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Working on atan2()

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This commit is contained in:
jespergravgaard 2019-06-28 17:05:54 +02:00
parent 13652f61f2
commit 83ed437553
8 changed files with 175 additions and 42 deletions
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14
src/main/fragment/vwsz1=vwsz2_ror_vbuxx.asm Normal file
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@ -0,0 +1,14 @@
lda {z2}
sta {z1}
lda {z2}+1
sta {z1}+1
cpx #0
beq !e+
!:
lda {z1}+1
cmp #$80
ror {z1}+1
ror {z1}
dex
bne !-
!e:

14
src/main/fragment/vwsz1=vwsz2_ror_vbuyy.asm Normal file
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@ -0,0 +1,14 @@
lda {z2}
sta {z1}
lda {z2}+1
sta {z1}+1
cpy #0
beq !e+
!:
lda {z1}+1
cmp #$80
ror {z1}+1
ror {z1}
dey
bne !-
!e:

7
src/main/fragment/vwuz1=vwuz1_plus_pwuc1_derefidx_vbuxx.asm Normal file
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@ -0,0 +1,7 @@
clc
lda {z1}
adc {c1},x
sta {z1}
lda {z1}+1
adc {c1}+1,x
sta {z1}+1

7
src/main/fragment/vwuz1=vwuz1_plus_pwuc1_derefidx_vbuyy.asm Normal file
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@ -0,0 +1,7 @@
clc
lda {z1}
adc {c1},y
sta {z1}
lda {z1}+1
adc {c1}+1,y
sta {z1}+1

87
src/main/kc/stdlib/atan2.kc Normal file
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@ -0,0 +1,87 @@
// Find atan2(x, y) using the CORDIC method
// See http://bsvi.ru/uploads/CORDIC--_10EBA/cordic.pdf
// The number of iterations performed during 16-bit CORDIC atan2 calculation
const byte CORDIC_ITERATIONS_16 = 15;
// Angles representing ATAN(0.5), ATAN(0.25), ATAN(0.125), ...
word* CORDIC_ATAN2_ANGLES_16 = 0x1000;
// Populate cordic angles table
kickasm(pc CORDIC_ATAN2_ANGLES_16, uses CORDIC_ITERATIONS_16) {{
.for (var i=0; i<CORDIC_ITERATIONS_16; i++)
.word 256*2*256*atan(1/pow(2,i))/PI/2
}}
// Find the atan2(x, y) - which is the angle of the line from (0,0) to (x,y)
// Finding the angle requires a binary search using CORDIC_ITERATIONS_16
// Returns the angle in hex-degrees (0=0, 0x8000=PI, 0x10000=2*PI)
word atan2_16(signed word x, signed word y) {
signed word yi = (y>0)?y:-y;
signed word xi = (x>0)?x:-x;
word angle = 0;
for( byte i: 0..CORDIC_ITERATIONS_16) {
if(yi==0) {
// We found the correct angle!
break;
}
signed word xd = xi>>i;
signed word yd = yi>>i;
if(yi>0) {
xi += yd;
yi -= xd;
angle += CORDIC_ATAN2_ANGLES_16[i];
} else {
xi -= yd;
yi += xd;
angle -= CORDIC_ATAN2_ANGLES_16[i];
}
}
angle /=2;
if(x<0) angle = 0x8000-angle;
if(y<0) angle = -angle;
// Iterations complete - return estimated angle
return angle;
}
// The number of iterations performed during 8-bit CORDIC atan2 calculation
const byte CORDIC_ITERATIONS_8 = 8;
// Angles representing ATAN(0.5), ATAN(0.25), ATAN(0.125), ...
byte* CORDIC_ATAN2_ANGLES_8 = 0x1100;
// Populate cordic angles table
kickasm(pc CORDIC_ATAN2_ANGLES_8, uses CORDIC_ITERATIONS_8) {{
.fill CORDIC_ITERATIONS_8, 2*256*atan(1/pow(2,i))/PI/2
}}
// Find the atan2(x, y) - which is the angle of the line from (0,0) to (x,y)
// Finding the angle requires a binary search using CORDIC_ITERATIONS
// Returns the angle in hex-degrees (0=0, 0x80=PI, 0x100=2*PI)
byte atan2_8(signed byte x, signed byte y) {
signed byte yi = (y>0)?y:-y;
signed byte xi = (x>0)?x:-x;
byte angle = 0;
for( byte i: 0..CORDIC_ITERATIONS_8) {
if(yi==0) {
// We found the correct angle!
break;
}
signed byte xd = xi>>i;
signed byte yd = yi>>i;
if(yi>0) {
xi += yd;
yi -= xd;
angle += CORDIC_ATAN2_ANGLES_8[i];
} else {
xi -= yd;
yi += xd;
angle -= CORDIC_ATAN2_ANGLES_8[i];
}
}
angle = angle/2;
if(x<0) angle = 128-angle;
if(y<0) angle = -angle;
// Iterations complete - return estimated angle
return angle;
}

