| 1 | /* | 
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| 2 | ** Please only distribute this with it's associated FHT routine. | 
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| 3 | ** This algorithm is apparently patented(!) and the code copyrighted. | 
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| 4 | ** See the comment with the fht routine for more info. | 
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| 5 | **   -Thanks, | 
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| 6 | **   Ron Mayer | 
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| 7 | */ | 
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| 8 |  | 
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| 9 | #ifdef REAL | 
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| 10 | #else | 
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| 11 | #define REAL double | 
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| 12 | #endif | 
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| 13 |  | 
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| 14 | #ifdef GOOD_TRIG | 
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| 15 | #else | 
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| 16 | #define FAST_TRIG | 
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| 17 | #endif | 
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| 18 |  | 
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| 19 | #if defined(GOOD_TRIG) | 
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| 20 | #define FHT_SWAP(a,b,t) {(t)=(a);(a)=(b);(b)=(t);} | 
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| 21 | #define TRIG_VARS                                                \ | 
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| 22 | int t_lam=0; | 
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| 23 | #define TRIG_INIT(k,c,s)                                         \ | 
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| 24 | {                                                           \ | 
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| 25 | int i;                                                     \ | 
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| 26 | for (i=2 ; i<=k ; i++)                                     \ | 
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| 27 | {coswrk[i]=costab[i];sinwrk[i]=sintab[i];}             \ | 
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| 28 | t_lam = 0;                                                 \ | 
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| 29 | c = 1;                                                     \ | 
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| 30 | s = 0;                                                     \ | 
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| 31 | } | 
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| 32 | #define TRIG_NEXT(k,c,s)                                         \ | 
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| 33 | {                                                           \ | 
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| 34 | int i,j;                                                \ | 
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| 35 | (t_lam)++;                                              \ | 
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| 36 | for (i=0 ; !((1<<i)&t_lam) ; i++);                      \ | 
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| 37 | i = k-i;                                                \ | 
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| 38 | s = sinwrk[i];                                          \ | 
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| 39 | c = coswrk[i];                                          \ | 
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| 40 | if (i>1)                                                \ | 
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| 41 | {                                                    \ | 
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| 42 | for (j=k-i+2 ; (1<<j)&t_lam ; j++);                 \ | 
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| 43 | j         = k - j;                                  \ | 
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| 44 | sinwrk[i] = halsec[i] * (sinwrk[i-1] + sinwrk[j]);  \ | 
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| 45 | coswrk[i] = halsec[i] * (coswrk[i-1] + coswrk[j]);  \ | 
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| 46 | }                                                    \ | 
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| 47 | } | 
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| 48 | #define TRIG_RESET(k,c,s) | 
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| 49 | #endif | 
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| 50 |  | 
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| 51 | #if defined(FAST_TRIG) | 
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| 52 | #define TRIG_VARS                                        \ | 
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| 53 | REAL t_c,t_s; | 
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| 54 | #define TRIG_INIT(k,c,s)                                 \ | 
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| 55 | {                                                    \ | 
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| 56 | t_c  = costab[k];                                   \ | 
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| 57 | t_s  = sintab[k];                                   \ | 
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| 58 | c    = 1;                                           \ | 
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| 59 | s    = 0;                                           \ | 
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| 60 | } | 
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| 61 | #define TRIG_NEXT(k,c,s)                                 \ | 
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| 62 | {                                                    \ | 
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| 63 | REAL t = c;                                         \ | 
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| 64 | c   = t*t_c - s*t_s;                                \ | 
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| 65 | s   = t*t_s + s*t_c;                                \ | 
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| 66 | } | 
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| 67 | #define TRIG_RESET(k,c,s) | 
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| 68 | #endif | 
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| 69 |  | 
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| 70 | static REAL halsec[20]= | 
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| 71 | { | 
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| 72 | 0, | 
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| 73 | 0, | 
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| 74 | .54119610014619698439972320536638942006107206337801, | 
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| 75 | .50979557910415916894193980398784391368261849190893, | 
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| 76 | .50241928618815570551167011928012092247859337193963, | 
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| 77 | .50060299823519630134550410676638239611758632599591, | 
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| 78 | .50015063602065098821477101271097658495974913010340, | 
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| 79 | .50003765191554772296778139077905492847503165398345, | 
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| 80 | .50000941253588775676512870469186533538523133757983, | 
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| 81 | .50000235310628608051401267171204408939326297376426, | 
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| 82 | .50000058827484117879868526730916804925780637276181, | 
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| 83 | .50000014706860214875463798283871198206179118093251, | 
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| 84 | .50000003676714377807315864400643020315103490883972, | 
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| 85 | .50000000919178552207366560348853455333939112569380, | 
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| 86 | .50000000229794635411562887767906868558991922348920, | 
