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This file was processed as: Mailbox/MIME Entity
(archive/mbox ).
You can browse this item here: cordic2.txt
Confidence Program Detection Match Type Support
100%
dexvert
Mailbox/MIME Entity (archive/mbox)
magic
Supported
100%
dexvert
Internet Message Format (text/imf)
magic
Supported
1%
dexvert
Swift 3D 3D Graphic (poly/swift3D3DGraphic)
ext
Unsupported
1%
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Boost Text serialization (other/boostTextSerialization)
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Unsupported
1%
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Text File (text/txt)
fallback
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100%
file
Mailbox text, 1st line "From steinmetz!uunet!seismo!sundc!pitstop!sun!decwrl!labrea!agate!pasteur!ames!ll-xn!vanhove Fri Feb 26 11:12:41 1988", ASCII text
default
100%
TrID
E-Mail message (Var. 2)
default
100%
checkBytes
Printable ASCII
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100%
perlTextCheck
Likely Text (Perl)
default
100%
siegfried
x-fmt/111 Plain Text File
default
100%
gt2
Textdatei (UNIX)
default
100%
detectItEasy
Format: plain text[LF]
default (weak)
100%
xdgMime
application/mbox
default
hex view +--------+-------------------------+-------------------------+--------+--------+ |00000000| 46 72 6f 6d 20 73 74 65 | 69 6e 6d 65 74 7a 21 75 |From ste|inmetz!u| |00000010| 75 6e 65 74 21 73 65 69 | 73 6d 6f 21 73 75 6e 64 |unet!sei|smo!sund| |00000020| 63 21 70 69 74 73 74 6f | 70 21 73 75 6e 21 64 65 |c!pitsto|p!sun!de| |00000030| 63 77 72 6c 21 6c 61 62 | 72 65 61 21 61 67 61 74 |cwrl!lab|rea!agat| |00000040| 65 21 70 61 73 74 65 75 | 72 21 61 6d 65 73 21 6c |e!pasteu|r!ames!l| |00000050| 6c 2d 78 6e 21 76 61 6e | 68 6f 76 65 20 46 72 69 |l-xn!van|hove Fri| |00000060| 20 46 65 62 20 32 36 20 | 31 31 3a 31 32 3a 34 31 | Feb 26 |11:12:41| |00000070| 20 31 39 38 38 0a 50 61 | 74 68 3a 20 62 65 6f 77 | 1988.Pa|th: beow| |00000080| 75 6c 66 21 73 74 65 69 | 6e 6d 65 74 7a 21 75 75 |ulf!stei|nmetz!uu| |00000090| 6e 65 74 21 73 65 69 73 | 6d 6f 21 73 75 6e 64 63 |net!seis|mo!sundc| |000000a0| 21 70 69 74 73 74 6f 70 | 21 73 75 6e 21 64 65 63 |!pitstop|!sun!dec| |000000b0| 77 72 6c 21 6c 61 62 72 | 65 61 21 61 67 61 74 65 |wrl!labr|ea!agate| |000000c0| 21 70 61 73 74 65 75 72 | 21 61 6d 65 73 21 6c 6c |!pasteur|!ames!ll| |000000d0| 2d 78 6e 21 76 61 6e 68 | 6f 76 65 0a 46 72 6f 6d |-xn!vanh|ove.From| |000000e0| 3a 20 76 61 6e 68 6f 76 | 65 40 58 4e 2e 4c 4c 2e |: vanhov|e@XN.LL.