Implement atan2() with integer operations and a lookup table

samhocevar · samhocevar · commit 4bfc33bf2437 · 2024-01-21T00:56:58.000+01:00
diff --git a/lpico8lib.c b/lpico8lib.c
@@ -1,7 +1,7 @@
 //
 //  ZEPTO-8 — Fantasy console emulator
 //
-//  Copyright © 2016–2023 Sam Hocevar <sam@hocevar.net>
+//  Copyright © 2016–2024 Sam Hocevar <sam@hocevar.net>
 //
 //  This program is free software. It comes without any warranty, to
 //  the extent permitted by applicable law. You can redistribute it
@@ -10,11 +10,8 @@
 //  See http://www.wtfpl.net/ for more details.
 //
 
-
-#include <cmath>
 #include <cctype>
 #include <cstring>
-#include <algorithm>
 
 #define lpico8lib_c
 #define LUA_LIB
@@ -25,9 +22,7 @@
 #include "llimits.h"
 #include "lobject.h"
 
-#include "sintable.h"
-
-#define TAU 6.2831853071795864769252867665590057683936
+#include "trigtables.h"
 
 static int pico8_max(lua_State *l) {
     lua_pushnumber(l, lua_Number::max(lua_tonumber(l, 1), lua_tonumber(l, 2)));
@@ -83,10 +78,21 @@ static int pico8_sin(lua_State *l) {
 static int pico8_atan2(lua_State *l) {
     lua_Number x = lua_tonumber(l, 1);
     lua_Number y = lua_tonumber(l, 2);
-    // This could simply be atan2(-y,x) but since PICO-8 decided that
-    // atan2(0,0) = 0.75 we need to do the same in our version.
-    double a = 0.75 + std::atan2((double)x, (double)y) / TAU;
-    lua_pushnumber(l, cast_num(a >= 1 ? a - 1 : a));
+    int32_t bits = 0x4000;
+    if (x) {
+        // Use std::abs() instead of fix32::abs() to emulate PICO-8’s behaviour
+        // with e.g. atan2(0x8000, 0x8000.0001)
+        auto q = (std::abs(int64_t(y.bits())) << 16) / std::abs(int64_t(x.bits()));
+        if (q > 0x10000)
+            bits -= atantable[(int64_t(1) << 32) / q >> 5];
+        else
+            bits = atantable[q >> 5];
+    }
+    if (x.bits() < 0) bits = 0x8000 - bits;
+    if (y.bits() > 0) bits = -bits & 0xffff;
+    // Emulate a bug in PICO-8 with e.g. atan2(1, 0x8000)
+    if (x && y.bits() == int32_t(0x80000000)) bits = -bits & 0xffff;
+    lua_pushnumber(l, lua_Number::frombits(bits));
     return 1;
 }
 
diff --git a/trigtables.h b/trigtables.h
@@ -1,7 +1,7 @@
