RealDoubleField: Exponentiation should not raise exceptions

[mkoeppe]

(from #32779)

RDF contains infinities and NaNs, which can appear as results of arithmetic operations.

sage: RDF(1.0)/RDF(0.0)
+infinity
sage: RDF(0.0)/RDF(0.0)
NaN

This is consistent with RR:

sage: RR(1.0)/RR(0.0)
+infinity
sage: RR(0.0)/RR(0.0)
NaN

(but is in contrast to float, which gives ZeroDivisionError).

However, RealDoubleElement_gsl.__pow__ raises exceptions:

sage: RDF('0.0').__pow__(RDF('-1'))
ZeroDivisionError: 0.0 cannot be raised to a negative power
sage: RDF('-0.0').__pow__(RDF('-1'))
ZeroDivisionError: 0.0 cannot be raised to a negative power
sage: RDF('-1').__pow__(RDF('0.5'))
ValueError: negative number cannot be raised to a fractional power

... in contrast to the other arithmetic operations and in contrast to RR:

sage: RR('0.0').__pow__(RR('-1'))
+infinity
age: RR('-0.0').__pow__(RR('-1'))
-infinity
sage: RR('-1').__pow__(RR('0.5'))
6.12323399573677e-17 + 1.00000000000000*I

Moreover, many RDF element methods do not handle -0.0 correctly.

CC: @sagetrac-tmonteil @dimpase @videlec @tscrim @slel

Component: basic arithmetic

Author: Matthias Koeppe, ...

Branch/Commit: u/mkoeppe/realdoublefield__exponentiation_should_not_raise_exceptions @ cf5a248

Issue created by migration from https://trac.sagemath.org/ticket/32963

[mkoeppe]

Description changed:

--- 
+++ 
@@ -20,17 +20,21 @@
 However, `RealDoubleElement_gsl.__pow__` raises exceptions:
 
 ```
-sage: RDF(0).__pow__(RDF(-1))
+sage: RDF('0.0').__pow__(RDF('-1'))
 ZeroDivisionError: 0.0 cannot be raised to a negative power
-sage: RDF(-1).__pow__(RDF(0.5))
+sage: RDF('-0.0').__pow__(RDF('-1'))
+ZeroDivisionError: 0.0 cannot be raised to a negative power
+sage: RDF('-1').__pow__(RDF('0.5'))
 ValueError: negative number cannot be raised to a fractional power
 ```
 ... in contrast to the other arithmetic operations and in contrast to `RR`:
 
 ```
-sage: RR(0).__pow__(RR(-1))
+sage: RR('0.0').__pow__(RR('-1'))
 +infinity
-sage: RR(-1).__pow__(RR(0.5))
+age: RR('-0.0').__pow__(RR('-1'))
+-infinity
+sage: RR('-1').__pow__(RR('0.5'))
 6.12323399573677e-17 + 1.00000000000000*I
 ```
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -16,6 +16,7 @@
 sage: RR(0.0)/RR(0.0)
 NaN
 ```
+(but is in contrast to `float`, which gives `ZeroDivisionError`).
 
 However, `RealDoubleElement_gsl.__pow__` raises exceptions:
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -39,3 +39,4 @@
 6.12323399573677e-17 + 1.00000000000000*I
 ```
 
+Moreover, many `RDF` element methods do not handle -0.0 correctly.

[mkoeppe]

Branch: u/mkoeppe/realdoublefield__exponentiation_should_not_raise_exceptions

[slel]

Commit: cf5a248

[slel]

Author: Matthias Koeppe

[slel]

Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 (from #32779)
 
-`RDF` contains infinities and NaNs, which can appear as results of arithmetic operations.
+`RDF` contains infinities and `NaN`s, which can appear as results of arithmetic operations.
 
 ```
 sage: RDF(1.0)/RDF(0.0)

[slel]

comment:5

@mkoeppe, did you mean to set this to "needs review"?

---

New commits:

cf5a248

RealDoubleElement_gsl.__pow_double: Do not raise exception on +/-0.0**negative

[mkoeppe]

Changed author from Matthias Koeppe to Matthias Koeppe, ...

[mkoeppe]

comment:6

No, it's not quite ready yet. I think there are still some corner cases, and test coverage should be improved. Any help is welcome