Accelerating Polynomial Evaluation

• Function approximation and spline interpolation

• Fast polynomial evaluation (N coefficients)

  • y(x) = c0 + c1 x + c2 x2 + c3 x3 Expanded form
  • y(x) = c0 + x (c1 + x (c2 + x (c3))) Horner’s form
  • POLY reduces 2 N cycles using MAC+ADD to N cycles

; ar2 contains address of array [c3 c2 c1 c0]; poly uses temporary register t for multiplicand x; first two times poly instruction executes gives; 1. a = c(3) + x * 0 = c(3); b = c2; 2. a = c(2) + x * c(3); b = c1

ld *ar2+,16,b ; b = c3 << 16 ld *ar3,t ; t = x (ar3 contains addr of x)

rptz a,#3 ; a = 0, repeat next inst. 4 times

poly *ar2+ ; a = b + x*a || b = c(i-1) << 16 sth a,*ar4 ; store result (ar4 is addr of y)

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