 //
 //  ZEPTO-8 — Fantasy console emulator
 //
-//  Copyright © 2016–2023 Sam Hocevar <sam@hocevar.net>
+//  Copyright © 2016–2024 Sam Hocevar <sam@hocevar.net>
 //
 //  This program is free software. It comes without any warranty, to
 //  the extent permitted by applicable law. You can redistribute it
@@ -274,3 +274,138 @@ static uint16_t sintable[] =
     0x01fb, 0x01eb, 0x01dc, 0x01cc, 0x01bc, 0x01ac, 0x019d, 0x018d, 0x017d, 0x016d, 0x015e, 0x014e, 0x013e, 0x012e, 0x011e, 0x010f,
     0x00ff, 0x00ef, 0x00df, 0x00cf, 0x00bf, 0x00af, 0x00a0, 0x0090, 0x0080, 0x0070, 0x0060, 0x0050, 0x0040, 0x0030, 0x0020, 0x0010,
 };
+
+// This table was generated using the following PICO-8 code:
+//   for i=0,1,0x.002 do printh('0x'..sub(tostr(atan2(1,-i),1),8,13)) end
+static uint16_t atantable[] =
+{
+    0x0000, 0x0005, 0x000a, 0x000f, 0x0014, 0x0019, 0x001f, 0x0024, 0x0029, 0x002e, 0x0033, 0x0038, 0x003d, 0x0042, 0x0047, 0x004c,
+    0x0051, 0x0057, 0x005c, 0x0061, 0x0066, 0x006b, 0x0070, 0x0075, 0x007a, 0x007f, 0x0084, 0x008a, 0x008f, 0x0094, 0x0099, 0x009e,
+    0x00a3, 0x00a8, 0x00ad, 0x00b2, 0x00b7, 0x00bc, 0x00c2, 0x00c7, 0x00cc, 0x00d1, 0x00d6, 0x00db, 0x00e0, 0x00e5, 0x00ea, 0x00ef,
+    0x00f4, 0x00fa, 0x00ff, 0x0104, 0x0109, 0x010e, 0x0113, 0x0118, 0x011d, 0x0122, 0x0127, 0x012c, 0x0131, 0x0137, 0x013c, 0x0141,
+    0x0146, 0x014b, 0x0150, 0x0155, 0x015a, 0x015f, 0x0164, 0x0169, 0x016f, 0x0174, 0x0179, 0x017e, 0x0183, 0x0188, 0x018d, 0x0192,
+    0x0197, 0x019c, 0x01a1, 0x01a6, 0x01ac, 0x01b1, 0x01b6, 0x01bb, 0x01c0, 0x01c5, 0x01ca, 0x01cf, 0x01d4, 0x01d9, 0x01de, 0x01e3,
+    0x01e9, 0x01ee, 0x01f3, 0x01f8, 0x01fd, 0x0202, 0x0207, 0x020c, 0x0211, 0x0216, 0x021b, 0x0220, 0x0226, 0x022b, 0x0230, 0x0235,
+    0x023a, 0x023f, 0x0244, 0x0249, 0x024e, 0x0253, 0x0258, 0x025d, 0x0262, 0x0268, 0x026d, 0x0272, 0x0277, 0x027c, 0x0281, 0x0286,
+    0x028b, 0x0290, 0x0295, 0x029a, 0x029f, 0x02a4, 0x02a9, 0x02af, 0x02b4, 0x02b9, 0x02be, 0x02c3, 0x02c8, 0x02cd, 0x02d2, 0x02d7,
+    0x02dc, 0x02e1, 0x02e6, 0x02eb, 0x02f0, 0x02f6, 0x02fb, 0x0300, 0x0305, 0x030a, 0x030f, 0x0314, 0x0319, 0x031e, 0x0323, 0x0328,
