Complex numbers in C#
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I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
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I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
If spacecraft or nuclear reactors are ever allowed to be run on .Net I will hide in a cave for the foreseeable future.
Wrong is evil and must be defeated. - Jeff Ello
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If spacecraft or nuclear reactors are ever allowed to be run on .Net I will hide in a cave for the foreseeable future.
Wrong is evil and must be defeated. - Jeff Ello
this gave me a good hearty chuckle. The kind of chuckle that can give a person a hernia. :thumbsup:
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I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
Do you really work on an Itanium system? That's what the IA-64 instruction was for - the Intel Itanium systems. The 64-bit instruction more commonly used today is called X64 and was originally developed by AMD.
"They have a consciousness, they have a life, they have a soul! Damn you! Let the rabbits wear glasses! Save our brothers! Can I get an amen?"
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Do you really work on an Itanium system? That's what the IA-64 instruction was for - the Intel Itanium systems. The 64-bit instruction more commonly used today is called X64 and was originally developed by AMD.
"They have a consciousness, they have a life, they have a soul! Damn you! Let the rabbits wear glasses! Save our brothers! Can I get an amen?"
Hmmm... how can I get .net on my Itanium (OpenVMS) system?
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I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
I have a guess. When dealing with stuff in mathematics that involves a degree of error, you want to treat all input consistently. Having some input that generates a value with error baked in and other input that generates a hard-coded exact value is a bad idea. With
Complex.Sqrt, they use [polar coordinates](https://referencesource.microsoft.com/#System.Numerics/System/Numerics/Complex.cs,d83f2d44d890c43f,references) to calculate the complex number. This is going to have some error baked in. If a developer usingComplexis adjusting for error, and the operations onComplextreat some input differently (like -1), then this adjustment would remove the error from some cases and introduce error in others. If you want an error-less representation ofComplex.Sqrt(-1)you can useComplex.ImaginaryOne. That would be my reasoning at least. -
I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
I hope you know you just induced me to have a flashback to the graduate linear systems course I took in 1988, the last time I cared that i = √-1 was a thing. I'm now going to have to spend the evening drinking hard apple cider, binge-watching Eureka[^], and talking to my sleeping greyhound in order to purge the memory from my neural cache.
Software Zen:
delete this; -
I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
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Do you really work on an Itanium system? That's what the IA-64 instruction was for - the Intel Itanium systems. The 64-bit instruction more commonly used today is called X64 and was originally developed by AMD.
"They have a consciousness, they have a life, they have a soul! Damn you! Let the rabbits wear glasses! Save our brothers! Can I get an amen?"
I work on whatever Tim Cook decides should be in my Macbook.
cheers Chris Maunder
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I was reading about complex numbers in C# and saw [this](https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex?view=net-5.0)
Complex minusOne = new Complex(-1, 0);
Console.WriteLine(Complex.Sqrt(minusOne));
// The example displays the following output:
// (6.12303176911189E-17, 1) on 32-bit systems.
// (6.12323399573677E-17,1) on IA64 systems.I'm curious: is there any reason one would not simply hardcode
Complex.Sqrt(-1)to equalnew Complex(0, 1);? The whole thing about complex numbers is they are based on the fundamental concept that i2 = -1. Why wouldn't you bake that in as an absolute and let the representational errors happen elsewhere? I get that actually detecting all cases of √-1 is tricky and messy at best, but it's not like you can actually compare, with arbitrary precision, two floating point values anyway. Future warning: if I ever get access to the .NET code in a way that lets me sneak in a change, then this will happen. It may cause manned spacecraft to veer off course and crash into the moon, or nuclear reactors to overheat and take out half a continent. But, dammit, √-1 will equal i.cheers Chris Maunder
Well, I had to [try it in C++](https://godbolt.org/z/9ajWdG5j5)... ```c++ #include #include #include int main() { const auto a = std::complex{-1, 0}; const auto b = std::sqrt(a); std::cout << std::setprecision(20) << "sqrt" << a << " -> " << b << "\n"; } ``` and that output ``` sqrt(-1,0) -> (0,1) ``` in gcc and clang. And, as you have been a physicist, I figured maybe [Fortran](https://godbolt.org/z/Tzvhxv7s1) might be an alternative... ```fortran program test implicit none COMPLEX*8 a,b a = (-1,0) b = sqrt(a) write (*,*) a,b endprogram test ``` Guess what - sqrt(-1) == i there too: ``` (-1.00000000,0.00000000) (0.00000000,1.00000000) ``` And all the [other](https://godbolt.org/z/Wqa3zc9MY) [non .NET](https://godbolt.org/z/9z553jvee) [languages](https://godbolt.org/z/b8rGrqYce) I tried also gave the same answer... So I guess .NET is the outlier here! With all that, though, they're still missing the negative root :doh:
Java, Basic, who cares - it's all a bunch of tree-hugging hippy cr*p
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If spacecraft or nuclear reactors are ever allowed to be run on .Net I will hide in a cave for the foreseeable future.
