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: 00 { 66-Byte Prgm } 01>LBL "ASINC" 02 ENTER 03 ENTER 04 ENTER 05 78 06 175 07 ÷ 08 × 09 456 10 175 11 ÷ 12 - 13 × 14 243 15 35 16 ÷ 17 + 18 × 19 2424 20 175 21 ÷ 22 - 23 × 24 1587 25 175 26 ÷ 27 + 28 SQRT 29 .END. $0.7 \rightarrow 1.4(0990334015)$ $0.8 \rightarrow 1.131(05968014)$ $0.9 \rightarrow 0.78668(1275111)$ $\frac{\sqrt{8}}{\pi }\rightarrow 0.78539(6392174)$ $0.95 \rightarrow 0.5519109(01224)$ $0.999 \rightarrow 0.077471290(5533)$ $0.999 \rightarrow 0.077471290316(5) (Free42)$ 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: 00 { 164-Byte Prgm } 01>LBL "ASINC" 02 ENTER 03 +/- 04 E^X 05 62 06 × 07 21 08 - 09 IP 10 STO 01 11 X<>Y 12 78 13 175 14 ÷ 15 RCL× ST Y 16 456 17 175 18 ÷ 19 - 20 RCL× ST Y 21 243 22 35 23 ÷ 24 + 25 RCL× ST Y 26 2424 27 175 28 ÷ 29 - 30 RCL× ST Y 31 1587 32 175 33 ÷ 34 + 35 STO 02 36 X<>Y 37 +/- 38 1 39 + 40 STO 03 41>LBL 00 42 RCL 03 43 4 44 RCL+ 01 45 Y^X 46 LASTX 47 -1.99209761578E-1 48 RCL× ST L 49 1.98659851625 50 + 51 E^X 52 X<>Y 53 -1.44092400765 54 Y^X 55 × 56 × 57 STO+ 02 58 DSE 01 59 GTO 00 60 RCL 02 61 SQRT 62 .END. 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)