Forward to the Past: The Case for Uniformly Strict Floating Point Arithmetic on the JVM
summary
Argues for restoring always-strict IEEE floating-point semantics via JEP 306, demonstrating a concrete double-rounding bug on x87 vs SSE by constructing a pair of hex doubles whose product falls on the subnormal-to-normal boundary and producing two different results. Shows the practical fix used on x87 — an x87 store-reload scaling trick (multiply by 2^-15360, operate, then rescale) — and notes modern x86 uses SSE2 so strict semantics cost no perf. Mentions fused-multiply-add API complications.
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chapters (17)
- 0:00Intro
- 0:34Overview
- 5:02Specifications and semantics Java source code
- 13:41The games of mathematics
- 15:09Levels of floating point
- 15:48Encoding and decoding IEEE 754 floating-point
- 20:43Round to nearest even rounding mode, illustrated
- 24:39Fun facts about floating-point arithmetic
- 25:39Completing floating point arithmetic
- 26:23Design of x87 floating point instructions, circa 1977
- 31:56A potential problem or a real problem?
- 36:28Toy example
- 36:50Abbreviated & abridged history of Java FP Proposals
- 38:54Features of default floating-point semantics
- 39:55Complexity in semantics or code generation
- 40:37JEP 306: Restore always strict floating point semantics
- 42:40Example: fused multiply add (fma)
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