Apparatus and method for performing division with an extended range of variables

Claim 2

Method of operating a data processing apparatus for obtaining the value of the quotient (u) of a dividend (v) and a divisor (w), characterized by the following steps: initially generating the inverse square root of the divisor (w) as an auxiliary value (g), by accumulating the sum value of a series C 0 +C 1 w+C 2 w 2 + . . . +C n w n in generating means (11; 11') comprising storage means (37 . . . 44; 77 . . . 81) furnishing appropriate values for C 0 , C 1 , C 2 , . . . C n , first multiplying means (25 . . . 29; 53, 55), and adding means (57, 59); multiplying in second multiplying means (17; 17') the dividend (v) by said auxiliary value (g) to obtain an intermediate value; and multiplying in third multiplying means (21; 21') said intermediate value by said auxiliary value (g) for generating the quotient value (u).

Claim 3

Arithmetic apparatus for furnishing the quotient (u) of a dividend (v) and a divisor (w), including first and second storage means (91, 51) for storing said dividend and divisor, respectively, said apparatus comprising: generating means (11') connected to receive the output of said second storage means (51), for generating at its output the reciprocal value of the square root of said divisor (w) as an auxiliary value (g), said generating means comprising circuitry (25 . . . 35; 61 . . . 75) for accumulating said auxiliary value as g={(C n ·w n-2 . . . +C 2 )w+C 1 }w+C 0 , by alternating multiplication and addition, and comprising third storage means (37 . . . 44; 77 . . . 81) for predetermined appropriate constant values C 0 , C 1 , C 2 , . . . C n ; first multiplying means (17') connected to receive the outputs of said first storage means (91) and of said generating means (11), for multiplying said dividend (v) by said auxiliary value (g) to obtain an intermediate product, and second multiplying means (21') connected to receive the outputs of said first multiplying means (17') and said generating means (11'), for multiplying said intermediate produce by said auxiliary value (g), thus producing at its output (13') a representation of the quotient (u) of said dividend and said divisor.

Claim 4

Arithmetic apparatus for furnishing the quotient (u) of a dividend (v) and a divisor (w), including first and second storage means (91, 51) for storing said dividend and divisor, respectively, said apparatus comprising: generating means (11') connected to receive the output of said second storage means (51), for generating at its output the reciprocal value of the square root of said divisor (w) as an auxiliary value (g), said generating means comprising circuitry (25 . . . 35; 61 . . . 75) for accumulating said auxiliary value as g={(C n ·w n-2 . . . +C 2 )w+C 1 }w+C 0 , by alternating multiplication and addition, and comprising third storage means (37 . . . 44; 77 . . . 81) for predetermined appropriate constant values C 0 , C 1 , C 2 , . . . C n ; first multiplying means (17') connected to receive the outputs of said first storage means (91) and of said generating means (11), for multiplying said dividend (v) by said auxiliary value (g) to obtain an intermediate product, and second multiplying means (21') connected to receive the outputs of said first multiplying means (17') and said generating means (11'), for multiplying said intermediate produce by said auxiliary value (g), thus producing at its output (13') a representation of the quotient (u) of said dividend and said divisor.

Claim 5

Arithmetic apparatus in accordance with claim 2, characterized in that said generating means (11') for generating the auxiliary value (g) comprises fourth, fifth, and sixth storage means (77, 79, 81) for furnishing first, second, and third constant values (C 2 , C 1 , C 0 ), respectively; third multiplying means (53) connected to receive the outputs of said second storage means (51) and said fourth storage means (77); first adding means (57) connected to receive the outputs of said third multiplying means (53) and said fifth storage means (79); fourth multiplying means (55) connected to receive the outputs of said first adding means (57) and said second storage means (51); and second adding means (59) connected to receive the outputs of said fourth multiplying means (55) and said sixth storage means (81), the output of this second adding means (59) furnishing the auxiliary value (g) on the output (13') of the generating means (11').