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Computer Arithmetic

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7 domain-specific abstractions whose origin domain is Computer Arithmetic.

  • Alpha max plus beta min algorithm — A low-cost approximation to two-dimensional Euclidean magnitude using a weighted maximum plus weighted minimum of component magnitudes.
  • Fixed-precision arithmetic — Arithmetic performed in a numeric format with a fixed finite number of digits or bits, requiring rounding, overflow and exceptional-value rules.
  • Logarithmic number system — A numerical representation encoding a real number by sign and the logarithm of its magnitude.
  • Offset binary — A signed-integer encoding that stores value n as the unsigned binary representation of n plus a fixed bias K.
  • Residue number system — A numeral representation encoding an integer as its residues modulo a set of pairwise coprime moduli.
  • Signed number representations — Encoding schemes that map positive, zero and negative numbers into fixed-width digit patterns without an external sign symbol.
  • Symmetric level-index arithmetic — A numerical representation and arithmetic system using signed nested logarithmic levels to span extremely large and small magnitudes.