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rsz: Reduce error in lerp formula #7604

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Jun 17, 2025
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rsz: Reduce error in lerp formula #7604

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da967ac
rsz: Use exact min on junction slack
povik Jun 17, 2025
fabacbc
rsz: Adjust lerp formula to reduce error
povik Jun 17, 2025
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18 changes: 10 additions & 8 deletions src/rsz/src/Rebuffer2.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -828,6 +828,11 @@ Delay Rebuffer::marginedSlackThreshold(Delay slack)
return slack - (ref_slack_ - slack) * 2e-6;
}

float lerp(float a, float b, float t)
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@maliberty maliberty Jun 17, 2025

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Use std::lerp

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@povik povik Jun 17, 2025

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I purposely open-coded it so we can see the formula and reason about the rounding errors (though I'm not fully sure compiler cannot rewrite it in optimization)

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@maliberty maliberty Jun 17, 2025

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Note the std version handles more corner cases but perhaps they don't arise here.

  template<typename _Fp>
    constexpr _Fp
    __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept
    {
      if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
	return __t * __b + (1 - __t) * __a;

      if (__t == 1)
	return __b;                        // exact

      // Exact at __t=0, monotonic except near __t=1,
      // bounded, determinate, and consistent:
      const _Fp __x = __a + __t * (__b - __a);
      return (__t > 1) == (__b > __a)
	? (__b < __x ? __x : __b)
	: (__b > __x ? __x : __b);  // monotonic near __t=1
    }

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@povik povik Jun 17, 2025

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Interesting they have different cases. I assume that's just one way it may be implemented.

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@maliberty maliberty Jun 17, 2025

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They handle overflow for one. The core formula is similar.

{
return a + (b - a) * t;
}

// Recover area on a rebuffering choice without regressing timing
BufferedNetPtr Rebuffer::recoverArea(const BufferedNetPtr& root,
Delay slack_target,
Expand Down Expand Up @@ -877,9 +882,8 @@ BufferedNetPtr Rebuffer::recoverArea(const BufferedNetPtr& root,
opts = recurse(inner, 0);
}

Delay threshold = marginedSlackThreshold(
(slack_target + node->arrivalDelay()) * alpha
+ node->slack() * (1.0 - alpha));
Delay threshold = marginedSlackThreshold(lerp(
node->slack(), slack_target + node->arrivalDelay(), alpha));
insertBufferOptions(opts,
level,
/*next_segment_wl=*/upstream_wl,
Expand All @@ -892,9 +896,8 @@ BufferedNetPtr Rebuffer::recoverArea(const BufferedNetPtr& root,
const BnetSeq& left_opts = recurse(node->ref(), upstream_wl);
const BnetSeq& right_opts = recurse(node->ref2(), upstream_wl);

Delay threshold = marginedSlackThreshold(
(slack_target + node->arrivalDelay()) * alpha
+ node->slack() * (1.0 - alpha));
Delay threshold = marginedSlackThreshold(lerp(
node->slack(), slack_target + node->arrivalDelay(), alpha));
BnetMetrics assured_envelope = node->metrics().withSlack(threshold);
BnetPtr assured_fallback;

Expand Down Expand Up @@ -1030,10 +1033,9 @@ void Rebuffer::annotateTiming(const BnetPtr& tree)
int ret = recurse(bnet->ref()) + recurse(bnet->ref2());
const BnetPtr& p = bnet->ref();
const BnetPtr& q = bnet->ref2();
const BnetPtr& min_req = fuzzyLess(p->slack(), q->slack()) ? p : q;
bnet->setSlackTransition(
combinedTransition(p->slackTransition(), q->slackTransition()));
bnet->setSlack(min_req->slack());
bnet->setSlack(std::min(p->slack(), q->slack()));
bnet->setCapacitance(p->cap() + q->cap());
return ret;
}
Expand Down