Apply RMS exponent without underflowing 2^exp first - #52
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This was referenced Aug 25, 2026
2.0.powi(-1075) is zero even when (nf/df)*2^-1075 is the smallest subnormal. Apply MIN_POSITIVE in 1022-bit steps so a scaled sample just above 2^-1075 still publishes rms_lsb = 2^-1074. This is not MAX_ERR_LSB. Co-authored-by: Steven Giacomelli <swgiacomelli@users.noreply.github.com>
Multiplying by 2^-1022 first can make a still-normal significand subnormal and round again on the leftover exponent, turning a three-unit residual into four and the five-sample RMS into two minimum-subnormal units. Co-authored-by: Steven Giacomelli <swgiacomelli@users.noreply.github.com>
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Follow-up to merged #50. Rebased onto
epic/36-surfaces-bakeafter #51 (S5 emit).Codex P2 on
07c0575: when both BigInt limbs are truncated and the shift difference is-1075,2.0.powi(exp)underflows to 0 beforenf / dfcan lift the result into the representable subnormal range.A later P2 on that same helper: multiplying by
MIN_POSITIVEfirst can make a still-normal significand subnormal and round again on the leftover exponent.Ratio::to_f64applies2^expby taking the remainder while the significand is still normal, then multiplying by2^-1022once. That keeps a significand just above2^-1075asf64::from_bits(1), and converts the[0, 17]lerp residual to three minimum-subnormal units rather than four.Proof:
f64::from_bits(0x0c70_0000_0000_0001)at scalef64::from_bits(0x3040_0000_0000_0001)quantize to a zero 2×2,MAX_ERR_LSB = 1,rms_lsb = 2^-1074(not0)[0, 17], rows[0, 1]/[0, 1], off-knotx = f64::from_bits(0x0088_0000_0000_0000),y = 0.5,value = f64::from_bits(0x0046_9696_9696_9697): residual converts to three minimum-subnormal units,MAX_ERR_LSB = 1, five-samplerms_lsb = f64::from_bits(1)(not2)This is the operator RMS path, not the bound. This PR does not add S6–S7 work.
Verification
cargo xtask cion798d19b(full profile, not release): all runnable checks PASS; baker line budget 1725 / 1800. SKIP: secret scan (gitleaks not installed). A skip is not a pass. This is not release evidence.PR base is
epic/36-surfaces-bake.