Search results
Results from the WOW.Com Content Network
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.
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
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 ...
The minimum strictly positive (subnormal) value is 2 −16494 ≈ 10 −4965 and has a precision of only one bit. The minimum positive normal value is 2 −16382 ≈ 3.3621 × 10 −4932 and has a precision of 113 bits, i.e. ±2 −16494 as well. The maximum representable value is 2 16384 − 2 16271 ≈ 1.1897 × 10 4932.
Exponents range from −1022 to +1023 because exponents of −1023 (all 0s) and +1024 (all 1s) are reserved for special numbers. The 53-bit significand precision gives from 15 to 17 significant decimal digits precision (2 −53 ≈ 1.11 × 10 −16). If a decimal string with at most 15 significant digits is converted to the IEEE 754 double ...
Julia: the built-in BigFloat and BigInt types provide arbitrary-precision floating point and integer arithmetic respectively. newRPL: integers and floats can be of arbitrary precision (up to at least 2000 digits); maximum number of digits configurable (default 32 digits) Nim: bigints and multiple GMP bindings. OCaml: The Num library supports ...
But if exact values for large factorials are desired, then special software is required, as in the pseudocode that follows, which implements the classic algorithm to calculate 1, 1×2, 1×2×3, 1×2×3×4, etc. the successive factorial numbers.