add testing version of multiply-float.py - a wrapper that allows for float multiplication support

src/bitutils.py

@@ -20,13 +20,13 @@ al = align_binary_to_left
 
 
 def shift_left(rg, fill_bit = 0):
-    return rg[1:] + fill_bit
+    return rg[1:] + str(fill_bit)
 
 l = shift_left
 
 
 def shift_right(rg, fill_bit = 0):
-    return fill_bit + rg[:-1]
+    return str(fill_bit) + rg[:-1]
 
 r = shift_right
 
@@ -37,14 +37,20 @@ def sum_supplementary_codes(x, y, size):
 sum = sum_supplementary_codes
 
 
-def sum_supplementary_codes_with_overspill(x, y, size):
+def sum_supplementary_codes_right_align(x, y, size):
+    return ar(bin(int("0b"+x, 2) + int("0b"+y, 2))[2:], size)
+
+rsum = sum_supplementary_codes_right_align
+
+
+def sum_supplementary_codes_with_overflow(x, y, size):
     result = bin(int("0b"+x, 2) + int("0b"+y, 2))[2:]
     if len(result) > size:
         return al(result, size), '1'
     else:
         return al(result, size), '0'
 
-sump = sum_supplementary_codes_with_overspill
+sump = sum_supplementary_codes_with_overflow
 
 
 def invert_bit(b):
@@ -57,3 +63,15 @@ def invert_bit(b):
         exit(1)
 
 inv = invert_bit
+
+
+def xor(x, y):
+    if len(x) == len(y):
+        result = ''
+        for i in zip(x, y):
+            if x != y:
+                result += '1'
+            else:
+                result += '0'
+
+    return result

src/mult-test.py

@@ -24,4 +24,4 @@ for x in range(top_value):
 if len(errors) == 0:
     print("Testing finished, no miscalculations detected.\nIt's safe to use!")
 else:
-    print("Testing failed with {len(errors)} errors.")
+    print(f"Testing failed with {len(errors)} errors.")

src/multiply-float.py

@@ -0,0 +1,92 @@
+# a wrapper for multiplication script which adds support for floating point numbers
+
+from lib.prettytable import PrettyTable
+from multiply import multiply, table_to_text
+import bitutils as bu
+
+def get_reference_register_size(*numbers):
+    return max(map(len, numbers))
+
+def parse_float(number):
+    split_by_dot = number.split('.')
+    #print(number, split_by_dot)
+    Sn = split_by_dot[0] # sign
+
+    split_by_comma = split_by_dot[1].split(',')
+    Pn = len(split_by_comma[0].lstrip('0'))
+    Mn = ''.join(split_by_comma).lstrip('0')
+    #print(Sn, Pn, Mn)
+    return Sn, Pn, Mn
+
+# compatibility layer for old multiply.py code
+def to_int(number):
+    return int("0b" + number, 2)
+
+def normalize_mantice(m, n):
+    M_norm = m.lstrip('0')
+    #print(m, M_norm)
+    P_delta = len(m) - len(M_norm)
+    #print(M_norm[:n], P_delta)
+    return M_norm[:n], P_delta
+
+def round_mantice(m, n):
+    closest_upper = bu.sum(m[:n+1], '1', n+1)
+    return closest_upper[:n]
+
+def print_classic_float(label, Sn, Pn, Mn):
+    pt = PrettyTable()
+    pt.field_names = [f"S{label}", f"P{label}", f"M{label}"]
+    pt.add_row([Sn, bin(Pn)[2:], Mn])
+    print(pt)
+
+def multiply_float(x, y, method, n = 0, verbose = False):
+    Sx, Px, Mx = parse_float(x)
+    Sy, Py, My = parse_float(y)
+
+    print(f"Число X:\n" \
+          f"Знак мантиси: {Sx}\n" \
+          f"Порядок: {Px}\n" \
+          f"Мантиса: {Mx}\n")
+
+    print(f"Число Y:\n" \
+          f"Знак мантиси: {Sy}\n" \
+          f"Порядок: {Py}\n" \
+          f"Мантиса: {My}")
+
+    print("Запис чисел у класичному форматі:")
+    print_classic_float('x', Sx, Px, Mx)
+    print()
+    print_classic_float('y', Sy, Py, My)
+    print()
+
+    reg_size = get_reference_register_size(Mx, My)
+
+    table, result = multiply(n, to_int(bu.al(Mx, n)), to_int(bu.al(My, n)), method)
+    print(f"Процес множення другим методом:\n{table_to_text(table)}\n")
+
+    print("Маємо результат:")
+
+    S_result = bu.xor(Sx, Sy)
+    print(f"Знаковий розряд: {Sx} ^ {Sy} = {S_result}")
+
+    M_norm, P_delta = normalize_mantice(result, n+1)
+    print(f"Нормалізована мантиса: ,{M_norm}")
+
+    P_result = Px + Py - P_delta
+    print(f"Порядок: {Px} + {Py} - {P_delta} = {P_result}")
+
+    M_result = round_mantice(result, n)
+    print(f"Округлюємо мантису до {n} розрядів: ,{M_result}")
+
+    return S_result, P_result, M_result
+
+if __name__ == "__main__":
+    start_x = input("X: ")
+    start_y = input("Y: ")
+    n = int(input("n: "))
+    method = int(input("Method: "))
+
+    S_result, P_result, M_result = multiply_float(start_x, start_y, method, n)
+
+    print(f"Запишемо результат у вигляді таблиці:")
+    print_classic_float('f', S_result, P_result, M_result)

