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In computing, double precision is a computer numbering format that occupies two storage locations in computer memory at address and address+1. A double precision number, sometimes simply a double, may be defined to be an integer, fixed point, or floating point. Originally, the word computing was synonymous with counting and calculating, and a science that deals with the original sense of computing mathematical calculations. ...
One of the common misunderstandings among computer users is a certain faith in the infallibility of numerical computations. ...
The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ...
In mathematics, a fixed point of a function f is an argument x such that f(x) = x; see fixed point (mathematics). ...
A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ...
Modern computers with 32-bit stores (single precision) provide 64-bit double precision. Double precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 8 bytes. This article is about the unit of information. ...
In computing, single precision is a computer numbering format that occupies one storage locations in computer memory at address. ...
The IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754) is the most widely-used standard for floating-point computation, and is followed by many CPU and FPU implementations. ...
Standardization, in the context related to technologies and industries, is the process of establishing a technical standard among competing entities in a market, where this will bring benefits without hurting competition. ...
A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ...
A byte is commonly used as a unit of storage measurement in computers, regardless of the type of data being stored. ...
Double precision memory format
Sign bit: 1 Exponent width: 11 Significand precision: 53 (one implicit) The format is written with an implicit integer bit with value 1 unless the written exponent is all zeros. With the 52 bits of the fraction appearing in the memory format the total precision is therefore 53 bits (approximately 16 decimal digits). The bits are laid out thus: In computer science the sign bit is the bit in a computer numbering format which indicates the sign of the number. ...
In mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. ...
The significand (also coefficient or, more informally, mantissa) is the part of a floating-point number that contains its significant digits. ...
The precision of a measurement or value describes the number of digits that are used to express that value. ...
syyy yyyy yyyy xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx where s is the sign bit, yyyyyyyyyyy are the bits encoding the exponent, and the x bits encode the significand.
Exponent encodings Emin (0x001) = -1022 Emax (0x7fe) = 1023 Exponent bias (0x3ff) = 1023 The true exponent = written exponent - exponent bias In IEEE 754 floating point numbers the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias. ...
0x000 and 0x7ff are reserved exponents 0x000 is used to represent zero and denormals 0x7ff is used to represent infinity and NaNs All bit patterns are valid encodings. 0 (zero), alternatively called naught, nil, nada, ought, zilch, zip, nothing or nought, is both a number and a numeral. ...
In computer science, denormal numbers (also called subnormal numbers) fill the gap around zero in floating point arithmetic: any non-zero number which is smaller than the smallest normal number is sub-normal. Producing a denormal is sometimes called gradual underflow because it allows the calculation to lose precision slowly...
Infinity refers to several distinct concepts which arise in theology, philosophy, mathematics and everyday life. ...
In computing, NaN (Not a Number) is a value or symbol that is usually produced as the result of an operation on invalid input operands, especially in floating-point calculations. ...
Double precision examples 3ff0 0000 0000 0000 = 1 c000 0000 0000 0000 = -2 7fef ffff ffff ffff ~ 1.7976931348623157 x 10308 (Max Double) 3fd5 5555 5555 5555 ~ 1/3 (1/3 rounds down instead of up like single precision, because of the odd number of bits in the significand.) In computing, single precision is a computer numbering format that occupies one storage locations in computer memory at address. ...
0000 0000 0000 0000 = 0 8000 0000 0000 0000 = -0 7ff0 0000 0000 0000 = Infinity fff0 0000 0000 0000 = -Infinity
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