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The IEEE standard IEEE 754 specifies a standard method for both floating-point calculations and storage of floating-point values in various formats, including single (32-bit, used in Java's float) or double (64-bit, used in Java's double) precision.
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits). The two most commonly used levels of precision for floating-point numbers are single precision and double precision.
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
Conversely, precision can be lost when converting representations from integer to floating-point, since a floating-point type may be unable to exactly represent all possible values of some integer type. For example, float might be an IEEE 754 single precision type, which cannot represent the integer 16777217 exactly, while a 32-bit integer type ...
2.1 Java. 2.2 C basic types. 2.3 ... Because floating-point numbers have limited precision, ... These are not objects and have no methods or properties; however, ...
push 2.0f on the stack fdiv 6e 0110 1110 value1, value2 → result divide two floats fload 17 0001 0111 1: index → value load a float value from a local variable #index: fload_0 22 0010 0010 → value load a float value from local variable 0 fload_1 23 0010 0011 → value load a float value from local variable 1 fload_2 24 0010 0100 → value