Analog Devices ADSP-BF535 Blackfin, Hardware Reference Manual

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Block Floating-Point Format
D-6 ADSP-BF535 Blackfin Processor Hardware Reference
The Blackfin family provides a means (a signed fractional mode) by which
the multiplier result is always shifted left one bit before being written to
the result register. This left shift eliminates the extra sign bit when both
operands are signed, yielding a correctly formatted result.
When both operands are in 1.15 format, the result is 2.30 (30 fractional
bits). A left shift causes the multiplier result to be 1.31 which can be
rounded to 1.15. Thus, if you use a signed fractional data format, it is
most convenient to use the 1.15 format.
For more information about data formats, see the data formats listed in
Table 2-2 on page 2-11 .
Block Floating-Point Format
A block floating-point format enables a fixed-point processor to gain some
of the increased dynamic range of a floating-point format without the
overhead needed to do floating-point arithmetic. Some additional pro-
gramming is required to maintain a block floating-point format, however.
A floating-point number has an exponent that indicates the position of the
radix point in the actual value. In block floating-point format, a set
(block) of data values share a common exponent. A block of fixed-point
values can be converted to block floating-point format by shifting each
value left by the same amount and storing the shift value as the block
exponent.
Typically, block floating-point format allows you to shift out non-signifi-
cant MSBs, increasing the precision available in each value. Block
floating-point format can also be used to eliminate the possibility of a data
value overflowing.
Figure D-4 shows an example. In the example, each of
the three data samples has at least two non-significant, redundant sign
bits. Each data value can grow by these two bits (two orders of magnitude)
before overflowing; thus, these bits are called guard bits.