FA-5463 / Integer arithmetic / Member archive

Arithmetic progression sum · case 03

The last term is multiplied by the count instead of using the endpoint average.

Member previewVariant 3 · 3 implementations · 4 checks per implementation

Case contract

Integer arguments; denominators, steps, moduli, and bit widths are positive. Unsigned word inputs fit the specified width except where masking is explicitly the operation. Sequence sizes are nonnegative. a and d may be signed; n>=0. Sum n terms starting with a and common difference d. Exact operational definition: n*(2*a+(n-1)*d)//2

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Integer mathematics results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: (2, 3, 4)	`44`	`26`	Failed

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