Search results
Results from the WOW.Com Content Network
This can express values in the range ±65,504, with the minimum value above 1 being 1 + 1/1024. Depending on the computer, half-precision can be over an order of magnitude faster than double precision, e.g. 550 PFLOPS for half-precision vs 37 PFLOPS for double precision on one cloud provider.
Single precision is termed REAL in Fortran; [1] SINGLE-FLOAT in Common Lisp; [2] float in C, C++, C# and Java; [3] Float in Haskell [4] and Swift; [5] and Single in Object Pascal , Visual Basic, and MATLAB. However, float in Python, Ruby, PHP, and OCaml and single in versions of Octave before 3.2 refer to double-precision numbers.
Information about the actual properties, such as size, of the basic arithmetic types, is provided via macro constants in two headers: <limits.h> header (climits header in C++) defines macros for integer types and <float.h> header (cfloat header in C++) defines macros for floating-point types. The actual values depend on the implementation.
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.
A 2-bit float with 1-bit exponent and 1-bit mantissa would only have 0, 1, Inf, NaN values. If the mantissa is allowed to be 0-bit, a 1-bit float format would have a 1-bit exponent, and the only two values would be 0 and Inf. The exponent must be at least 1 bit or else it no longer makes sense as a float (it would just be a signed number).
The minimum strictly positive (subnormal) value is 2 −262378 ≈ 10 −78984 and has a precision of only one bit. The minimum positive normal value is 2 −262142 ≈ 2.4824 × 10 −78913. The maximum representable value is 2 262144 − 2 261907 ≈ 1.6113 × 10 78913.
Where standard libraries do not provide precomputed values (as <float.h> does with FLT_EPSILON, DBL_EPSILON and LDBL_EPSILON for C and <limits> does with std::numeric_limits<T>::epsilon() in C++), the best way to determine machine epsilon is to refer to the table, above, and use the appropriate power formula. Computing machine epsilon is often ...
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.