CORDIC: Difference between revisions

=={{header|jq}}==

'''Adapted from [[#Wren|Wren]]'''

{{works with|jq}}

'''Works with gojq, the Go implementation of jq'''

'''Preliminaries'''

<syntaxhighlight lang="jq">

# like while/2 but emit the final term rather than the first one

def whilst(cond; update):

def _whilst:

if cond then update | (., _whilst) else empty end;

_whilst;

# Simplistic approach to rounding:

def round($ndec): pow(10;$ndec) as $p | . * $p | round / $p;

def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;

</syntaxhighlight>

'''The task'''

<syntaxhighlight lang="jq">

# The following are pre-computed to avoid using atan and sqrt functions.

def angles: [

0.78539816339745, 0.46364760900081, 0.24497866312686, 0.12435499454676,

0.06241880999596, 0.03123983343027, 0.01562372862048, 0.00781234106010,

0.00390623013197, 0.00195312251648, 0.00097656218956, 0.00048828121119,

0.00024414062015, 0.00012207031189, 0.00006103515617, 0.00003051757812,

0.00001525878906, 0.00000762939453, 0.00000381469727, 0.00000190734863,

0.00000095367432, 0.00000047683716, 0.00000023841858, 0.00000011920929,

0.00000005960464, 0.00000002980232, 0.00000001490116, 0.00000000745058

];

def kvalues: [

0.70710678118655, 0.63245553203368, 0.61357199107790, 0.60883391251775,

0.60764825625617, 0.60735177014130, 0.60727764409353, 0.60725911229889,

0.60725447933256, 0.60725332108988, 0.60725303152913, 0.60725295913894,

0.60725294104140, 0.60725293651701, 0.60725293538591, 0.60725293510314,

0.60725293503245, 0.60725293501477, 0.60725293501035, 0.60725293500925,

0.60725293500897, 0.60725293500890, 0.60725293500889, 0.60725293500888

];

def PI: (1 | atan * 4);

def radians: . * PI / 180;

def Cordic($alpha; $n):

PI as $PI

| (if (($alpha / (2 * $PI))|floor % 2 == 1) then 1 else -1 end) as $newsgn

| if ($alpha < -$PI/2)

then Cordic($alpha + $PI; $n) | map(. * $newsgn)

elif ($alpha > $PI/2)

then Cordic($alpha - $PI; $n) | map(. * $newsgn)

else kvalues[ [$n-1, (kvalues|length-1)] | min] as $kn

| reduce angles[0:$n][] as $atan ({ theta: 0, x: 1, y: 0, pow2: 1};

(if .theta < $alpha then 1 else -1 end) as $sigma

| .theta += $sigma * $atan

| .x as $t

| .x = (.x - $sigma * .y * .pow2)

| .y = (.y + $sigma * $t * .pow2)

| .pow2 /= 2 )

| [.x * $kn, .y * $kn]

end;

def example:

def format: map(round(8) | lpad(11)) | join(" ");

" x sin(x) diff. sine cos(x) diff. cosine",

({ th: -90 }

| whilst (.th <= 90;

(.th | radians) as $thr

| Cordic($thr; 24) as [ $cos, $sin ]

| .out = [.th, $sin, $sin - ($thr|sin), $cos, $cos - ($thr|cos) ]

| .th += 15 )

| .out

| format),

"\n x(rads) sin(x) diff. sine cos(x) diff. cosine",

((-9, 0, 1.5, 6) as $thr

| Cordic($thr; 24) as [$cos, $sin]

| [$thr, $sin, $sin - ($thr|sin), $cos, $cos - ($thr|cos)]

| format) ;

example

</syntaxhighlight>

'''Invocation:''' jq -ncr -f cordic.jq

{{output}}

<pre>

x sin(x) diff. sine cos(x) diff. cosine

-90 -1 0 -7e-08 -7e-08

-75 -0.96592585 -3e-08 0.25881895 -9e-08

-60 -0.86602545 -5e-08 0.49999992 -8e-08

-45 -0.70710684 -6e-08 0.70710672 -6e-08

-30 -0.49999992 8e-08 0.86602545 5e-08

-15 -0.25881895 9e-08 0.96592585 3e-08

0 7e-08 7e-08 1 -0

15 0.25881895 -9e-08 0.96592585 3e-08

30 0.49999992 -8e-08 0.86602545 5e-08

45 0.70710684 6e-08 0.70710672 -6e-08

60 0.86602545 5e-08 0.49999992 -8e-08

75 0.96592585 3e-08 0.25881895 -9e-08

90 1 -0 -7e-08 -7e-08

x(rads) sin(x) diff. sine cos(x) diff. cosine

-9 -0.41211842 6e-08 -0.91113029 -3e-08

0 7e-08 7e-08 1 -0

1.5 0.99749499 0 0.07073719 -2e-08

6 -0.27941552 -2e-08 0.96017028 -1e-08

</pre>