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Merged
Zaneham merged 1 commit into from
Jan 19, 2026
Merged

Add L1-L4 tests for interpolation and diff_integ modules #4

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118 changes: 111 additions & 7 deletions TESTING.md
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Expand Up @@ -36,9 +36,9 @@ These are the tests we run continuously. They verify basic functionality and cat
| special_functions | Partial (Bessel) | `test/test_bessel_regression.f90` |
| linear (BLAS) | ✓ **18/18 PASS** | `test/level1_regression/test_l1_linear_blas.f90` |
| linear (LINPACK) | ⏳ In Progress | `test/level1_regression/test_l1_linear_linpack.f90` |
| diff_integ | Partial (QUADPACK) | `test/test_diff_integ_quadpack.f90` |
| diff_integ | ✓ **12/12 PASS** | `test/level1_regression/test_l1_diff_integ.f90` |
| diff_integ_eq | Partial | `test/test_diff_integ_eq.f90` |
| interpolation | ⏳ Pending | — |
| interpolation | ✓ **9/9 PASS** | `test/level1_regression/test_l1_interpolation.f90` |
| integ_trans | ⏳ Pending | — |
| approximation (MINPACK) | ✓ **9/9 PASS** | `test/level1_regression/test_l1_minpack.f90` |
| nonlin_eq | ⏳ Pending | — |
Expand All @@ -65,7 +65,8 @@ These tests compare computed values against authoritative mathematical reference
|--------|--------|------------------|
| special_functions | Partial | A&S Tables 9.1, 9.8 (Bessel) |
| linear (BLAS) | ✓ **16/16 PASS** | Lawson et al., ACM TOMS 5(3), 1979 |
| diff_integ | Partial | Closed-form integrals |
| diff_integ | ✓ **17/17 PASS** | Closed-form integrals, A&S, NIST DLMF |
| interpolation | ⚠ **14/17 PASS** | de Boor (1978), Fritsch & Carlson (1980) |
| approximation (MINPACK) | ✓ **17/17 PASS** | Moré, Garbow, Hillstrom (1981) |

**Test Files:**
Expand All @@ -74,6 +75,8 @@ These tests compare computed values against authoritative mathematical reference
- `test/test_specfun_bessel.f90` — Edge cases
- `test/level2_mathematical/test_l2_linear_blas.f90` — BLAS linearity, orthogonality, Pythagorean properties
- `test/level2_mathematical/test_l2_minpack_mgh.f90` — MGH test functions (Rosenbrock, Powell, Helical Valley, Freudenstein-Roth)
- `test/level2_mathematical/test_l2_diff_integ.f90` — Gauss-Kronrod exactness, classical integrals, infinite intervals
- `test/level2_mathematical/test_l2_interpolation.f90` — B-spline, PCHIP, polynomial interpolation properties

---

Expand Down Expand Up @@ -196,6 +199,11 @@ Code modifications required to compile on IBM FORTRAN G (1966):
| approximation (MINPACK) | DQRFAC | Pending |
| approximation (MINPACK) | DNLS1 | Pending |
| approximation (MINPACK) | DNSQ | Pending |
| interpolation | DPLINT, DPOLVL (polynomial) | **4/4 PASS** |
| interpolation | DPCHIM, DPCHFE (PCHIP) | N/A (post-1980) |
| interpolation | DBINT4, DBVALU (B-spline) | N/A (post-1978) |
| diff_integ | Trapezoidal rule | **2/2 PASS** |
| diff_integ | QUADPACK routines | N/A (post-1983) |

### Historical Context

Expand Down Expand Up @@ -289,22 +297,22 @@ See [DEVIATIONS.md](DEVIATIONS.md#critical-deviation-subnormal-flush-with--ffast

## Module Coverage Summary

*Last updated: 1 January 2026*
*Last updated: 18 January 2026*

| Module | Routines | L1 | L2 | L3 | L4 | Overall |
|--------|----------|----|----|----|----|---------|
| **service** | 3 | — | — | ✓ | — | ~33% |
| **special_functions** | 270 | ~20 | ~20 | 4 | ~20 | ~9% |
| **linear (BLAS)** | 217 | 18 | 16 | 9 | 65 | ~50% |
| **diff_integ** | 81 | ~10 | ~10 | — | — | ~12% |
| **diff_integ** | 81 | 12 | 17 | 2 | 12 | ~53% |
| **diff_integ_eq** | 225 | ~5 | — | — | — | ~2% |
| **interpolation** | 80 | — | — | — | — | 0% |
| **interpolation** | 80 | 9 | 14 | 4 | 19 | ~58% |
| **integ_trans** | 48 | — | — | — | — | 0% |
| **approximation** | 78 | 9 | 17 | 7 | 45 | ~100% |
| **nonlin_eq** | 15 | — | — | — | — | 0% |
| **optimisation** | 46 | — | — | — | — | 0% |
| **data_handling** | 16 | — | — | — | — | 0% |
| **TOTAL** | **1,079** | ~62 | ~63 | ~22 | ~130 | **~18%** |
| **TOTAL** | **1,079** | ~83 | ~98 | ~28 | ~161 | **~25%** |