+    0x032d, 0x0332, 0x0337, 0x033c, 0x0341, 0x0347, 0x034c, 0x0351, 0x0356, 0x035b, 0x0360, 0x0365, 0x036a, 0x036f, 0x0374, 0x0379,
+    0x037e, 0x0383, 0x0388, 0x038d, 0x0392, 0x0397, 0x039c, 0x03a2, 0x03a7, 0x03ac, 0x03b1, 0x03b6, 0x03bb, 0x03c0, 0x03c5, 0x03ca,
+    0x03cf, 0x03d4, 0x03d9, 0x03de, 0x03e3, 0x03e8, 0x03ed, 0x03f2, 0x03f7, 0x03fc, 0x0401, 0x0407, 0x040c, 0x0411, 0x0416, 0x041b,
+    0x0420, 0x0425, 0x042a, 0x042f, 0x0434, 0x0439, 0x043e, 0x0443, 0x0448, 0x044d, 0x0452, 0x0457, 0x045c, 0x0461, 0x0466, 0x046b,
+    0x0470, 0x0475, 0x047a, 0x047f, 0x0484, 0x0489, 0x048e, 0x0494, 0x0499, 0x049e, 0x04a3, 0x04a8, 0x04ad, 0x04b2, 0x04b7, 0x04bc,
+    0x04c1, 0x04c6, 0x04cb, 0x04d0, 0x04d5, 0x04da, 0x04df, 0x04e4, 0x04e9, 0x04ee, 0x04f3, 0x04f8, 0x04fd, 0x0502, 0x0507, 0x050c,
+    0x0511, 0x0516, 0x051b, 0x0520, 0x0525, 0x052a, 0x052f, 0x0534, 0x0539, 0x053e, 0x0543, 0x0548, 0x054d, 0x0552, 0x0557, 0x055c,
+    0x0561, 0x0566, 0x056b, 0x0570, 0x0575, 0x057a, 0x057f, 0x0584, 0x0589, 0x058e, 0x0593, 0x0598, 0x059d, 0x05a2, 0x05a7, 0x05ac,
+    0x05b1, 0x05b6, 0x05bb, 0x05c0, 0x05c5, 0x05ca, 0x05cf, 0x05d4, 0x05d9, 0x05de, 0x05e3, 0x05e8, 0x05ed, 0x05f2, 0x05f7, 0x05fc,
+    0x0601, 0x0606, 0x060b, 0x0610, 0x0615, 0x061a, 0x061f, 0x0624, 0x0629, 0x062e, 0x0633, 0x0638, 0x063d, 0x0642, 0x0647, 0x064c,
+    0x0651, 0x0656, 0x065b, 0x0660, 0x0665, 0x066a, 0x066e, 0x0673, 0x0678, 0x067d, 0x0682, 0x0687, 0x068c, 0x0691, 0x0696, 0x069b,
+    0x06a0, 0x06a5, 0x06aa, 0x06af, 0x06b4, 0x06b9, 0x06be, 0x06c3, 0x06c8, 0x06cd, 0x06d2, 0x06d7, 0x06dc, 0x06e1, 0x06e5, 0x06ea,
+    0x06ef, 0x06f4, 0x06f9, 0x06fe, 0x0703, 0x0708, 0x070d, 0x0712, 0x0717, 0x071c, 0x0721, 0x0726, 0x072b, 0x0730, 0x0735, 0x0739,
+    0x073e, 0x0743, 0x0748, 0x074d, 0x0752, 0x0757, 0x075c, 0x0761, 0x0766, 0x076b, 0x0770, 0x0775, 0x077a, 0x077e, 0x0783, 0x0788,
+    0x078d, 0x0792, 0x0797, 0x079c, 0x07a1, 0x07a6, 0x07ab, 0x07b0, 0x07b5, 0x07b9, 0x07be, 0x07c3, 0x07c8, 0x07cd, 0x07d2, 0x07d7,
+    0x07dc, 0x07e1, 0x07e6, 0x07eb, 0x07ef, 0x07f4, 0x07f9, 0x07fe, 0x0803, 0x0808, 0x080d, 0x0812, 0x0817, 0x081c, 0x0820, 0x0825,
+    0x082a, 0x082f, 0x0834, 0x0839, 0x083e, 0x0843, 0x0848, 0x084c, 0x0851, 0x0856, 0x085b, 0x0860, 0x0865, 0x086a, 0x086f, 0x0873,
