Where does round collide?

In music a round is a song for several voices in which each voice enters in turn with the same melody, chasing the others so the piece can loop without end: a perpetual canon in which every voice sings at the same pitch. The oldest known example is the mid-13th-century Sumer is icumen in, the Reading Rota (British Library, Harley MS 978, copied about 1250), and the form was later gathered into print in Thomas Ravenscroft's 1609 collection Pammelia. Here the referent is a musical form built from staggered voices, not a number trimmed to fit a machine, a stage of a repeated game, or a pass of a cipher over its data.[1][2]

Unit

One melody sung as a canon by several voices entering in turn

Recovery means

Not applicable

Measured by

Described by the number of voices, the entry interval between them, and the melody's length in bars

In numerical computing to round is to replace a number with the nearest value a machine can actually store, and the small discrepancy left behind is the rounding error or round-off. Von Neumann and Goldstine's 1947 Numerical inverting of matrices of high order gave the first systematic study of how these errors accumulate through a long calculation, and Turing's 1948 Rounding-off errors in matrix processes refined that analysis. The referent is an unavoidable approximation forced by finite precision, not a looping song, a stage of a repeated game, or a step inside a cipher.[3][4]

Unit

One number replaced by its nearest representable value, leaving a residual error

Recovery means

Not applicable

Measured by

Quantified by the difference between the exact and stored value, and bounded by the machine's unit in the last place

In cryptography a round is one pass of a repeated scrambling step inside a block cipher, applied over and over so many simple, reversible operations together produce output that looks random: each round mixes the data with part of the key. Feistel's 1973 Cryptography and computer privacy introduced the iterated round structure that later block ciphers such as DES and AES adopted, stacking many rounds for security. The referent is a keyed transformation repeated in sequence, counted by how many passes the cipher makes, not a looping melody, a rounded-off number, or a play in a repeated game.[5]

Unit

One keyed transformation step of the cipher, repeated a fixed number of times

Recovery means

Not applicable

Measured by

Counted as the number of rounds a cipher applies, a design parameter set against known attacks