SINE/COSINE GENERATOR

• US 20090300088A1
• Filed: 05/29/2008
• Published: 12/03/2009
• Est. Priority Date: 05/29/2008
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Michaels, Alan J., Chester, David B.
• Granted Patent: US 8,200,728 B2
• Time in Patent Office: Days
• US Class Current: 708/276
• CPC Class Codes: G06F 1/03 working, at least partly, by table look-up G06F1/025 takes precedence
• CPC Class Codes: G06F 7/49942 Significance control
• CPC Class Codes: G06F 7/548 Trigonometric functions; Co-ordinate transformations

Abstract

A method (30°) for generating a sine and cosine of an input angle (Ø₁₀₂). The method involves decomposing Ø₁₀₂ to an octant or quadrant, a coarse angle (A), and a fine angle (B), determining cos(A), and determining sin(A). The method also involves decomposing cos(A) and sin(A) to a most significant word (MSW) and a least significant word (LSW). The method further involves computing an approximation of 1−cos(B), an approximation of sin(B), and a plurality of products (P₁, . . . , P₄) using the MSWs and approximations. The method involves computing approximations of cos(Ø′₁₀₂) and sin(Ø′₁₀₂) using the values for cos(A), sin(A), and P₁, . . . , P₄. The method involves scaling the approximations of cos(Ø′₁₀₂) and sin(Ø′₁₀₂) to a desired resolution.

Claims

1. A method for generating a sine and cosine of an input angle, comprising the steps of:

decomposing said input angle into an octant or quadrant, a coarse angle, and a fine angle;

determining a cosine and a sine of said coarse angle;

decomposing said cosine of said coarse angle to a first most significant word and a first least significant word and said sine of said coarse angle to a second most significant word and a second least significant word;

computing an approximation of one minus a cosine of said fine angle and an approximation of a sine of said fine angle;

computing a first product by multiplying said first most significant word by said approximation of a sine of said fine angle, a second product by multiplying said first most significant word by said approximation of one minus a cosine of said fine angle, a third product by multiplying said second most significant word by said approximation of one minus a cosine of said fine angle, and a fourth product by multiplying said second most significant word by said approximation of a sine of said fine angle; and

generating approximations of a cosine of said input angle modulo π

/k and a sine of said input angle modulo π

/k using said cosine of said coarse angle, said sine of said coarse angle, and each of said products, wherein k is an integer selected in accordance with octant or quadrant symmetry.

2. The method according to claim 1, wherein said generating step further comprises

computing a first difference by subtracting said second product from said cosine of said coarse angle and a second difference by subtracting said third product from said sine of said coarse angle,

subtracting said fourth product from said first difference to yield said approximation of said cosine of said input angle modulo π

/k, and

combining said first product and said second difference to yield said approximation of said sine of said input angle modulo π

/k.

3. The method according to claim 1, further comprising the steps of scaling said approximation of said sine of said input angle by a first scale factor, and combining said scaled approximation of said sine of said input angle with said approximation of said cosine of said input angle to yield said cosine of said input angle.

4. The method according to claim 3, further comprising the steps of scaling said approximation of said cosine of said input angle by a second scale factor, and combining said scaled approximation of said cosine of said input angle with said approximation of said sine of said input angle to yield said sine of said input angle.

5. The method according to claim 4, wherein said first and second scale factors are a function of a weighting of said first and second most significant words.

6. The method according to claim 1, wherein said cosine and sine of said coarse angle are pre-computed values selected from at least one look up table.

7. The method according to claim 1, wherein said approximations of one minus a cosine of said fine angle and said sine of said fine angle are computed using Taylor Series Approximations.

8. The method according to claim 7, wherein each of said approximations of one minus a cosine of said fine angle and said sine of said fine angle is computed using a Taylor Series of an N^th order selected for providing an n bit precision.

9. The method according to claim 1, wherein said first and second most and least significant words are pre-computed values selected from at least one look up table.

10. The method according to claim 9, wherein said first and second least significant words are scaled such that bits stored in said at least one look up table are significant.

