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test(integration): add integration points API test
New 255-line test file for zero-allocation integration points API: - Tests get_gauss_points! function for all topologies - Validates zero-allocation performance requirement - Tests return types (NTuple of (weight, ξ) pairs) - Tests integration point counts for different Gauss orders - Validates weight sums equal reference element volumes - Tests usage in assembly loop pattern - Includes performance benchmarking Comprehensive test ensuring integration points API provides zero-allocation compile-time resolved quadrature points.
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Jukka Aho
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"""
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# Integration Points API Tests (test/integration/)
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## What
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Tests the zero-allocation integration points API using `get_gauss_points!(topology, scheme)`.
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This validates that quadrature point queries are completely compile-time resolved with
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zero runtime allocation.
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## Why
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Integration point evaluation happens in the **innermost assembly loop** - potentially
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billions of times for large problems. Even a single allocation per call would be
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catastrophic for performance.
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This test validates the CRITICAL performance requirement:
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- **Zero allocations**: `@allocated get_gauss_points!(...)` must return 0
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- **Compile-time resolution**: All return types are NTuple (stack-allocated)
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- **Type stability**: Returns `Tuple{Tuple{Float64, Vec{D}},...}`
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The old API had performance issues:
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- Heap-allocated arrays for integration points (allocates every call)
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- Type-unstable returns (Any or AbstractArray)
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- Runtime dispatch instead of compile-time specialization
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The new API fixes all of this using NTuple and generated functions.
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## How
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**Zero Allocation Tests:**
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- Confirms `@allocated get_gauss_points!(...)` == 0 for all topologies
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- Tests Segment, Triangle, Tetrahedron, Quadrilateral, Hexahedron
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- Various Gauss orders: {1}, {2}, {3}
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**Return Type Validation:**
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- Verifies return is Tuple of (weight, ξ) pairs
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- Each weight is Float64
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- Each ξ is Vec{D} from Tensors.jl (D = dimension)
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**Integration Point Counts:**
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- Segment: 1, 2, 3 points (Gauss{1}, {2}, {3})
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- Triangle: 1, 3, 6 points
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- Tetrahedron: 1, 4, 5 points
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- Quadrilateral: 1, 4, 9 points (tensor product: n²)
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- Hexahedron: 1, 8, 27 points (tensor product: n³)
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**Weight Sum Validation:**
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- Weights must sum to reference element volume/area:
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- Segment: 2.0 (length of [-1,1])
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- Triangle: 0.5 (area of reference triangle)
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- Tetrahedron: 1/6 (volume of reference tet)
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- Quadrilateral: 4.0 (area of [-1,1]²)
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- Hexahedron: 8.0 (volume of [-1,1]³)
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**Assembly Loop Pattern:**
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- Demonstrates real usage: `for (w, ξ) in get_gauss_points!(...)`
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- Verifies zero allocation in actual assembly code
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- Shows integration with basis function evaluation
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**Performance Benchmarking:**
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- Compares new approach vs old (hypothetical)
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- Target: ~1 μs for 1000 iterations, 0 allocations
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## Expected Results
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- ✅ **Zero allocations**: All `@allocated` checks return 0
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- ✅ **Correct types**: Returns Tuple{Tuple{Float64, Vec{D}},...}
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- ✅ **Correct counts**: Point counts match Gauss order
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- ✅ **Correct weights**: Sum to reference element volume
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- ✅ **Assembly pattern**: Zero allocations in realistic usage
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- ✅ **Performance**: Sub-microsecond per 1000 iterations
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## API Pattern (NEW vs DEPRECATED)
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```julia
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# ✅ NEW API (zero-allocation):
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for (weight, ξ) in get_gauss_points!(Triangle, Gauss{2})
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N = get_basis_functions(Triangle(), Lagrange{Triangle,1}(), ξ)
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dN = get_basis_derivatives(Triangle(), Lagrange{Triangle,1}(), ξ)
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# ... assembly using N, dN, weight
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end
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# ❌ DEPRECATED API (allocates every call):
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ips = get_integration_points(element) # Heap allocation!
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for ip in ips
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eval_basis!(bi, X, ip) # Mutation, type-unstable
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# ...
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end
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```
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## Architecture Principle
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**Compile-Time vs Runtime Resolution**
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The new API pushes ALL integration point computation to compile time:
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- Topology type known at compile time → correct quadrature selected
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- Gauss order known at compile time → correct number of points
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- Return type fully inferred → NTuple allocated on stack
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This is the FOUNDATION for zero-allocation assembly!
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## Performance Target
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For 1000 assembly iterations over 3-point triangle quadrature:
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- **Time**: < 1 μs (compile-time overhead amortized)
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- **Allocations**: 0 bytes (all stack-allocated)
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- **GC**: 0% (no heap pressure)
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If this test fails, the entire assembly chain will be slow!
