first stab at trig

fix16.tal

@@ -144,3 +144,62 @@
 
 @x16-div-mod ( x* y* -> x/y* x%y* )
     ;x16-mod-div JSR2 SWP2 JMP2r
+
+( trigonometry                                      )
+(                                                   )
+( this uses there different angle representations:  )
+(                                                   )
+( 1. angle representation (#0080 = pi, #0100 = 2pi) )
+( 2. fix16 representation (#0324 = pi, #0648 = 2pi) )
+( 3. degrees              (#00b4 = pi, #0168 = 2pi) )
+(                                                   )
+( angles are the most precise, but may require some )
+( conversion.                                       )
+
+( calculate the sin of the given angle.  )
+(                                        )
+( the input should be an angle and the   )
+( result will be 16-bit fixed point.     )
+(                                        )
+( cos(x) = sin(x + pi/2)                 )
+@cos-angle ( x* -> cos(x)* )
+    #0080 ADD2 ;sin-angle JMP2
+
+( calculate the sin of the given angle.  )
+(                                        )
+( the input should be an angle and the   )
+( result will be 16-bit fixed point.     )
+(                                        )
+( sin table offset math:                 )
+(       0 <= x <  64 ->  table[x]        )
+(      64 <= x < 128 ->  table[127 - x]  )
+(     128 <= x < 192 -> -table[x - 128]  )
+(     192 <= x < 256 -> -table[255 - x]  )
+@sin-angle ( x* -> sin(x)* )
+    NIP DUP #7f GTH ,&d180+ JCN
+            #0001 STH2
+            DUP #3f GTH ,&d90 ,&load JMP
+        &d90     #7f SWP SUB ,&load JMP
+    &d180+
+            #ffff STH2
+            DUP #bf GTH ,&d270 #80 SUB ,&load JMP
+        &d270             #ff SWP SUB ,&load JMP
+    &load ,sin-table ADD LDR2 STH2r MUL2 JMP2r
+
+( sin table with 64 entries for 1/4 of a unit circle. )
+(                                                     )
+( there is no need for interpolation when using       )
+( angle values, since 256 distinct values can be      )
+( produced using reflection.                          )
+(                                                     )
+( these table values go from 0 until pi/2 (i.e. from  )
+( angles #00 until #80).                              )
+@sin-table ( 0 - pi/2: 64 steps )
+    0000 0006 000d 0013 0019 001f 0026 002c
+    0032 0038 003e 0044 004a 0050 0056 005c
+    0062 0068 006d 0073 0079 007e 0084 0089
+    008e 0093 0098 009d 00a2 00a7 00ac 00b1
+    00b5 00b9 00be 00c2 00c6 00ca 00ce 00d1
+    00d5 00d8 00dc 00df 00e2 00e5 00e7 00ea
+    00ed 00ef 00f1 00f3 00f5 00f7 00f8 00fa
+    00fb 00fc 00fd 00fe 00ff 00ff 0100 0100