Apparatus for rapidly determining the trigonometric functions of an input angle
First Claim
1. Apparatus responsive to a signal representation of an input angle (INPUT) having Nin binary places for providing a signal representation of an approximation of the function SIN(INPUT) having Nout bits, comprising:
- input means for receiving the Nin binary places of INPUT and identifying a set of at least three progressively smaller subangles A, B, C . . . LAST-1, and LAST formed by consecutive groups of sequential binary places such that;
space="preserve" listing-type="equation">INPUT = A + B + C + . . . LAST-1, + LAST, and
space="preserve" listing-type="equation">INPUT >
A >
B >
C . . . LAST-1, >
LAST;
a set of function generator means responsive to the input means, each of which provides a term of the approximate sine relationship;
space="preserve" listing-type="equation">SIN(INPUT) ≅
SIN(A) + COS(A)SIN(B) + COS(A)SIN(C) + . . . + COS(A)SIN(LAST-1) + COS(A)SIN(LAST);
andadder means responsive to each function generator for combining the terms therefrom to form the approximate sine relationship.
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Accused Products
Abstract
High-speed hardware is employed to:
(1) subdivide an input angle into a series of smaller subangles according to the sine approximation algorithm:
SIN(INPUT) ≅ SIN(A) + COS(A)SIN(B) + COS(A)SIN(C) + COS(A)SIN(D);
(2) process the above terms separately through individual look-up tables; and
(3) sum the table results to provide the sine function of the input angle.
The above algorithm is derived from a series of approximations relating to the sine and cosine functions of very small angles. The relative sizes of the above subangles is expressed by:
A >> B > C > D
the actual size of each subangle is dependent on the number of input bits, the size of the look-up tables available, and the accuracy desired.
20 Citations
14 Claims
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1. Apparatus responsive to a signal representation of an input angle (INPUT) having Nin binary places for providing a signal representation of an approximation of the function SIN(INPUT) having Nout bits, comprising:
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input means for receiving the Nin binary places of INPUT and identifying a set of at least three progressively smaller subangles A, B, C . . . LAST-1, and LAST formed by consecutive groups of sequential binary places such that;
space="preserve" listing-type="equation">INPUT = A + B + C + . . . LAST-1, + LAST,and
space="preserve" listing-type="equation">INPUT >
A >
B >
C . . . LAST-1, >
LAST;a set of function generator means responsive to the input means, each of which provides a term of the approximate sine relationship;
space="preserve" listing-type="equation">SIN(INPUT) ≅
SIN(A) + COS(A)SIN(B) + COS(A)SIN(C) + . . . + COS(A)SIN(LAST-1) + COS(A)SIN(LAST);and adder means responsive to each function generator for combining the terms therefrom to form the approximate sine relationship. - View Dependent Claims (2)
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3. Apparatus responsive to a signal representation of an input angle (INPUT) having Nin binary places for providing a signal representation of an approximation of the function SIN (INPUT) having Nout bits, comprising:
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input means for receiving the Nin binary places of INPUT and identifying a set of at least three progressively smaller subangles A, B, C . . . LAST - 1, and LAST formed by consecutive groups of sequential binary places such that;
space="preserve" listing-type="equation">INPUT = A + B + C + . . . LAST - 1, + LAST,
space="preserve" listing-type="equation">input >
a >
b >
c . . . last - 1,>
last,
space="preserve" listing-type="equation">a = (the MSB of A) + (the remaining LSB of A) = Ap + As;and a set of function generator means responsive to the input means, each of which provides a term of the approximate sine relationship;
space="preserve" listing-type="equation">SIN(INPUT ≅
SIN(Ap + As) + COS(Apb + Asb) SIN(B) + COS(Apc + Asc) SIN(C) + . . . + COS(Aplast - 1 + Aslast -
1) SIN(LAST -
1) + COS(Aplast + Aslast) SIN(LAST)in which the Ap- portion for subangles B through LAST is any group of the most significant bits of A, and the As- portion for subangles B through LAST is at least the most significant bits of the remaining least significant bits of A; and adder means responsive to each function generator for combining the terms therefrom to the approximate sine relationship.
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4. Apparatus responsive to a signal representation of an input angle (INPUT) having Nin binary places for providing a signal representation of an approximation of the function SIN(INPUT) having Nout bits, comprising:
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input means for receiving the Nin binary places of INPUT and identifying a set of at least three progressively smaller subangles A, B, C . . . LAST - 1, and LAST formed by consecutive groups of sequential binary places such that;
space="preserve" listing-type="equation">INPUT = A + B + C + . . . LAST - 1 + LAST,
space="preserve" listing-type="equation">input a >
b >
c . . . last - 1 >
last,
space="preserve" listing-type="equation">a = (the MSB of A) + (the remaining LSB of A) = Ap + As;and a set of function generator means responsive to the input means, each of which provides a term of the approximate sine relationship;
space="preserve" listing-type="equation">SIN(INPUT) ≅
SIN(Ap + As) + COS(Apb + Kb)SIN(B) + COS(Apc + Kc)SIN(C) + . . . + COS(Aplast - 1 + Klast -
1)SIN(Last -
1) + COS(Aplast + Klast)SIN(Last)in which the Ap- portion for subangle B through LAST is any group of the most significant bits of A, and the K- is a constant having a predetermined value; and
adder means responsive to each function generator for combining the terms therefrom to form the approximate sine relationship. - View Dependent Claims (5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
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Specification