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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.
→ value load a double from local variable 1 dload_2 28 0010 1000 → value load a double from local variable 2 dload_3 29 0010 1001 → value load a double from local variable 3 dmul 6b 0110 1011 value1, value2 → result multiply two doubles dneg 77 0111 0111 value → result negate a double drem 73 0111 0011 value1, value2 → result
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.
Java bytecode is the instruction set of the Java virtual machine ... while dconst_1 will push a double (64 bit floating point value) with the value 1 onto the stack.
The Java virtual machine's set of primitive data types consists of: [12] byte, short, int, long, char (integer types with a variety of ranges) float and double, floating-point numbers with single and double precisions; boolean, a Boolean type with logical values true and false; returnAddress, a value referring to an executable memory address ...
The value distribution is similar to floating point, but the value-to-representation curve (i.e., the graph of the logarithm function) is smooth (except at 0). Conversely to floating-point arithmetic, in a logarithmic number system multiplication, division and exponentiation are simple to implement, but addition and subtraction are complex.
strictfp, an obsolete keyword in the Java programming language that previously restricted arithmetic to IEEE 754 single and double precision to ensure reproducibility across common hardware platforms (as of Java 17, this behavior is required) Table-maker's dilemma for more about the correct rounding of functions; Standard Apple Numerics Environment
Choosing an acceptable range is a complex topic. A common technique is to use a comparison epsilon value to perform approximate comparisons. [6] Depending on how lenient the comparisons are, common values include 1e-6 or 1e-5 for single-precision, and 1e-14 for double-precision.