Overview

Calculates the unscaled area under a fourth order polynomial using the rectangular method. The result is the sum of y-values. To get the area, multiply by the rectangle/bin width.

Expressed as a formula, this function calculates

Dispatcher Prototype

void volk_32f_x3_sum_of_poly_32f(float* target, float* src0, float* center_point_array,
float* cutoff, unsigned int num_points) 

Inputs

• src0: x values
• center_point_array: polynomial coefficients in order {c1, c2, c3, c4, c0}
• cutoff: the minimum x value to use (will clamp to cutoff if input < cutoff)
• num_points: The number of values in both input vectors.

Outputs

• complexVector: The sum of y values generated by polynomial.

Example The following estimates by using the Taylor expansion centered around ,

  int npoints = 4096;
  float* coefficients = (float*)volk_malloc(sizeof(float) * 5, volk_get_alignment());
  float* input        = (float*)volk_malloc(sizeof(float) * npoints,
volk_get_alignment()); float* result       = (float*)volk_malloc(sizeof(float),
volk_get_alignment()); float* cutoff       = (float*)volk_malloc(sizeof(float),
volk_get_alignment());
  // load precomputed Taylor series coefficients
  coefficients[0] = 4.48168907033806f;            // c1
  coefficients[1] = coefficients[0] * 0.5f;       // c2
  coefficients[2] = coefficients[0] * 1.0f/6.0f;  // c3
  coefficients[3] = coefficients[0] * 1.0f/24.0f; // c4
  coefficients[4] = coefficients[0];              // c0
  *cutoff = -2.0;
  *result = 0.0f;
  // generate uniform input data
  float dx = (float)M_PI/ (float)npoints;
  for(unsigned int ii=0; ii < npoints; ++ii){
      input[ii] = dx * (float)ii - 1.5f;
  }
  volk_32f_x3_sum_of_poly_32f(result, input, coefficients, cutoff, npoints);
  // multiply by bin width to get approximate area
  std::cout << "result is " << *result * (input[1]-input[0]) << std::endl;
  volk_free(coefficients);
  volk_free(input);
  volk_free(result);
  volk_free(cutoff);