What is Catastrophic cancellation?

Loss of significant digits when subtracting two nearly equal numbers, as their leading digits cancel and the relative weight of existing rounding error grows. It is avoided by rearranging formulas.

Field: Computer Arithmetic

Catastrophic cancellation in the explanations

Questions that mention Catastrophic cancellation (2)

  1. For very large x, computing √(x + 1) − √x in floating point suffers catastrophic cancellation. Which rewrite computes it accurately?
  2. What is the phenomenon called in which subtracting two nearly equal floating-point numbers greatly reduces the significant digits?

Related terms

Arithmetic shift bfloat16 Booth's algorithm Carry-lookahead adder Carry-save adder Exponent field Fixed point Floating-point absorption FP8 Fused multiply-add

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