"TMS320C55x DSP Library DSPLIB Programmer's Reference"

Calculating the Reciprocal of a Q15 NumberThe method chosen in this example is (c). Successive approximation yieldsthe most optimum code versus speed versus accuracy option. The methodoutlined below yields an accuracy of 15 bits.Assume Ym(new) exact value of1Xnorm :Ym(new) 1XnormorYm(new)*X 1(c1)(c2)Assume Ym(old) estimate of value 1 X :Ym(old)*Xnorm 1 DyxorDxy Ym(old)*Xnorm 1where Dyx = error in calculationAssume that Ym(new) and Ym(old) are related as follows:Ym(new) Ym(old) Dywhere Dy = difference in valuesSubstituting (c2) and (c4) into (c3):Ym(old)*Xnorm Ym(new)*Xnorm Dxy(Ym(new) Dy)*Xnorm Ym(new)*Xnorm DxyYm(new)*Xnorm Dy * Xnorm Ym(new)*Xnorm DxyDy * Xnorm DxyDy Dxy *1XnormAssume that 1/Xnorm is approximately equal to Ym(old):Dy Dxy * Ym(old) (approx)Substituting (c6) into (c4):Ym(new) Ym(old) Dxy * Ym(old)Substituting for Dxy from (c3) into (c7):Ym(new) Ym(old) (Ym(old)*Xnorm 1) * Ym(old)Ym(new) Ym(old) Ym(old) 2 * Xnorm Ym(old)Ym(new) 2*Ym(old) Ym(old) 2 * Xnorm(c3)(c4)(c5)(c6)(c7)(c8)B-2