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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.
C# has a built-in data type decimal consisting of 128 bits resulting in 28–29 significant digits. It has an approximate range of ±1.0 × 10 −28 to ±7.9228 × 10 28. [1] Starting with Python 2.4, Python's standard library includes a Decimal class in the module decimal. [2]
Fastest integer types that are guaranteed to be the fastest integer type available in the implementation, that has at least specified number n of bits. Guaranteed to be specified for at least N=8,16,32,64. Pointer integer types that are guaranteed to be able to hold a pointer. Included only if it is available in the implementation.
In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary), x = 2.0 ⇒ result is 2 (10.00 in binary)
A double (eight bytes) will be 8-byte aligned. A long long (eight bytes) will be 8-byte aligned. A long double (eight bytes with Visual C++, sixteen bytes with GCC) will be 8-byte aligned with Visual C++ and 16-byte aligned with GCC. Any pointer (eight bytes) will be 8-byte aligned. Some data types are dependent on the implementation.
C and C++ perform such promotion for objects of Boolean, character, wide character, enumeration, and short integer types which are promoted to int, and for objects of type float, which are promoted to double. Unlike some other type conversions, promotions never lose precision or modify the value stored in the object. In Java:
This functionality is also available in wider versions in the SSE2 and AVX2 integer instruction sets. It is also available in ARM NEON instruction set. Saturation arithmetic for integers has also been implemented in software for a number of programming languages including C , C++ , such as the GNU Compiler Collection , [ 2 ] LLVM IR, and Eiffel .
From binary32 to bfloat16. When bfloat16 was first introduced as a storage format, [15] the conversion from IEEE 754 binary32 (32-bit floating point) to bfloat16 is truncation (round toward 0). Later on, when it becomes the input of matrix multiplication units, the conversion can have various rounding mechanisms depending on the hardware platforms.