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 2-3 shows the coefficients for the arctangent approximation obtained from the Sollya program. The table shows the error expected given the range reduction and order of the polynomial.
| Range | Terms | Abs err | Polynomial |
|---|---|---|---|
| -1 : 1 | 4 | 8.00E-05 |
Equation 21. x *
(0.99921381473541259765625 + x2 *
(-0.321175038814544677734375 + x2 *
(0.146264731884002685546875 + x2 *
(-3.8986742496490478515625e-2))))
|
| -1 : 1 | 5 | 2.30E-05 |
Equation 22. x *
(0.999970018863677978515625 + x2 *
(-0.3317006528377532958984375 + x2 *
(0.1852150261402130126953125 + x2 *
(-9.1925732791423797607421875e-2 + x2 *
2.386303804814815521240234375e-2))))
|
| -1 : 1 | 6 | 3.40E-06 |
Equation 23. x *
(0.999995648860931396484375 + x2 *
(-0.3329949676990509033203125 + x2 *
(0.19563795626163482666015625 + x2 *
(-0.121243648231029510498046875 + x2 *
(5.7481847703456878662109375e-2 + x2 *
(-1.3482107780873775482177734375e-2))))))
|
| tan(pi/12) | 3 | 2.00E-07 |
Equation 24. x *
(0.999994814395904541015625 + x2 *
(-0.3327477872371673583984375 + x2 *
0.18327605724334716796875))
|
| tan(pi/12) | 4 | 3.00E-09 |
Equation 25. x *
(0.999999940395355224609375 + x2 *
(-0.333319008350372314453125 + x2 *
(0.19920165836811065673828125 + x2 *
(-0.12685041129589080810546875))))
|
| tan(pi/12) | 5 | 8.70E-11 |
Equation 26. x * (1 +
x2 * (-0.333333194255828857421875 + x2
* (0.19998063147068023681640625 + x2 *
(-0.14202083647251129150390625 + x2 *
9.6703059971332550048828125e-2))))
|