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When the program requires the sine of a value, it can use the lookup table to retrieve the closest sine value from a memory address, and may also interpolate to the sine of the desired value, instead of calculating by mathematical formula. Lookup tables can thus used by mathematics coprocessors in computer systems.
Shift register lookup table. A shift register lookup table, also shift register LUT or SRL, refers to a component in digital circuitry. It is essentially a shift register of variable length. The length of SRL is set by driving address pins high or low and can be changed dynamically, if necessary. [1] The SRL component is used in FPGA devices ...
CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
In mathematics, the values of the trigonometric functions can be expressed approximately, as in (/), or exactly, as in (/) = /.While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots.
The company's field-programmable gate array (FPGA) chips were marketed as 3-D programmable logic devices or 3PLDs. The chips have 220-630 thousand 4-input lookup table (LUT) from the user point of view and are capable of working at 1.6 GHz physical clock speed.
One way to reduce the truncation in the address lookup is to have several smaller lookup tables in parallel and use the upper bits to index into the tables and the lower bits to weigh them for linear or quadratic interpolation. Ie use a 24-bit phase accumulator to look up into two 16-bit LUTS. Address into the truncated 16 MSBs, and that plus 1.
Simplified example illustration of a logic cell (LUT – lookup table, FA – full adder, DFF – D-type flip-flop) The most common FPGA architecture consists of an array of logic blocks called configurable logic blocks (CLBs) or logic array blocks (LABs) (depending on vendor), I/O pads, and routing channels. [1]