Amplitude

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
typedef struct {
  double amp;
  double t;
} data_t;
static data_t **read_data(FILE *in, int *size);
static double max_data(data_t **data, int size);
static double linear_interpolation(data_t **data, int size, double target_amp);
static void free_data(data_t **data, int size);
int main(void);
static data_t **read_data(FILE *in, int *size) {
  data_t **ret = NULL;
  char line[BUFSIZ];
  double amp, t;
  *size = 0;
  while (fgets(line, BUFSIZ, in)) {
    sscanf(line, "%lf%lf", &amp, &t);
    ret = (data_t **) realloc(ret, ++(*size) * sizeof(data_t *));
    ret[*size - 1] = (data_t *) malloc(sizeof(data_t));
    ret[*size - 1]->amp = amp;
    ret[*size - 1]->t = t;
  }
  return ret;
}
static double max_data(data_t **data, int size) {
  int i;
  double max, max_abs;
  max = data[0]->amp;
  max_abs = fabs(max);
  for (i = 1; i < size; i++)
    if (fabs(data[i]->amp) > max_abs) {
      max = data[i]->amp;
      max_abs = fabs(max);
    }
  return max;
}
static double linear_interpolation(data_t **data, int size, double target_amp) {
  int i;
  double a0, a1, t0, t1;
  a0 = data[0]->amp;
  t0 = data[0]->t;
  if (fabs(a0 - target_amp) < 1e-6) return t0;
  for (i = 1; i < size; i++) {
    if (a0 < target_amp && data[i]->amp > target_amp) {
      a0 = data[i - 1]->amp;
      t0 = data[i - 1]->t;
      a1 = data[i]->amp;
      t1 = data[i]->t;
      break;
    } else if (a0 > target_amp && data[i]->amp < target_amp) {
      a0 = data[i - 1]->amp;
      t0 = data[i - 1]->t;
      a1 = data[i]->amp;
      t1 = data[i]->t;
      break;
    }
  }
  return t0 + (target_amp - a0) / (a1 - a0) * (t1 - t0);
}
static void free_data(data_t **data, int size) {
  int i;
  for (i = 0; i < size; i++)
    free(data[i]);
  free(data);
}
int main(void) {
  data_t **data;
  int size;
  double max, time;
  data = read_data(stdin, &size);
  max = max_data(data, size);
  time = linear_interpolation(data, size, .2 * max);
  printf("max: %lf, 0.2 * max: %lf, time: %lf\n", max, .2 * max, time);
  free_data(data, size);
  return 0;
}