Inverse Sinc Approximation (HP-42S) - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: General Forum (/forum-4.html) +--- Thread: Inverse Sinc Approximation (HP-42S) (/thread-2914.html) |
Inverse Sinc Approximation (HP-42S) - Gerson W. Barbosa - 01-24-2015 03:30 AM The approximation is good only when the arguments approach 1 (better on Free42). Anyway, this might be useful in some situations. Sinc Function Code:
\[0.7 \rightarrow 1.4(0990334015)\] \[0.8 \rightarrow 1.131(05968014)\] \[0.9 \rightarrow 0.78668(1275111)\] \[\frac{\sqrt{8}}{\pi }\rightarrow 0.78539(6392174)\] \[0.95 \rightarrow 0.5519109(01224)\] \[0.999 \rightarrow 0.077471290(5533)\] \[0.999 \rightarrow 0.077471290316(5) (Free42)\] Edited to add plot. RE: Inverse Sinc Approximation (HP-42S) - Gerson W. Barbosa - 01-29-2015 05:52 PM A rough improvement over the previous one: Code:
0.999 7.7471290(5533)e-2 [ 1.2 seconds ] 0.999 7.74712903165e-2 (Free42) 0.990 2.45317808(947)e-1 0.990 2.45317808854e-1 (Free42) 0.950 5.51910978(573)e-1 0.950 5.51910978(542)e-1 (Free42) 0.900 7.866830720(53)e-1 0.900 7.866830720(28)e-1 (Free42) 0.800 1.1311025855(6) 0.800 1.131102585(58) (Free42) 0.700 1.41018537(706) 0.700 1.41018537(705) (Free42) 0.600 1.660034813(68) 0.600 1.660034813(67) (Free42) 0.500 1.89549426(538) [ 7.8 seconds ] 0.500 1.89549426(538) (Free42) 0.400 2.1253451(8634) 0.400 2.1253451(8634) (Free42) 0.300 2.3564411(3218) 0.300 2.3564411(3218) (Free42) 0.200 2.59573(889746) 0.200 2.59573(889746) (Free42) 0.100 2.85234(009548) 0.100 2.85234(009547) (Free42) 0.050 2.99145(085513) 0.050 2.99145(085514) (Free42) 0.000 3.1415(7574992) [ 17.7 seconds ] 0.000 3.1415(7574992) (Free42) |