So apparently some folder/package named -ip + some numbers was installed at `c:\python39\lib\site-packages`.

Once I checked my site packages at the link it provided and removed the `ip(random numbers)` package it stopped giving me errors.


I&#39;m trying to initiate a Springboot project using Open Jdk 15, Springboot 2.6.0, Springfox 3.
We are working on a project that replaced Netty as the webserver and used Jetty instead because we do not need a non-blocking environment.

In the code we depend primarily on Reactor API (Flux, Mono), so we can not remove `org.springframework.boot:spring-boot-starter-webflux` dependencies.

I replicated the problem that we have in a new project.: https://github.com/jvacaq/spring-fox.

I figured out that these lines in our build.gradle file are the origin of the problem.

```
compile(&quot;org.springframework.boot:spring-boot-starter-web&quot;) {
   exclude module: &quot;spring-boot-starter-tomcat&quot;
}
compile(&quot;org.springframework.boot:spring-boot-starter-jetty&quot;)
```

Here is the `build.gradle` file:
```
plugins {
	id &#39;org.springframework.boot&#39; version &#39;2.6.0&#39;
	id &#39;io.spring.dependency-management&#39; version &#39;1.0.11.RELEASE&#39;
	id &#39;java&#39;
}

group = &#39;com.example&#39;
version = &#39;0.0.1-SNAPSHOT&#39;
sourceCompatibility = &#39;11&#39;

repositories {
	mavenCentral()
}

dependencies {
	compile(&quot;org.springframework.boot:spring-boot-starter-web&quot;) {
		exclude module: &quot;spring-boot-starter-tomcat&quot;
	}
	compile(&quot;org.springframework.boot:spring-boot-starter-jetty&quot;)
	implementation &#39;org.springframework.boot:spring-boot-starter-webflux&#39;
	testImplementation &#39;org.springframework.boot:spring-boot-starter-test&#39;
	testImplementation &#39;io.projectreactor:reactor-test&#39;
	implementation &quot;io.springfox:springfox-boot-starter:3.0.0&quot;
}

test {
	useJUnitPlatform()
}

