docs: fix fsin.bas.md page

Author: boriel

docs/library/fsin.bas.md

@@ -2,84 +2,91 @@
 
 ## Introduction
 
+This function implements fast `Fixed` point `sin`, `cos` and `tan` functions.
+The ones that uses `Float` type (calling the Sinclair ROM) are much slower as FP Calculations
+are expensive. This variant is less precise but more suitable for games, for example.
+
 `fSin` is the basis for the alternatives, since `COS(x)` can be calculated
-from `SIN(x)` and `TAN(x)` from `COS(x)` and `SIN(x)`.
+from `SIN(x)` and `TAN(x)` as `SIN(x)` / `COS(x)`.
+
+!!! info "Note"
+    This library is already bundled with Boriel BASIC.<br />
+    To use it just add `#include <fmath.bas>`
+    at the beginning of your program.
 
 The functions should be accurate to about 0.25%, and significantly faster.
 If you need a lot of trig in your code, and it doesn't need to be pinpoint accuracy, these are good alternatives.
-Note that they more or less acknowledge they are less accurate by returning values of type `Fixed` instead of type `Float`.
-I did this because it should be fine for the actual accuracy returned,
+Note that they more or less acknowledge they are less accurate by returning values of type `Fixed` instead
+of type `Float`.
+It should be fine for the actual accuracy returned,
 and `Fixed` numbers process faster and smaller than `Float` ones.
 
-* Note that you need only include `fSin` if you only want Sines, but you need fSin to use `fCos` or `fTan`.
+* Note that you need only include `fSin` if you only want Sines, but you need `fSin` to use `fCos` or `fTan`.
 
 * Note that these functions use degrees, not radians.
 
 ## SINE Function
 
-```
+```vbnet
 FUNCTION fSin(num as FIXED) as FIXED
-DIM quad as byte
-DIM est1,dif as uByte
-
-'This change made now that MOD works with FIXED types.
-'This is much faster than the repeated subtraction method for large angles (much > 360)
-'while having some tiny rounding errors that should not significantly affect our results.
-'Note that the result may be positive or negative still, and for SIN(360) might come out
-'fractionally above 360 (which would cause issued) so the below code still is required.
-
-IF num >= 360 THEN
-  num = num MOD 360
-ELSEIF num < 0 THEN
-  num = 360 - ABS(num) MOD 360
-END IF
-
-IF num>180 then
-  quad=-1
-  num=num-180
-ELSE
-  quad=1
-END IF
-
-IF num>90 then num=180-num
-
-num=num/2
-dif=num : rem Cast to byte loses decimal
-num=num-dif : rem so this is just the decimal bit
-
-
-est1=PEEK (@sinetable+dif)
-dif=PEEK (@sinetable+dif+1)-est1 : REM this is just the difference to the next up number.
-
-num=est1+(num*dif): REM base +interpolate to the next value.
-
-return (num/255)*quad
-
-
-sinetable:
-asm
-DEFB 000,009,018,027,035,044,053,062
-DEFB 070,079,087,096,104,112,120,127
-DEFB 135,143,150,157,164,171,177,183
-DEFB 190,195,201,206,211,216,221,225
-DEFB 229,233,236,240,243,245,247,249
-DEFB 251,253,254,254,255,255
-end asm
+  DIM quad as byte
+  DIM est1,dif as uByte
+
+  'This change made now that MOD works with FIXED types.
+  'This is much faster than the repeated subtraction method for large angles (much > 360)
+  'while having some tiny rounding errors that should not significantly affect our results.
+  'Note that the result may be positive or negative still, and for SIN(360) might come out
+  'fractionally above 360 (which would cause issued) so the below code still is required.
+
+  IF num >= 360 THEN
+    num = num MOD 360
+  ELSEIF num < 0 THEN
+    num = 360 - ABS(num) MOD 360
+  END IF
+
+  IF num > 180 then
+    quad = -1
+    num = num - 180
+  ELSE
+    quad = 1
+  END IF
+
+  IF num > 90 THEN num = 180 - num
+
+  num = num / 2
+  dif = num : REM Cast to byte loses decimal
+  num = num - dif : REM so this is just the decimal bit
+
+  est1 = PEEK(@sinetable + dif)
+  dif = PEEK(@sinetable + dif + 1) - est1 : REM this is just the difference to the next up number.
+  num = est1 + (num * dif) : REM base + interpolate to the next value.
+
+  Return (num / 255) * quad
+
+  sinetable:
+  Asm
+    DEFB 000,009,018,027,035,044,053,062
+    DEFB 070,079,087,096,104,112,120,127
+    DEFB 135,143,150,157,164,171,177,183
+    DEFB 190,195,201,206,211,216,221,225
+    DEFB 229,233,236,240,243,245,247,249
+    DEFB 251,253,254,254,255,255
+  End Asm
 END FUNCTION
 ```
 
 ## COSINE Function
 
-```
+```vbnet
 FUNCTION fCos(num as FIXED) as FIXED
-    return fSin(90-num)
+    Return fSin(90 - num)
 END FUNCTION
 ```
 
 ## TANGENT Function
 
-```
+```vbnet
 FUNCTION fTan(num as FIXED) as FIXED
-    return fSin(num)/fSin(90-num)
+    Return fSin(num) / fSin(90 - num)
 END FUNCTION
 ```