/*
Copyright 2016 Ian Jauslin

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

/*
  Base functions for real polynomials

  see polynomial_*.h for the values taken by POLYNOMIAL_FUNC, etc...
*/


// init
int POLYNOMIAL_FUNC(init) (POLYNOMIAL_TYPENAME* poly, unsigned int memory){
  POLYNOMIAL_COEFSARRAY_FUNC(init) (&(poly->coefficients), memory);
  POLYNOMIAL_ORDERSARRAY_FUNC(init) (&(poly->orders), memory);
  return(0);
}
int POLYNOMIAL_FUNC(free) (POLYNOMIAL_TYPENAME poly){
  POLYNOMIAL_COEFSARRAY_FUNC(free) (poly.coefficients);
  POLYNOMIAL_ORDERSARRAY_FUNC(free) (poly.orders);
  return(0);
}

// resize memory
int POLYNOMIAL_FUNC(resize) (POLYNOMIAL_TYPENAME* poly, unsigned int newsize){
  POLYNOMIAL_COEFSARRAY_FUNC(resize) (&(poly->coefficients), newsize);
  POLYNOMIAL_ORDERSARRAY_FUNC(resize) (&(poly->orders), newsize);
  return(0);
}

// add a monomial
int POLYNOMIAL_FUNC(add_monomial) (POLYNOMIAL_COEF_TYPE val, POLYNOMIAL_ORDER_TYPE order, POLYNOMIAL_TYPENAME* output){
  unsigned int i;
  if((output->coefficients.length != output->orders.length) || (output->coefficients.memory != output->orders.memory)){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  // check whether the order already exists in the polynomial
  for(i=0;i< output->coefficients.length;i++){
    if(POLYNOMIAL_ORDER_CMP(order, output->orders.values[i])==0){
      POLYNOMIAL_COEF_ADD(output->coefficients.values[i], output->coefficients.values[i], val);
      return(0);
    }
  }
  // if the order does not already exist
  if(output->coefficients.length >= output->coefficients.memory){
    POLYNOMIAL_FUNC(resize) (output,2*output->coefficients.memory+1);
  }
  POLYNOMIAL_COEF_CPY(val, output->coefficients.values[output->coefficients.length]);
  POLYNOMIAL_ORDER_CPY(order, output->orders.values[output->coefficients.length]);
  output->coefficients.length++;
  output->orders.length++;
  return(0);
}
// from a double-valued coefficient and an unsigned int order
int POLYNOMIAL_FUNC(add_monomial_dui) (double val, unsigned int order, POLYNOMIAL_TYPENAME* output){
  unsigned int i;
  if((output->coefficients.length != output->orders.length) || (output->coefficients.memory != output->orders.memory)){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  // check whether the order already exists in the polynomial
  for(i=0;i< output->coefficients.length;i++){
    if(POLYNOMIAL_ORDER_CMP_UI(output->orders.values[i], order)==0){
      POLYNOMIAL_COEF_ADD_D(output->coefficients.values[i], output->coefficients.values[i], val);
      return(0);
    }
  }
  // if the order does not already exist
  if(output->coefficients.length >= output->coefficients.memory){
    POLYNOMIAL_FUNC(resize) (output,2*output->coefficients.memory+1);
  }
  POLYNOMIAL_COEF_CPY_D(val, output->coefficients.values[output->coefficients.length]);
  POLYNOMIAL_ORDER_CPY_UI(order, output->orders.values[output->coefficients.length]);
  output->coefficients.length++;
  output->orders.length++;
  return(0);
}

// copy
int POLYNOMIAL_FUNC(cpy) (POLYNOMIAL_TYPENAME input, POLYNOMIAL_TYPENAME* output){
  POLYNOMIAL_COEFSARRAY_FUNC(cpy) (input.coefficients, &(output->coefficients));
  POLYNOMIAL_ORDERSARRAY_FUNC(cpy) (input.orders, &(output->orders));
  return(0);
}
int POLYNOMIAL_FUNC(cpy_noinit) (POLYNOMIAL_TYPENAME input, POLYNOMIAL_TYPENAME* output){
  int ret;
  ret=POLYNOMIAL_COEFSARRAY_FUNC(cpy_noinit) (input.coefficients, &(output->coefficients));
  if(ret<0){
    return(ret);
  }
  POLYNOMIAL_ORDERSARRAY_FUNC(cpy_noinit) (input.orders, &(output->orders));
  return(ret);
}