11. The method according to claim 1, wherein said coarse angle is in a quadrant or octant of a two dimensional space.

12. The method according claim 11, wherein said coarse angle is one of a plurality of angles in said quadrant or octant of a two dimensional space.

13. The method according to claim 1, wherein said fine angle is bounded by a smallest coarse angle existing in a two dimensional space.

14. The method according to claim 4, further comprising the steps of mapping said sine of said input angle modulo π

/k to a sine of said input angle using N most significant bits from said input angle and mapping said cosine of said input angle modulo π

/k to a cosine of said input angle using said N most significant bits, wherein N is an integer.

15. A sine/cosine generator, comprising:

a decomposition device configured for decomposing said input angle into an octant or quadrant, a coarse angle, and a fine angle;

at least one coarse angle device configured for determining a cosine of said coarse angle, determining a sine of said coarse angle, decomposing said cosine of said coarse angle to a first most significant word and a first least significant word, and decomposing said sine of said coarse angle to a second most significant word and a second least significant word;

at least one fine angle device configured for computing an approximation of one minus a cosine of said fine angle and an approximation of a sine of said fine angle;

a product computation device configured for computing a first product by multiplying said first most significant word by said approximation of a sine of said fine angle, a second product by multiplying said first most significant word by said approximation of one minus a cosine of said fine angle, a third product by multiplying said second most significant word by said approximation of one minus a cosine of said fine angle, and a fourth product by multiplying said second most significant word by said approximation of a sine of said fine angle; and

an output computation device coupled to said product computation device and said at least one coarse angle device, said output computation device configured for generating approximations of a cosine of said input angle modulo π

/k and a sine of said input angle modulo π

/k using said cosine of said coarse angle, said sine of said coarse angle, and each of said products, wherein k is an integer selected in accordance with octant or quadrant symmetry.

16. The sine/cosine generator according to claim 15, wherein said output computation device is further configured for

computing a first difference by subtracting said second product from said cosine of said coarse angle and a second difference by subtracting said third product from said sine of said coarse angle,

subtracting said fourth product from said first difference to yield said approximation of said cosine of said input angle modulo π

/k, and

combining said first product and said second difference to yield said approximation of said sine of said input angle modulo π

/k.

17. The sine/cosine generator according to claim 15, wherein said output computation device is further configured for scaling said approximation of said sine of said input angle by a first scale factor, and combining said scaled approximation of said sine of said input angle with said approximation of said cosine of said input angle to yield said cosine of said input angle.

18. The sine/cosine generator according to claim 17, wherein said output computation device is further configured for scaling said approximation of said cosine of said input angle by a second scale factor, and combining said scaled approximation of said cosine of said input angle with said approximation of said sine of said input angle to yield said sine of said input angle.

19. The sine/cosine generator according to claim 18, wherein said first and second scale factors are a function of a weighting of said first and second most significant words.

20. The sine/cosine generator according to claim 15, wherein said at least one coarse angle device is comprised of at least one look up table and said cosine and sine of said coarse angle are pre-computed values selected from said at least one look up table.

21. The sine/cosine generator according to claim 15, wherein said at least one fine angle device is further configured for computing said approximations of one minus a cosine of said fine angle and said sine of said fine angle using Taylor Series Approximations.

22. The sine/cosine generator according to claim 21, wherein said at least one fine angle device is further configured for computing said each of said approximations of one minus a cosine of said fine angle and said sine of said fine angle using a Taylor Series of an N^th order selected for providing an n bit precision.

23. The sine/cosine generator according to claim 15, wherein said at least one coarse angle device is comprised of at least one look up table and said first and second most and least significant words are pre-computed values selected from said at least one look up table.

24. The sine/cosine generator according to claim 15, wherein said coarse angle is in a octant or quadrant of a two dimensional space and said fine angle is bounded by a smallest coarse angle existing in a two dimensional space.

25. The sine/cosine generator according to claim 18, wherein said output computation device is further configured for mapping said sine of said input angle modulo π

/k to a sine of said input angle using N most significant bits from said input angle and for mapping said cosine of said input angle modulo π

/k to a cosine of said input angle using said N most significant bits, wherein N is an integer.