Abstract: In a general aspect, a method can include: executing an operation of a program that loads an arbitrarily chosen value of an initial data item of a series of ordered data; executing a series of calculation operations distributed in the program, that calculate a current data item based on a preceding data item; performing a final calculation operation of the series of operations that calculates a final data item of the data series; and executing an operation of the program that detects a program execution error by comparing the current data item of the data series with an expected value of the current data item or the final data item, the final data item having an expected value that is independent of the number of data items in the data series and is calculated based on the current data item of the data series and a final compensation data item.

Abstract: In a general aspect, a method can include: executing an operation of a program that loads an arbitrarily chosen value of an initial data item of a series of ordered data; executing a series of calculation operations distributed in the program, that calculate a current data item based on a preceding data item; performing a final calculation operation of the series of operations that calculates a final data item of the data series; and executing an operation of the program that detects a program execution error by comparing the current data item of the data series with an expected value of the current data item or the final data item, the final data item having an expected value that is independent of the number of data items in the data series and is calculated based on the current data item of the data series and a final compensation data item.