```

I issued the command `gradle clean bootrun`. The result is this error:
```
 gradle clean bootrun                                                                                                                                                                                                               

&gt; Task :bootRun FAILED

  .   ____          _            __ _ _
 /\\ / ___&#39;_ __ _ _(_)_ __  __ _ \ \ \ \
( ( )\___ | &#39;_ | &#39;_| | &#39;_ \/ _` | \ \ \ \
 \\/  ___)| |_)| | | | | || (_| |  ) ) ) )
  &#39;  |____| .__|_| |_|_| |_\__, | / / / /
 =========|_|==============|___/=/_/_/_/
 :: Spring Boot ::                (v2.6.0)

2021-11-19 09:41:06.665  INFO 16666 --- [           main] c.e.springfox.SpringFoxApplication       : Starting SpringFoxApplication using Java 15.0.2 on advance-Inspiron-5379 with PID 16666 (/home/advance/projects/spring-fox/build/classes/java/main started by advance in /home/advance/projects/spring-fox)
2021-11-19 09:41:06.666  INFO 16666 --- [           main] c.e.springfox.SpringFoxApplication       : No active profile set, falling back to default profiles: default
2021-11-19 09:41:07.294  INFO 16666 --- [           main] org.eclipse.jetty.util.log               : Logging initialized @1132ms to org.eclipse.jetty.util.log.Slf4jLog
2021-11-19 09:41:07.396  INFO 16666 --- [           main] o.s.b.w.e.j.JettyServletWebServerFactory : Server initialized with port: 8080
2021-11-19 09:41:07.398  INFO 16666 --- [           main] org.eclipse.jetty.server.Server          : jetty-9.4.44.v20210927; built: 2021-09-27T23:02:44.612Z; git: 8da83308eeca865e495e53ef315a249d63ba9332; jvm 15.0.2+7-27
2021-11-19 09:41:07.417  INFO 16666 --- [           main] o.e.j.s.h.ContextHandler.application     : Initializing Spring embedded WebApplicationContext
2021-11-19 09:41:07.417  INFO 16666 --- [           main] w.s.c.ServletWebServerApplicationContext : Root WebApplicationContext: initialization completed in 713 ms
2021-11-19 09:41:07.474  INFO 16666 --- [           main] org.eclipse.jetty.server.session         : DefaultSessionIdManager workerName=node0
2021-11-19 09:41:07.474  INFO 16666 --- [           main] org.eclipse.jetty.server.session         : No SessionScavenger set, using defaults
2021-11-19 09:41:07.475  INFO 16666 --- [           main] org.eclipse.jetty.server.session         : node0 Scavenging every 660000ms
2021-11-19 09:41:07.480  INFO 16666 --- [           main] o.e.jetty.server.handler.ContextHandler  : Started o.s.b.w.e.j.JettyEmbeddedWebAppContext@6aa3bfc{application,/,[file:///tmp/jetty-docbase.8080.2024342829220941812/, jar:file:/home/advance/.gradle/caches/modules-2/files-2.1/io.springfox/springfox-swagger-ui/3.0.0/1e665fbe22148f7c36fa8a08e515a0047cd4390b/springfox-swagger-ui-3.0.0.jar!/META-INF/resources],AVAILABLE}
2021-11-19 09:41:07.480  INFO 16666 --- [           main] org.eclipse.jetty.server.Server          : Started @1318ms
2021-11-19 09:41:07.920  INFO 16666 --- [           main] o.e.j.s.h.ContextHandler.application     : Initializing Spring DispatcherServlet &#39;dispatcherServlet&#39;
2021-11-19 09:41:07.920  INFO 16666 --- [           main] o.s.web.servlet.DispatcherServlet        : Initializing Servlet &#39;dispatcherServlet&#39;
2021-11-19 09:41:07.921  INFO 16666 --- [           main] o.s.web.servlet.DispatcherServlet        : Completed initialization in 1 ms
2021-11-19 09:41:07.931  INFO 16666 --- [           main] o.e.jetty.server.AbstractConnector       : Started ServerConnector@2643d762{HTTP/1.1, (http/1.1)}{0.0.0.0:8080}
2021-11-19 09:41:07.932  INFO 16666 --- [           main] o.s.b.web.embedded.jetty.JettyWebServer  : Jetty started on port(s) 8080 (http/1.1) with context path &#39;/&#39;
2021-11-19 09:41:07.934  WARN 16666 --- [           main] ConfigServletWebServerApplicationContext : Exception encountered during context initialization - cancelling refresh attempt: org.springframework.context.ApplicationContextException: Failed to start bean &#39;documentationPluginsBootstrapper&#39;; nested exception is java.lang.NullPointerException: Cannot invoke &quot;org.springframework.web.servlet.mvc.condition.PatternsRequestCondition.getPatterns()&quot; because &quot;this.condition&quot; is null
