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The integer n is called the exponent and the real number m is called the significand or mantissa. [1] The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes m, as in ordinary decimal notation.
In 1946, Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number (Burks [11] et al.) by analogy with the then-prevalent common logarithm tables: the characteristic is the integer part of the logarithm (i.e. the exponent), and the mantissa is the fractional part.
Then, the fractional part can be formulated as a difference: frac ( x ) = x − ⌊ x ⌋ , x > 0 {\displaystyle \operatorname {frac} (x)=x-\lfloor x\rfloor ,\;x>0} . The fractional part of logarithms , [ 2 ] specifically, is also known as the mantissa ; by contrast with the mantissa, the integral part of a logarithm is called its ...
The part of the representation that contains the significant figures (1.30 or 1.23) is known as the significand or mantissa. The digits in the base and exponent ( 10 3 or 10 −2 ) are considered exact numbers so for these digits, significant figures are irrelevant.
The TensorFloat-32 [31] format combines the 8 bits of exponent of the Bfloat16 with the 10 bits of trailing significand field of half-precision formats, resulting in a size of 19 bits. This format was introduced by Nvidia, which provides hardware support for it in the Tensor Cores of its GPUs based on the Nvidia Ampere architecture. The ...
In a normal floating-point value, there are no leading zeros in the significand (also commonly called mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as 1.23 × 10 −2). Conversely, a denormalized floating-point value has a significand with a leading digit of zero.
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).
- Different understanding of significand as integer or fraction, and acc. different bias to apply for the exponent (for decimal64 what is stored in bits can be decoded as base to the power of 'stored value for the exponent minus bias of 383' times significand understood as d 0. d −1 d −2 d −3 d −4 d −5 d −6 d −7 d −8 d −9 d ...