NXP Semiconductors K32 L2A Series, Reference Manual, Page: 864 / 1379

For the unsigned integer format used in the MMDVSQ's square root calculation, an
u(nsigned)Qm.n notation requires m+n bits (m+n = 32) for the input radicand. An uQm.n
format produces an uQ(m/2).(n/2) square root. As examples, consider the following
tables involving the square root of 2 and square root of “pi” calculations. As expected, as
the number of fractional bits (n) increases, the error between the calculated square root
and the “actual” result decreases.
Table 32-2. Square Root of 2 Calculations (√2 = 1.4142135623)
RCND [Hex] RCND Q format Results [Hex] RES Q Format Decimal % Error
0x0000_0002 uQ32.00 0x0000_0001 uQ16.00 1.0 -29.289%
0x0002_0000 uQ16.16 0x0000_016A uQ08.08 1.4140625 -0.011%
0x0200_0000 uQ08.24 0x0000_16A0 uQ04.12 1.4140625 -0.011%
0x2000_0000 uQ04.28 0x0000_5A82 uQ02.14 1.4141845703 -0.002%
0x8000_0000 uQ02.30 0x0000_B504 uQ01.15 1.4141845703 -0.002%
Table 32-3. Square Root of Pi Calculations (√Pi = 1.7724538509)
RCND [Hex] RCND Q format Results [Hex] RES Q Format Decimal % Error
0x0000_0003 uQ32.0 0x0000_0001 uQ16.00 1.0 -43.581%
0x0003_243F uQ16.16 0x0000_01C5 uQ08.08 1.76953125 -0.165%
0x0324_3F6A uQ08.24 0x0000_1C5B uQ04.12 1.772216769 -0.013%
0x3243_F6A8 uQ04.28 0x0000_716F uQ02.14 1.7723999023 -0.003%
0xC90F_DAA0 uQ02.30 0x0000_E2DF uQ01.15 1.7724304199 -0.001%
The application of the Q notation for square root calculations provides a powerful
extension for these types of fractional numeric computations using fixed-point integer
processing hardware.
32.4.2 Execution times
The MMDVSQ module includes early termination logic to finish both divide and square
root calculations as quickly as possible, based on the magnitude of the input operand.
Accordingly, the execution time for the calculations is data dependent as defined in
Table
32-4 and Table 32-5 . In this context, the execution time is defined from the register write
to initiate the calculation until the result register has been updated and available to read.
Stated differently, it represents the time CSR[BUSY] is asserted for a given calculation.
In the following two tables, “x” signals a bit with a don’t care value.
Integer square root
K32 L2A Reference Manual, Rev. 2, 01/2020
864 NXP Semiconductors