numerical_analysis.theory.txt

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Rounding:
  - setting to closest lower|upper number among a sequence of numbers with lower precisions
     - goal: lowering precision
  - notation: ≈ or =~
  - deciding between lower|upper number:
     - directed rounding: closer to:
        - towards infinity: +∞|-∞
        - up|ceiling: +∞
           - notation: ⌈x⌉
        - down|floor: -∞
           - notation: ⌊x⌋
        - towards 0|truncating: 0
     - nearest: closer to number itself
        - if equally close, use another rounding method
           - e.g. round half up: closer to +∞
     - unbiased:
        - no bias towards +∞|-∞|0
        - often used only as nearest rounding's second rounding
        - types:
           - odd|even:
              - prefer odd|even number
              - even is often used, called convergent|statistician|Dutch|Gaussian|banker|odd-even rounding
           - alternating:
              - between rounding up|down or rounding towards infinity|0
           - random|stochastic: probability proportional to how close to each number
  - sequence can be:
     - modulo: sequence of multiples
        - rounding to simple fraction: when modulo is 1/n, result can be represented as fraction
     - discrete exponation
     - logarithmic rounding: discrete logarithm
     - preferred numbers|values|series: specific series of numbers