1.2 On-Chip Boot ROM IQ Math Tables
On-Chip Boot ROM IQ Math Tables
3K x 16 words of the boot ROM memory is reserved for IQ math tables. These math tables are provided
to help improve performance and save RAM space.
The math tables included in the boot ROM are used by the Texas Instruments™ C28x™ IQMath Library -
A Virtual Floating Point Engine (literature number SPRC087). The 28x IQmath Library is a collection of
highly optimized and high precision mathematical functions for C/C++ programmers to seamlessly port a
floating-point algorithm into fixed-point code on TMS320C28x devices.
These routines are typically used in computational-intensive real-time applications where optimal
execution speed and high accuracy is critical. By using these routines you can achieve execution speeds
that are considerably faster than equivalent code written in standard ANSI C language. In addition, by
providing ready-to-use high precision functions, the TI IQmath Library can shorten significantly your DSP
application development time. The C28x™ IQMath Library - A Virtual Floating Point Engine (literature
number SPRC087) can be downloaded from the TI website.
The following math tables are included in the Boot ROM:
• Sine/Cosine Table
– Table size: 1282 words
– Q format: Q30
– Contents: 32-bit samples for one and a quarter period sine wave
This is useful for accurate sine wave generation and 32-bit FFTs. This can also be used for 16-bit
math, just skip over every second value.
• Normalized Inverse Table
– Table size: 528 words
– Q format: Q29
– Contents: 32-bit normalized inverse samples plus saturation limits
This table is used as an initial estimate in the Newton-Raphson inverse algorithm. By using a more
accurate estimate the convergence is quicker and hence cycle time is faster.
• Normalized Square Root Table
– Table size: 274 words
– Q format: Q30
– Contents: 32-bit normalized inverse square root samples plus saturation
This table is used as an initial estimate in the Newton-Raphson square-root algorithm. By using a more
accurate estimate the convergence is quicker and hence cycle time is faster.
• Normalized Arctan Table
– Table size: 452 words
– Q format: Q30
– Contents 32-bit second order coefficients for line of best fit plus normalization table
This table is used as an initial estimate in the Arctan iterative algorithm. By using a more accurate
estimate the convergence is quicker and hence cycle time is faster.
• Rounding and Saturation Table
– Table size: 360 words
– Q format: Q30
– Contents: 32-bit rounding and saturation limits for various Q values
SPRU722C – November 2004 – Revised October 2006 Boot ROM Overview 13
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