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| 87 | .50000000057448658687873302235147272458812263401372 | 
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| 88 | }; | 
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| 89 | static REAL costab[20]= | 
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| 90 | { | 
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| 91 | .00000000000000000000000000000000000000000000000000, | 
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| 92 | .70710678118654752440084436210484903928483593768847, | 
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| 93 | .92387953251128675612818318939678828682241662586364, | 
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| 94 | .98078528040323044912618223613423903697393373089333, | 
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| 95 | .99518472667219688624483695310947992157547486872985, | 
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| 96 | .99879545620517239271477160475910069444320361470461, | 
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| 97 | .99969881869620422011576564966617219685006108125772, | 
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| 98 | .99992470183914454092164649119638322435060646880221, | 
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| 99 | .99998117528260114265699043772856771617391725094433, | 
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| 100 | .99999529380957617151158012570011989955298763362218, | 
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| 101 | .99999882345170190992902571017152601904826792288976, | 
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| 102 | .99999970586288221916022821773876567711626389934930, | 
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| 103 | .99999992646571785114473148070738785694820115568892, | 
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| 104 | .99999998161642929380834691540290971450507605124278, | 
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| 105 | .99999999540410731289097193313960614895889430318945, | 
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| 106 | .99999999885102682756267330779455410840053741619428 | 
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| 107 | }; | 
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| 108 | static REAL sintab[20]= | 
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| 109 | { | 
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| 110 | 1.0000000000000000000000000000000000000000000000000, | 
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| 111 | .70710678118654752440084436210484903928483593768846, | 
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| 112 | .38268343236508977172845998403039886676134456248561, | 
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| 113 | .19509032201612826784828486847702224092769161775195, | 
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| 114 | .09801714032956060199419556388864184586113667316749, | 
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| 115 | .04906767432741801425495497694268265831474536302574, | 
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| 116 | .02454122852291228803173452945928292506546611923944, | 
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| 117 | .01227153828571992607940826195100321214037231959176, | 
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| 118 | .00613588464915447535964023459037258091705788631738, | 
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| 119 | .00306795676296597627014536549091984251894461021344, | 
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| 120 | .00153398018628476561230369715026407907995486457522, | 
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| 121 | .00076699031874270452693856835794857664314091945205, | 
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| 122 | .00038349518757139558907246168118138126339502603495, | 
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| 123 | .00019174759731070330743990956198900093346887403385, | 
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| 124 | .00009587379909597734587051721097647635118706561284, | 
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| 125 | .00004793689960306688454900399049465887274686668768 | 
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| 126 | }; | 
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| 127 | static REAL coswrk[20]= | 
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| 128 | { | 
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| 129 | .00000000000000000000000000000000000000000000000000, | 
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| 130 | .70710678118654752440084436210484903928483593768847, | 
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| 131 | .92387953251128675612818318939678828682241662586364, | 
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| 132 | .98078528040323044912618223613423903697393373089333, | 
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| 133 | .99518472667219688624483695310947992157547486872985, | 
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| 134 | .99879545620517239271477160475910069444320361470461, | 
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| 135 | .99969881869620422011576564966617219685006108125772, | 
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| 136 | .99992470183914454092164649119638322435060646880221, | 
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| 137 | .99998117528260114265699043772856771617391725094433, | 
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| 138 | .99999529380957617151158012570011989955298763362218, | 
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| 139 | .99999882345170190992902571017152601904826792288976, | 
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| 140 | .99999970586288221916022821773876567711626389934930, | 
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| 141 | .99999992646571785114473148070738785694820115568892, | 
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| 142 | .99999998161642929380834691540290971450507605124278, | 
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| 143 | .99999999540410731289097193313960614895889430318945, | 
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| 144 | .99999999885102682756267330779455410840053741619428 | 
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| 145 | }; | 
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| 146 | static REAL sinwrk[20]= | 
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| 147 | { | 
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| 148 | 1.0000000000000000000000000000000000000000000000000, | 
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| 149 | .70710678118654752440084436210484903928483593768846, | 
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| 150 | .38268343236508977172845998403039886676134456248561, | 
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| 151 | .19509032201612826784828486847702224092769161775195, | 
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| 152 | .09801714032956060199419556388864184586113667316749, | 
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| 153 | .04906767432741801425495497694268265831474536302574, | 
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| 154 | .02454122852291228803173452945928292506546611923944, | 
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| 155 | .01227153828571992607940826195100321214037231959176, | 
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| 156 | .00613588464915447535964023459037258091705788631738, | 
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| 157 | .00306795676296597627014536549091984251894461021344, | 
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| 158 | .00153398018628476561230369715026407907995486457522, | 
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| 159 | .00076699031874270452693856835794857664314091945205, | 
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| 160 | .00038349518757139558907246168118138126339502603495, | 
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| 161 | .00019174759731070330743990956198900093346887403385, | 
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| 162 | .00009587379909597734587051721097647635118706561284, | 
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| 163 | .00004793689960306688454900399049465887274686668768 | 
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| 164 | }; | 
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