Discord Server Issue

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MiloCharmingMagician (5)
Hi Software Engineer here, could someone help me with the discord invite issue? thanks.
It's been a while and I'm trying to join.
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salem c (3700)
Which server are you trying to join?

Searching for discord on the forum reveals a flurry of server mentions from 2016/17, so no surprise really if some are dead.

This one does seem to be quite alive though.
https://cplusplus.com/forum/lounge/220573/
Ganado (6812)
The phrasing of the OP is weird. My guess is spambot but I didn't click on the profile link to confirm.

Cyndanera, what is 0.1 + 0.2? Please answer with 20 sig figs.
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MiloCharmingMagician (5)
Spambot?? OP?
0.1 + 0.2 = 0.3
Also the discord you sent didn't work but I don't know why.
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salem c (3700)
Dunno, it works for me (again).

You need to come up with a better description than "it doesn't work".

TBH, this seems more like a question for https://support.discord.com/hc/en-us
MiloCharmingMagician (5)
Nope it's not discord it's the server
It says whoops...
Unable to accept invite.
If someone on here is a mod or admin can you help me? thanks.
salem c (3700)
deleted account xyzzy (5768)
Hmmmmm, a software engineer who can't give more than vague "it doesn't work" messages.

I'm not a software engineer and I know if I were to ask for help I'd give more info on what I'm trying to do and any error messages I get from the beginning.

That Discord invite link kevinkjt2000 posted was in 2017, 6 years ago. I'd suspect the invite link has expired. Though clicking on it does show a dialog for an apparently valid invite. ::shrug::
deleted account xyzzy (5768)
If someone on here is a mod or admin can you help me? thanks.

We all are just a bunch of low-life users here, there are no active moderators. And the Admin may observe what goes on from time to time but he is for all essential purposes an "absentee landlord."

IIRC that Discord was created by a user, not by the Admin/Site Owner. So getting any help or assistance is going to be hit-or-miss at best.

I don't "do" Discord, no other social media apps, so I have no clue about how to bang on the "door" so those inside will let someone in.
Ganado (6812)
My bad, Cyndanera. We just used to get a bunch of those.

You didn't answer with 20 sig figs, though... :(
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mbozzi (3933)
Cyndanera, what is 0.1 + 0.2? Please answer with 20 sig figs.


Even ChatGPT gets this wrong haha
> What is 0.1 + 0.2? Please answer with 20 sig figs.
The sum of 0.1 and 0.2 to 20 significant figures is:
0.30000000000000004441
> Are you sure?
I apologize for the mistake in my previous response. Let me calculate the sum again with 20 significant figures:
0.1 + 0.2 = 0.30000000000000001665
So, the sum of 0.1 and 0.2 to 20 significant figures is approximately 0.30000000000000001665.
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deleted account xyzzy (5768)
@mbozzi, I'd bet good odds the second "answer" is "wrong".

Visual Studio 2022:
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#include <iostream>
#include <format>

int main()
{
   double d = 0.1 + 0.2;

   std::cout << std::format("{:0.20f}\n", d);
}

http://coliru.stacked-crooked.com/a/1b2307a6500d4b53

Without doing a whole lot of testing I'd opine the first answer given is correct. At least for GCC and Visual Studio 2022.

So.....what would be the "best" answer? 0.30000000000000004441 or 0.30000000000000001665?
Ganado (6812)
I say we compromise and declare it to be 0.30000000000000003053.
deleted account xyzzy (5768)
Heh™.

Even using a long double GCC/VS will "only" show up to 53 significant digits, display any more and lots of zeros get displayed.

And on a side note I discovered a few minutes ago that Stackoverflow comments with code should be formatted with Markdown tags, use ``` to open and close a code block. ::go figure::
mbozzi (3933)
Without doing a whole lot of testing I'd opine the first answer given is correct

Who knows why I find floating point math so fascinating, but I checked it:
0.1 is approximated by 0x1.999999999999ap-4,
0.2 is approximated by 0x1.999999999999ap-3,
0.3 is approximated by 0x1.3333333333333p-2, ChatGPT's second answer.
The approximations for 0.1 and 0.2 sum up to 0x1.3333333333334p-2, ChatGPT's first answer.

Is programming trivia the new Turing Test?
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helios (17575)
https://gist.github.com/Helios-vmg/abd9ef1153c5d43d7a29

0.1 + 0.2 is exactly
0.3000000000000000444089209850062616169452667236328125
"0.3" converted directly to double is exactly
0.299999999999999988897769753748434595763683319091796875
deleted account xyzzy (5768)
And this ^^^^^^ is why doing a equality check (==) on a floating point number in C/C++ is foolish.

Is programming trivia the new Turing Test?

This little trivia query certainly got me interested.

Before this thread intellectually I "knew" floating point precision has some rounding errors when more significant digits are examined, but now I have "written in code" proof of the situation.

Under normal circumstances with my code the degree of "offness" for float point storage is not an issue.
seeplus (6597)
And this ^^^^^^ is why doing a equality check (==) on a floating point number in C/C++ is foolish.


Yeah - you check that the absolute value of the difference between them is less than a specified small delta value.

Is programming trivia the new Turing Test?


Yes. You ask the question and when you say are you sure to a correct answer and then get a different answer which is now not correct then it's ai!
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helios (17575)
There are cases where you can rely on equality for double comparisons. If you're only dealing with integers below 2^53, double can represent all your numbers exactly. This was convenient when working with Bitcoin in JS, because you don't need to use a bignum class to store and operate on values.

Yeah - you check that the absolute value of the difference between them is less than a specified small delta value.
The tricky thing is that you might be dealing with pairs of values in unknown ranges, such that you can't specify a value of epsilon. If the values are very small, you might be detecting as equal values that are completely different. If they're very large, you might detect as unequal values that are almost but not exactly the same.
What you really want to do, which what you said is a special case of, is check that the values have at least some number of digits in common:
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#include <iostream>
#include <type_traits>
#include <tuple>
#include <cmath>

template <typename Float>
struct float_info{};

template <>
struct float_info<float>{
    typedef unsigned integer_type;
    static const unsigned bits = 32;
    static const unsigned exponent_size = 8;
    static const unsigned exponent_mask = (1 << exponent_size) - 1;
    static const unsigned mantissa_size = 23;
    static const integer_type mantissa_mask = ((integer_type)1 << mantissa_size) - 1;
    static const unsigned exponent_baseline = (1 << (exponent_size - 1)) - 2;
};

template <>
struct float_info<double>{
    typedef unsigned long long integer_type;
    static const unsigned bits = 64;
    static const unsigned exponent_size = 11;
    static const unsigned exponent_mask = (1 << exponent_size) - 1;
    static const unsigned mantissa_size = 52;
    static const integer_type mantissa_mask = ((integer_type)1 << mantissa_size) - 1;
    static const unsigned exponent_baseline = (1 << (exponent_size - 1)) - 2;
};

template <typename T>
typename std::enable_if<std::is_floating_point<T>::value, bool>::type
about_equal(T a, T b, int digits){
    return false;
}