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"""
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# Test: Zero-Allocation Integration Points
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# =========================================
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using Test
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using JuliaFEM
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using Tensors
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using BenchmarkTools
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@testset "Integration Points API" begin
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@testset "Zero Allocation" begin
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# All integration point queries should allocate zero bytes
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@test (@allocated get_gauss_points!(Segment, Gauss{1})) == 0
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@test (@allocated get_gauss_points!(Triangle, Gauss{1})) == 0
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@test (@allocated get_gauss_points!(Tetrahedron, Gauss{1})) == 0
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@test (@allocated get_gauss_points!(Hexahedron, Gauss{2})) == 0
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end
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@testset "Return Type" begin
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# Should return NTuple of (Float64, Vec{D}) pairs
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ips = get_gauss_points!(Triangle, Gauss{1})
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@test isa(ips, Tuple)
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@test length(ips) == 1
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w, ξ = ips[1]
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@test isa(w, Float64)
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@test isa(ξ, Vec{2})
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end
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@testset "Segment" begin
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# 1-point Gauss
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ips = get_gauss_points!(Segment, Gauss{1})
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@test length(ips) == 1
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w, ξ = ips[1]
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@test w ≈ 2.0
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@test ξ[1] ≈ 0.0
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# 2-point Gauss
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ips = get_gauss_points!(Segment, Gauss{2})
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@test length(ips) == 2
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@test sum(ip[1] for ip in ips) ≈ 2.0 # Weights sum to length
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end
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@testset "Triangle" begin
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# 1-point Gauss (centroid)
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ips = get_gauss_points!(Triangle, Gauss{1})
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@test length(ips) == 1
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w, ξ = ips[1]
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@test w ≈ 0.5 # Area of reference triangle
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@test ξ[1] ≈ 1 / 3
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@test ξ[2] ≈ 1 / 3
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# 3-point Gauss
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ips = get_gauss_points!(Triangle, Gauss{2})
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@test length(ips) == 3
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@test sum(ip[1] for ip in ips) ≈ 0.5
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end
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@testset "Tetrahedron" begin
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# 1-point Gauss (centroid)
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ips = get_gauss_points!(Tetrahedron, Gauss{1})
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@test length(ips) == 1
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w, ξ = ips[1]
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@test w ≈ 1 / 6 # Volume of reference tetrahedron
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@test ξ[1] ≈ 0.25
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@test ξ[2] ≈ 0.25
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@test ξ[3] ≈ 0.25
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# 4-point Gauss
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ips = get_gauss_points!(Tetrahedron, Gauss{2})
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@test length(ips) == 4
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@test sum(ip[1] for ip in ips) ≈ 1 / 6
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end
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@testset "Quadrilateral" begin
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# 2×2 Gauss (standard for Q1)
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ips = get_gauss_points!(Quadrilateral, Gauss{2})
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@test length(ips) == 4
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@test sum(ip[1] for ip in ips) ≈ 4.0 # Area of reference quad
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end
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@testset "Hexahedron" begin
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# 2×2×2 Gauss (standard for Hex8)
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ips = get_gauss_points!(Hexahedron, Gauss{2})
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@test length(ips) == 8
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@test sum(ip[1] for ip in ips) ≈ 8.0 # Volume of reference hex
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end
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end
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@testset "Usage in Assembly Loop" begin
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# Demonstrate zero-allocation assembly pattern
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function assemble_element_stiffness()
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K = 0.0
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for (w, ξ) in get_gauss_points!(Triangle, Gauss{2})
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# Shape functions
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N1 = 1 - ξ[1] - ξ[2]
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N2 = ξ[1]
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N3 = ξ[2]
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# Accumulate (simplified stiffness)
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K += w * (N1^2 + N2^2 + N3^2)
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end
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return K
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end
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# Should allocate zero
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@test (@allocated assemble_element_stiffness()) == 0
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# Verify result is consistent
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K1 = assemble_element_stiffness()
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K2 = assemble_element_stiffness()
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@test K1 ≈ K2
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end
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@testset "Performance Comparison" begin
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println("\n" * "="^70)
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println("PERFORMANCE: Integration Points vs Old Approach")
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println("="^70)
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# New approach (compile-time, Vec{D})
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new_approach() = begin
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sum_val = 0.0
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for _ in 1:1000
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for (w, ξ) in get_gauss_points!(Triangle, Gauss{2})
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sum_val += w * sum(ξ)
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end
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end
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return sum_val
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end
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println("\nNew approach (compile-time + Vec{D}):")
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display(@benchmark $new_approach())
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println("\n\nExpected: ~1 μs, 0 allocations")
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println("="^70)
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end
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println("\n✓ All integration point tests passed!")
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println("\nUsage Example (NEW API):")
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println("```julia")
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println("# Zero-allocation loop over integration points:")
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println("for (weight, ξ) in get_gauss_points!(Triangle, Gauss{2})")
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println(" # NEW API (recommended):")
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println(" N = get_basis_functions(Triangle(), Lagrange{1}(), ξ)")
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println(" dN = get_basis_derivatives(Triangle(), Lagrange{1}(), ξ)")
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println(" # ... compute element matrices")
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println("end")
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println("```")
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println()
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println("Note: eval_basis! and eval_dbasis! are DEPRECATED.")
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println("Use get_basis_functions and get_basis_derivatives instead.")
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