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di_dar
TA的每日心情 | 无聊 2015-1-15 22:05 |
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签到天数: 79 天 [LV.6]常住居民II
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本帖最后由 大笨象 于 2011-6-7 12:26 编辑 $ S+ @, \2 a& _" C
$ P8 A8 e$ q/ u' K! o8 ~2 q
不知道有木有人研究这个,比较偏向于硬件描述。
) r6 z9 W" r( {; Z* L+ L& i今天先发一个sine cose函数的实现。
8 L, F% ]: G* _有兴趣的可以看一下,m文件见附件。
2 u+ f+ I8 H4 V5 T* ~" Ofunction v=f_cordic(beta,n)
1 a6 ?: V0 E X! rif beta < -pi/2 || beta > pi/25 G4 u9 G% K5 T0 ^/ N, K5 J: I
if beta < 0# m# q8 ?. B0 K& I* |: Y6 c) H. I6 b1 }
v=f_cordic(beta + pi,n);, ?1 [' F2 {+ j. W5 J: P
else8 j" D" z: H/ k2 l8 X
v=f_cordic(beta - pi,n);
; p2 Y8 u. w' O4 F: n2 d* ^ end
2 L) c) c* m6 L v = -v;% flip the sign for second or third quadrant
/ t( F5 F/ s, K return
! s4 o6 s& |: E( b' Y7 V. wend
5 x* O# v4 G$ U" A& s# k% Initialization of tables of constants used by CORDIC
& D& d% v; q+ a% T8 e! W% need a table of arctangents of negative powers of two, in radians:
. K" L4 F3 o v/ p% angles = atan(2.^-(0:27)); F, [' {7 b' o* }! Q: q6 i
angles = [ ...( g1 }8 r0 y: A! t7 z+ R
0.78539816339745 0.46364760900081 0.24497866312686 0.12435499454676 ...- X8 `( U+ f5 o4 K$ f
0.06241880999596 0.03123983343027 0.01562372862048 0.00781234106010 ...1 O& _4 D% b: P7 h" g s0 n
0.00390623013197 0.00195312251648 0.00097656218956 0.00048828121119 ...
; {3 L9 P5 B( v5 g U* {3 n9 x 0.00024414062015 0.00012207031189 0.00006103515617 0.00003051757812 ...
! G2 }( _1 M5 w4 ^ r 0.00001525878906 0.00000762939453 0.00000381469727 0.00000190734863 ...
3 I' `# C. u/ N/ I3 U9 z6 d 0.00000095367432 0.00000047683716 0.00000023841858 0.00000011920929 ...
# x Z% {# c# ?9 ] 0.00000005960464 0.00000002980232 0.00000001490116 0.00000000745058 ];
- b0 U: O( L+ u, Q' y' S% and a table of products of reciprocal lengths of vectors [1, 2^-j]:
( I4 C% D/ {) @- A- v8 m- E( sKvalues = [ ...7 D( O* X+ Y, p2 W5 B
0.70710678118655 0.63245553203368 0.61357199107790 0.60883391251775 ...2 k% p; O. \) [+ l$ B
0.60764825625617 0.60735177014130 0.60727764409353 0.60725911229889 ...
* I4 @6 p( ]" {( \; e 0.60725447933256 0.60725332108988 0.60725303152913 0.60725295913894 ...+ u6 p0 H4 e2 P) Z% E9 Q, h
0.60725294104140 0.60725293651701 0.60725293538591 0.60725293510314 ...
5 |5 k/ K/ I5 | 0.60725293503245 0.60725293501477 0.60725293501035 0.60725293500925 ...2 K# O8 F) b- D; l5 I* p
0.60725293500897 0.60725293500890 0.60725293500889 0.60725293500888 ];
9 r" B G0 }* b4 i$ ~% _Kn = Kvalues(min(n, length(Kvalues)));+ l5 Y; G$ O5 I. o2 I
D j9 x" O+ r' [' E1 w: @. o
% Initialize loop variables:
' u) i$ K+ k p* Z7 Sv = [1;0]; % start with 2-vector cosine and sine of zero( L8 F: i- j" v3 s; K
poweroftwo = 1;
3 s- B8 P) w6 W% Iterations
% U1 Y3 ~& r' G; jfor j = 1:n;0 e5 |; V6 ~; Q+ I
if beta < 0
4 R: \* O. n: a; B/ `1 T8 d sigma = -1;! _6 m% i0 [. q2 G& T% q
else
) ]' t7 {5 L6 [) ?* B* H sigma = 1;! v( M8 s8 D- t8 S3 q# b
end; O; G m/ S, S% T8 K8 |
% update the angle from table, or eventually by just dividing by two
V g0 a; p9 v; u8 r- ^ N+ p if j <= length(angles)
k/ w2 u, i( O% g0 C+ \ angle = angles(j);
" u: i/ a3 M. g% R else. ` z C# w) ^5 E; P: M
angle = angle/2;' f, G }. v* y) G0 o( E3 Q. J
end
* F# @% r3 P N5 L factor = sigma * poweroftwo;* H9 k7 K4 P, T8 a& s C9 D5 `
R = [1, -factor; factor, 1];8 j0 l+ {/ w; k" M( g
v = R * v; % 2-by-2 mtrix multiply& L' e( [. a. B5 ` O
beta = beta - sigma * angle; % update the remaining angle
0 G6 ~ ]+ A0 C3 e. g/ B poweroftwo = poweroftwo / 2;
: c+ p2 M2 d# k' ?5 ]6 xend% ]% g5 y6 D& Y. a( F9 K
% Adjust length of output vector to be [cos(beta), sin(beta)]:* B0 K p7 S L4 s% w
v = v * Kn;
, P3 R1 ~; l1 i j; Oreturn% X; E$ W6 O6 @0 X7 T6 ?* r9 l
( M U4 T; s2 a' B( q2 I
使用20位寄存器,仿真波形如下:
0 i8 g* b3 [# K7 z; l
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f_cordic.m
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CORDIC算法
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