Wrong is evil and must be defeated. - Jeff Ello
Ehm.. As a fellow swedish developer, I suggest you hide right now, because software I've written in C# is actually in a control room for a unnamed reactor. =)
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If spacecraft or nuclear reactors are ever allowed to be run on .Net I will hide in a cave for the foreseeable future.
Wrong is evil and must be defeated. - Jeff Ello
It is not related to language-specific issues, but to floating point representation. Every language has these problems with basic floating-point data structures.
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Ehm.. As a fellow swedish developer, I suggest you hide right now, because software I've written in C# is actually in a control room for a unnamed reactor. =)
But is it actually controlling the reactor?
Wrong is evil and must be defeated. - Jeff Ello
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It is not related to language-specific issues, but to floating point representation. Every language has these problems with basic floating-point data structures.
My concern isn't language specific nor floating point specific. I'd rather not trust anything running on a PC for high security purposes.
Wrong is evil and must be defeated. - Jeff Ello
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But is it actually controlling the reactor?
Wrong is evil and must be defeated. - Jeff Ello
Not directly but a crash will cause an emergency stop. // E
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Not directly but a crash will cause an emergency stop. // E
Ok, that's interesting. :~ I suppose it's not an off the shelf PC it's running on?
Wrong is evil and must be defeated. - Jeff Ello
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Ok, that's interesting. :~ I suppose it's not an off the shelf PC it's running on?
Wrong is evil and must be defeated. - Jeff Ello
Everything runs on off the shelf pcs. That are 5+ years old. But on the other hand, the backups have backups. There's some really, REALLY old stuff in there that's custom built, but that's even more scary. That's it, I better stop before I bust some NDA and get SÄPO after my ass. =) // E
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Everything runs on off the shelf pcs. That are 5+ years old. But on the other hand, the backups have backups. There's some really, REALLY old stuff in there that's custom built, but that's even more scary. That's it, I better stop before I bust some NDA and get SÄPO after my ass. =) // E
Oh fuck. :wtf: It's not like as if it's an unknown problem: Malware Discovered in German Nuclear Power Plant - Security News[^] But I really thought critical systems were running on a Safety-Critical System[^].
Wrong is evil and must be defeated. - Jeff Ello
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Oh fuck. :wtf: It's not like as if it's an unknown problem: Malware Discovered in German Nuclear Power Plant - Security News[^] But I really thought critical systems were running on a Safety-Critical System[^].
Wrong is evil and must be defeated. - Jeff Ello
Two more words: Windows. XP. :'( // E
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Well, I had to [try it in C++](https://godbolt.org/z/9ajWdG5j5)... ```c++ #include #include #include int main() { const auto a = std::complex{-1, 0}; const auto b = std::sqrt(a); std::cout << std::setprecision(20) << "sqrt" << a << " -> " << b << "\n"; } ``` and that output ``` sqrt(-1,0) -> (0,1) ``` in gcc and clang. And, as you have been a physicist, I figured maybe [Fortran](https://godbolt.org/z/Tzvhxv7s1) might be an alternative... ```fortran program test implicit none COMPLEX*8 a,b a = (-1,0) b = sqrt(a) write (*,*) a,b endprogram test ``` Guess what - sqrt(-1) == i there too: ``` (-1.00000000,0.00000000) (0.00000000,1.00000000) ``` And all the [other](https://godbolt.org/z/Wqa3zc9MY) [non .NET](https://godbolt.org/z/9z553jvee) [languages](https://godbolt.org/z/b8rGrqYce) I tried also gave the same answer... So I guess .NET is the outlier here! With all that, though, they're still missing the negative root :doh:
Java, Basic, who cares - it's all a bunch of tree-hugging hippy cr*p
Are we sure that we are comparing like-with-like? The original answers were (6.12303176911189E-17, 1) or (6.12323399573677E-17,1) Your answers were (0.00000000,1.00000000) If you display 6.12303176911189E-17 in a non-exponent form, it will come out as 0.00000000 because it is a rounded version of 0.000000000000000006123... (I may have miscounted the zeros) So both answers may be representations of the same number. This is easy to test e.g. in FORTRAN which has an E format type for exponential and F for floating point.