2021-11-19 09:41:07.949  INFO 16666 --- [           main] o.e.jetty.server.AbstractConnector       : Stopped ServerConnector@2643d762{HTTP/1.1, (http/1.1)}{0.0.0.0:8080}
2021-11-19 09:41:07.950  INFO 16666 --- [           main] org.eclipse.jetty.server.session         : node0 Stopped scavenging
2021-11-19 09:41:07.951  INFO 16666 --- [           main] o.e.j.s.h.ContextHandler.application     : Destroying Spring FrameworkServlet &#39;dispatcherServlet&#39;
2021-11-19 09:41:07.951  INFO 16666 --- [           main] o.e.jetty.server.handler.ContextHandler  : Stopped o.s.b.w.e.j.JettyEmbeddedWebAppContext@6aa3bfc{application,/,[file:///tmp/jetty-docbase.8080.2024342829220941812/, jar:file:/home/advance/.gradle/caches/modules-2/files-2.1/io.springfox/springfox-swagger-ui/3.0.0/1e665fbe22148f7c36fa8a08e515a0047cd4390b/springfox-swagger-ui-3.0.0.jar!/META-INF/resources],STOPPED}
2021-11-19 09:41:07.958  INFO 16666 --- [           main] ConditionEvaluationReportLoggingListener : 

Error starting ApplicationContext. To display the conditions report re-run your application with &#39;debug&#39; enabled.
2021-11-19 09:41:07.970 ERROR 16666 --- [           main] o.s.boot.SpringApplication               : Application run failed

org.springframework.context.ApplicationContextException: Failed to start bean &#39;documentationPluginsBootstrapper&#39;; nested exception is java.lang.NullPointerException: Cannot invoke &quot;org.springframework.web.servlet.mvc.condition.PatternsRequestCondition.getPatterns()&quot; because &quot;this.condition&quot; is null
        at org.springframework.context.support.DefaultLifecycleProcessor.doStart(DefaultLifecycleProcessor.java:181) ~[spring-context-5.3.13.jar:5.3.13]
        at org.springframework.context.support.DefaultLifecycleProcessor.access$200(DefaultLifecycleProcessor.java:54) ~[spring-context-5.3.13.jar:5.3.13]
        at org.springframework.context.support.DefaultLifecycleProcessor$LifecycleGroup.start(DefaultLifecycleProcessor.java:356) ~[spring-context-5.3.13.jar:5.3.13]
        at java.base/java.lang.Iterable.forEach(Iterable.java:75) ~[na:na]
        at org.springframework.context.support.DefaultLifecycleProcessor.startBeans(DefaultLifecycleProcessor.java:155) ~[spring-context-5.3.13.jar:5.3.13]
        at org.springframework.context.support.DefaultLifecycleProcessor.onRefresh(DefaultLifecycleProcessor.java:123) ~[spring-context-5.3.13.jar:5.3.13]
        at org.springframework.context.support.AbstractApplicationContext.finishRefresh(AbstractApplicationContext.java:935) ~[spring-context-5.3.13.jar:5.3.13]
        at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:586) ~[spring-context-5.3.13.jar:5.3.13]
        at org.springframework.boot.web.servlet.context.ServletWebServerApplicationContext.refresh(ServletWebServerApplicationContext.java:145) ~[spring-boot-2.6.0.jar:2.6.0]
        at org.springframework.boot.SpringApplication.refresh(SpringApplication.java:730) ~[spring-boot-2.6.0.jar:2.6.0]
        at org.springframework.boot.SpringApplication.refreshContext(SpringApplication.java:412) ~[spring-boot-2.6.0.jar:2.6.0]
        at org.springframework.boot.SpringApplication.run(SpringApplication.java:302) ~[spring-boot-2.6.0.jar:2.6.0]
        at org.springframework.boot.SpringApplication.run(SpringApplication.java:1301) ~[spring-boot-2.6.0.jar:2.6.0]
        at org.springframework.boot.SpringApplication.run(SpringApplication.java:1290) ~[spring-boot-2.6.0.jar:2.6.0]
        at com.example.springfox.SpringFoxApplication.main(SpringFoxApplication.java:10) ~[main/:na]
Caused by: java.lang.NullPointerException: Cannot invoke &quot;org.springframework.web.servlet.mvc.condition.PatternsRequestCondition.getPatterns()&quot; because &quot;this.condition&quot; is null
        at springfox.documentation.spring.web.WebMvcPatternsRequestConditionWrapper.getPatterns(WebMvcPatternsRequestConditionWrapper.java:56) ~[springfox-spring-webmvc-3.0.0.jar:3.0.0]
        at springfox.documentation.RequestHandler.sortedPaths(RequestHandler.java:113) ~[springfox-core-3.0.0.jar:3.0.0]
