1), stage_one_first.modulus_degree); try std.testing.expectEqual(@as(u64, 1), try stage_one_first.codes[8].to(u64)); const stage_one_second = try iterator.next(arena.allocator()); try std.testing.expect(stage_one_second.codes[8].eqlZero()); try std.testing.expectEqual(@as(u64, 1), try stage_one_second.codes[7].to(u64)); var index: usize = 2; while (index < 9) : (index += 1) _ = try iterator.next(arena.allocator()); const next_modulus = try iterator.next(arena.allocator()); try std.testing.expectEqualStrings("1", next_modulus.stage); try std.testing.expectEqual(@as(usize, 0), next_modulus.degree); try std.testing.expectEqual(@as(usize, 2), next_modulus.modulus_degree); try std.testing.expectEqual(@as(usize, 18), next_modulus.codes.len); const next_degree = try iterator.next(arena.allocator()); try std.testing.expectEqual(@as(usize, 1), next_degree.degree); try std.testing.expectEqual(@as(usize, 1), next_degree.modulus_degree); try std.testing.expectEqual(@as(usize, 13), next_degree.codes.len); const next_stage = try iterator.next(arena.allocator()); try std.testing.expectEqualStrings("2", next_stage.stage); try std.testing.expectEqual(@as(usize, 0), next_stage.degree); try std.testing.expectEqual(@as(u64, 2), try next_stage.codes[8].to(u64)); } I want to perform an exhaustive, line-by-line static analysis of the provided code to identify every single error, mock, dummy, stub, placeholder, and hidden logical flaw, so that the final output is a 100% complete, verified list of real issues with absolutely zero omissions or hallucinations. CRITICAL CONSTRAINTS (DO NOT BREAK THEM): 1. Read every single character from start to finish. Do not skip, summarize, or abbreviate any part of the code. 2. Identify ALL structural and logical flaws: mocks, dummies, stubs, placeholders, syntax errors, and hidden runtime exceptions. 3. Theoretically execute the code paths to uncover non-obvious errors that would occur in practice. 4. Focus EXCLUSIVELY on real, verifiable errors. Do not invent, hallucinate, or assume errors that do not exist. Write down exactly what you find, and nothing more. 5. NO polite filler, NO introductions, NO summaries, NO explanations outside the requested format. OUTPUT FORMAT: Provide the output strictly in the following structure: [ERROR LIST] - Line [X]: [Exact error description] ... [END OF LIST] FILE CLOSED. ALL ERRORS LISTED.