| |000000f0| 4d 49 54 2e 45 44 55 20 | 28 50 61 74 72 69 63 6b |MIT.EDU |(Patrick| |00000100| 20 56 61 6e 20 48 6f 76 | 65 29 0a 4e 65 77 73 67 | Van Hov|e).Newsg| |00000110| 72 6f 75 70 73 3a 20 63 | 6f 6d 70 2e 67 72 61 70 |roups: c|omp.grap| |00000120| 68 69 63 73 0a 53 75 62 | 6a 65 63 74 3a 20 52 65 |hics.Sub|ject: Re| |00000130| 3a 20 43 4f 52 44 49 43 | 53 0a 4d 65 73 73 61 67 |: CORDIC|S.Messag| |00000140| 65 2d 49 44 3a 20 3c 39 | 32 33 40 78 6e 2e 4c 4c |e-ID: <9|23@xn.LL| |00000150| 2e 4d 49 54 2e 45 44 55 | 3e 0a 44 61 74 65 3a 20 |.MIT.EDU|>.Date: | |00000160| 32 36 20 46 65 62 20 38 | 38 20 31 36 3a 31 32 3a |26 Feb 8|8 16:12:| |00000170| 34 31 20 47 4d 54 0a 4f | 72 67 61 6e 69 7a 61 74 |41 GMT.O|rganizat| |00000180| 69 6f 6e 3a 20 4d 49 54 | 20 4c 69 6e 63 6f 6c 6e |ion: MIT| Lincoln| |00000190| 20 4c 61 62 6f 72 61 74 | 6f 72 79 2c 20 4c 65 78 | Laborat|ory, Lex| |000001a0| 69 6e 67 74 6f 6e 2c 20 | 4d 41 0a 4c 69 6e 65 73 |ington, |MA.Lines| |000001b0| 3a 20 35 37 0a 49 6e 2d | 72 65 70 6c 79 2d 74 6f |: 57.In-|reply-to| |000001c0| 3a 20 74 75 72 6b 40 61 | 70 70 6c 65 2e 55 55 43 |: turk@a|pple.UUC| |000001d0| 50 27 73 20 6d 65 73 73 | 61 67 65 20 6f 66 20 31 |P's mess|age of 1| |000001e0| 38 20 46 65 62 20 38 38 | 20 30 32 3a 31 39 3a 30 |8 Feb 88| 02:19:0| |000001f0| 36 20 47 4d 54 0a 0a 0a | 09 54 68 61 6e 6b 73 20 |6 GMT...|.Thanks | |00000200| 74 6f 20 22 54 75 72 6b | 22 20 66 6f 72 20 70 6f |to "Turk|" for po| |00000210| 73 74 69 6e 67 20 74 68 | 65 20 43 4f 52 44 49 43 |sting th|e CORDIC| |00000220| 20 73 63 68 65 6d 65 20 | 2b 20 63 6f 64 65 2e 0a | scheme |+ code..| |00000230| 0a 49 20 68 61 76 65 20 | 61 20 66 65 77 20 63 6f |.I have |a few co| |00000240| 6d 6d 65 6e 74 73 20 77 | 68 69 63 68 20 72 65 61 |mments w|hich rea| |00000250| 64 65 72 73 20 6d 61 79 | 20 66 69 6e 64 20 75 73 |ders may| find us| |00000260| 65 66 75 6c 0a 0a 0a 46 | 69 72 73 74 2c 20 49 20 |eful...F|irst, I | |00000270| 74 68 69 6e 6b 20 74 68 | 65 20 65 78 70 72 65 73 |think th|e expres| |00000280| 73 69 6f 6e 20 66 6f 72 | 20 74 68 65 20 72 6f 74 |sion for| the rot| |00000290| 61 74 69 6f 6e 20 73 68 | 6f 75 6c 64 20 62 65 0a |ation sh|ould be.| |000002a0| 20 69 6e 20 74 65 72 6d | 73 20 6f 66 20 50 52 4f | in term|s of PRO| |000002b0| 44 55 43 54 53 20 69 6e | 73 74 65 61 64 20 6f 66 |DUCTS in|stead of| |000002c0| 20 53 55 4d 53 0a 0a 09 | 20 20 20 20 20 20 20 20 | SUMS...| | |000002d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | | |000002e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | | |000002f0| 2d 69 0a 09 5b 20 78 27 | 20 5d 20 20 20 20 20 20 |-i..[ x'| ] | |00000300| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | | |00000310| 5b 20 31 20 20 20 20 20 | 2d 64 20 32 20 20 20 5d |[ 1 |-d 2 ]| |00000320| 20 5b 20 78 20 5d 0a 09 | 5b 20 20 20 20 5d 20 20 | [ x ]..|[ ] | |00000330| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | | |00000340| 20 20 20 20 5b 20 20 20 | 20 20 20 20 20 20 69 20 | [ | i | |00000350| 20 20 20 5d 20 5b 20 20 | 20 5d 0a 09 5b 20 20 20 | ] [ | ]..[ | |00000360| 20 5d 20 3d 20 50 72 6f | 64 20 7b 20 43 20 20 7d | ] = Pro|d { C }| |00000370| 20 50 72 6f 64 20 7b 20 | 5b 20 20 20 20 2d 69 20 | Prod { |[ -i | |00000380| 20 20 20 20 20 20 20 5d | 20 5b 20 20 20 5d 20 7d | ]| [ ] }| |00000390| 0a 09 5b 20 79 27 20 5d | 20 20 20 20 69 20 20 20 |..