<P> There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digits each (ca . 16.2 kB). An arithmetic unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots . Initially (1838) it was conceived as a difference engine curved back upon itself, in a generally circular layout, with the long store exiting off to one side . Later drawings (1858) depict a regularized grid layout . Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify . </P> <P> The programming language to be employed by users was akin to modern day assembly languages . Loops and conditional branching were possible, and so the language as conceived would have been Turing - complete as later defined by Alan Turing . Three different types of punch cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back . There were three separate readers for the three types of cards . Babbage developed some two dozen programs for the Analytical Engine between 1837 and 1840, and one program later . These programs treat polynomials, iterative formulas, Gaussian elimination, and Bernoulli numbers . </P> <P> In 1842, the Italian mathematician Luigi Federico Menabrea published a description of the engine based on a lecture by Babbage in French . In 1843, the description was translated into English and extensively annotated by Ada Lovelace, who had become interested in the engine eight years earlier . In recognition of her additions to Menabrea's paper, which included a way to calculate Bernoulli numbers using the machine, she has been described as the first computer programmer . </P> <P> Late in his life, Babbage sought ways to build a simplified version of the machine, and assembled a small part of it before his death in 1871 . </P>

Who wrote a program for the analytical engine to calculate a series of bernoulli numbers