+    0x0878, 0x087d, 0x0882, 0x0887, 0x088c, 0x0891, 0x0896, 0x089a, 0x089f, 0x08a4, 0x08a9, 0x08ae, 0x08b3, 0x08b8, 0x08bd, 0x08c1,
+    0x08c6, 0x08cb, 0x08d0, 0x08d5, 0x08da, 0x08df, 0x08e3, 0x08e8, 0x08ed, 0x08f2, 0x08f7, 0x08fc, 0x0901, 0x0905, 0x090a, 0x090f,
+    0x0914, 0x0919, 0x091e, 0x0922, 0x0927, 0x092c, 0x0931, 0x0936, 0x093b, 0x093f, 0x0944, 0x0949, 0x094e, 0x0953, 0x0958, 0x095c,
+    0x0961, 0x0966, 0x096b, 0x0970, 0x0975, 0x0979, 0x097e, 0x0983, 0x0988, 0x098d, 0x0992, 0x0996, 0x099b, 0x09a0, 0x09a5, 0x09aa,
+    0x09ae, 0x09b3, 0x09b8, 0x09bd, 0x09c2, 0x09c6, 0x09cb, 0x09d0, 0x09d5, 0x09da, 0x09de, 0x09e3, 0x09e8, 0x09ed, 0x09f2, 0x09f6,
+    0x09fb, 0x0a00, 0x0a05, 0x0a0a, 0x0a0e, 0x0a13, 0x0a18, 0x0a1d, 0x0a22, 0x0a26, 0x0a2b, 0x0a30, 0x0a35, 0x0a39, 0x0a3e, 0x0a43,
+    0x0a48, 0x0a4d, 0x0a51, 0x0a56, 0x0a5b, 0x0a60, 0x0a64, 0x0a69, 0x0a6e, 0x0a73, 0x0a77, 0x0a7c, 0x0a81, 0x0a86, 0x0a8b, 0x0a8f,
+    0x0a94, 0x0a99, 0x0a9e, 0x0aa2, 0x0aa7, 0x0aac, 0x0ab1, 0x0ab5, 0x0aba, 0x0abf, 0x0ac4, 0x0ac8, 0x0acd, 0x0ad2, 0x0ad7, 0x0adb,
+    0x0ae0, 0x0ae5, 0x0ae9, 0x0aee, 0x0af3, 0x0af8, 0x0afc, 0x0b01, 0x0b06, 0x0b0b, 0x0b0f, 0x0b14, 0x0b19, 0x0b1e, 0x0b22, 0x0b27,
+    0x0b2c, 0x0b30, 0x0b35, 0x0b3a, 0x0b3f, 0x0b43, 0x0b48, 0x0b4d, 0x0b51, 0x0b56, 0x0b5b, 0x0b60, 0x0b64, 0x0b69, 0x0b6e, 0x0b72,
+    0x0b77, 0x0b7c, 0x0b80, 0x0b85, 0x0b8a, 0x0b8f, 0x0b93, 0x0b98, 0x0b9d, 0x0ba1, 0x0ba6, 0x0bab, 0x0baf, 0x0bb4, 0x0bb9, 0x0bbd,
+    0x0bc2, 0x0bc7, 0x0bcb, 0x0bd0, 0x0bd5, 0x0bd9, 0x0bde, 0x0be3, 0x0be7, 0x0bec, 0x0bf1, 0x0bf5, 0x0bfa, 0x0bff, 0x0c03, 0x0c08,
+    0x0c0d, 0x0c11, 0x0c16, 0x0c1b, 0x0c1f, 0x0c24, 0x0c29, 0x0c2d, 0x0c32, 0x0c37, 0x0c3b, 0x0c40, 0x0c45, 0x0c49, 0x0c4e, 0x0c53,
+    0x0c57, 0x0c5c, 0x0c60, 0x0c65, 0x0c6a, 0x0c6e, 0x0c73, 0x0c78, 0x0c7c, 0x0c81, 0x0c86, 0x0c8a, 0x0c8f, 0x0c93, 0x0c98, 0x0c9d,
+    0x0ca1, 0x0ca6, 0x0cab, 0x0caf, 0x0cb4, 0x0cb8, 0x0cbd, 0x0cc2, 0x0cc6, 0x0ccb, 0x0ccf, 0x0cd4, 0x0cd9, 0x0cdd, 0x0ce2, 0x0ce6,
+    0x0ceb, 0x0cf0, 0x0cf4, 0x0cf9, 0x0cfd, 0x0d02, 0x0d07, 0x0d0b, 0x0d10, 0x0d14, 0x0d19, 0x0d1e, 0x0d22, 0x0d27, 0x0d2b, 0x0d30,