[ y' ]| i | |000003a0| 20 20 20 69 20 20 20 20 | 69 20 20 20 20 20 5b 20 | i |i [ | |000003b0| 64 20 32 20 20 20 20 20 | 20 31 20 20 20 5d 20 5b |d 2 | 1 ] [| |000003c0| 20 79 20 5d 0a 09 09 09 | 09 20 20 20 20 20 20 20 | y ]....|. | |000003d0| 69 0a 0a 28 61 20 6c 6f | 6f 6b 20 61 74 20 74 68 |i..(a lo|ok at th| |000003e0| 65 20 63 6f 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|000007c0| 35 30 30 34 37 35 36 2c | 20 34 32 36 36 37 33 33 |5004756,| 4266733| |000007d0| 31 2c 0a 3e 09 32 31 33 | 35 34 34 36 35 2c 20 31 |1,.>.213|54465, 1| |000007e0| 30 36 37 39 38 33 38 2c | 20 35 33 34 30 32 34 35 |0679838,| 5340245| |000007f0| 2c 20 32 36 37 30 31 36 | 33 2c 20 31 33 33 35 30 |, 267016|3, 13350| |00000800| 38 37 2c 20 36 36 37 35 | 34 34 2c 20 33 33 33 37 |87, 6675|44, 3337| |00000810| 37 32 2c 20 31 36 36 38 | 38 36 2c 0a 3e 09 38 33 |72, 1668|86,.>.83| |00000820| 34 34 33 2c 20 34 31 37 | 32 32 2c 20 32 30 38 36 |443, 417|22, 2086| |00000830| 31 2c 20 31 30 34 33 30 | 2c 20 35 32 31 35 2c 20 |1, 10430|, 5215, | |00000840| 32 36 30 38 2c 20 31 33 | 30 34 2c 20 36 35 32 2c |2608, 13|04, 652,| |00000850| 20 33 32 36 2c 20 31 36 | 33 2c 20 38 31 2c 20 34 | 326, 16|3, 81, 4| |00000860| 31 2c 0a 3e 09 32 30 2c | 20 31 30 2c 20 35 2c 20 |1,.>.20,| 10, 5, | |00000870| 33 2c 20 31 2c 20 31 2c | 20 0a 3e 23 20 65 6e 64 |3, 1, 1,| .># end| |00000880| 69 66 0a 3e 23 20 65 6e | 64 69 66 0a 3e 0a 0a 69 |if.># en|dif.>..i| |00000890| 74 20 74 75 72 6e 73 20 | 6f 75 74 20 74 68 61 74 |t turns |out that| |000008a0| 20 43 4f 53 43 41 4c 45 | 20 69 73 20 74 68 65 20 | COSCALE| is the | |000008b0| 70 72 6f 64 75 63 74 20 | 6f 66 20 61 6c 6c 20 74 |product |of all t| |000008c0| 68 65 20 43 5f 69 27 73 | 2c 0a 61 6e 64 20 74 68 |he C_i's|,.and th| |000008d0| 61 74 20 74 68 65 20 6e | 75 6d 62 65 72 73 20 69 |at the n|umbers i| |000008e0| 6e 20 61 72 63 74 61 6e | 74 61 62 20 61 72 65 20 |n arctan|tab are | |000008f0| 74 68 65 20 73 65 71 75 | 65 6e 63 65 20 6f 66 20 |the sequ|ence of | |00000900| 61 6e 67 6c 65 73 3a 0a | 0a 09 61 72 63 74 61 6e |angles:.|..arctan| |00000910| 20 28 20 32 5e 2d 69 20 | 29 2c 20 66 6f 72 20 69 | ( 2^-i |), for i| |00000920| 20 3d 20 2d 31 2c 20 30 | 2c 20 2e 2e 2e 2c 20 33 | = -1, 0|, ..., 3| |00000930| 30 0a 0a 6e 6f 72 6d 61 | 6c 69 7a 65 64 20 73 6f |0..norma|lized so| |00000940| 20 74 68 61 74 20 39 30 | 20 64 65 67 72 65 65 73 | that 90| degrees| |00000950| 20 69 73 20 65 71 75 61 | 6c 20 74 6f 20 51 55 41 | is equa|l to QUA| |00000960| 52 54 45 52 2e 0a 0a 49 | 20 68 6f 70 65 20 49 20 |RTER...I| hope I | |00000970| 73 61 76 65 64 20 74 68 | 65 20 74 69 6d 65 20 6f |saved th|e time o| |00000980| 66 20 73 6f 6d 65 20 72 | 65 61 64 65 72 73 20 69 |f some r|eaders i| |00000990| 6e 20 66 69 67 75 72 69 | 6e 67 20 74 68 69 73 20 |n figuri|ng this | |000009a0| 6f 75 74 2e 0a 0a 09 50 | 61 74 72 69 63 6b 20 56 |out....P|atrick V| |000009b0| 61 6e 20 48 6f 76 65 0a | 0a 0a |an Hove.|.. | +--------+-------------------------+-------------------------+--------+--------+