SPRAD27A July 2022 – August 2022 AM2431 , AM2432 , AM2434 , AM2631 , AM2631-Q1 , AM2632 , AM2632-Q1 , AM2634 , AM2634-Q1 , AM2732 , AM2732-Q1 , AM6411 , AM6412 , AM6421 , AM6422 , AM6441 , AM6442
Table 2-1 and Table 2-2 show the coefficients for the sine and cosine approximation obtained from the Sollya program. The table shows the error expected given the range reduction and order of the polynomial. If you are trying to achieve full single precision floating-point accuracy, then you need to get to ~1e-7.
Range | Number of Terms | Absolute Error | Polynomial |
---|---|---|---|
−π/2 : π/2 | 3 | 1.00E-04 |
Equation 8. x *
(0.999891757965087890625 + x2 *
(-0.165960013866424560546875 + x2 *
7.602870464324951171875e-3))
|
−π/2 : π/2 | 4 | 6.00E-07 |
Equation 22. x *
(0.999996483325958251953125 + x2 *
(-0.166647970676422119140625 + x^2 * (8.306086063385009765625e-3
+ x2 * (-1.83582305908203125e-4))))
|
−π/2 : π/2 | 5 | 6.00E-09 |
Equation 10. x * (1 +
x2 * (-0.1666665971279144287109375 +
x2 * (8.333069272339344024658203125e-3 +
x2 * (-1.98097783140838146209716796875e-4 +
x2 *
2.6061034077429212629795074462890625e-6))))
|
−π/4 : π/4 | 2 | 1.50E-04 |
Equation 11. x *
(0.99903142452239990234375 + x2 *
(-0.16034401953220367431640625))
|
−π/4 : π/4 | 3 | 5.60E-07 |
Equation 12. x *
(0.9999949932098388671875 + x2 *
(-0.166601598262786865234375 + x2 *
8.12153331935405731201171875e-3))
|
−π/4 : π/4 | 4 | 1.80E-09 |
Equation 13. x * (1 +
x2 * (-0.166666507720947265625 + x2 *
(8.331983350217342376708984375e-3 + x2 *
(-1.94961365195922553539276123046875e-4))))
|
−π/4 : π/4 | 5 | 6.00E-11 |
Equation 14. x * (1 +
x2 * (-0.16666667163372039794921875 +
x2 * (8.33337195217609405517578125e-3 +
x2 * (-1.98499110410921275615692138671875e-4 +
x2 *
2.800547008519060909748077392578125e-6))))
|
Range | Number of Terms | Absolute Error | Polynomial |
---|---|---|---|
−π/2 : π/2 | 3 | 6.00E-04 |
Equation 15. 0.9994032382965087890625 + x2 *
(-0.495580852031707763671875 + x2 *
3.679168224334716796875e-2)
|
−π/2 : π/2 | 4 | 6.70E-06 |
Equation 16. 0.99999332427978515625 + x2 *
(-0.4999125301837921142578125 + x2 *
(4.1487820446491241455078125e-2 + x2 *
(-1.27122621051967144012451171875e-3)))
|
−π/2 : π/2 | 5 | 6.00E-08 |
Equation 17. 0.999999940395355224609375 + x2 *
(-0.499998986721038818359375 + x2 *
(4.1663490235805511474609375e-2 + x2 *
(-1.385320327244699001312255859375e-3 + x2 *
2.31450176215730607509613037109375e-5)))
|
−π/4 : π/4 | 3 | 1.00E-05 |
Equation 18. 0.999990046024322509765625 + x2 *
(-0.4997082054615020751953125 + x2 *
4.03986163437366485595703125e-2)
|
−π/4 : π/4 | 4 | 3.30E-08 |
Equation 19. 1 + x2 *
(-0.49999892711639404296875 + x2 *
(4.16561998426914215087890625e-2 + x2 *
(-1.35968066751956939697265625e-3)))
|
−π/4 : π/4 | 5 | 1.00E-10 |
Equation 20. 1 + x2 *
(-0.5 + x2 * (4.16666455566883087158203125e-2 +
x2 * (-1.388731296174228191375732421875e-3 +
x2 *
2.4432971258647739887237548828125e-5)))
|