+    0x0d34, 0x0d39, 0x0d3e, 0x0d42, 0x0d47, 0x0d4b, 0x0d50, 0x0d54, 0x0d59, 0x0d5e, 0x0d62, 0x0d67, 0x0d6b, 0x0d70, 0x0d74, 0x0d79,
+    0x0d7d, 0x0d82, 0x0d87, 0x0d8b, 0x0d90, 0x0d94, 0x0d99, 0x0d9d, 0x0da2, 0x0da6, 0x0dab, 0x0daf, 0x0db4, 0x0db9, 0x0dbd, 0x0dc2,
+    0x0dc6, 0x0dcb, 0x0dcf, 0x0dd4, 0x0dd8, 0x0ddd, 0x0de1, 0x0de6, 0x0dea, 0x0def, 0x0df3, 0x0df8, 0x0dfc, 0x0e01, 0x0e05, 0x0e0a,
+    0x0e0f, 0x0e13, 0x0e18, 0x0e1c, 0x0e21, 0x0e25, 0x0e2a, 0x0e2e, 0x0e33, 0x0e37, 0x0e3c, 0x0e40, 0x0e45, 0x0e49, 0x0e4e, 0x0e52,
+    0x0e56, 0x0e5b, 0x0e5f, 0x0e64, 0x0e68, 0x0e6d, 0x0e71, 0x0e76, 0x0e7a, 0x0e7f, 0x0e83, 0x0e88, 0x0e8c, 0x0e91, 0x0e95, 0x0e9a,
+    0x0e9e, 0x0ea3, 0x0ea7, 0x0eac, 0x0eb0, 0x0eb4, 0x0eb9, 0x0ebd, 0x0ec2, 0x0ec6, 0x0ecb, 0x0ecf, 0x0ed4, 0x0ed8, 0x0edc, 0x0ee1,
+    0x0ee5, 0x0eea, 0x0eee, 0x0ef3, 0x0ef7, 0x0efc, 0x0f00, 0x0f04, 0x0f09, 0x0f0d, 0x0f12, 0x0f16, 0x0f1b, 0x0f1f, 0x0f23, 0x0f28,
+    0x0f2c, 0x0f31, 0x0f35, 0x0f3a, 0x0f3e, 0x0f42, 0x0f47, 0x0f4b, 0x0f50, 0x0f54, 0x0f58, 0x0f5d, 0x0f61, 0x0f66, 0x0f6a, 0x0f6e,
+    0x0f73, 0x0f77, 0x0f7c, 0x0f80, 0x0f84, 0x0f89, 0x0f8d, 0x0f91, 0x0f96, 0x0f9a, 0x0f9f, 0x0fa3, 0x0fa7, 0x0fac, 0x0fb0, 0x0fb5,
+    0x0fb9, 0x0fbd, 0x0fc2, 0x0fc6, 0x0fca, 0x0fcf, 0x0fd3, 0x0fd7, 0x0fdc, 0x0fe0, 0x0fe5, 0x0fe9, 0x0fed, 0x0ff2, 0x0ff6, 0x0ffa,
+    0x0fff, 0x1003, 0x1007, 0x100c, 0x1010, 0x1014, 0x1019, 0x101d, 0x1021, 0x1026, 0x102a, 0x102e, 0x1033, 0x1037, 0x103b, 0x1040,
+    0x1044, 0x1048, 0x104d, 0x1051, 0x1055, 0x105a, 0x105e, 0x1062, 0x1067, 0x106b, 0x106f, 0x1073, 0x1078, 0x107c, 0x1080, 0x1085,
+    0x1089, 0x108d, 0x1092, 0x1096, 0x109a, 0x109e, 0x10a3, 0x10a7, 0x10ab, 0x10b0, 0x10b4, 0x10b8, 0x10bc, 0x10c1, 0x10c5, 0x10c9,
+    0x10ce, 0x10d2, 0x10d6, 0x10da, 0x10df, 0x10e3, 0x10e7, 0x10eb, 0x10f0, 0x10f4, 0x10f8, 0x10fd, 0x1101, 0x1105, 0x1109, 0x110e,
+    0x1112, 0x1116, 0x111a, 0x111f, 0x1123, 0x1127, 0x112b, 0x1130, 0x1134, 0x1138, 0x113c, 0x1140, 0x1145, 0x1149, 0x114d, 0x1151,
+    0x1156, 0x115a, 0x115e, 0x1162, 0x1166, 0x116b, 0x116f, 0x1173, 0x1177, 0x117c, 0x1180, 0x1184, 0x1188, 0x118c, 0x1191, 0x1195,
