Block floating point (BFP) is a method used to provide an arithmetic approaching

floating point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be r ...

while using a

fixed-point Fixed point may refer to: * Fixed point (mathematics), a value that does not change under a given transformation * Fixed-point arithmetic, a manner of doing arithmetic on computers * Fixed point, a benchmark (surveying) The term benchmark, be ...

processor. BFP assigns a group of ''

significand The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on ...

s'' (the non-exponent part of the floating-point number) to a single exponent, rather than single significand being assigned its own exponent. BFP can be advantageous to limit space use in hardware to perform the same functions as floating-point algorithms, by reusing the exponent; some operations over multiple values between blocks can also be done with a reduced amount of computation. The common exponent is found by data with the largest amplitude in the block. To find the value of the exponent, the number of leading zeros must be found (

count leading zeros In computer software and hardware, find first set (ffs) or find first one is a bit operation that, given an unsigned machine word, designates the index or position of the least significant bit set to one in the word counting from the least signifi ...

). For this to be done, the number of left shifts needed for the data must be normalized to the dynamic range of the processor used. Some processors have means to find this out themselves, such as exponent detection and normalization instructions. Block floating-point algorithms were extensively studied by

James Hardy Wilkinson James Hardy Wilkinson FRS (27 September 1919 – 5 October 1986) was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering. Edu ...

. BFP can be recreated in software for smaller performance gains.

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