        at springfox.documentation.spi.service.contexts.Orderings.lambda$byPatternsCondition$3(Orderings.java:89) ~[springfox-spi-3.0.0.jar:3.0.0]
        at java.base/java.util.Comparator.lambda$comparing$77a9974f$1(Comparator.java:469) ~[na:na]
        at java.base/java.util.TimSort.countRunAndMakeAscending(TimSort.java:355) ~[na:na]
        at java.base/java.util.TimSort.sort(TimSort.java:220) ~[na:na]
        at java.base/java.util.Arrays.sort(Arrays.java:1306) ~[na:na]
        at java.base/java.util.ArrayList.sort(ArrayList.java:1721) ~[na:na]
        at java.base/java.util.stream.SortedOps$RefSortingSink.end(SortedOps.java:392) ~[na:na]
        at java.base/java.util.stream.Sink$ChainedReference.end(Sink.java:258) ~[na:na]
        at java.base/java.util.stream.Sink$ChainedReference.end(Sink.java:258) ~[na:na]
        at java.base/java.util.stream.Sink$ChainedReference.end(Sink.java:258) ~[na:na]
        at java.base/java.util.stream.Sink$ChainedReference.end(Sink.java:258) ~[na:na]
        at java.base/java.util.stream.AbstractPipeline.copyInto(AbstractPipeline.java:485) ~[na:na]
        at java.base/java.util.stream.AbstractPipeline.wrapAndCopyInto(AbstractPipeline.java:474) ~[na:na]
        at java.base/java.util.stream.ReduceOps$ReduceOp.evaluateSequential(ReduceOps.java:913) ~[na:na]
        at java.base/java.util.stream.AbstractPipeline.evaluate(AbstractPipeline.java:234) ~[na:na]
        at java.base/java.util.stream.ReferencePipeline.collect(ReferencePipeline.java:578) ~[na:na]
        at springfox.documentation.spring.web.plugins.WebMvcRequestHandlerProvider.requestHandlers(WebMvcRequestHandlerProvider.java:81) ~[springfox-spring-webmvc-3.0.0.jar:3.0.0]
        at java.base/java.util.stream.ReferencePipeline$3$1.accept(ReferencePipeline.java:195) ~[na:na]
        at java.base/java.util.ArrayList$ArrayListSpliterator.forEachRemaining(ArrayList.java:1625) ~[na:na]
        at java.base/java.util.stream.AbstractPipeline.copyInto(AbstractPipeline.java:484) ~[na:na]
        at java.base/java.util.stream.AbstractPipeline.wrapAndCopyInto(AbstractPipeline.java:474) ~[na:na]
        at java.base/java.util.stream.ReduceOps$ReduceOp.evaluateSequential(ReduceOps.java:913) ~[na:na]
        at java.base/java.util.stream.AbstractPipeline.evaluate(AbstractPipeline.java:234) ~[na:na]
        at java.base/java.util.stream.ReferencePipeline.collect(ReferencePipeline.java:578) ~[na:na]
        at springfox.documentation.spring.web.plugins.AbstractDocumentationPluginsBootstrapper.withDefaults(AbstractDocumentationPluginsBootstrapper.java:107) ~[springfox-spring-web-3.0.0.jar:3.0.0]
        at springfox.documentation.spring.web.plugins.AbstractDocumentationPluginsBootstrapper.buildContext(AbstractDocumentationPluginsBootstrapper.java:91) ~[springfox-spring-web-3.0.0.jar:3.0.0]
        at springfox.documentation.spring.web.plugins.AbstractDocumentationPluginsBootstrapper.bootstrapDocumentationPlugins(AbstractDocumentationPluginsBootstrapper.java:82) ~[springfox-spring-web-3.0.0.jar:3.0.0]
        at springfox.documentation.spring.web.plugins.DocumentationPluginsBootstrapper.start(DocumentationPluginsBootstrapper.java:100) ~[springfox-spring-web-3.0.0.jar:3.0.0]
        at org.springframework.context.support.DefaultLifecycleProcessor.doStart(DefaultLifecycleProcessor.java:178) ~[spring-context-5.3.13.jar:5.3.13]
        ... 14 common frames omitted


FAILURE: Build failed with an exception.

* What went wrong:
Execution failed for task &#39;:bootRun&#39;.
&gt; Process &#39;command &#39;/home/advance/.sdkman/candidates/java/15.0.2-open/bin/java&#39;&#39; finished with non-zero exit value 1

* Try:
Run with --stacktrace option to get the stack trace. Run with --info or --debug option to get more log output. Run with --scan to get full insights.

* Get more help at https://help.gradle.org

Deprecated Gradle features were used in this build, making it incompatible with Gradle 7.0.
Use &#39;--warning-mode all&#39; to show the individual deprecation warnings.
See https://docs.gradle.org/6.9.1/userguide/command_line_interface.html#sec:command_line_warnings

BUILD FAILED in 2s
5 actionable tasks: 5 executed
```

