From c7ab5c9d07bce82f9c60a9d9ce97dad43186f89e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Juhani=20Krekel=C3=A4?= <juhani@krekelä.fi>
Date: Fri, 11 Mar 2022 19:42:50 +0200
Subject: [PATCH] Add trigonometric functions

---
 dosclock.asm | 190 ++++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 180 insertions(+), 10 deletions(-)

diff --git a/dosclock.asm b/dosclock.asm
index 1d0d8cb..d4a73a3 100644
--- a/dosclock.asm
+++ b/dosclock.asm
@@ -51,18 +51,18 @@ mainloop:
 		mov [minute], cl
 		mov [second], dh
 
-		mov bp, 0
-		add bp, [hour]
-		mov byte [es:bp], 1
+		mov ax, [second]
+		mul word [six]
+		mov bx, ax
+		mov ax, [width]
+		shr ax, 1
+		shr ax, 1
+		call sinx
 
 		mov bp, [width]
-		add bp, [minute]
-		mov byte [es:bp], 2
-
-		mov bp, [width]
-		add bp, [width]
-		add bp, [second]
-		mov byte [es:bp], 4
+		shr bp, 1
+		mov bp, ax
+		mov byte [es:bp], 7
 
 	.unchanged:
 	hlt
@@ -89,10 +89,180 @@ clear_screen:
 	pop bp
 	ret
 
+; in:
+;  ax = scale
+;  bx = angle
+; out:
+;  ax = scale·cos(angle)
+cosx:
+	push bx
+
+	; cos(x) = sin(x + 90°)
+	add bx, 90
+	call sinx
+
+	pop bx
+	ret
+
+; in:
+;  ax = scale
+;  bx = angle
+; out:
+;  ax = scale·sin(angle)
+sinx:
+	push bx
+	push dx
+
+	.get_in_range:
+		cmp bx, 360
+		jb .in_range
+
+		sub bx, 360
+		jmp .get_in_range
+
+		.in_range:
+
+	; sin(90°) = 1
+	.angle_90:
+		cmp bx, 90
+		je .end
+
+	; Main branch of function 0 ≤ bx < 90
+	.q1:
+		cmp bx, 90
+		ja .q2
+
+		; Load sin(bx) * 2¹⁶ into bx
+		shl bx, 1
+		mov bx, [sin_table + bx]
+		; Compute ax·bx and take high 16 bits, which cancel out the
+		; pre-multiplication of the sin_table
+		mul bx
+		mov ax, dx
+
+		jmp .end
+
+	; sin(bx) = sin(180° - bx) for 90 < bx ≤ 180
+	.q2:
+		cmp bx, 180
+		ja .q3_q4
+
+		mov dx, 180
+		sub dx, bx
+		mov bx, dx
+		call sinx
+
+		jmp .end
+
+	; sin(bx) = -sin(bx - 180°) for 180 < bx < 360
+	.q3_q4:
+		sub bx, 180
+		call sinx
+		neg ax
+
+	.end:
+	pop dx
+	pop bx
+	ret
+
 section .rodata
 width dw 320
 height dw 200
 
+sin_table:
+	dw 0 ; sin(0°)
+	dw 1143 ; sin(1°)
+	dw 2287 ; sin(2°)
+	dw 3429 ; sin(3°)
+	dw 4571 ; sin(4°)
+	dw 5711 ; sin(5°)
+	dw 6850 ; sin(6°)
+	dw 7986 ; sin(7°)
+	dw 9120 ; sin(8°)
+	dw 10252 ; sin(9°)
+	dw 11380 ; sin(10°)
+	dw 12504 ; sin(11°)
+	dw 13625 ; sin(12°)
+	dw 14742 ; sin(13°)
+	dw 15854 ; sin(14°)
+	dw 16961 ; sin(15°)
+	dw 18064 ; sin(16°)
+	dw 19160 ; sin(17°)
+	dw 20251 ; sin(18°)
+	dw 21336 ; sin(19°)
+	dw 22414 ; sin(20°)
+	dw 23486 ; sin(21°)
+	dw 24550 ; sin(22°)
+	dw 25606 ; sin(23°)
+	dw 26655 ; sin(24°)
+	dw 27696 ; sin(25°)
+	dw 28729 ; sin(26°)
+	dw 29752 ; sin(27°)
+	dw 30767 ; sin(28°)
+	dw 31772 ; sin(29°)
+	dw 32767 ; sin(30°)
+	dw 33753 ; sin(31°)
+	dw 34728 ; sin(32°)
+	dw 35693 ; sin(33°)
+	dw 36647 ; sin(34°)
+	dw 37589 ; sin(35°)
+	dw 38521 ; sin(36°)
+	dw 39440 ; sin(37°)
+	dw 40347 ; sin(38°)
+	dw 41243 ; sin(39°)
+	dw 42125 ; sin(40°)
+	dw 42995 ; sin(41°)
+	dw 43852 ; sin(42°)
+	dw 44695 ; sin(43°)
+	dw 45525 ; sin(44°)
+	dw 46340 ; sin(45°)
+	dw 47142 ; sin(46°)
+	dw 47929 ; sin(47°)
+	dw 48702 ; sin(48°)
+	dw 49460 ; sin(49°)
+	dw 50203 ; sin(50°)
+	dw 50931 ; sin(51°)
+	dw 51643 ; sin(52°)
+	dw 52339 ; sin(53°)
+	dw 53019 ; sin(54°)
+	dw 53683 ; sin(55°)
+	dw 54331 ; sin(56°)
+	dw 54963 ; sin(57°)
+	dw 55577 ; sin(58°)
+	dw 56175 ; sin(59°)
+	dw 56755 ; sin(60°)
+	dw 57319 ; sin(61°)
+	dw 57864 ; sin(62°)
+	dw 58393 ; sin(63°)
+	dw 58903 ; sin(64°)
+	dw 59395 ; sin(65°)
+	dw 59870 ; sin(66°)
+	dw 60326 ; sin(67°)
+	dw 60763 ; sin(68°)
+	dw 61183 ; sin(69°)
+	dw 61583 ; sin(70°)
+	dw 61965 ; sin(71°)
+	dw 62328 ; sin(72°)
+	dw 62672 ; sin(73°)
+	dw 62997 ; sin(74°)
+	dw 63302 ; sin(75°)
+	dw 63589 ; sin(76°)
+	dw 63856 ; sin(77°)
+	dw 64103 ; sin(78°)
+	dw 64331 ; sin(79°)
+	dw 64540 ; sin(80°)
+	dw 64729 ; sin(81°)
+	dw 64898 ; sin(82°)
+	dw 65047 ; sin(83°)
+	dw 65176 ; sin(84°)
+	dw 65286 ; sin(85°)
+	dw 65376 ; sin(86°)
+	dw 65446 ; sin(87°)
+	dw 65496 ; sin(88°)
+	dw 65526 ; sin(89°)
+
+six dw 6
+
 section .data
 hour dw 0
 minute dw 0