TheAlgorithms · zhbi98 · May 18, 2020 · May 20, 2020 · May 20, 2020 · May 20, 2020
diff --git a/maths/maths.py b/maths/maths.py
@@ -0,0 +1,135 @@
+
+# package maths.py
+# implement some math.py
+# trigonometric algorithm
+
+Pi = 3.14159265358979323846
+
+
+def _abs(value):
+    # >>> _abs(-10)
+    # 10
+    # >>> _abs(10)
+    # 10
-    # >>> _abs(-10)
-    # 10
-    # >>> _abs(10)
-    # 10
+    """
+    >>> _abs(-10)
+    10
+    >>> _abs(-.5)
+    0.5
+    >>> _abs(0)
+    0
+    >>> _abs(.5)
+    0.5
+    >>> _abs(10)
+    10
+    """
-    # >>> _abs(-10)
-    # 10
-    # >>> _abs(10)
-    # 10
+    """
+    >>> _abs(-10)
+    10
+    >>> _abs(-.5)
+    0.5
+    >>> _abs(0)
+    0
+    >>> _abs(.5)
+    0.5
+    >>> _abs(10)
+    10
+    """
+    return -value if value < 0 else value
+
+
+def _power(value, n):
-def _power(value, n):
+def _power(value, n):
+    """
+    >>> from math import pow
+    >>> for i in range 360:
+    >>>     assert _power(10, i) == pow(10, i), (i, _power(10, i), pow(10, i))
+    """
-def _power(value, n):
+def _power(value, n):
+    """
+    >>> from math import pow
+    >>> for i in range 360:
+    >>>     assert _power(10, i) == pow(10, i), (i, _power(10, i), pow(10, i))
+    """
+    # >>> _power(-10, 2)
+    # 100
+    # >>> _power(10, 2)
+    # 100
+    result = 1
+
+    if n == 0:
+        result = 1
+    else:
+        for i in range(n):
+            result = result * value
+
+    return result
+
+
+# newton iteration method
+def _sqrt(value):
-def _sqrt(value):
+def _sqrt(value):
+    """
+    >>> _sqrt(9)
+    3
+    >>> _sqrt(25)
+    5
+    """
-def _sqrt(value):
+def _sqrt(value):
+    """
+    >>> _sqrt(9)
+    3
+    >>> _sqrt(25)
+    5
+    """
+    if value < 0:
+        print("_sqrt: Value must be greater than or equal to 0")
+    else:
+        x = value
+        t = 0
+        # X(k+1) = 1/2 * (X(k) + vale/X(k))
+        while _abs(x - t) > 1e-15:
+            t = x
+            x = 0.5 * (x + (value / x))
+
+    # >>> _sqrt(9)
+    # 3
+    # >>> _sqrt(25)
+    # 5
+    return x
+
+
+# factorial
+def _factor(value):
+    # regulations 0! = 1
-    # regulations 0! = 1
+    """
+    regulations 0! = 1
+    >>> from math import factorial
+    >>> for i in range 360:
+    >>>     assert _factor(i) == factorial(i), (i, _factor(i), factorial(i))
+    """
-    # regulations 0! = 1
+    """
+    regulations 0! = 1
+    >>> from math import factorial
+    >>> for i in range 360:
+    >>>     assert _factor(i) == factorial(i), (i, _factor(i), factorial(i))
+    """
+    f = 1
+    if value:
+        for i in range(value):
+            f = f * (i + 1)
+    else:
+        f = 1
+
+    # >>> _factor(5)
+    # 120
+    # >>> _factor(2)
+    # 2  
+    return f
+
+
+# Another way to 
+# implement sin(x)
+def __sin(value):
+    value = value * Pi / 180
+    t = value
+    x = 0
+    n = 1
+
+    while _abs(t) > 1e-15:
+        x = x + t
+        n = n + 1
+        t = -t * value * value / (2 * n - 1) / (2 * n - 2)
+
+    if x > 0 and x < 1e-15:
+        x = 0
+
+    # >>> _sin(90)
+    # 1
+    # >>> _sin(0)
+    # 0    
+    return x
+
+
+def _sin(value):
+    value = value * Pi / 180
+    t = 1
+    x = 0
+    n = 1
+
+    while _power(value, n) / _factor(n) > 1e-15:
+        x += t * _power(value, n) / _factor(n)
+        t = -1 * t
+        n = n + 2
+
+    # >>> _sin(90)
+    # 1
+    # >>> _sin(0)
+    # 0 
+    return x
+
+
+def _cos(value):
+    value = value * Pi / 180
+    n = 0
+    t = 1 
+    x = 0
+
+    while _power(value, n) / _factor(n) > 1e-15:
+        x += t * _power(value, n) / _factor(n)
+        t = -1 * t
+        n = n + 2
+
+    # >>> _cos(90)
+    # 0
+    # >>> _cos(0)
+    # 1     
+    return x
+
+
+def _tan(value):
+    x = _sin(value) / _cos(value)
+
+    # >>> _tan(90)
+    # 0
+    # >>> _tan(45)
+    # 1      
+    return x
-def _tan(value):
-    x = _sin(value) / _cos(value)
-    
-    # >>> _tan(90)
-    # 0
-    # >>> _tan(45)
-    # 1      
-    return x
+def _tan(value):
+    """
+    >>> _tan(90)
+    0
+    >>> _tan(45)
+    1
+    >>> from math import tan
+    >>> for i in range 360:
+    >>>     assert _tan(i) == tan(i), (i, _tan(i), tan(i))
+    """
+    return _sin(value) / _cos(value)
-def _tan(value):
-    x = _sin(value) / _cos(value)
-    
-    # >>> _tan(90)
-    # 0
-    # >>> _tan(45)
-    # 1      
-    return x
+def _tan(value):
+    """
+    >>> _tan(90)
+    0
+    >>> _tan(45)
+    1
+    >>> from math import tan
+    >>> for i in range 360:
+    >>>     assert _tan(i) == tan(i), (i, _tan(i), tan(i))
+    """
+    return _sin(value) / _cos(value)