/*
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 multivariable polynomials

  see polynomialMV_*.h for the values taken by POLYNOMIALMV_FUNC, etc...
*/

// init
int POLYNOMIALMV_FUNC(init) (POLYNOMIALMV_TYPENAME* polynomial, int size){
  polynomial->factors=calloc(size, sizeof(POLYNOMIALMV_FACTOR_TYPE));
  polynomial->coefficients=calloc(size, sizeof(POLYNOMIALMV_COEF_TYPE));
  polynomial->length=0;
  polynomial->memory=size;
  return(0);
}

// free memory
int POLYNOMIALMV_FUNC(free) (POLYNOMIALMV_TYPENAME polynomial){
  unsigned int i;
  for(i=0;i<polynomial.length;i++){
    POLYNOMIALMV_FACTOR_FUNC(free) (polynomial.factors[i]);
    #ifdef POLYNOMIALMV_COEF_FREE
      POLYNOMIALMV_COEF_FREE(polynomial.coefficients[i]);
    #endif
  }
  free(polynomial.factors);
  free(polynomial.coefficients);
  return(0);
}

// resize the memory allocated to a polynomial
int POLYNOMIALMV_FUNC(resize) (POLYNOMIALMV_TYPENAME* polynomial, int new_size){
  POLYNOMIALMV_TYPENAME new_poly;
  unsigned int i;

  POLYNOMIALMV_FUNC(init) (&new_poly, new_size);
  for(i=0;i<polynomial->length;i++){
    new_poly.factors[i]=polynomial->factors[i];
    POLYNOMIALMV_COEF_SET(new_poly.coefficients[i], polynomial->coefficients[i]);
  }
  new_poly.length=polynomial->length;

  free(polynomial->factors);
  free(polynomial->coefficients);

  *polynomial=new_poly;
  return(0);
}

// copy a polynomial
int POLYNOMIALMV_FUNC(cpy) (POLYNOMIALMV_TYPENAME input, POLYNOMIALMV_TYPENAME* output){
  POLYNOMIALMV_FUNC(init) (output, input.length);
  POLYNOMIALMV_FUNC(cpy_noinit) (input, output);
  return(0);
}
int POLYNOMIALMV_FUNC(cpy_noinit) (POLYNOMIALMV_TYPENAME input, POLYNOMIALMV_TYPENAME* output){
  unsigned int i;
  if(output->memory<input.length){
    return(LIBINUM_ERROR_ILLEGAL_MEMORY_ACCESS);
  }
  for(i=0;i<input.length;i++){
    POLYNOMIALMV_FACTOR_FUNC(cpy) (input.factors[i],output->factors+i);
    POLYNOMIALMV_COEF_CPY(output->coefficients[i], input.coefficients[i]);
  }
  output->length=input.length;
  
  return(0);
}

// append an element to a polynomial
int POLYNOMIALMV_FUNC(append) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output){
  unsigned int offset=output->length;

  if(output->length>=output->memory){
    POLYNOMIALMV_FUNC(resize) (output,2*output->memory+1);
  }

  // copy and allocate
  POLYNOMIALMV_FACTOR_FUNC(cpy) (factor, output->factors+offset);
  POLYNOMIALMV_COEF_CPY(output->coefficients[offset], coef);
  //increment length
  output->length++;

  return(0);
}
// if there already exists an element with the same factor, then just add coefficients
// requires the factors to be ordered
int POLYNOMIALMV_FUNC(append_inplace) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output){
  unsigned int i;
  unsigned short int foundit=0;
  for(i=0;i<output->length;i++){
    if(POLYNOMIALMV_FACTOR_FUNC(cmp) (factor, output->factors[i])==0){
      POLYNOMIALMV_COEF_ADD(output->coefficients[i], output->coefficients[i], coef);
      foundit=1;
      break;
    }
  }
  if(foundit==0){
    POLYNOMIALMV_FUNC(append) (factor, coef, output);
  }
  return(0);
}
// do not allocate memory for the factor or the coefficient
int POLYNOMIALMV_FUNC(append_noinit) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output){
  int offset=output->length;

  if(output->length>=output->memory){
    POLYNOMIALMV_FUNC(resize) (output,2*output->memory+1);
  }

  // copy without allocating
  output->factors[offset]=factor;
  POLYNOMIALMV_COEF_SET(output->coefficients[offset], coef);
  // increment length
  output->length++;
  return(0);
}
// noinit factor but init coefficient
int POLYNOMIALMV_FUNC(append_noinitfactor) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output){
  int offset=output->length;

  if(output->length>=output->memory){
    POLYNOMIALMV_FUNC(resize) (output,2*output->memory+1);
  }

