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Update "exact expt" #53

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bcd1ad3
Update exact expt
jpellegrini Sep 9, 2023
ded1b09
Fix typo 2.0 -> 3.0
jpellegrini Sep 9, 2023
e17f7c4
Include SCM
jpellegrini Sep 9, 2023
b4c11fc
Fix LIPS result for (expt 81 1/4)
jpellegrini Apr 7, 2024
f7af938
Fix thinko (inexact -> exact)
jpellegrini Apr 7, 2024
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78 changes: 74 additions & 4 deletions surveys/exact-expt.md
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# Exact expt

This tests whether exponentiation of exact numbers produces an exact result. The test expression was `(expt 1/3 3)`, except on systems without inexact rationals, where `(expt 3 3)` was substituted.
## Exact rational base

Exact exponentiation supported: Racket, Gauche, MIT, Gambit, Chicken with the `numbers` egg, Bigloo, Scheme48/scsh, Guile, Kawa, SISC, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, STklos, KSi, TinyScheme, Scheme 9, RScheme, S7, XLisp, Rep, UBM, Sizzle, Oaklisp, Sagittarius, Picrin, Owl Lisp, Chibi, Loko
This tests whether exponentiation of exact numbers produces an exact result.
The test expression was `(expt 1/3 3)`, except on systems without exact rationals, where `(expt 3 3)` was substituted.

Only inexact exponentiation supported: plain Chicken, SCM, NexJ, JScheme, Unlikely, Elk, SXM, Dfsch, Inlab

No support or broken support for `expt`: SigScheme, Shoe, Mini-Scheme, SIOD, Schemik, Llava, FemtoLisp, LMU
| System | `(expt 1/3 3)` | `(expt 3 3)` |
|-------------|-----------------------|--------------|
| Bigloo | | 27 |
| Biwa | | 27 |
| Chez | 1/27 | |
| Chibi | 1/27 | |
| Chicken | 1/27 | |
| Elk | | 27 |
| Gambit | 1/27 | |
| Gauche | 1/27 | |
| Guile | 1/27 | |
| Kawa | 1/27 | |
| LIPS | 1/27 | |
| Loko | 1/27 | |
| MIT | 1/27 | |
| Racket | 1/27 | |
| Sagittarius | 1/27 | |
| Scheme48 | 1/27 | |
| Scheme9 | | 27 |
| SCM | 3.7037037037037035e-2 | |
| STklos | 1/27 | |
| Tinyscheme | | 27 |


## Exact rational exponent

What happens when the exponent is an exact rational, the base is exact, and it *would* be possible to return an exact result?

The following expression was evaluated:

```
(expt 81 1/4)
```

Implementations that do not support rationals are not included.
Some Common Lisp systems were also checked, for comparison.

| system | `(expt 81 1/4)` |
|-------------|--------------------|
| Chez | 3.0 |
| Chibi | 3.0 |
| Chicken | 3 |
| Gambit | 3 |
| Gauche | 3 |
| Guile | 3.0 |
| Kawa | 3.0 |
| LIPS | 3 |
| Loko | 3.000000238418579 |
| MIT | 3.0 |
| Racket | 3.0 |
| Sagittarius | 3.0 |
| Scheme48 | 3.0000000000000004 |
| SCM | 3.0 |
| STklos | 3.0000000000000004 |
|-------------|--------------------|
| ABCL | 3.0 |
| CCL | 3.0 |
| Clisp | 3 |
| ECL | 3.0 |
| GCL | 3.0000000000000006 |
| SBCL | 3.0 |

* The systems with result `3.0` in the first column are those where `(= 3.0 (expt 81 1/4))` is true.
In the other systems, which do not return the precise `3.0` floating-point representation, the
returned value indicates at least one digit where it differs from 3.0.

* The test `(= 3.0 (expt 81 1/4))` was necessary, since we do not know if `3.0` actually means a
precise representation of the number. For example, STklos will answer `3.0`, but after changing
the default print precision with `(real-precision 50)`, it will show that the number is not
the same as `3.0`.