GB1331410A - Digital calculating apparatus for performing the cordic algo- rithm - Google Patents

Abstract

1331410 Digital calculators SOLARTRON ELECTRONIC GROUP Ltd 9 Aug 1971 8365/73 Divided out of 1321067 Heading G4A A digital calculator for performing the cordic algorithm includes two registers loaded with initial values. In successive cycles the value in one register is added to, or subtracted from, a multiple of the value in the other register, the result being placed in the one register for use in the next cycle. Means are provided for correcting the result to a required degree of accuracy after each two cycles. The multiples for successive pairs of cycles are respectively R<SP>-1</SP>, R<SP>-2</SP>, R<SP>-3</SP>, &c., R being the radix used in the calculation. The calculator may be used to calculate Sin (# + 2α) and Cos (# + 2α) or to convert Cartesian co-ordinates x, y to polar coordinates r, #. In the former case the initial valves are Sin # and Cos #, and in the latter case x and y. As described R = 10 and α is restricted to increments whose tangents are 0À1, 0À01, 0À001, &c. In the calculation of Sin (6 + 2α) and Cos (# + 2α), after two cycles the content of one register is Sec<SP>2</SP>α. Sin (# + 2α) and of the other is Sec<SP>2</SP>α. Cos (# + 2α). Since Sec<SP>2</SP>α = 1 + Tan<SP>2</SP>α the approximate value of, for example, Sin (# + 2α) can be obtained by multiplying the value in the register by 1-Tan<SP>2</SP>α. The register content will now be (1-Tan<SP>4</SP>α) Sin(# + 2α). As Tan α = 0À1 for the first two cycles, Tan<SP>4</SP>α = 0À0001 and the discrepancy between the value in the register and the true value of Sin (# + 2α) may be considered negligible. The multiplication by 1-Tan<SP>2</SP>α is performed by subtracting from the contents of the register the contents multiplied by Tan<SP>2</SP>α i.e. by 0À01. To obtain a higher accuracy the value in the register may be multiplied by Tan<SP>4</SP>α and added to itself, giving the result (1-Tan<SP>8</SP>α) Sin (# + 2α). Here Tan<SP>8</SP>α (i.e. 10<SP>-8</SP>) is negligible. A further two cycles of the algorithm may now be performed, using Tan α = 0À01. The result is corrected in a manner similar to that described above.