---

Expand Down Expand Up @@ -403,6 +411,102 @@ See [DEVIATIONS.md](DEVIATIONS.md#critical-deviation-subnormal-flush-with--ffast

---

## Diff_Integ Test Details

*Testing QUADPACK and GAUS8 numerical integration routines*

### Complete 4-Level Results (18 January 2026)

| Level | Tests | Result | Notes |
|-------|-------|--------|-------|
| **L1 Regression** | 12 | ✓ **12/12 PASS** | DGAUS8, DQAGS, DQAGI, DQNG |
| **L2 Mathematical** | 17 | ✓ **17/17 PASS** | Gauss-Kronrod exactness, classical integrals |
| **L3 Historical** | 2 | ✓ **2/2 PASS** | Trapezoidal rule (QUADPACK N/A - post-1983) |
| **L4 Hostile** | 12 | ✓ **12/12 PASS** | Extreme values, oscillatory, reproducibility |
| **TOTAL** | **43** | **43/43 PASS** | |

### Test Files

| Level | File | Description |
|-------|------|-------------|
| L1 | `test/level1_regression/test_l1_diff_integ.f90` | Basic integration regression tests |
| L2 | `test/level2_mathematical/test_l2_diff_integ.f90` | Gauss-Kronrod exactness, special functions |
| L3 | `test/level3_historical/test_l3_diff_integ.f90` | IBM 360 trapezoidal golden values |
| L4 | `test/level4_hostile/test_l4_diff_integ.f90` | Hostile environment tests |

### Mathematical Properties Tested (Level 2)

| Property | Test |
|----------|------|
| Gauss-Kronrod exactness | QK15 exact for degree ≤ 29 |
| Gauss-Kronrod exactness | QK21 exact for degree ≤ 41 |
| Gauss-Kronrod exactness | QK31 exact for degree ≤ 61 |
| Classical integrals | ∫sin(x)dx, ∫exp(-x)dx, ∫1/√x dx |
| Infinite intervals | ∫₀^∞ exp(-x)dx = 1 |
| Gaussian integral | ∫_{-∞}^{∞} exp(-x²)dx = √π |

### Hostile Tests (Level 4) — 12 Tests in 6 Categories

| Category | Tests | What It Catches |
|----------|-------|-----------------|
| Tiny Intervals | 2 | Very small [a,b], A≈B handling |
| Extreme Values | 3 | 1e-100 to 1e100 function scaling |
| Narrow Peaks | 2 | Sharp Gaussian, narrow Lorentzian |
| Discontinuities | 2 | Step functions, kinks |
| Oscillatory | 2 | sin(10x), cos(10x) moderate oscillation |
| Reproducibility | 1 | Identical results across runs |

### Historical Note (Level 3)

QUADPACK was developed by Piessens, de Doncker, et al. and published in 1983. The algorithms post-date the IBM 360 era, so no authentic L3 golden values exist. Level 3 tests use trapezoidal rule integration (1960s compatible) for IBM 360 validation.

---

## Interpolation Test Details

*Testing B-spline, PCHIP, and polynomial interpolation routines*

### Complete 4-Level Results (18 January 2026)

| Level | Tests | Result | Notes |
|-------|-------|--------|-------|
| **L1 Regression** | 9 | ✓ **9/9 PASS** | DBINT4, DBVALU, DPCHIM, DPCHFE, DPLINT, DPOLVL |
| **L2 Mathematical** | 17 | ⚠ **14/17 PASS** | B-spline issues identified |
| **L3 Historical** | 4 | ✓ **4/4 PASS** | IBM 360 polynomial golden values |
| **L4 Hostile** | 19 | ✓ **19/19 PASS** | Runge phenomenon, subnormals, cancellation |
| **TOTAL** | **49** | **46/49 PASS** | 3 B-spline mathematical issues |

### Test Files

| Level | File | Description |
|-------|------|-------------|
| L1 | `test/level1_regression/test_l1_interpolation.f90` | Basic interpolation regression |
| L2 | `test/level2_mathematical/test_l2_interpolation.f90` | Mathematical property verification |
| L3 | `test/level3_historical/test_l3_interpolation.f90` | IBM 360 golden comparisons |
| L3 | `/c/dev/vintage/fortran360/tests/slatec/interpolation/test_poly.f` | FORTRAN IV for Hercules |
| L4 | `test/level4_hostile/test_l4_interpolation.f90` | Hostile environment tests |

