ST20-C1 datasheet(65/205 Pages) STMICROELECTRONICS

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5 Multiply accumulate

5.7

Data formats

This section gives details of the data formats used by the

smacloop and biquad

instructions.

A signed fractional number of N bits is characterized as x.y, where x+y=N. This means

the number is made up from x bits before the binary point, an implied binary point, and

y fractional bits. Some examples are listed in Table 5.7.

5.7.1

Range

A value

n in x.y format has a range -2x-1

≤ n < 2x-1.

For example, a value in the format 1.15 has range -1

≤ n < 1, and the format 2.14 has

range -2

≤ n <2.

5.7.2

Multiplication

The characteristic of the product of two fractional values is given by:

a.b * c.d = a+c.b+d

5.7.3

Supported formats

Table 5.8 shows the data formats for multiply-accumulate operations supported by the

ST20-C1.

Note that a Q15 value may be (optimally) stored in a 16-bit field, or a wider (>16-bit)

field with redundant sign bits . The two storage methods are described below.

5.7.4

Q15 in 16 bits

Q15 format is a 16-bit signed fractional value in the range -1

≤ n < 1. The value is

stored in two’s-complement form with a sign bit (bit 15), an implied binary point

between bits 15 and 14, and 15 significant fractional bits (bit 14 to bit 0).

Total bits

Range

Format

Short name

-1

≤ n < 1

1.31

Q31

-1

≤ n< 1

1.15

Q15

-2

≤ n < 2

2.14

Q14

Table 5.7 Example data formats

Description

Name

Format

Signed 16-bit fractional

Q14

14 significant fr actional bits

Signed 16-bit fractional

Q15

15 significant fr actional bits

Signed 16-bit fractional

Q31

31 significant fr actional bits

Table 5.8 Supported multiply accumulate data formats

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