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 Math Products
GoFast® for ARM / Cortex and CrossWorks
Fast Floating Point Library
Features
- Fast
- Reentrant
- ROMable
- Conforms to IEEE 754 Format
- "Link and Go" compiler support for CrossWorks ARM
- Includes complete source, test programs, project files, and startup code
Description
GoFast® for ARM / Cortex was carefully designed for high performance operation in embedded applications and ease of use including “link and go” compatibility with the CrossWorks C compiler. GoFast provides ROMable, reentrant IEEE and ANSI compatible ARM floating point support. It boosts the performance of an application’s math calculations or eliminates the need for a hardware floating-point coprocessor, in order to reduce product manufacturing cost. It is delivered with full assembly source code.
Currently GoFast is offered only for the ARM and Thumb-2 instruction sets, not Thumb.
Functionality
GoFast ARM / Cortex offers the following reentrant floating point routines, for both single and double precision:
- intrinsic basic operations + - * /
- intrinsic conversions
- sqrt
- sin, cos, tan
- asin, acos, atan, atan2
- sinh, cosh, atanh
- log, log10, exp, pow
- floor, ceil, fabs
- modf, fmod, frexp, ldexp
Floating Point Technology
GoFast is based on “Architecture Independent Technology” (AIT) and proven floating point algorithms that were developed for over a decade. The algorithms have been thoroughly tested using automated methods.
Conformance and Testing
The accuracy of each GoFast Floating Point Library is within one (least significant) bit for arithmetic functions and two bits for transcendental functions, in most cases. The IEEE 754 Floating Point Format defines special representations for underflow, overflow, and invalid operation. The GoFast routines use these formats and adhere to the IEEE 754 error handling procedures in all applicable cases. Quality assurance and testing procedures have assured proper product operation. In addition, each delivery includes target specific test programs assuring confidence of product operation.
Timings
The following tables give the times for all floating point operations, for GoFast and the CrossWorks floating point library. The times, in microseconds, were measured using the indicated processor and evaluation board. The basic operations (add, subtract, multiply, divide, conversions, and comparisons) in the CrossWorks C library are hand-coded and faster than those in GoFast, so the CrossWorks versions are used instead. (If you only need these basic operations, you don’t need GoFast.) Thus, the routines linked are a mixture of both libraries, as indicated in bold below. GoFast provides the greatest benefit for the more complex operations, typically offering a 2x to 3x performance boost.
Microsecond Timings
ARM7: AT91SAM7X256-EK, 48 MHz, RAM
| |
Double Precision |
Single Precision |
| Function |
GoFast |
CrossWorks |
GoFast |
CrossWorks |
| add |
2.5 |
1.6 |
1.6 |
1.0 |
| subtract |
3.0 |
2.0 |
1.9 |
1.4 |
| multiply |
2.7 |
2.2 |
1.6 |
1.0 |
| divide |
16.5 |
9.2 |
8.3 |
2.3 |
| sqrt |
32.3 |
46.6 |
16.7 |
15.3 |
| exp |
13.1 |
46.6 |
4.3 |
32.4 |
| log |
27.2 |
60.2 |
11.3 |
28.9 |
| log10 |
28.3 |
62.4 |
11.6 |
30.0 |
| sin |
11.6 |
41.9 |
4.0 |
21.0 |
| cos |
10.6 |
53.1 |
4.0 |
25.2 |
| tan |
28.2 |
59.9 |
11.3 |
28.5 |
| asin |
45.1 |
109.2 |
34.8 |
48.2 |
| acos |
43.8 |
107.6 |
42.2 |
46.8 |
| atan |
27.1 |
64.4 |
11.6 |
30.2 |
| atan 2 |
42.8 |
75.5 |
19.2 |
34.6 |
| pow |
40.5 |
112.9 |
16.7 |
65.8 |
| tanh |
30.7 |
62.5 |
19.2 |
40.1 |
| sinh |
30.4 |
65.0 |
12.1 |
39.0 |
| cosh |
29.8 |
63.9 |
11.6 |
40.6 |
| modf |
1.4 |
1.9 |
1.1 |
1.3 |
| fmod |
1.6 |
16.5 |
1.0 |
8.0 |
| fabs |
0.5 |
0.5 |
0.3 |
0.3 |
| floor |
1.1 |
1.9 |
0.7 |
1.2 |
| ceil |
1.2 |
1.9 |
0.7 |
1.2 |
| ldexp |
2.2 |
2.3 |
1.4 |
1.6 |
| frexp |
1.3 |
1.8 |
0.8 |
1.3 |
| cmp |
1.7 |
1.0 |
1.2 |
0.8 |
| fp to long |
1.0 |
0.6 |
0.7 |
0.5 |
| fp to ulong |
1.0 |
0.5 |
0.7 |
0.5 |
| long to fp |
4.6 |
0.8 |
4.3 |
0.7 |
| ulong to fp |
4.5 |
0.7 |
4.2 |
0.7 |
| sgl to dbl |
0.9 |
0.5 |
— |
— |
| dbl to sgl |
1.1 |
0.6 |
— |
— |
GoFast is a registered trademark of Lantronix Inc. ARM is a registered trademark of ARM Ltd.
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