
118 GPGPU Programming for Games and Science
TABLE 3. 8: Minimax polynomial approximations to f(x)=tan(x)
d coefficients d coefficients
3 p
0
=1 5 p
0
=1
p
1
=4.4295926544736286 ∗ 10
−1
p
1
=3.1401320403542421 ∗ 10
−1
e =1.1661892256204731 ∗ 10
−2
p
2
=2.0903948109240345 ∗ 10
−1
e =5.8431854390143118 ∗ 10
−4
7 p
0
=1 9 p
0
=1
p
1
=3.3607213284422555 ∗ 10
−1
p
1
=3.3299232843941784 ∗ 10
−1
p
2
=1.1261037305184907 ∗ 10
−1
p
2
=1.3747843432474838 ∗ 10
−1
p
3
=9.8352099470524479 ∗ 10
−2
p
3
=3.7696344813028304 ∗ 10
−2
e =3.5418688397723108 ∗ 10
−5
p
4
=4.6097377279281204 ∗ 10
−2
e =2.2988173242199927 ∗ 10
−6
11 p
0
=1 13 p
0
=1
p
1
=3.3337224456224224 ∗ 10
−1
p
1
=3.3332916426394554 ∗ 10
−1
p
2
=1.3264516053824593 ∗ 10
−1
p
2