Welcome to Ordner, a catalog of real numbers in Fungrim. Ordner is indexed by 30-digit floating-point decimal keys such as `0.707106781186547524400844362105`. For each key, Ordner lists constant symbolic expressions (for example `Div(1, Sqrt(2))`) with numerical value within ±1 ulp of the key. For each expression `x`, Ordner also links to the Fungrim entries where `x` appears. Ordner currently contains 3249 decimal keys (of which 1462 are integers) and 5847 symbolic expressions.

Find out which real numbers have real significance!

Browse [0, ∞). To keep the page sizes reasonable, the listing is split into intervals with a few hundred keys per page. The splitting points are not permanent and will change when Fungrim is updated.

- [
`0.00000000000000000000000000000, 0.381966011250105151795413165634`] - [
`0.381966011250105151795413165634, 1.00000005960818905125947961244`] - [
`1.00000005960818905125947961244, 2.07440022977064900739949056948`] - [
`2.07440022977064900739949056948, 6.28318530717958647692528676656`] - [
`6.28318530717958647692528676656, 77.1448400688748053726826648563`] - [
`77.1448400688748053726826648563, 218.000000000000000000000000000`] - [
`218.000000000000000000000000000, 369.000000000000000000000000000`] - [
`369.000000000000000000000000000, 528.406213900000000000000000000`] - [
`528.406213900000000000000000000, 786.461147500000000000000000000`] - [
`786.461147500000000000000000000, 30240.0000000000000000000000000`] - [
`30240.0000000000000000000000000, 232792560.000000000000000000000`] - [
`232792560.000000000000000000000, 279238341033925.000000000000000`] - [
`279238341033925.000000000000000, ∞`)

Ordner is generated automatically by searching all Fungrim formulas for constant subexpressions that Arb can evaluate numerically. Only expressions that appear explicitly in Fungrim are covered, with the following exceptions. For tables with numerical data, all the listed instances of the ground expression are included. All decimal keys in Ordner are normalized to be nonnegative, so expressions `x` representing negative values are indexed as `Neg(x)` in Ordner. Complex numbers are indexed by the real and imaginary parts (`Re(x)`, `Im(x)`), as well as the absolute value and complex argument (`Abs(x)`, `Arg(x)`) when both the real and imaginary parts are nonzero. The number 0 is a special case: a vanishing expression is only included when the numerical evaluation code can prove that the expression exactly represents 0. Some trivially zero-valued expressions are excluded to prevent bloat. Finally, since the Fungrim formula language normally uses `Exp(x)` instead of `Pow(ConstE, x)` to represent the exponential function, formulas containing `Exp(...)` are listed under `2.71828182845904523536028747135` as a special case, so as to represent this fundamental constant fairly!

ORDNER stands for Online Real Decimal Number Encyclopedia Reference.

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC