C#

// calculate a sum of order rows:
double total = 0;
foreach (row in rows)
{
    row.Amount = Math.Round(row.Quantity * row.UnitPrice, 2);
    total = Math.Round(total + row.Amount, 2);
    // note: total += Math.Round(...) can cause very small
    // roundoff errors (caused by binary encoding) to build
    // up and become visible.
}
 
// check for a = b:
if (Math.Round(Math.Abs(a - b), 2) < 0.001)
{
    // consider a and b sufficiently equal,
    // assuming two significant decimals.
}
 
// check for a < b:
if (Math.Round(b - a, 2) > 0.001)
{
    // consider a (sufficiently) less than b
}

float Result1 = TotalBonus * Worker1 / (Worker1 + Worker2);

float Result2 = TotalBonus * Worker2 / (Worker1 + Worker2);

string Result1String = Result1.ToString();
string Result2String = Result2.ToString();

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TestFloat
{
    class Program
    {
        static void Main(string[] args)
        {
            float TotalBonus = 199.321F;
            float Worker1 = 100F;
            float Worker2 = 300F;

            float Result1 = TotalBonus * Worker1 / (Worker1 + Worker2);

            float Result2 = TotalBonus * Worker2 / (Worker1 + Worker2);

            float ResultTotalSent = Result1 + Result2;


            string Result1String = Result1.ToString();
            string Result2String = Result2.ToString();

            // sending to another computer using string

            // received from another computer using string
            string ReceivedString1 = Result1String;
            string ReceivedString2 = Result2String;
            float Received1 = float.Parse(ReceivedString1);
            float Received2 = float.Parse(ReceivedString2);
            float ResultTotalReceived = Received1 + Received2;

            // sanity checking failed, since ResultTotalReceived > TotalBonus

            if ((ResultTotalReceived - ResultTotalSent) < float.Epsilon)
            {
                // not executed here
                Console.WriteLine("Treated the same. ");
            }
        }
    }
}

PeterTheSwede wrote:

The type float only gives you 7 digits of precision

George_George wrote:

"binary 0.1 is representable as decimal 0.5" -- you get it from 0 + 1 * 2 ^ (-1) = 0.5?

George_George wrote:

1. Why using Decimal type, we can represent 0.1 precisely? Because Decimal type will use base 10 other than base 2 to represent a number?

George_George wrote:

2. For the numbers (which can be precisely represented by base 2), are there any possibilities which they can not be represented by base 10 precisely? If yes, I think it is not correct to say Decimal has less issues compared with float type?

George_George wrote:

3. Both float and double will use base 2 as internal representation?

PeterTheSwede wrote:

One exception: Binary floating point types can confuse people who don't understand a) that they are binary or b) what that means. Decimal types don't have that issue. In all other respects (precision limits, error accumulation and whatever) they are identical.

George_George wrote:

What means "a scaled binary integer"?

George_George wrote:

Do you have an adverse sample, which could be represented by base 2, but not be able to represented to base 10?

George_George wrote:

I think item a means Float and Double are both using base 2 as internal number represetation, correct? Your point b means?

PeterTheSwede wrote:

It is saved as an integer in binary (base 2)

PeterTheSwede wrote:

o if the number is 12345678 and the number of decimals is 5, the actual value is 123.45678.