Does anyone have an idea how to solve it?

Springboot 2.6.0 / Spring fox 3 - Failed to start bean &#39;documentationPluginsBootstrapper&#39;

Stetho and Google Chrome DevTools have become unusable after a macOS update (I doubt that macOS update is the origin of this bug, but I prefer to mention it).

Here is the appearance of DevTools after the open of &quot;inspect mode&quot; on a device (provided by Facebook Stetho library for Android &amp; OKHttp).

![DevTools window](https://i.stack.imgur.com/8AK7W.png)


There are no longer &quot;CSS&quot; stylesheets on the page and fonts have changed.
Many tab pages aren&#39;t displayed (i.e. Network Requests), I only have access to some error messages :

```
There were 84 bytes that were not consumed while processing request 4
There were 84 bytes that were not consumed while processing request 5
There were 84 bytes that were not consumed while processing request 6
Failed to clear temp storage: undefined
```

I followed instructions on this issue : https://stackoverflow.com/questions/31358446/failed-to-clear-temp-storage/35172470 and this one : https://stackoverflow.com/questions/36850053/failed-to-clear-temp-storage-securityerror-in-chrome?noredirect=1&amp;lq=1 but I haven&#39;t been able to fix the problem. 

Here is what I tried :
 - Uninstall and reinstall Chrome with AppCleaner
 - Remove chrome cache from disk
 - Remove chrome profiles from `~/Library/Application\ Support/Google/Chrome`
 - Create and use a new Chrome profile
 - Try to connect on Firefox distant debug (unfonctionnal)
 - Restart system

Have any of you ever encountered this problem ?
Thanks !



Chrome DevTools broken - Stetho unusable

[![Error][1]][1]

  [1]: https://i.stack.imgur.com/Jn9TG.png

I keep getting this error: 

```
WARNING: Ignoring invalid distribution -ip (c:\python39\lib\site-packages)
```

How do I fix this and what does it mean?

I have `anaconda` and Python installed. I use Jupyter Notebook and Python in VS Code.

This is in Git Bash command line.

My operating system is Windows 10 Home.

I have Python 3.9.2 and `pip` 21.1.1.

WARNING: Ignoring invalid distribution -ip (c:\python39\lib\site-packages) How do I fix this and what does it mean?

<a href="https://i.stack.imgur.com/Jn9TG.png" target="_blank" rel="noopener noreferrer"><img src="https://i.stack.imgur.com/Jn9TG.png" alt="Error"></a>
I keep getting this error:
<pre><code class="hljs language-vbnet">WARNING: Ignoring invalid distribution -ip (c:\python39\lib\site-packages)
</code></pre>
How do I fix this and what does it mean?
I have <code>anaconda</code> and Python installed. I use Jupyter Notebook and Python in VS Code.
This is in Git Bash command line.
My operating system is Windows 10 Home.
I have Python 3.9.2 and <code>pip</code> 21.1.1.

