Math.Round(double,int,MidpointRounding) Math.Round(decimal,int,MidpointRounding) different result

[erikzhouxin]

Description

            // 单精度浮点数(Float)
            Console.WriteLine(Math.Round(18.254550f, 4, MidpointRounding.ToEven)); // 18.2546
            Console.WriteLine(Math.Round(18.745450f, 4, MidpointRounding.ToEven)); // 18.7454
            // 双精度浮点数(Double)
            Console.WriteLine(Math.Round(18.254550d, 4, MidpointRounding.ToEven)); // 18.2545
            Console.WriteLine(Math.Round(18.745450d, 4, MidpointRounding.ToEven)); // 18.7455
            // 高精度浮点数(Decimal)
            Console.WriteLine(Math.Round(18.254550m, 4, MidpointRounding.ToEven)); // 18.2546
            Console.WriteLine(Math.Round(18.745450m, 4, MidpointRounding.ToEven)); // 18.7454

            Console.WriteLine(string.Format("{0:f4}", 18.254550d));
            Console.WriteLine(string.Format("{0:f4}", 18.745450d));

Why this is different result?

in fact string.Format("{0:f4}", double) not consistent with Math.Round Method

Reproduction Steps

Math.Round(double,int,MidpointRounding)
Math.Round(decimal,int,MidpointRounding)

Expected behavior

Math.Round(double,int,MidpointRounding)
Math.Round(decimal,int,MidpointRounding)
by useful digit precision these can return the same number,and string.format use math.round default MidpointRounding

Actual behavior

Math.Round(double,int,MidpointRounding)
Math.Round(decimal,int,MidpointRounding)
// 18.254550 and 18.745450 is different

Regression?

netcoreapp3.1 or net6.0

Known Workarounds

No response

Configuration

No response

Other information

No response

Tagging subscribers to this area: @dotnet/area-system-numerics
See info in area-owners.md if you want to be subscribed.

Issue Details

---

Description

`
// 单精度浮点数(Float)
Console.WriteLine(Math.Round(18.254550f, 4, MidpointRounding.ToEven)); // 18.2546
Console.WriteLine(Math.Round(18.745450f, 4, MidpointRounding.ToEven)); // 18.7454
// 双精度浮点数(Double)
Console.WriteLine(Math.Round(18.254550d, 4, MidpointRounding.ToEven)); // 18.2545
Console.WriteLine(Math.Round(18.745450d, 4, MidpointRounding.ToEven)); // 18.7455
// 高精度浮点数(Decimal)
Console.WriteLine(Math.Round(18.254550m, 4, MidpointRounding.ToEven)); // 18.2546
Console.WriteLine(Math.Round(18.745450m, 4, MidpointRounding.ToEven)); // 18.7454

        Console.WriteLine(string.Format("{0:f4}", 18.254550d));
        Console.WriteLine(string.Format("{0:f4}", 18.745450d));

`
Why this is different result?

in fact string.Format("{0:f4}", double) not consistent with Math.Round Method

Reproduction Steps

Math.Round(double,int,MidpointRounding)
Math.Round(decimal,int,MidpointRounding)

Expected behavior

Math.Round(double,int,MidpointRounding)
Math.Round(decimal,int,MidpointRounding)
by useful digit precision these can return the same number,and string.format use math.round default MidpointRounding

Actual behavior

Math.Round(double,int,MidpointRounding)
Math.Round(decimal,int,MidpointRounding)
// 18.254550 and 18.745450 is different

Regression?

netcoreapp3.1 or net6.0

Known Workarounds

No response

Configuration

No response

Other information

No response

Author:	erikzhouxin
Assignees:	-
Labels:	area-System.Numerics
Milestone:	-

[tannergooding]

These aren't equivalent operations.

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To start lets look at the actual values at play here:

18.254550f is actually 18.254550933837890625
18.254550d is actually 18.254549999999998277644408517517149448394775390625
18.254550m is actually 18.25455

18.745450f is actually 18.745449066162109375
18.745450d is actually 18.74549999999999982946974341757595539093017578125
18.745450m is actually 18.7454

---

Round will take the inputs as given, round to the specified number of digits, and return a value in the original format.

18.254550f will become 18.2546f which is actually 18.25460052490234375
18.254550d will become 18.2545d which is actually 18.25450000000000017053025658242404460906982421875
18.254550m will become 18.2546m which is actually 18.2546

18.745450f will become 18.7455f which is actually 18.74539947509765625
18.745450d will become 18.2546d which is actually 18.74549999999999982946974341757595539093017578125
18.745450m will become 18.7454m which is actually 18.7454

-- Noting there are some known bugs with Round(T value, int digits) and Round(T value, int digits, MidpointRounding mode) for float and double. These issues don't appear to be present for these inputs however

---

ToString("G") (which is what Console.WriteLine(value) will do) prints the "shortest roundtrippable string" since .NET Core 3.1.

In the case that you directly do x.ToString("F4") you are taking the original value and directly rounding and it can be "infinitely precise" with regards to the underlying value.

In the case where you are doing Math.Round(x, 4, MidpointRounding.ToEven).ToString("F4") then there are three rounding operations that happen:

1. The original value x is rounded to 4 digits (as with ToString("F4"))
2. The result of 1 is then rounded to the nearest representable float/double/decimal
3. The result of 2 is then itself rounded to 4 digits in order to display it

If you consider the floating-point case of 18.745450f you can see that 18.745449066162109375 rounded to 4 digits should be 18.7454 however since 18.7454 is not exactly representable this ends up becoming 18.74539947509765625. Printed to 4 digits, this ends up displaying as 18.7454 still simply because the 5th digit is 9 and causes it to round up. If you were to display to 7 digits you'd see 18.7453995 instead vs 18.7454491 for the original input, which helps display the error introduced via the multiple rounding operations.