Improve automatic evaluation of arg(exp()) #25953

gschintgen · 2023-12-04T19:46:52Z

References to other Issues or PRs

Brief description of what is fixed or changed

Before this commit, expressions of the form arg(exp()) are not special cased and the argument to arg(), including exp(), ends up being split apart by .as_real_imag(). The real and imaginary parts are then passed to atan2. This often leads to poor results. See issue #17300 for examples.

This commit adds a special case for arg(exp()) to better handle these expressions.

BEFORE:

>>> arg(exp(1 + 5*I))
atan(sin(5)/cos(5))
>>> arg(exp(1 + I*pi/8))
atan(sqrt(1/2 - sqrt(2)/4)/sqrt(sqrt(2)/4 + 1/2))

AFTER:

>>> arg(exp(1 + 5*I))
5 - 2⋅π
>>> arg(exp(1 + I*pi/8))
π
-
8

Other comments

Release Notes

functions
- Improved automatic evaluation of arg(exp()).

Fixes sympy#17300. Before this commit, expressions of the form arg(exp()) are not special cased and the argument to arg(), including exp(), ends up being split apart by .as_real_imag(). The real and imaginary parts are then passed to atan2. This often leads to poor results. See issue sympy#17300 for examples. This commit adds a special case for arg(exp()) to better handle these expressions. BEFORE: >>> arg(exp(1 + 5*I)) atan(sin(5)/cos(5)) >>> arg(exp(1 + I*pi/8)) atan(sqrt(1/2 - sqrt(2)/4)/sqrt(sqrt(2)/4 + 1/2)) AFTER: >>> arg(exp(1 + 5*I)) 5 - 2⋅π >>> arg(exp(1 + I*pi/8)) π - 8

sympy-bot · 2023-12-04T19:47:00Z

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functions
- Improved automatic evaluation of arg(exp()). (#25953 by @gschintgen)

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#### References to other Issues or PRs
<!-- If this pull request fixes an issue, write "Fixes #NNNN" in that exact
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Fixes #17300

#### Brief description of what is fixed or changed

Before this commit, expressions of the form `arg(exp())` are not special cased and the argument to `arg()`, including `exp()`, ends up being split apart by `.as_real_imag()`. The real and imaginary parts are then passed to `atan2`. This often leads to poor results. See issue #17300 for examples.

This commit adds a special case for `arg(exp())` to better handle these expressions.

BEFORE:
```
>>> arg(exp(1 + 5*I))
atan(sin(5)/cos(5))
>>> arg(exp(1 + I*pi/8))
atan(sqrt(1/2 - sqrt(2)/4)/sqrt(sqrt(2)/4 + 1/2))
```
AFTER:
```
>>> arg(exp(1 + 5*I))
5 - 2⋅π
>>> arg(exp(1 + I*pi/8))
π
-
8
```

#### Other comments


#### Release Notes

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  * Added a new solver for logarithmic equations.

* functions
  * Fixed a bug with log of integers. Formerly, `log(-x)` incorrectly gave `-log(x)`.

* physics.units
  * Corrected a semantical error in the conversion between volt and statvolt which
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<!-- BEGIN RELEASE NOTES -->
* functions
  * Improved automatic evaluation of `arg(exp())`.

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Update

The release notes on the wiki have been updated.

github-actions · 2023-12-04T20:32:11Z

Benchmark results from GitHub Actions

Lower numbers are good, higher numbers are bad. A ratio less than 1
means a speed up and greater than 1 means a slowdown. Green lines
beginning with + are slowdowns (the PR is slower then master or
master is slower than the previous release). Red lines beginning
with - are speedups.

