Sine/cosine generator and method
First Claim
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1. A sin/cos generator, comprising:
- (a) a coarse memory storing sines and cosines of coarse angles with said coarse angles within the first octant;
(b) a fine memory storing sines .[.and cosines.]. of fine angles with the magnitudes of said fine angles within .Iadd.half .Iaddend.the difference between successive coarse angles;
(c) a phase input decoder, said decoder decoding an input phase to yield a coarse memory address and a fine memory address; and
(d) arithmetic circuitry .[.coupling said first and second memories with addition, multiplication, and sign circuitry whereby.]. .Iadd.coupled to said memories for computing .Iaddend.the sine and cosine of an angle encoded by said input phase .[.is computed.]. using .[.the.]. trigonometric formulas .[.sin(A+B)=sin(A)cos(B)+cos(A)sin(B) and cos(A+B)=cos(A)cos(B)-sin(A)sin(B).]..
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Abstract
A sine/cosine generator with coarse and fine angles having compressed sine and cosine read only memories (ROMS) by use of symmetry of coarse angles about π/4 and, optionally, symmetry of fine angles about 0. The output of the ROMs directly feed multiplexers for utilization of the compressed storage. Addressing of complementary coarse angles is with one'"'"'s complementing of the address and of complementary fine angles is with two'"'"'s commplementing of the address. Fine sines and cosines are stored in recoded version for direct use in multipliers for computations using the sum of angles formulas.
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Citations
20 Claims
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1. A sin/cos generator, comprising:
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(a) a coarse memory storing sines and cosines of coarse angles with said coarse angles within the first octant; (b) a fine memory storing sines .[.and cosines.]. of fine angles with the magnitudes of said fine angles within .Iadd.half .Iaddend.the difference between successive coarse angles; (c) a phase input decoder, said decoder decoding an input phase to yield a coarse memory address and a fine memory address; and (d) arithmetic circuitry .[.coupling said first and second memories with addition, multiplication, and sign circuitry whereby.]. .Iadd.coupled to said memories for computing .Iaddend.the sine and cosine of an angle encoded by said input phase .[.is computed.]. using .[.the.]. trigonometric formulas .[.sin(A+B)=sin(A)cos(B)+cos(A)sin(B) and cos(A+B)=cos(A)cos(B)-sin(A)sin(B).].. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 18)
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13. A method of generating the sine and cosine of an angle, comprising the steps of:
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(a) partitioning an input angle into an input quadrant indicator, an input coarse angle, and an input fine angle where said input coarse angle is one of a plurality of coarse angles located in the first quadrant and said input fine angle is one of a plurality of fine angles located .[.in a range of extent equal to the difference.]. between successive coarse angles; (b) providing a first lookup table of sines and cosines of coarse angles for coarse angles in the first octant; (c) using said first lookup table to find the sine and cosine of said input coarse angle, and when said input coarse angle is in the second octant its complementary angle is used in said first lookup table; (d) providing a second lookup table of sines .[.and cosines.]. of fine angles; (e) using said second lookup table to find the sine .[.and cosine.]. of said input fine angle; and (f) combining said sine and cosine of said input coarse angle and said sine and .Iadd.a .Iaddend.cosine of said fine angle according to said quadrant indicator to yield the sine .Iadd.and cosine .Iaddend.of said input angle. - View Dependent Claims (14, 15, 16)
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19. Iaddend..Iadd.32. In a circuit having means for computing the sine and cosine of any phase angle 0°
- to 360°
using trigonometric formulas and means for storing values related to phase angles, the improvement wherein said computing means comprises means for performing calculations using trigonometric formulas (1) sin(A+B)=sin(A)-Dsin(A)+cos(A)sin(B) and (2) cos(A+B)=cos(A)-Dcos(A)-sin(A)sin(B), where A is one of said coarse angles, B is one of said fine angles, and D is one minus cos(B). .Iaddend..Iadd.33. The circuit of claim 32 wherein said means for storing values related to phase angles is limited to values within a contiguous
- to 360°
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20. 45°
- . .Iaddend..Iadd.34. The circuit of claim 32 wherein said means for storing values includes a coarse memory for coarse angles within said contiguous 45° and
a fine memory for fine angles within one-half of the difference between successive coarse angles. .Iaddend..Iadd.35. The circuit of claim 34 wherein said fine memory stores values of one minus the cosines of said fine angles. .Iaddend..Iadd.36. In a sin/cos generator having input means for receiving an input signal related to a selected one of 360°
phase angles, storage means for storing data related to the sin/cos of phase angles within a contiguous 45°
of the 360°
, and circuit means for calculating the sin/cos of any selected phase angle of the 360°
using the data from said storage means, the improvement wherein said calculating means includes means for calculating any selected angle of the 360°
using only said input signal and the stored data related to the sin/cos of the phase angles within said contiguous 45°
. .Iaddend.
- . .Iaddend..Iadd.34. The circuit of claim 32 wherein said means for storing values includes a coarse memory for coarse angles within said contiguous 45° and
Specification