math: add sin and cos 1.12 fixed point functions.

.gitignore

@@ -7,4 +7,5 @@ __pycache__
 *.nds
 .~lock*
 *.csv
-*.dsi
+*.dsi
+*.out

math/cos_table_fp12.c

@@ -0,0 +1,95 @@
+#include <stdint.h>
+
+const uint16_t cos_table_fp12[91] = {
+  4096,
+  4095,
+  4094,
+  4090,
+  4086,
+  4080,
+  4074,
+  4065,
+  4056,
+  4046,
+  4034,
+  4021,
+  4006,
+  3991,
+  3974,
+  3956,
+  3937,
+  3917,
+  3896,
+  3873,
+  3849,
+  3824,
+  3798,
+  3770,
+  3742,
+  3712,
+  3681,
+  3650,
+  3617,
+  3582,
+  3547,
+  3511,
+  3474,
+  3435,
+  3396,
+  3355,
+  3314,
+  3271,
+  3228,
+  3183,
+  3138,
+  3091,
+  3044,
+  2996,
+  2946,
+  2896,
+  2845,
+  2793,
+  2741,
+  2687,
+  2633,
+  2578,
+  2522,
+  2465,
+  2408,
+  2349,
+  2290,
+  2231,
+  2171,
+  2110,
+  2048,
+  1986,
+  1923,
+  1860,
+  1796,
+  1731,
+  1666,
+  1600,
+  1534,
+  1468,
+  1401,
+  1334,
+  1266,
+  1198,
+  1129,
+  1060,
+  991,
+  921,
+  852,
+  782,
+  711,
+  641,
+  570,
+  499,
+  428,
+  357,
+  286,
+  214,
+  143,
+  71,
+  0
+};

math/gen_cos_table.py

@@ -0,0 +1,21 @@
+from math import cos, pi
+
+fixed_point_bits = 12
+divisor = 2 ** fixed_point_bits
+tau = pi * 2
+
+if __name__ == "__main__":
+    print("#include <stdint.h>")
+    print()
+    print(f"const uint16_t cos_table_fp{fixed_point_bits}[91] = {{")
+    for i in range(0, 91):
+        radians = i / 360 * tau
+        n = cos(radians)
+        assert n >= 0
+        integer = round(n)
+        decimal = round((n - integer) * divisor)
+        assert decimal < divisor
+        fixed_point = (integer * divisor) + decimal
+        comma = "" if i == 90 else ","
+        print(f"  {fixed_point}{comma}")
+    print("};")

math/math.h

@@ -0,0 +1,10 @@
+#pragma once
+
+#define abs __builtin_abs
+
+int cos_fp12(int theta);
+
+static inline int sin_fp12(int theta)
+{
+  return cos_fp12(theta - 90);
+}

math/sincos.c

@@ -0,0 +1,23 @@
+#include <stdint.h>
+
+#include "math.h"
+
+extern const uint16_t cos_table_fp12[];
+
+int cos_fp12(int theta)
+{
+  theta = abs(theta);
+  while (theta > 360) {
+    theta -= 360;
+  }
+
+  if (theta <= 90) {
+    return cos_table_fp12[theta];
+  } else if (theta <= 180) {
+    return - cos_table_fp12[180 - theta];
+  } else if (theta <= 270) {
+    return - cos_table_fp12[theta - 180];
+  } else {
+    return cos_table_fp12[360 - theta];
+  }
+}

math/sincos_test.c

@@ -0,0 +1,10 @@
+#include <stdio.h>
+
+#include "math.h"
+
+int main()
+{
+  for (int i = -360; i <= 360; i++) {
+    printf("%d %d\n", i, sin_fp12(i));
+  }
+}

math/sincos_verify.py

@@ -0,0 +1,16 @@
+from math import cos, sin
+
+import sys
+from gen_cos_table import fixed_point_bits, divisor, tau
+
+for i in range(-360, 360 + 1):
+    line = sys.stdin.readline()
+    ix, value = map(int, line.strip().split())
+    assert i == ix
+    radians = i / 360 * tau
+    n = sin(radians)
+    integer = round(n)
+    decimal = round((n - integer) * divisor)
+    fixed_point = (integer * divisor) + decimal
+    if fixed_point != value:
+        print("error", i, fixed_point, value)