Significantly changed benchmark results (PR vs master)

Significantly changed benchmark results (master vs previous release)

| Change   | Before [a00718ba]    | After [4adf8d24]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 67.5±0.7ms           | 43.5±0.3ms          |    0.64 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 67.3±1ms             | 44.1±0.4ms          |    0.66 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 18.0±0.2μs           | 29.1±0.4μs          |    1.62 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.18±0.03ms          | 2.83±0.03ms         |    0.55 | logic.LogicSuite.time_load_file                                      |
| -        | 73.6±0.2ms           | 28.1±0.1ms          |    0.38 | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 25.8±0.08ms          | 16.7±0.05ms         |    0.65 | polys.TimeGCD_GaussInt.time_op(1, 'expr')                            |
| -        | 72.1±0.6ms           | 28.4±0.1ms          |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 254±1ms              | 123±0.9ms           |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 255±2ms              | 126±1ms             |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 661±5ms              | 374±2ms             |    0.57 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 660±3ms              | 369±3ms             |    0.56 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 492±2μs              | 281±2μs             |    0.57 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.74±0.01ms          | 1.05±0ms            |    0.6  | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.71±0.02ms          | 3.06±0.02ms         |    0.54 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 449±2μs              | 233±2μs             |    0.52 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.46±0.01ms          | 658±4μs             |    0.45 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.83±0.02ms          | 1.62±0.01ms         |    0.33 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 372±2μs              | 202±2μs             |    0.54 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.43±0.02ms          | 1.21±0.01ms         |    0.5  | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 10.0±0.07ms          | 4.24±0.02ms         |    0.42 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 360±2μs              | 165±0.9μs           |    0.46 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.47±0.01ms          | 877±10μs            |    0.36 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.39±0.07ms          | 2.59±0.02ms         |    0.28 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 999±10μs             | 419±2μs             |    0.42 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.71±0.02ms          | 499±3μs             |    0.29 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 5.68±0.05ms          | 1.76±0.01ms         |    0.31 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.27±0.04ms          | 1.50±0ms            |    0.18 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 288±2μs              | 63.1±0.5μs          |    0.22 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.29±0.03ms          | 389±2μs             |    0.12 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 3.90±0.02ms          | 279±2μs             |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 6.78±0.1ms           | 1.23±0.01ms         |    0.18 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.47±0.05ms          | 838±4μs             |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 5.00±0.03ms          | 2.96±0.01ms         |    0.59 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 11.8±0.09ms          | 6.38±0.03ms         |    0.54 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.2±0.1ms           | 9.05±0.03ms         |    0.41 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.26±0.01ms          | 860±2μs             |    0.16 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.6±0.03ms          | 7.04±0.04ms         |    0.56 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 98.7±0.7ms           | 25.4±0.2ms          |    0.26 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 165±2ms              | 54.4±0.2ms          |    0.33 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 176±2μs              | 114±3μs             |    0.64 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 366±2μs              | 213±2μs             |    0.58 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.20±0.01ms          | 823±3μs             |    0.2  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.22±0.04ms          | 377±1μs             |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 19.2±0.09ms          | 2.78±0.01ms         |    0.14 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 22.2±0.2ms           | 623±2μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 490±5μs              | 132±0.8μs           |    0.27 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.64±0.06ms          | 601±3μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.22±0.03ms          | 136±0.6μs           |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 12.7±0.1ms           | 1.29±0ms            |    0.1  | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 13.4±0.09ms          | 138±1μs             |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 131±0.3μs            | 74.1±0.4μs          |    0.57 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 251±2μs              | 87.5±1μs            |    0.35 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 24.1±0.06ms          | 10.2±0.03ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |

Full benchmark results can be found as artifacts in GitHub Actions
(click on checks at the top of the PR).

smichr · 2023-12-05T03:38:04Z

Looks ok to me. I don't prefer the i_ variable but understand that in context it is probably being distinguished from i (or I). Just a nit.

Will commit in 12 hours if there is no other argument. This is a nice clean up to automatic evaluation of such expressions!

sympy/functions/elementary/complexes.py

oscarbenjamin reviewed Dec 5, 2023

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sympy/functions/elementary/complexes.py Show resolved Hide resolved

smichr merged commit cec82f2 into sympy:master Dec 5, 2023

gschintgen deleted the fix-arg-exp branch December 5, 2023 19:09

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gschintgen commented Dec 4, 2023

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