+    0x1199, 0x119d, 0x11a1, 0x11a6, 0x11aa, 0x11ae, 0x11b2, 0x11b6, 0x11bb, 0x11bf, 0x11c3, 0x11c7, 0x11cb, 0x11cf, 0x11d4, 0x11d8,
+    0x11dc, 0x11e0, 0x11e4, 0x11e9, 0x11ed, 0x11f1, 0x11f5, 0x11f9, 0x11fd, 0x1202, 0x1206, 0x120a, 0x120e, 0x1212, 0x1216, 0x121a,
+    0x121f, 0x1223, 0x1227, 0x122b, 0x122f, 0x1233, 0x1237, 0x123c, 0x1240, 0x1244, 0x1248, 0x124c, 0x1250, 0x1254, 0x1259, 0x125d,
+    0x1261, 0x1265, 0x1269, 0x126d, 0x1271, 0x1275, 0x127a, 0x127e, 0x1282, 0x1286, 0x128a, 0x128e, 0x1292, 0x1296, 0x129a, 0x129f,
+    0x12a3, 0x12a7, 0x12ab, 0x12af, 0x12b3, 0x12b7, 0x12bb, 0x12bf, 0x12c3, 0x12c7, 0x12cc, 0x12d0, 0x12d4, 0x12d8, 0x12dc, 0x12e0,
+    0x12e4, 0x12e8, 0x12ec, 0x12f0, 0x12f4, 0x12f8, 0x12fc, 0x1301, 0x1305, 0x1309, 0x130d, 0x1311, 0x1315, 0x1319, 0x131d, 0x1321,
+    0x1325, 0x1329, 0x132d, 0x1331, 0x1335, 0x1339, 0x133d, 0x1341, 0x1345, 0x1349, 0x134d, 0x1351, 0x1355, 0x135a, 0x135e, 0x1362,
+    0x1366, 0x136a, 0x136e, 0x1372, 0x1376, 0x137a, 0x137e, 0x1382, 0x1386, 0x138a, 0x138e, 0x1392, 0x1396, 0x139a, 0x139e, 0x13a2,
+    0x13a6, 0x13aa, 0x13ae, 0x13b2, 0x13b6, 0x13ba, 0x13be, 0x13c2, 0x13c6, 0x13ca, 0x13ce, 0x13d2, 0x13d6, 0x13da, 0x13de, 0x13e2,
+    0x13e6, 0x13e9, 0x13ed, 0x13f1, 0x13f5, 0x13f9, 0x13fd, 0x1401, 0x1405, 0x1409, 0x140d, 0x1411, 0x1415, 0x1419, 0x141d, 0x1421,
+    0x1425, 0x1429, 0x142d, 0x1431, 0x1435, 0x1439, 0x143d, 0x1440, 0x1444, 0x1448, 0x144c, 0x1450, 0x1454, 0x1458, 0x145c, 0x1460,
+    0x1464, 0x1468, 0x146c, 0x1470, 0x1473, 0x1477, 0x147b, 0x147f, 0x1483, 0x1487, 0x148b, 0x148f, 0x1493, 0x1497, 0x149b, 0x149e,
+    0x14a2, 0x14a6, 0x14aa, 0x14ae, 0x14b2, 0x14b6, 0x14ba, 0x14be, 0x14c1, 0x14c5, 0x14c9, 0x14cd, 0x14d1, 0x14d5, 0x14d9, 0x14dd,
+    0x14e0, 0x14e4, 0x14e8, 0x14ec, 0x14f0, 0x14f4, 0x14f8, 0x14fb, 0x14ff, 0x1503, 0x1507, 0x150b, 0x150f, 0x1513, 0x1516, 0x151a,
+    0x151e, 0x1522, 0x1526, 0x152a, 0x152d, 0x1531, 0x1535, 0x1539, 0x153d, 0x1541, 0x1544, 0x1548, 0x154c, 0x1550, 0x1554, 0x1558,
+    0x155b, 0x155f, 0x1563, 0x1567, 0x156b, 0x156e, 0x1572, 0x1576, 0x157a, 0x157e, 0x1581, 0x1585, 0x1589, 0x158d, 0x1591, 0x1594,
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+    0x2000,
+};