Suppose we want to compute some Fibonacci numbers, modulo 997.

For `n=500` in C++ we can run
```cpp
#include &lt;iostream&gt;
#include &lt;array&gt;

std::array&lt;int, 2&gt; fib(unsigned n) {
	if (!n)
		return {1, 1};
	auto x = fib(n - 1);
	return {(x[0] + x[1]) % 997, (x[0] + 2 * x[1]) % 997};
}

int main() {
	std::cout &lt;&lt; fib(500)[0];
}
```
and in Python
```py
def fib(n):
    if n==1:
        return (1, 2)
    x=fib(n-1)
    return ((x[0]+x[1]) % 997, (x[0]+2*x[1]) % 997)

if __name__==&#39;__main__&#39;:
    print(fib(500)[0])
```

Both will find the answer 996 without issues. We are taking modulos to keep the output size reasonable and using pairs to avoid exponential branching.

For `n=5000`, the C++ code outputs 783, but Python will complain
```none
RecursionError: maximum recursion depth exceeded in comparison
```
If we add a couple of lines
```py
import sys

def fib(n):
    if n==1:
        return (1, 2)
    x=fib(n-1)
    return ((x[0]+x[1]) % 997, (x[0]+2*x[1]) % 997)

if __name__==&#39;__main__&#39;:
    sys.setrecursionlimit(5000)
    print(fib(5000)[0])
```
then Python too will give the right answer.

For `n=50000` C++ finds the answer 151 within milliseconds while Python crashes (at least on my machine).

Why are recursive calls so much cheaper in C++? Can we somehow modify the Python compiler to make it more receptive to recursion?

Of course, one solution is to replace recursion with iteration. For Fibonacci numbers, this is easy to do. However, this will swap the initial and the terminal conditions, and the latter is tricky for many problems (e.g. alpha–beta pruning). So generally, this will require a lot of hard work on the part of the programmer.

Why is Python recursion so expensive and what can we do about it?

As we all know, the pythonic way to swap the values of two items ``a`` and ``b`` is 
```
a, b = b, a
```
and it should be equivalent to 
```
b, a = a, b
```
However, today when I was working on some code, I accidentally found that the following two swaps give different results:
```
nums = [1, 2, 4, 3]
i = 2
nums[i], nums[nums[i]-1] = nums[nums[i]-1], nums[i]
print(nums)
# [1, 2, 4, 3]

nums = [1, 2, 4, 3]
i = 2
nums[nums[i]-1], nums[i] = nums[i], nums[nums[i]-1]
print(nums)
# [1, 2, 3, 4]
```
This is mind-boggling to me. Can someone explain to me what happened here? I thought in a Python swap the two assignments happen simultaneously and independently.

Understand Python swapping: why is a, b = b, a not always equivalent to b, a = a, b?

I recently came across a weird discrepancy when trying to sort self-referential lists using `.sort()` and `sorted()`. I was hoping someone could shed some light on this. The code in question is the following:

```python
lst = [1, 2, 3]

lst[0] = lst
lst[1] = lst
lst[2] = lst

print(lst)

print(sorted(lst))

lst.sort()

print(lst)
```

The above code produces the following output:

```sh
[[...], [...], [...]]
[[[...], [...], [...]], [[...], [...], [...]], [[...], [...], [...]]]
[[...], [...], [...]]
```

It&#39;s the output from `print(sorted(lst))` that baffles me. Wonder if it is some form of recursion that&#39;s causing it?

Python self-referential list produces weird output on sorted

Two similar ways to check whether a list contains an odd number:
```
any(x % 2 for x in a)
any(True for x in a if x % 2)
```
 Timing results with `a = [0] * 10000000` (five attempts each, times in seconds):
```none
0.60  0.60  0.60  0.61  0.63  any(x % 2 for x in a)
0.36  0.36  0.36  0.37  0.37  any(True for x in a if x % 2)
```

Why is the second way almost twice as fast?