2
src/main/kc/stdlib/print.kc
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@ -49,6 +49,8 @@ void print_sword(signed word w) {
if(w<0) {
print_char('-');
w = -w;
} else {
print_char(' ');
}
print_word((word)w);
}

41
src/test/kc/cordic-atan2-16.kc Normal file
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@ -0,0 +1,41 @@
// Find atan2(x, y) using the CORDIC method
// See http://bsvi.ru/uploads/CORDIC--_10EBA/cordic.pdf
import "font-hex"
import "atan2"
import "c64"
const byte* CHARSET = 0x2000;
const byte* SCREEN = 0x2800;
const byte* SCREEN_REF = 0x2c00;
kickasm(pc SCREEN_REF) {{
.for(var y=-12;y<=12;y++)
.for(var x=-19;x<=20;x++)
.byte round(256*atan2(y, x)/PI/2)
}}
void main() {
init_font_hex(CHARSET);
*D018 = toD018(SCREEN, CHARSET);
byte* screen = SCREEN;
byte* screen_ref = SCREEN_REF;
for(signed byte y: -12..12) {
for(signed byte x: -19..20) {
//byte angle_b = atan2_8(x, y);
signed word xw = (signed word)(word){ (byte)x, 0 };
signed word yw = (signed word)(word){ (byte)y, 0 };
word angle_w = atan2_16(xw, yw);
//*screen++ = (>angle_w)-angle_b;
//*screen++ = >angle_w;
*screen++ = (>(angle_w+0x0080)) - *screen_ref++;
//*screen++ = angle_b - *screen_ref++;
//*screen++ = *screen_ref++;
}
}
byte* col00 = COLS+12*40+19;
while(true) (*col00)++;
}

45
src/test/kc/cordic-atan2.kc
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@ -3,6 +3,8 @@
import "font-hex"
import "c64"
import "atan2"
const byte* CHARSET = 0x2000;
const byte* SCREEN = 0x2800;
@ -14,7 +16,7 @@ void main() {
byte* screen = SCREEN;
for(signed byte y: -12..12) {
for(signed byte x: -19..20) {
byte angle = atan2(x, y);
byte angle = atan2_8(x, y);
*screen++ = angle;
}
}
@ -24,44 +26,3 @@ void main() {
}
// The number of iterations performed during CORDIC atan2 calculation
const byte CORDIC_ITERATIONS = 8;
// Angles representing ATAN(0.5), ATAN(0.25), ATAN(0.125), ...
byte* CORDIC_ATAN2_ANGLES = 0x1000;
// Populate cordic angles table
kickasm(pc CORDIC_ATAN2_ANGLES) {{
.fill CORDIC_ITERATIONS, 2*256*atan(1/pow(2,i))/PI/2
}}
// Find the atan2(x, y) - which is the angle of the line from (0,0) to (x,y)
// Finding the angle requires a binary search using CORDIC_ITERATIONS
// Returns the angle in hex-degrees (0=0, 128=PI, 256=2*PI)
byte atan2(signed byte x, signed byte y) {
signed byte yi = (y>0)?y:-y;
signed byte xi = (x>0)?x:-x;
byte angle = 0;
for( byte i: 0..CORDIC_ITERATIONS) {
if(yi==0) {
// We found the correct angle!
break;
}
signed byte xd = xi>>i;
signed byte yd = yi>>i;
if(yi>0) {
xi += yd;
yi -= xd;
angle += CORDIC_ATAN2_ANGLES[i];
} else {
xi -= yd;
yi += xd;
angle -= CORDIC_ATAN2_ANGLES[i];
}
}
angle /=2;
if(x<0) angle = 128-angle;
if(y<0) angle = -angle;
// Iterations complete - return estimated angle
return angle;
}