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With downcasting off, EvalNumerical loses small divisors and both ends of the exponent range

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Issue 类型
缺陷
描述清晰度
基本清楚
活跃度
活跃
技术栈
csharp
领域
backend

调研方向

Start at EvalNumerical and inspect Number.IsZero, DecimalPrecisionContext, and LostToExponentRange, comparing their behavior with the interval evaluation mentioned in the issue. Use the three expressions and affected Rubi derivative-check cases as regression coverage; done means small divisors and extreme exponent products produce finite, correct results instead of NaN or zero.

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描述

With downcasting off, EvalNumerical loses decimals at three limits:

using var _ = MathS.Settings.DowncastingEnabled.Set(false);
"1 / 1.37^(-200)".EvalNumerical()                    // NaN, not 2.21e27
"1.37^(-1500) * 1.37^1500".EvalNumerical()           // 0, not 1
"(1.37^8000 + 1) / (1.37^8000 + 2)".EvalNumerical()  // NaN, not 1.00...
  • A small divisor. A divisor below PrecisionErrorZeroRange (1e-16) counts as zero (Number.IsZero), so the quotient is NaN.
  • Both ends of the exponent range. DecimalPrecisionContext is new EContext(100, ERounding.HalfUp, -100, 1000, false), which bounds exponents to [-100, 1000]. At 100 digits, a decimal below about 1e-199 becomes zero and one above 1e1000 becomes infinite. LostToExponentRange works around this for an exact ratio, but a decimal has no exact value to fall back on.

The integrator's derivative check hit these and rejected correct antiderivatives in Rubi's suites (#1338). Five of those were large rational expressions: a factor near 1e-316 times one near 1e+316 came out 0, and a factor flushed to 0 times one saturated to infinity came out NaN. Another divided 2.40e-45 by 2.23e-91. The check now uses interval evaluation (#1497), which has none of these limits.

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