My testing code:
```
from timeit import repeat

setup = &#39;a = [0] * 10000000&#39;

expressions = [
    &#39;any(x % 2 for x in a)&#39;,
    &#39;any(True for x in a if x % 2)&#39;,
]

for expression in expressions:
    times = sorted(repeat(expression, setup, number=1))
    print(*(&#39;%.2f &#39; % t for t in times), expression)
```
[Try it online!](https://tio.run/##TY47DoMwEER7n2IaZBuhKJ8misQt0kUURFkUF9jWepHg9AQ7BWzhZsbzXlzkG/ztHnldBw4jxI3kBG6MgQVMkXpRKpFMES10vz2vc4cal/P/tFI0R6aUXPApxwrb6d4vZkaFK4bAmOE8equbPXzyRIcMbkDp51KnVE724Vw5YB5lJrtmYtpU6WP@smavNSjeDfw0vonbi7XlX2TnxdRGV6frAL1BpYhIppRR2xxodl1/ &quot;Python 3.8 (pre-release) – Try It Online&quot;)

Why is any (True for ... if cond) much faster than any (cond for ...)?

I have the following code:

    class Test:

        def __init__(self, name):
            self.name = name

        def __enter__(self):
            print(f&#39;entering {self.name}&#39;)

        def __exit__(self, exctype, excinst, exctb) -&gt; bool:
            print(f&#39;exiting {self.name}&#39;)
            return True

    with Test(&#39;first&#39;) as test:
        print(f&#39;in {test.name}&#39;)

    test = Test(&#39;second&#39;)
    with test:
        print(f&#39;in {test.name}&#39;)

Running it produces the following output:

```lang-none
entering first
exiting first
entering second
in second
exiting second
```

But I expected it to produce:

```lang-none
entering first
in first
exiting first
entering second
in second
exiting second
```

Why isn&#39;t the code within my first example called?




Invoking a constructor in a &#39;with&#39; statement

I know Python `//` rounds towards negative infinity and in C++ `/` is truncating, rounding towards 0.

And here&#39;s what I know so far:

```lang-none
               |remainder|
-12 / 10  = -1,   - 2      // C++
-12 // 10 = -2,   + 8      # Python

12 / -10  = -1,     2      // C++
12 // -10 = -2,   - 8      # Python

12 / 10  = 1,      2       // Both
12 // 10 = 1,      2

-12 / -10 = 1,    - 2      // Both
          = 2,    + 8

C++:
1. m%(-n) == m%n
2. -m%n == -(m%n)
3. (m/n)*n + m%n == m

Python:
1. m%(-n) == -8 == -(-m%n)
2. (m//n)*n + m%n == m
```

But why Python `//` choose to round towards negative infinity? I didn&#39;t find any resources explain that, but only find and hear people say vaguely: *&quot;for mathematics reasons&quot;*.

For example, in *https://stackoverflow.com/questions/22030342/why-is-1-2-evaluated-to-0-in-c-but-1-in-python*:

&gt; People dealing with these things in the abstract tend to feel that
&gt; rounding toward negative infinity makes more sense (**that means it&#39;s
&gt; compatible with the modulo function as defined in mathematics, rather
&gt; than % having a somewhat funny meaning**).

But I don&#39;t see C++ &#39;s `/` not being compatible with the modulo function. In C++, `(m/n)*n + m%n == m` also applies.

So what&#39;s the (mathematical) reason behind Python choosing rounding towards negative infinity?


----------

See also [Guido van Rossum&#39;s old blog post on the topic][1].

  [1]: http://python-history.blogspot.com/2010/08/why-pythons-integer-division-floors.html









Content Type	Original Author	Original Content on Stackoverflow
Question	ralphiecodes	View Question on Stackoverflow
Solution 1 - Python	ralphiecodes	View Answer on Stackoverflow

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