A system comprising: a four element dot product circuit configured to-- (a) receive four first inputs (v1, v2, v3, v4) and four second inputs (ul, u2, u3, u4); (b) input the four first inputs and four second inputs to four multipliers (Mull, Mul2, Mul3, and Mul4); (c) input outputs of multipliers Mull and Mul2 to an adder Adder12; (d) input outputs of multipliers Mul3 and Mul4 to an adder Adder34; (e) input outputs of Adder12 and Adder34 into an adder AdderAll; (f) output an output of AdderAll; a trigonometric circuit configured to-- calculate an estimate of x/pi by inputting a representation of 1/pi and x to the multipliers Mull, Mul2, Mul3, Mul4; process the outputs of the multipliers Mull, Mul2, Mul3, and Mul4 using adders Adder12, Adder34, and AdderAll to compute t effective to increase an accuracy of an output of a trigonometric function circuit receiving t as an input argument with respect to a theoretically correct value for a trigonometric function corresponding to the trigonometric function circuit and taking x/pi as an input as compared to the output of the trigonometric function circuit for Mull + Mul2 + Mul3 + Mul4 as the input argument. a four element dot product circuit configured to-- (a) receive four first inputs (v1, v2, v3, v4) and four second inputs (ul, u2, u3, u4); (b) input the four first inputs and four second inputs to four multipliers (Mull, Mul2, Mul3, and Mul4); (c) input outputs of multipliers Mull and Mul2 to an adder Adder12; (d) input outputs of multipliers Mul3 and Mul4 to an adder Adder34; (e) input outputs of Adder12 and Adder34 into an adder AdderAll; (f) output an output of AdderAll; (a) receive four first inputs (v1, v2, v3, v4) and four second inputs (ul, u2, u3, u4); (b) input the four first inputs and four second inputs to four multipliers (Mull, Mul2, Mul3, and Mul4); (c) input outputs of multipliers Mull and Mul2 to an adder Adder12; (d) input outputs of multipliers Mul3 and Mul4 to an adder Adder34; (e) input outputs of Adder12 and Adder34 into an adder AdderAll; (f) output an output of AdderAll; a trigonometric circuit configured to-- calculate an estimate of x/pi by inputting a representation of 1/pi and x to the multipliers Mull, Mul2, Mul3, Mul4; process the outputs of the multipliers Mull, Mul2, Mul3, and Mul4 using adders Adder12, Adder34, and AdderAll to compute t effective to increase an accuracy of an output of a trigonometric function circuit receiving t as an input argument with respect to a theoretically correct value for a trigonometric function corresponding to the trigonometric function circuit and taking x/pi as an input as compared to the output of the trigonometric function circuit for Mull + Mul2 + Mul3 + Mul4 as the input argument. calculate an estimate of x/pi by inputting a representation of 1/pi and x to the multipliers Mull, Mul2, Mul3, Mul4; process the outputs of the multipliers Mull, Mul2, Mul3, and Mul4 using adders Adder12, Adder34, and AdderAll to compute t effective to increase an accuracy of an output of a trigonometric function circuit receiving t as an input argument with respect to a theoretically correct value for a trigonometric function corresponding to the trigonometric function circuit and taking x/pi as an input as compared to the output of the trigonometric function circuit for Mull + Mul2 + Mul3 + Mul4 as the input argument.