What is the difference between scales and floats

Precision is the number of digits available to represent a number. The more precision, the less you need to round. No data type has infinite precision. Thecrocodilehunter: You're assuming that the value that is being measured is exactly 0.

Any finite storage format will conflate an infinite number of possible values to a finite number of bit patterns. For example, float will conflate 0. Sure, within a given range , certain values can be represented in any format with zero loss of accuracy e. Thecrocodilehunter: You missed my point.

The only thing that makes 0. And even with a float value, if you initialize two values with 0. It's just that that value won't be exactly 0. Sure, with binary floats, 1. Neither is perfectly precise. Thecrocodilehunter: You still don't understand.

It's just that a and b will both not exactly equal 0. In both cases, some accuracy is lost due to representation. You stubbornly say that decimal has "infinite" precision, which is false. Show 30 more comments. Net Framework Signed? Sbyte Yes 1 to short System. Int16 Yes 2 , to 32, int System. Int32 Yes 4 -2,,, to 2,,, long System.

Int64 Yes 8 -9,,,,,, to 9,,,,,, byte System. Byte No 1 0 to ushort System. Uint16 No 2 0 to 65, uint System. UInt32 No 4 0 to 4,,, ulong System. Uint64 No 8 0 to 18,,,,,, float System. Brady Davis 3 3 3 bronze badges. You left out the biggest difference, which is the base used for the decimal type decimal is stored as base 10, all other numeric types listed are base 2.

The value ranges for the Single and Double are not depicted correctly in the above image or the source forum post. Also, MSDN has the float with a range of Single and System. Double in case of link changes. Single: msdn.

Decimal is bits Decimals are not adequate for scientific applications, however, for several reasons: A certain loss of precision is acceptable in many scientific calculations because of the practical limits of the physical problem or artifact being measured. Loss of precision is not acceptable in finance. Decimal is much much slower than float and double for most operations, primarily because floating point operations are done in binary, whereas Decimal stuff is done in base 10 i.

Decimal has an unacceptably smaller value range than double, despite the fact that it supports more digits of precision. Therefore, Decimal can't be used to represent many scientific values.

Mark Jones Mark Jones 1, 18 18 silver badges 12 12 bronze badges. If you're doing financial calculations, you absolutely have to roll your own datatypes or find a good library that matches your exact needs. Accuracy in a financial setting is defined by human standards bodies and they have very specific localized both in time and geography rules about how to do calculations.

Things like correct rounding aren't captured in the simple numeric datatypes in. The ability to do calculations is only a very small part of the puzzle. I won't reiterate tons of good and some bad information already answered in other answers and comments, but I will answer your followup question with a tip: When would someone use one of these? I really like this answer, especially the question "do we count or measure money?

I have seen some applications that use decimal simply because double has too few significant digits. In other words, decimal might be used because C does not have a quadruple type en. ABCD 15 15 silver badges 38 38 bronze badges. CharithJ CharithJ RogerLipscombe: I would consider double proper in accounting applications in those cases and basically only those cases where no integer type larger than 32 bits was available, and the double was being used as though it were a bit integer type e.

Not much use for such things nowadays, but many languages gained the ability to use double-precision floating-point values long before they gained bit or in some cases even bit! Your answer implies precision is the only difference between these data types. Given binary floating point arithmetic is typically implemented in hardware FPU , performance is a significant difference. This may be inconsequential for some applications, but is critical for others. Because Double can only approximate decimal values even within the range of its own precision.

This is because double stores the values in a base-2 binary -centric format. BrainSlugs Use of floating-point types to hold non-whole-number quantities would be improper, but it was historically very common for languages to have floating-point types that could precisely represent larger whole-number values than their integer types could represent.

I would think it would be much saner for an accounting application to use Real to represent a whole number of pennies than For most other languages the difference wasn't that extreme, but for a long time it has been very common for languages not to have any integer type that went beyond 4E9 but have a double type which had unit accuracy up to 9E Floating point operations can have small rounding errors, especially when the operands have different precision or scale.

