8.14 Rounding Variance Tolerance

When performing invoice reconciliation between the Cost and Usage dataset and an invoice (either the payable invoice itself, or the Invoice Detail dataset), the totals may not be perfectly equal due to precision differences (e.g., 6 decimals in detailed cost data vs. 2 decimals in invoice data). The following tolerance formula allows for a maximum rounding error based on the statistical probability of rounding variance, which grows with the square root of the row count.

8.14.1 Tolerance Formula

The tolerance used when comparing aggregated BilledCost values is defined as:

Tolerance = MAX(100 × Subunit, (SQRT(Rows) × 0.5) × Subunit)

Where:

• Rows — The number of CostAndUsage rows included in the aggregation for the relevant CostAndUsage.InvoiceIssuerName, CostAndUsage.InvoiceId, and (if applicable) CostAndUsage.InvoiceDetailId.
• Subunit — The numeric value of the smallest subunit of CostAndUsage.BillingCurrency (for example, 0.01 for USD or 1 for JPY).

The tolerance is the greater of the following values:

• 100 × Subunit — Establishes a fixed minimum tolerance equal to 100 units of the smallest currency subunit.
• (SQRT(Rows) × 0.5) × Subunit — Provides a tolerance that increases with the square root of the number of rows to account for rounding accumulation in larger datasets.

8.14.2 Scenario 1: Small Invoice (Pass)

• Data: A small invoice with 5 underlying CostAndUsage rows.
• Values: CostAndUsage sums to $12.50. InvoiceDetail sums to $12.52. Difference is $0.02.
• Limit Calculation:
  • Statistical Limit: SQRT(5) * 0.5 * 0.01 = $0.011.
  • Floor Limit: 100 * 0.01 = $1.00.
  • Effective Tolerance: $1.00 (Greater of $0.011 and $1.00).
• Result: Pass (Difference $0.02 < Tolerance $1.00).

8.14.3 Scenario 2: Small Invoice (Fail)

• Data: A small invoice with 5 underlying CostAndUsage rows where a $5.00 charge is missing from CostAndUsage.
• Values: CostAndUsage sums to $10.00. InvoiceDetail sums to $15.00. Difference is $5.00.
• Limit Calculation:
  • Effective Tolerance: $1.00.
• Result: Fail (Difference $5.00 > Tolerance $1.00).

8.14.4 Scenario 3: Large Invoice (Pass)

• Data: An enterprise invoice with 1,000,000 underlying CostAndUsage rows.
• Values: CostAndUsage sums to $5,000,000.00. InvoiceDetail sums to $5,000,004.50. Difference is $4.50.
• Limit Calculation:
  • Statistical Limit: SQRT(1,000,000) * 0.5 * 0.01 = $5.00.
  • Floor Limit: 100 * 0.01 = $1.00.
  • Effective Tolerance: $5.00 (Greater of $5.00 and $1.00).
• Result: Pass (Difference $4.50 < Tolerance $5.00).

8.14.5 Scenario 4: Large Invoice (Fail)

• Data: An enterprise invoice with 1,000,000 underlying CostAndUsage rows with a systematic rounding error (truncation bias).
• Values: CostAndUsage sums to $5,000,000.00. InvoiceDetail sums to $5,000,015.00. Difference is $15.00.
• Limit Calculation:
  • Effective Tolerance: $5.00.
• Result: Fail (Difference $15.00 > Tolerance $5.00).