// add
int POLYNOMIAL_FUNC(add_inplace) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME* poly2){
  unsigned int i;
  if(poly1.coefficients.length != poly1.orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  for(i=0;i<poly1.coefficients.length;i++){
    POLYNOMIAL_FUNC(add_monomial) (poly1.coefficients.values[i], poly1.orders.values[i], poly2);
  }
  return(0);
}
int POLYNOMIAL_FUNC(add) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME poly2, POLYNOMIAL_TYPENAME* output){
  int ret;
  POLYNOMIAL_FUNC(cpy) (poly2, output);
  ret=POLYNOMIAL_FUNC(add_inplace) (poly1, output);
  return(ret);
}

// multiply by a scalar
int POLYNOMIAL_FUNC(mul_scalar_inplace) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_TYPENAME* poly){
  unsigned int i;
  if(poly->coefficients.length != poly->orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  for(i=0;i<poly->coefficients.length;i++){
    POLYNOMIAL_COEF_MUL(poly->coefficients.values[i], poly->coefficients.values[i], x);
  }
  return(0);
}
int POLYNOMIAL_FUNC(mul_scalar) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_TYPENAME poly, POLYNOMIAL_TYPENAME* output){
  int ret;
  POLYNOMIAL_FUNC(cpy) (poly, output);
  ret=POLYNOMIAL_FUNC(mul_scalar_inplace) (x, output);
  return(ret);
}

// multiply by a monomial
int POLYNOMIAL_FUNC(mul_monomial_inplace) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_ORDER_TYPE order, POLYNOMIAL_TYPENAME* poly){
  unsigned int i;
  if(poly->coefficients.length != poly->orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  for(i=0;i<poly->coefficients.length;i++){
    POLYNOMIAL_COEF_MUL(poly->coefficients.values[i], poly->coefficients.values[i], x);
    POLYNOMIAL_ORDER_ADD(poly->orders.values[i], poly->orders.values[i], order);
  }
  return(0);
}
int POLYNOMIAL_FUNC(mul_monomial) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_ORDER_TYPE order, POLYNOMIAL_TYPENAME poly, POLYNOMIAL_TYPENAME* output){
  int ret;
  POLYNOMIAL_FUNC(cpy) (poly,output);
  ret=POLYNOMIAL_FUNC(mul_monomial_inplace) (x, order, output);
  return(ret);
}

// multiply two polynomials
int POLYNOMIAL_FUNC(mul_inplace) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME* poly2){
  unsigned int i;
  int ret;
  if(poly1.coefficients.length != poly1.orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  for(i=0;i<poly1.coefficients.length;i++){
    ret=POLYNOMIAL_FUNC(mul_monomial_inplace) (poly1.coefficients.values[i], poly1.orders.values[i], poly2);
    if(ret<0){
      return(ret);
    }
  }
  return(0);
}
int POLYNOMIAL_FUNC(mul) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME poly2, POLYNOMIAL_TYPENAME* output){
  int ret;
  POLYNOMIAL_FUNC(cpy) (poly2, output);
  ret=POLYNOMIAL_FUNC(mul_inplace) (poly1, output);
  return(ret);
}

// derive
int POLYNOMIAL_FUNC(derive_inplace) (POLYNOMIAL_TYPENAME* poly){
  unsigned int i;
  if(poly->coefficients.length != poly->orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }
  for(i=0;i<poly->coefficients.length;i++){
    if(POLYNOMIAL_ORDER_CMP_UI(poly->orders.values[i], 0)>0){
      POLYNOMIAL_COEF_MUL_ORDER(poly->coefficients.values[i], poly->coefficients.values[i], poly->orders.values[i]);
      POLYNOMIAL_ORDER_SUB_UI(poly->orders.values[i], poly->orders.values[i], 1);
    }
    else{
      // remove the term by setting it to the last term and reducing the length
      #ifdef POLYNOMIAL_COEF_FREE
	POLYNOMIAL_COEF_FREE(poly->coefficients.values[i]);
      #endif
      #ifdef POLYNOMIAL_ORDER_FREE
	POLYNOMIAL_ORDER_FREE(poly->orders.values[i]);
      #endif
      if(i<poly->coefficients.length-1){
	POLYNOMIAL_COEF_SET(poly->coefficients.values[i], poly->coefficients.values[poly->coefficients.length-1]);
	POLYNOMIAL_ORDER_SET(poly->orders.values[i], poly->orders.values[poly->coefficients.length-1]);
	i--;
      }
      poly->coefficients.length--;
      poly->orders.length--;
    }
  }
  return(0);
}
int POLYNOMIAL_FUNC(derive) (POLYNOMIAL_TYPENAME poly, POLYNOMIAL_TYPENAME* output){
  int ret;
  POLYNOMIAL_FUNC(cpy) (poly, output);
  ret=POLYNOMIAL_FUNC(derive_inplace) (output);
  return(ret);
}

