Numeric Representation & Encoding Schemes

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Abstractions about encoding numbers for computation, covering signed and biased integer encodings (offset binary, signed number representations), alternative arithmetic systems (logarithmic number system, residue number system, symmetric level-index arithmetic), and approximation techniques like the alpha max plus beta min algorithm.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• 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.