Errors can accumulate, especially when aggregate functions e. Errors can vary each time the query is executed if the rows are processed in a different order e. Casting to a fixed-point data type before aggregating can reduce or eliminate these errors. Snowflake supports the fixed-point data type NUMBER , which allows greater precision, although a smaller range of exponents.

The symbols 'NaN' , 'inf' , and '-inf' must be in single quotes, and are case-insensitive. In Snowflake, 'NaN' values are all equal. Snowflake treats 'NaN' as greater. This is a known issue in Snowflake.

Constants also known as literals refers to fixed data values. The following sections describe the types in detail. The types smallint , integer , and bigint store whole numbers, that is, numbers without fractional components, of various ranges. Attempts to store values outside of the allowed range will result in an error.

The type integer is the common choice, as it offers the best balance between range, storage size, and performance. The smallint type is generally only used if disk space is at a premium.

The bigint type is designed to be used when the range of the integer type is insufficient. SQL only specifies the integer types integer or int , smallint , and bigint. The type names int2 , int4 , and int8 are extensions, which are also used by some other SQL database systems. The type numeric can store numbers with a very large number of digits. It is especially recommended for storing monetary amounts and other quantities where exactness is required. Calculations with numeric values yield exact results where possible, e.

However, calculations on numeric values are very slow compared to the integer types, or to the floating-point types described in the next section.

We use the following terms below: The precision of a numeric is the total count of significant digits in the whole number, that is, the number of digits to both sides of the decimal point. The scale of a numeric is the count of decimal digits in the fractional part, to the right of the decimal point.

So the number Integers can be considered to have a scale of zero. Both the maximum precision and the maximum scale of a numeric column can be configured. To declare a column of type numeric use the syntax:. A column of this kind will not coerce input values to any particular scale, whereas numeric columns with a declared scale will coerce input values to that scale. The SQL standard requires a default scale of 0, i. We find this a bit useless.

If you're concerned about portability, always specify the precision and scale explicitly. The maximum allowed precision when explicitly specified in the type declaration is ; NUMERIC without a specified precision is subject to the limits described in Table 8.

If the scale of a value to be stored is greater than the declared scale of the column, the system will round the value to the specified number of fractional digits. Submit a Pull Request Report a Bug.

Warning Floating point precision Floating point numbers have limited precision. Converting to float From strings If the string is numeric or leading numeric then it will resolve to the corresponding float value, otherwise it is converted to zero 0. From other types For values of other types, the conversion is performed by converting the value to int first and then to float. Comparing floats As noted in the warning above, testing floating point values for equality is problematic, due to the way that they are represented internally.

General computing hint: If you're keeping track of money, do yourself and your users the favor of handling everything internally in cents and do as much math as you can in integers. Store values in cents if at all possible. Add and subtract in cents. At every operation that wii involve floats, ask yourself "what will happen in the real world if I get a fraction of a cent here" and if the answer is that this operation will generate a transaction in integer cents, do not try to carry fictional fractional accuracy that will only screw things up later.

However, since 2 is a factor of 10, any number that terminates in binary also terminates in decimal. I'd like to point out a "feature" of PHP's floating point support that isn't made clear anywhere here, and was driving me insane. I should point out that I originally thought this was an issue with the floats being stored as strings, so I forced them to be floats and they still didn't get evaluated properly probably 2 different problems there. There's some hidden precision there that was making me tear my hair out.

Perhaps this should be added to the documentation? Concider the following: It doesn't - it returns 0. So, that's all lovely then. In some cases you may want to get the maximum value for a float without getting "INF". It comes with a configurable multiplicator and affine values so you can share more CPU to get a more accurate estimate. I haven't seen better values with more affine, but well, the possibility is here so if you really thing it's worth the cpu time, just try to affine more.

You can play with the values and see what you get. The good thing is this method will work on any system.