Merge pull request #104 from icelal-kskn/master

Created ikram_celal_keskin's Week06 homework

Week06/halfprecision_ikram_celal_keskin.py

@@ -0,0 +1,147 @@
+import numpy as np
+
+class HalfPrecision:
+    """
+    This class converting a floating point number to half precision format.
+    The half precision format is a 16-bit format with 1 sign bit, 5 exponent bits, and 10 mantissa bits.
+    The sign bit is 0 for positive numbers and 1 for negative numbers. 
+
+    Attributes:
+        number: float
+
+    Raises:
+        TypeError: If the input is the string, bool, list, tuple, or set.
+        TypeError: If the input cannot be converted to a float.
+
+    Returns:
+        str: The half precision format of the input number.
+    """
+    def __init__(self,number):
+        if isinstance(number,(str,bool,list,tuple,set)):
+            raise TypeError(f"Invalid input {type(number)}")
+        try:
+            self.__number = number / 1
+        except Exception as e:
+            raise TypeError("Input {} cannot be converted to a float".format(e.args[0]))
+
+    def __str__(self)->str:
+        """
+        Returns the half precision format of the input number.
+
+        Returns:
+            str: The half precision format of the input number.
+        """
+        return self.__calculate_precision(5,10,self.__number) #for half precision
+
+    def __calculate_precision(self,exponent_length:int,mantissa_length:int,number:float)->str:
+        """
+        This function calculates the half precision format of the input number.
+        """
+        sign= False
+
+        if number < 0 or np.signbit(number):
+            sign = True
+            number = -number
+
+        number = self.__is_calculatable_mantissa(number,mantissa_length,exponent_length)
+
+        if np.isinf(number):
+            return f"{int(sign)}{'1'*exponent_length}{'0'*mantissa_length}"
+
+        bias= 2**(exponent_length-1)-1
+        mantissa,power = self.__calculate_mantissa(mantissa_length,number)
+
+        if power == None:
+            return f"{int(sign)}{'0'*exponent_length}{'0'*mantissa_length}"
+
+        exponent = self.__calculate_exponent(bias,power,exponent_length)
+
+        return f"{int(sign)}{exponent}{mantissa}"
+
+    def __calculate_exponent(self,bias:int,power:int,exponent_length)->str:
+        """
+        This function calculates the exponent part of the half precision format.
+        """
+        binary_exponent = self.__integer_to_binary(bias+power)
+
+        if len(binary_exponent) < exponent_length:
+            binary_exponent = '0' * (exponent_length - len(binary_exponent)) + binary_exponent
+
+        return binary_exponent
+
+    def __calculate_mantissa(self,mantissa_length:int,number:float)->str:
+        """
+        This function calculates the mantissa part of the half precision format.
+        """
+        integer_part,decimal_part = f"{number:.20f}".split(".")
+        integer_part = self.__integer_to_binary(integer_part)
+        decimal_part = self.__decimal_to_binary(decimal_part)
+
+        mantissa = f'{integer_part}.{decimal_part}'
+
+        if not '1' in mantissa:
+            return '0'*mantissa_length,None
+
+        power = 0
+        index1 = mantissa_length
+
+        indexdot = mantissa.index(".")
+        index1 = mantissa.index("1")
+        mantissa = mantissa[index1+1:].replace(".","")
+        power = indexdot - index1 if indexdot < index1 else indexdot - index1 -1
+
+        if len(mantissa)< mantissa_length:
+            mantissa += '0' * (mantissa_length - len(mantissa))
+        elif len(mantissa)> mantissa_length:
+            mantissa = mantissa[:mantissa_length] #Truncating
+            # mantissa = mantissa[:mantissa_length-1] + '1' #Rounding
+
+        return mantissa,power
+
+    def __is_calculatable_mantissa(self, number: float, mantissa_length: int, exponent_length: int) -> float:
+        """
+        This function checks if the input number is calculatable in custom precision format.
+        """
+        max_number = 2**(2**(exponent_length-1)-1) * (2-2**(-mantissa_length))
+
+        if number > max_number:
+            return np.inf
+
+        return number
+
+    def __integer_to_binary(self,number:int)->str:
+
+        result = ""
+        number = int(number)
+
+        if number == 0:
+            return "0"
+
+        while number != 0:
+            remainder = number % 2
+            result += str(remainder)
+            number //= 2
+
+        return result[::-1]
+
+    def __decimal_to_binary(self,number:float)->str:
+        number=float(f"0.{number.split("0")[0]}")
+
+        if number == 0:
+            return ''
+
+        binary = ''
+        while number > 0 and len(binary) < 100:
+
+            number *= 2
+            if number >= 1:
+                binary += '1'
+                number -= 1
+            else:
+                binary += '0'
+
+        return binary
+
+
+
+