math and docs

docs/math.md

@@ -10,7 +10,7 @@ Same as in C++.
 |        1         | `%` `*` `/`                          |
 |        2         | `+` `-`                              |
 |        3         | bit shifts (NI)                      |
-|        4         | `<=>` (NI)                           |
+|        4         | `<=>` (1)                            |
 |        5         | `<=` `>=` `<` `>`                    |
 |        6         | `==` `!=`                            |
 |        7         | bitwise and `&` (NI)                 |
@@ -18,7 +18,11 @@ Same as in C++.
 |        10        | `&&`                                 |
 |  11<br/>lowest   | `\|\|`                               |
 
-- (NI) stands for not yet implemented.
+(NI) 
+: not yet implemented.
+
+(1)
+: Shuttle operator: `a <=> b` returns 0 if a == b, negative Int if a < b and positive Int otherwise. It is necessary to override shuttle operator to make a class comparable. 
 
 ## Operators
 
@@ -43,22 +47,39 @@ or transformed `Real` otherwise.
 | floor(x) | Computes the largest integer value not greater than x  |
 | ceil(x)  | Computes the least integer value value not less than x |
 | round(x) | Rounds x                                               |
-|          |                                                        |
+| abs(x)   | absolute value, Int for integer x, Real otherwise      |
 |          |                                                        |
 
-## Scientific functions
+## Mathematical functions
 
-| name                | meaning |
-|---------------------|---------|
-| `sin(x:Real): Real` | sine    |
-|                     |         |
-|                     |         |
-|                     |         |
+| name      | meaning                                              |
+|-----------|------------------------------------------------------|
+| sin(x)    | sine                                                 |
+| cos(x)    | cosine                                               |
+| tan(x)    | tangent                                              |
+| asin(x)   | $sin^-1(x)$                                          |
+| acos(x)   | $cos^-1(x)$                                          |
+| atan(x)   | $tg^-1(x)$                                           |
+| sinh(x)   | hyperbolic sine                                      |
+| cosh(x)   | hyperbolic cosine                                    |
+| tanh(x)   | hyperbolic tangent                                   |
+| asinh(x)  | $sinh^-1(x)$                                         |
+| acosh(x)  | $cosh^-1(x)$                                         |
+| atanh(x)  | $tgh^-1(x)$                                          |
+| ln(x)     | $ln(x)$, $ log_e(x) $                                |
+| exp(x)    | $e^x$                                                |
+| log10(x)  | $log_{10}(x)$                                        |
+| pow(x, y) | ${x^y}$                                              |
+| sqrt(x)   | $ \sqrt {x}$                                         |
+| abs(x)    | absolute value of x. Int if x is Int, Real otherwise |
 
-For example: 
 
-    sin(π/2)
-    >>> 1.0
+For example:
+
+    assert( sin(π/2) == 1.0)
+    assert( cos(π/2) < 0.000001)
+    assert( abs(ln(exp(1))) - 1 < 0.00001)
+    >>> void
 
 ## Scientific constant