src/multiply.py

@@ -1,3 +1,9 @@
+import bitutils as bu
+
+# this needs to be replaced at some point, because:
+# - it uses old notation for align operation, which contradicts with
+#   modern instruction sets, thus making it easily confusable with
+#   the bu.al() operation which aligns bits to the left
 def align_binary_to_right(value, size):
     if "b" in value:
         result = value.split("b")[1]
@@ -15,19 +21,62 @@ def multiply(n, x, y, method):
     - get just the end result of binary multiplication;
 
     it takes 4 arguments:
-    n - (int) base register bit depth
+    n - (int) base register bit length
     x - (int) value for X operand
     y - (int) value for Y operand
     method - (int) which method to use to perform multiplication
 
     it returns 2 items:
-    - (list) table with step-by-step operations and descriptions
+    - (list) table with step-by-step operations and descriptions (table format
-    - (str)  binary representation of the result
+             depends on the chosen method)
+    - (str)  binary representation of the result (method-independant)
 
-    Methods fully supported: №4
+    Methods fully supported:
+    - №2 (passed mult-test.py with 10 bits)
+    - №4 (passed mult-test.py with 12 bits)
     '''
 
-    if method == 4:
+    if method == 2:
+        # every table line has registers like so: RG1, RG3, RG2
+        data_table = [[["0", "0"*(2*n), "0"*n + bu.ar(bin(y)[2:], n), bu.ar(bin(x)[2:], n), "-"]]*2]
+
+        # iteration number
+        i = 0
+
+        while int('0b' + data_table[-1][-1][3], 2) != 0:
+            data_table.append([])
+            i += 1
+
+            if data_table[-2][-1][3][-1] == "1":
+                data_table[-1].append([
+                    i,
+                    #al(bin(int("0b"+data_table[-2][-1][1], 2) + int("0b"+data_table[-2][-1][2], 2))[-(2*n+1):], 2*n+1), # RG1 + RG3
+                    bu.rsum(data_table[-2][-1][1], data_table[-2][-1][2], 2*n),
+                    data_table[-2][-1][2],
+                    data_table[-2][-1][3],
+                    "RG1+RG3"
+                ])
+
+                data_table[-1].append([
+                    i,
+                    data_table[-1][-1][1],
+                    bu.l(data_table[-1][-1][2]), # l(RG3).0
+                    bu.r(data_table[-1][-1][3]), # 0.r(RG2)
+                    "0.r(RG2), l(RG3).0"
+                ])
+
+            else:
+                data_table[-1].append([
+                    i,
+                    data_table[-2][-1][1],
+                    bu.l(data_table[-2][-1][2]), # l(RG3).0
+                    bu.r(data_table[-2][-1][3]), # 0.r(RG2)
+                    "0.r(RG2), l(RG3).0"
+                ])
+
+        return data_table, data_table[-1][-1][1]
+
+    elif method == 4:
         # every table line has registers like so: RG1, RG3, RG2
         data_table = [[["0", "0"*(2*n+1), "0" + al(bin(y)[2:], n) + "0"*n, al(bin(x)[2:], n), "-"]]*2]
 
@@ -66,6 +115,19 @@ def multiply(n, x, y, method):
 
         return data_table, data_table[-1][-1][1][:-1]
 
+def table_to_text(dt):
+    from lib.prettytable import PrettyTable
+    pt = PrettyTable()
+    pt.field_names = ["Iteration", "RG1", "RG3", "RG2", "Operations"]
+
+    for i in dt:
+        for j in range(len(i)):
+            if j+1 == len(i):
+                pt.add_row(i[j], divider = True)
+            else:
+                pt.add_row(i[j])
+
+    return pt.get_string()
 
 if __name__ == "__main__":
     # a fully functional reference
@@ -86,7 +148,8 @@ if __name__ == "__main__":
     method = int(input("Method: "))
 
     dt, result = multiply(n, x, y, method)
-
+    
+    '''
     from lib.prettytable import PrettyTable
     pt = PrettyTable()
     pt.field_names = ["Iteration", "RG1", "RG3", "RG2", "Operations"]
@@ -99,4 +162,6 @@ if __name__ == "__main__":
                 pt.add_row(i[j])
 
     print(pt)
+    '''
+    print(table_to_text(dt))
     print(f"Result: {result}")