### IBM 360 Golden Values (Level 3)

Captured via Hercules/TK4- on 18 January 2026:

| Test | y = x³ at midpoints | IBM 360 Value |
|------|---------------------|---------------|
| p(0.5) | 0.125 | 0.125000000000000D 00 |
| p(1.5) | 3.375 | 0.337500000000000D 01 |
| p(2.5) | 15.625 | 0.156250000000000D 02 |
| p(3.5) | 42.875 | 0.428750000000000D 02 |

### Known Issues (Level 2)

- **DBINT4 natural spline**: Does not interpolate exactly (max error: 3.56e-03)
- **DBINT4 clamped spline**: Does not interpolate exactly (max error: 0.36)
- **Natural spline boundary**: S''(1) = 60.1 instead of 0

PCHIP and polynomial interpolation work correctly.

---

## Contributing Tests

When adding tests, consider which level they belong to:
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14 changes: 11 additions & 3 deletions TEST_RESULTS.md
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@@ -1,6 +1,6 @@
# SLATEC-Modern Test Results

*Comprehensive test execution log — 1 January 2026*
*Comprehensive test execution log — 18 January 2026*
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## Executive Summary

Expand All @@ -10,9 +10,17 @@
| **MINPACK** | 9/9 | 17/17 | 7/7 | 45/45 | **78/78** |
| **LINPACK** | 15/15 | 26/26 | 19/19 | 36/36 | **96/96** |
| **Special Functions** | 26/26 | 18/18 | 21/21 | 28/32 | **93/97** |
| **Combined** | 68/68 | 77/77 | 56/56 | 174/178 | **375/379** |
| **Interpolation** | 9/9 | 14/17 | 4/4 | 19/19 | **46/49** |
| **Diff_Integ** | 12/12 | 17/17 | 2/2 | 12/12 | **43/43** |
| **Combined** | 89/89 | 108/111 | 62/62 | 205/209 | **464/471** |

**All tests pass with safe compiler flags (`-O2` or `-O3`).**
**All tests pass with safe compiler flags (`-O2` or `-O3`).** 3 B-spline mathematical issues documented.

### Latest Additions (18 January 2026)

- **Interpolation**: Full L1-L4 coverage for DBINT4, DBVALU, DPCHIM, DPCHFE, DPLINT, DPOLVL
- **Diff_Integ**: Full L1-L4 coverage for DGAUS8, DQAGS, DQAGI, DQNG, DQK15/21/31
- **L3 Historical**: IBM 360 golden values captured via Hercules/TK4- for polynomial interpolation

---

Expand Down
17 changes: 15 additions & 2 deletions test/level1_regression/README.md
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Expand Up @@ -28,19 +28,32 @@ When code changes, Level 1 tests may need updating. This is expected and accepta
| test_l1_minpack.f90 | approximation | DENORM/ENORM | 9 | ✓ **9/9 PASS** |
| test_l1_linear_blas.f90 | linear | DAXPY, DSCAL, DCOPY, DSWAP, DROT, DROTG | 18 | ✓ **18/18 PASS** |
| test_l1_linear_linpack.f90 | linear | DGEFA/DGESL, DPOFA/DPOSL | — | ⏳ In Progress |
| test_l1_interpolation.f90 | interpolation | DBINT4, DBVALU, DPCHIM, DPCHFE, DPCHIA, DPLINT, DPOLCF, DPOLVL | 9 | ✓ **9/9 PASS** |
| test_l1_diff_integ.f90 | diff_integ | DGAUS8, DQAGS, DQAGI, DQNG | 12 | ✓ **12/12 PASS** |

## Running

```bash
cd /c/dev/slatec-modern

# Build library first (if needed)
cmake -B build && cmake --build build

# MINPACK
gfortran -o test_l1_minpack test/level1_regression/test_l1_minpack.f90
gfortran -O2 -I build/modules -o test_l1_minpack test/level1_regression/test_l1_minpack.f90 -L build/lib -lslatec
./test_l1_minpack

# BLAS
gfortran -o test_l1_blas test/level1_regression/test_l1_linear_blas.f90
gfortran -O2 -I build/modules -o test_l1_blas test/level1_regression/test_l1_linear_blas.f90 -L build/lib -lslatec
./test_l1_blas

# Interpolation
gfortran -O2 -I build/modules -o test_l1_interpolation test/level1_regression/test_l1_interpolation.f90 -L build/lib -lslatec
./test_l1_interpolation

# Diff_Integ
gfortran -O2 -I build/modules -o test_l1_diff_integ test/level1_regression/test_l1_diff_integ.f90 -L build/lib -lslatec
./test_l1_diff_integ
```

Or via fpm:
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