Write exact results past the range of a double (closes #16)
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An exact result outside the normal range of a double, such as 2^1200, 10^400 or 2^-1200, was refused because format wrote every result through float64. Such a result is now written from its exact value, rounded to 17 significant digits with trailing zeros dropped, through a big.Float precise enough to round as the exact value would. Results inside the range are written as before, and a power computed in float64 must still be a normal double. The tests check the written text of these results, the refusals just past the 4096-bit limit, and the time taken to write the largest and smallest numbers under it. Model: opus-5-5
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@@ -335,16 +335,20 @@ container.
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refused, exact powers are capped, and every number is held as a
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fraction, whole numbers too, under the 4096-bit limit below, so a
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message cannot make the bot do unbounded work. Whole numbers below
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10<sup>21</sup> are written exactly; other results in the shortest
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form that reads back as the same double, in exponent notation from
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10<sup>21</sup> up and below 10<sup>-6</sup>. Refused as too large or
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too small: any number whose numerator or denominator reaches 4096
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bits, wherever it appears, as `go/constant` rounds a fraction that
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grows that large (`1e-1300 + 1`); a power computed as a double whose
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base or result is outside the normal range of a double, about 2.2e-308
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to 1.8e308 in magnitude, where a double keeps all its digits
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(`1e-400^0.5`); and a result other than zero outside that range, as it
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is written through a double (`1e400`, `2^-1400`).
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10<sup>21</sup> are written exactly. Other results inside the normal
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range of a double, about 2.2e-308 to 1.8e308 in magnitude, where a
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double keeps all its digits, are written in the shortest form that
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reads back as the same double, in exponent notation from
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10<sup>21</sup> up and below 10<sup>-6</sup>. Results outside that
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range are written from their exact value in exponent notation, rounded
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to 17 significant digits, the most the shortest form of a double
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takes, with trailing zeros dropped: `2^1200` is
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`1.7218479456385751e+361`, `10^400` is `1e+400` and `2^-1074` is
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`4.9406564584124654e-324`. Refused as too large or too small: any
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number whose numerator or denominator reaches 4096 bits, wherever it
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appears, as `go/constant` rounds a fraction that grows that large
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(`2^4095`, `1e-1300 + 1`); and a power computed as a double whose base
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or result is outside the normal range of a double (`1e-400^0.5`).
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- **Failure is an exit.** If the chat client exits or the connection to
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it drops, the bot exits with an error and the container's restart
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policy starts both again. `SIGTERM` stops the bot, which stops the
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