Why it matters

IEEE 754 is the language of numeric computing. Understanding shapes correctness in ML and finance.

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The architecture

Sign, exponent, mantissa fields.

Special values: Inf, NaN, subnormals.

Rounding modes; not associative.

IEEE 754 floating pointFormatsign, exp, mantissaSpecialsInf, NaN, subnormalPitfallsnot exact, not assocUniversal FP; NaN propagates; subnormals slow on some CPUs
IEEE 754 floating point.
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How it works end to end

FP32 vs FP64 vs BF16 vs FP16.

NaN propagates; equality fails.

Subnormals may trap or run slow.