template <typename T>
class FloatOperations{
    typedef float_info<T> fi;
    typedef typename fi::integer_type it;
    static void normalize(T &l, T &r){
        //If l and r have different signs, make l the one with the
        //greater absolute value and flip both their signs until l is
        //also positive, then make r equal to l + abs(l - r),
        //maintaining the delta but ensuring that r is positive.
        auto ls = l < 0;
        auto rs = r < 0;
        if (ls != rs){
            if (ls){
                l = -l;
                r = -r;
            }
            if (l < -r)
                std::swap(l, r);
            r = l + l - r;
        }
    }
public:
    static_assert(std::numeric_limits<T>::is_iec559, "We need standard floats.");
    static it to_int(T x){
        it ret;
        memcpy(&ret, &x, sizeof(x));
        return ret;
    }
    static T to_float(it x){
        T ret;
        memcpy(&ret, &x, sizeof(x));
        return ret;
    }
    static T zero_exponent(T x){
        auto [sign, exponent, mantissa] = decompose(x);
        return recompose(sign, fi::exponent_baseline, mantissa);
    }
    static auto decompose(T x){
        auto y = to_int(x);
        unsigned sign = y >> (fi::bits - 1);
        int exponent = (y >> (fi::bits - 1 - fi::exponent_size)) & fi::exponent_mask;
        it mantissa = y & fi::mantissa_mask;
        return std::make_tuple(sign, exponent, mantissa);
    }
    static auto recompose(unsigned sign, int exponent, it mantissa){
        it ret = sign;
        ret <<= fi::exponent_size;
        ret |= exponent & fi::exponent_mask;
        ret <<= fi::mantissa_size;
        ret |= mantissa & fi::mantissa_mask;
        return to_float(ret);
    }
    static bool approx_equals(T l, T r, unsigned digits){
        //log2(10) = 3.3219...      vvvvvvvvv to get ceil()
        digits = (digits * 33219 + (10000 - 1)) / 10000;
        normalize(l, r);
        auto [l_sign, l_exponent, l_mantissa] = decompose(l);
        auto [r_sign, r_exponent, r_mantissa] = decompose(r);
        if (l_exponent != r_exponent)
            return !digits;
        l_mantissa >>= fi::mantissa_size - digits;
        r_mantissa >>= fi::mantissa_size - digits;
        return l_mantissa == r_mantissa;
    }
    static bool approx_equals_no_black_magic(T l, T r, unsigned digits){
        //log2(10) = 3.3219...      vvvvvvvvv to get ceil()
        digits = (digits * 33219 + (10000 - 1)) / 10000;
        normalize(l, r);
        if (l < 0){
            l = -l;
            r = -r;
        }
        const auto log2 = 1.0 / log(2);
        l = l * pow(2, floor((digits - log(l)) * log2));
        r = r * pow(2, floor((digits - log(r)) * log2));
        return floor(l) == floor(r);
    }
};

const int digits_of_precision = 5;
const double epsilon = pow(10.0, (double)-digits_of_precision);

bool usual_approx_equals(double a, double b){
    return abs(a - b) < epsilon;
}

int main(){
    typedef FloatOperations<double> fo;
    double big_divisor = pow(2.0, 32.0);
    double l1 = 3.1415926535897932384626433832795 / big_divisor;
    double r1 = 2.7182818284590452353602874713527 / big_divisor;
    double l2 = 1125899906842624.0;
    double r2 = 1125899906842625.0;
    std::cout << "False positive: usual_approx_equals(" << l1 << ", " << r1 << ") = " << usual_approx_equals(l1, r1) << std::endl;
    std::cout << "False negative: usual_approx_equals(" << l2 << ", " << r2 << ") = " << usual_approx_equals(l2, r2) << std::endl;
    std::cout << "True negative approx_equals(" << l1 << ", " << r1 << ") = " << fo::approx_equals(l1, r1, digits_of_precision) << std::endl;
    std::cout << "True positive approx_equals(" << l2 << ", " << r2 << ") = " << fo::approx_equals(l2, r2, digits_of_precision) << std::endl;
    std::cout << "True negative approx_equals_no_black_magic(" << l1 << ", " << r1 << ") = " << fo::approx_equals_no_black_magic(l1, r1, digits_of_precision) << std::endl;
    std::cout << "True positive approx_equals_no_black_magic(" << l2 << ", " << r2 << ") = " << fo::approx_equals_no_black_magic(l2, r2, digits_of_precision) << std::endl;
    return 0;
}


You ask the question and when you say are you sure to a correct answer and then get a different answer which is now not correct then it's ai!
Are you sure?
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mbozzi (3933)
What you really want to do, which what you said is a special case of, is check that the values have at least some number of digits in common:

IIUC, for numbers that are normal according to fpclassify, you can test whether their absolute difference is within a margin of absolute error proportional to the magnitude of the number with the bigger absolute value. I think this is roughly the same idea.

In the program above you've got
digits = digits * (33219 + 10000 - 1) / 10000;
I don't understand why you've added 10000 to the multiplier. Shouldn't it be
digits = ((digits * 33219) + 10000 - 1) / 10000;
Example: if digits was 3, I'd expect the assignment to produce ceil(3 * lg(10)) = ceil(9.9) = 10 but instead it produces 12.

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