Floats in Java

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Floats
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The SQL Standard provides three data types for columns that contain floats: REAL, FLOAT, and DOUBLE PRECISION (or DOUBLE) Table 7-6 shows the SQL Standard requirements and the level of support (data type and precision) the Big Eight have for these data types Notes on Table 7-6:
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The letters IEEE mean "according to the IEEE 754 Standard for Binary Floating-Point Arithmetic" Informix and PostgreSQL use "the native C float," which coincidentally corresponds to IEEE 754 for any common C compiler IEEE single storage is 32 bits (four bytes) It allows for seven-digit precision, with a usual range from 3402E+38 to 1175E 37 for negative numbers, zero, and from +1175E-37 to +3402E+38 for positive numbers REAL and FLOAT(n) where n <= 23 are usually synonymous and refer to a 32-bit floating-point number, IEEE single precision InterBase, though, allows you to define a column with a specific precision for FLOAT, for example:
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CREATE TABLE Table1 ( column1 FLOAT(20))
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but ignores the precision specified InterBase FLOAT(n) is always 64-bit IEEE double precision even though FLOAT alone is always 32-bit IEEE single precision
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IEEE double storage is 64 bits (eight bytes) It allows for 15-digit precision, with a usual range from 1798E+308 to 2225E-307 for negative numbers, zero, and from +2225E-307 to +1798E+308 for positive numbers DOUBLE PRECISION and FLOAT(n) where n BETWEEN 24 AND 53 are usually synonymous and refer to a 64-bit floating-point number, IEEE double precision For MySQL, REAL is synonymous with DOUBLE, rather than with FLOAT Oracle accepts columns defined as REAL, FLOAT, or DOUBLE PRECISION, but treats all numbers differently from other DBMSs; see the sidebar "Oracle Numbers" Table 7-6 ANSI/DBMS Float Support
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ANSI SQL IBM Informix Ingres InterBase Microsoft MySQL Oracle Sybase
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REAL Yes IEEE single IEEE single IEEE single IEEE single IEEE single IEEE double Yes IEEE single
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FLOAT Yes IEEE double IEEE double IEEE double IEEE single IEEE double IEEE single Yes IEEE double
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DOUBLE PRECISION Yes IEEE double IEEE double IEEE double IEEE double IEEE double IEEE double Yes IEEE double
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The official SQL term for FLOAT, REAL, and DOUBLE PRECISION values is "approximate numeric" but "floating point" or simply "float" is common The key point for all such values is that the decimal point is floating (If the decimal point is fixed, see the next section) You should use float literals when working with floats For example, use this type of expression:
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UPDATE Table1 SET float_column = 125E02
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instead of:
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UPDATE Table1 SET float_column = 125
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Portability MySQL won't accept a float literal unless it has a two-digit exponent That is, the literal 125E02 is acceptable, but 125E2 is not All other DBMSs allow you to drop the leading zero
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Floating-point operations are fast if they go through the computer's Floating Point Unit (FPU), but a compiler can make the cautious assumption that no FPU is present In that case, floating-point operations are slow because they are emulated instead of performed with the FPU When you install a DBMS, the installer should detect the FPU automatically and bring in the right code, whether FPU dependent or emulated, so make sure you rerun the install program after hardware upgrades or moves Take another look at Table 7-6 and the precisions shown for the float data types The range of IEEE single-precision float is from 1175E-37 to +3402E+38, to 7 decimal digits precision, although some DBMSs are more cautious in stating the actual range supported The range of IEEE double-precision float is from 2225E-307 to +1798E+308, to 15 decimal digits precision Again, some DBMSs give a slightly smaller range These sizes are shown in Table 7-7 Table 7-7 shows that the range of a single-precision float is 1175E-37 to +3402E+38 In reality it isn't possible to store all the real numbers in that range in a four-byte space; it isn't even possible to store all the integers in that range in four bytes (the range of a four-byte INTEGER is from 214E9 to +214E9) So for most numbers in the single-precision range, you'll need to use whatever number is closest that can be represented in a single float In other words, a floating-point number is exact in bit
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combinations that is, all bit combinations are exact but it might not be exactly the same as the number that was inserted originally Hence the name approximate The question that arises from this is Is it better to use DOUBLE PRECISION for float columns or REAL (We'll ignore FLOAT entirely because REAL and DOUBLE are just synonyms for predefined sizes of FLOAT) We checked the Big Eight to see what happens if the same number is stored both ways First, we created this table:
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CREATE TABLE Table1 ( real_column REAL, double_column DOUBLE PRECISION)
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Table 7-7 IEEE 754 Floats Precision in Bits Precision in Decimal (effective mantissa size) Digits(inexact) <=23 7 >=24 AND <=53 15 Min Max 1175E- +3402E+38 37 2225E- +1798E+308 307
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