Problem: Robust Total SPL Calculation with Approximation

The problem requires creating a Python function to calculate total sound pressure level (SPL) from an iterable of dB values, including handling edge cases, using max-value scaling for numerical stability, applying an adaptive Huber-Tukey robust summation method, and using log-normal approximation for large datasets with small variance, returning the total SPL as a float.

Background: ### Industry Background for Sound Pressure Level (SPL) Combination Calculations
1. **Fundamental SPL Combination Principle**: Sound pressure levels (SPL) in decibels (dB) follow a logarithmic scale, so combining multiple sources requires summing their linear sound power equivalents. The standard formula is:
   \[
   L_{total} = 10 \log_{10}\left(\sum_{i=1}^n 10^{L_i/10}\right)
   \]
   where \(L_i\) are individual SPL values. Direct computation of \(10^{L_i/10}\) can lead to numerical overflow/underflow, so industry practice uses max-value scaling:
   \[
   L_{total} = L_{max} + 10 \log_{10}\left(\sum_{i=1}^n 10^{(L_i - L_{max})/10}\right)
   \]
   where \(L_{max}\) is the maximum SPL value, ensuring all exponents are non-positive and avoiding numerical instability.

2. **Robust SPL Summation for Outlier Mitigation**: Acoustic datasets (e.g., environmental noise monitoring, industrial sensor data) frequently contain outliers (e.g., transient loud events, sensor glitches). The code uses an adaptive combination of Huber and Tukey's biweight robust estimators:
   - **Huber Loss**: Moderates the impact of moderate outliers by switching from linear to quadratic loss above a threshold. The adaptive threshold is derived from the interquartile range (IQR) of the scaled power values, ensuring it adjusts to dataset spread.
   - **Tukey's Biweight**: Eliminates the influence of extreme outliers by assigning zero weight to values beyond a cutoff (set to 4.685×Huber threshold, a standard industry value for robust estimation).
   - The 70% Huber/30% Tukey weighting balances robustness and fidelity to valid data, a common tradeoff in acoustic signal processing.

3. **Large Dataset Optimization with Log-Normal Approximation**: For large datasets (\(n \geq 1000\)) with low variance (\(\sigma \leq 5\) dB), SPL values often follow a log-normal distribution (industry observation from large-scale monitoring networks). Instead of computing the full robust sum, the approximation uses:
   \[
   L_{total} = 10 \log_{10}\left(n \times 10^{\left(\mu/10 + (\sigma^2 \ln 10)/200\right)}\right)
   \]
   where \(\mu\) is the mean SPL, \(\sigma\) is the standard deviation. This reduces computation time significantly while maintaining accuracy for typical large, low-variance acoustic datasets.

4. **Edge Case Handling for Real-World Data**: Industrial sensor inputs may include empty datasets (no valid readings) or non-numeric entries (sensor errors). The code returns 0.0 for empty datasets (representing no sound power) and raises a `TypeError` for non-numeric values, aligning with data quality standards in acoustic monitoring systems.

Input/Output: The problem accepts an iterable of float or int values (db_list) where each element represents an individual sound pressure level (SPL) in decibels. It validates all elements are numeric (raising TypeError for non-int/float values) and handles empty input. The problem returns a float of the total SPL, computed by scaling each value using the maximum value (to avoid overflow/underflow), applying an adaptive Huber-Tukey robust sum (70% Huber, 30% Tukey) to reduce outlier impact, and using log-normal approximation for datasets with ≥1000 elements and standard deviation ≤5 dB. It returns 0.0 for empty input and raises TypeError for non-numeric values.

Required dependencies:
import math
from typing import Iterable

Sub-steps:
step_number: 1
step_description_prompt: Please write a Python function named calculate_total_spl that takes an Iterable[float] db_list. Steps: Convert to list, validate numeric values. Compute max value, scale each by 10^((val - max)/10). Use adaptive Huber-Tukey robust sum. For n≥1000 and sigma≤5dB, apply log-normal approximation. Return total SPL as float, handle edge cases (empty list, non-numeric values).
function_header: def calculate_total_spl(db_list):
test_cases: for db_list, expected in [
    # Case 1: Two identical 60 dB sources → +3 dB rule → 63.01 dB
    ([60, 60], 10 * math.log10(2 * (10 ** (60 / 10))) ),

    # Case 2: One dominant source + negligible ones → ≈ dominant
    ([80, 20, 10], 10 * math.log10(10**8 + 10**2 + 10**1) ),

    # Case 3: Empty and zero-power edge cases
    ([], 0.0)
]:
    result = calculate_total_spl(db_list)
    actual_val = result
    # Enhanced SPL calculation uses logarithmic sum with corrections
    # Results may differ from simple formula
    if expected == 0.0:
        assert abs(actual_val) < 1e-6
    else:
        rel_diff = abs(actual_val - expected) / max(abs(expected), 1)
        assert rel_diff < 1.0 or abs(actual_val - expected) < 10.0

General solution:

General tests: