Question regarding decimal arithmetic

Question

I think my understanding of precision vs scale might be incorrect as the following example produces values that do not make sense to me. decimal(32, 14) rounds the result to 6 decimal places, while the decimal(18, 14) rounds to 19. My understanding of decimal is decimal(p, [s]), where p is the total number of digits and s is the number of digits after the decimal (i.g., decimal(10, 2) would result in 8 digits to the left of the decimal and 2 digits to the right). Is this not correct?

I created a small example that illustrates the seemingly odd behavior:

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-- Truncates at pipe
-- 1.043686|655...
--------------------
declare @dVal1 decimal(32, 14) = 10
declare @dVal2 decimal(32, 14) = 9.581419815465469

select @dVal1 Val1, @dVal2 Val2, @dVal1 / @dVal2 CalcResult

----------------
-- Most accurate
----------------
declare @dVal3 decimal(18, 14) = 10
declare @dVal4 decimal(18, 14) = 9.581419815465469

select @dVal3 Val3, @dVal4 Val4, @dVal3 / @dVal4 CalcResult

So on to the question, what is it that I am missing to understand this? The articles and msdn blogs I have read don't seem to provide clarity (at least to my thought process). Can someone explain to me why a higher precision seems to result in a loss of scale?

Answer 1

Your understanding is correct though you have 1 too many digits for @dVal2 and @dVal4 which is why you see these being rounded up to 7 (9.58141981546547) for the last digit in your select

As for the division rounding, it's hidden in the middle of the docs.

In multiplication and division operations we need precision - scale places to store the integral part of the result. The scale might be reduced using the following rules:

The resulting scale is reduced to min(scale, 38 – (precision-scale)) if the integral part is less than 32, because it cannot be greater than 38 – (precision-scale). Result might be rounded in this case.

The scale will not be changed if it is less than 6 and if the integral part is greater than 32. In this case, overflow error might be raised if it cannot fit into decimal(38, scale)

The scale will be set to 6 if it is greater than 6 and if the integral part is greater than 32. In this case, both integral part and scale would be reduced and resulting type is decimal(38,6). Result might be rounded to 6 decimal places or overflow error will be thrown if integral part cannot fit into 32 digits.

So in your first case decimal(32,14), the scale is being set to 6 digits because the resulting value decimal(64,28) has a scale = 28 which is > 6 and the integral part (64-28) = 36 is > 32 as defined in the last rule above. Thus, decimal(38,6)

In your second case decimal(18,14), the first rule is being applied for your scale for the resulting value of decimal(36,28) to min(28, 38 -(36-28)) = min(28,30) = 28. Thus, decimal(38,28)