// evaluate
int POLYNOMIAL_FUNC(evaluate) (POLYNOMIAL_COEF_TYPE* out, POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_TYPENAME poly){
  unsigned int i;
  POLYNOMIAL_COEF_TYPE tmp;

  #ifdef POLYNOMIAL_COEF_INIT
    POLYNOMIAL_COEF_INIT(tmp);
  #endif

  if(poly.coefficients.length != poly.orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }

  POLYNOMIAL_COEF_SET_UI(*out, 0);
  for(i=0;i<poly.coefficients.length;i++){
    POLYNOMIAL_COEF_POW_UI(tmp, x, poly.orders.values[i]);
    POLYNOMIAL_COEF_MUL(tmp, tmp, poly.coefficients.values[i]);
    POLYNOMIAL_COEF_ADD(*out, *out, tmp);
  }
  #ifdef POLYNOMIAL_COEF_FREE
    POLYNOMIAL_COEF_FREE(tmp);
  #endif
  return(0);
}

// print
int POLYNOMIAL_FUNC(print) (POLYNOMIAL_TYPENAME poly){
  unsigned int j;

  if(poly.coefficients.length != poly.orders.length){
    return(LIBINUM_ERROR_SIZE_MISMATCH);
  }

  printf("  ");
  for(j=0;j<poly.coefficients.length;j++){
    if(j>0){
      printf("+ ");
    }
    POLYNOMIAL_COEF_PRINT(poly.coefficients.values[j]);
    printf(" x^");
    POLYNOMIAL_ORDER_PRINT(poly.orders.values[j]);
    printf("\n");
  }

  return(0);
}


// n-th Legendre polynomial
int POLYNOMIAL_FUNC(legendre) (unsigned int n, POLYNOMIAL_TYPENAME* output){
  POLYNOMIAL_TYPENAME prevpoly, tmppoly;
  unsigned int i;
  int j;
  POLYNOMIAL_COEF_TYPE tmp;
  POLYNOMIAL_ORDER_TYPE tmp_o;
  
  if(n==0){
    POLYNOMIAL_FUNC(init) (output, 1);
    POLYNOMIAL_FUNC(add_monomial_dui) (1., 0, output);
    return(0);
  }
  else if(n==1){
    POLYNOMIAL_FUNC(init) (output, n);
    POLYNOMIAL_FUNC(add_monomial_dui) (1., 1, output);
    return(0);
  }

  #ifdef POLYNOMIAL_COEF_INIT
    POLYNOMIAL_COEF_INIT(tmp);
  #endif
  #ifdef POLYNOMIAL_ORDER_INIT
    POLYNOMIAL_ORDER_INIT(tmp_o);
  #endif

  // init: prevpoly=1
  POLYNOMIAL_FUNC(init) (&prevpoly, n-1);
  POLYNOMIAL_FUNC(add_monomial_dui) (1., 0, &prevpoly);
  // init: output=x
  POLYNOMIAL_FUNC(init) (output, n);
  POLYNOMIAL_FUNC(add_monomial_dui) (1., 1, output);

  // implement i*p_i=(2*i-1)*p_{i-1}-(i-1)*p_{i-2}
  for(i=2;i<=n;i++){
    // save current poly to copy it to prevpoly at the end of the loop
    POLYNOMIAL_FUNC(cpy) (*output, &tmppoly);

    // (2*i-1)/i*p_{i-1}
    POLYNOMIAL_COEF_SET_UI(tmp, 2*i-1);
    POLYNOMIAL_COEF_DIV_UI(tmp, tmp, i);
    POLYNOMIAL_ORDER_SET_UI(tmp_o, 1);
    POLYNOMIAL_FUNC(mul_monomial_inplace) (tmp, tmp_o, output);

    // -(i-1)/i*p_{i-2}
    // copy i to a signed int
    j=i;
    POLYNOMIAL_COEF_SET_SI(tmp, -j+1);
    POLYNOMIAL_COEF_DIV_UI(tmp, tmp, i);
    POLYNOMIAL_FUNC(mul_scalar_inplace) (tmp, &prevpoly);

    // add it to p_n
    POLYNOMIAL_FUNC(add_inplace) (prevpoly, output);

    // replace prevpoly
    POLYNOMIAL_FUNC(free) (prevpoly);
    prevpoly=tmppoly;
  }

  POLYNOMIAL_FUNC(free) (prevpoly);
  #ifdef POLYNOMIAL_COEF_FREE
    POLYNOMIAL_COEF_FREE(tmp);
  #endif
  #ifdef POLYNOMIAL_ORDER_FREE
    POLYNOMIAL_ORDER_FREE(tmp_o);
  #endif

  return(0);
}