  // copy without allocating
  output->factors[offset]=factor;
  POLYNOMIALMV_COEF_CPY(output->coefficients[offset], coef);
  // increment length
  output->length++;
  return(0);
}
// noinit
// if there already exists an element with the same factor, then just add coefficients
// requires the factors to be ordered
int POLYNOMIALMV_FUNC(append_noinit_inplace) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output){
  unsigned int i;
  unsigned short int foundit=0;
  for(i=0;i<output->length;i++){
    if(POLYNOMIALMV_FACTOR_FUNC(cmp) (factor, output->factors[i])==0){
      POLYNOMIALMV_COEF_ADD(output->coefficients[i], output->coefficients[i], coef);
      foundit=1;
      // free
      POLYNOMIALMV_FACTOR_FUNC(free) (factor);
      #ifdef POLYNOMIALMV_COEF_FREE
	POLYNOMIALMV_COEF_FREE(coef);
      #endif
      break;
    }
  }
  if(foundit==0){
    POLYNOMIALMV_FUNC(append_noinit) (factor, coef, output);
  }
  return(0);
}
// noinit factor but init coefficient
// if there already exists an element with the same factor, then just add coefficients
// requires the factors to be ordered
int POLYNOMIALMV_FUNC(append_noinitfactor_inplace) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output){
  unsigned int i;
  unsigned short int foundit=0;
  for(i=0;i<output->length;i++){
    if(POLYNOMIALMV_FACTOR_FUNC(cmp) (factor, output->factors[i])==0){
      POLYNOMIALMV_COEF_ADD(output->coefficients[i], output->coefficients[i], coef);
      foundit=1;
      // free factor
      POLYNOMIALMV_FACTOR_FUNC(free) (factor);
      break;
    }
  }
  if(foundit==0){
    POLYNOMIALMV_FUNC(append_noinitfactor) (factor, coef, output);
  }
  return(0);
}

// add polynomials (inplace)
int POLYNOMIALMV_FUNC(add_inplace) (POLYNOMIALMV_TYPENAME input, POLYNOMIALMV_TYPENAME* inout){
  unsigned int i;
  for(i=0;i<input.length;i++){
    POLYNOMIALMV_FUNC(append_inplace) (input.factors[i], input.coefficients[i], inout);
  }
  return(0);
}
// not inplace
int POLYNOMIALMV_FUNC(add) (POLYNOMIALMV_TYPENAME input1, POLYNOMIALMV_TYPENAME input2, POLYNOMIALMV_TYPENAME* output){
  POLYNOMIALMV_FUNC(cpy) (input1, output);
  POLYNOMIALMV_FUNC(add_inplace) (input2, output);
  return(0);
}

// multiply a polynomial by a scalar
int POLYNOMIALMV_FUNC(multiply_scalar) (POLYNOMIALMV_TYPENAME polynomial, POLYNOMIALMV_COEF_TYPE num){
  unsigned int i;
  for(i=0;i<polynomial.length;i++){
    POLYNOMIALMV_COEF_MUL(polynomial.coefficients[i], polynomial.coefficients[i], num);
  }
  return(0);
}

// multiply polynomials
int POLYNOMIALMV_FUNC(prod) (POLYNOMIALMV_TYPENAME input1, POLYNOMIALMV_TYPENAME input2, POLYNOMIALMV_TYPENAME* output){
  // position in polys
  unsigned int pos1, pos2;
  POLYNOMIALMV_FACTOR_TYPE out_factor;
  POLYNOMIALMV_COEF_TYPE out_num;

  POLYNOMIALMV_FUNC(init) (output, input1.length);
  #ifdef POLYNOMIALMV_COEF_INIT
    POLYNOMIALMV_COEF_INIT(out_num);
  #endif

  // loop over terms
  for(pos1=0;pos1<input1.length;pos1++){
    for(pos2=0;pos2<input2.length;pos2++){
      // allocate
      POLYNOMIALMV_FACTOR_FUNC(init) (&out_factor, input1.factors[pos1].length + input2.factors[pos2].length);

      // concatenate factor
      POLYNOMIALMV_FACTOR_FUNC(concat) (input1.factors[pos1],&out_factor);
      POLYNOMIALMV_FACTOR_FUNC(concat) (input2.factors[pos2],&out_factor);
      // sort factor
      POLYNOMIALMV_FACTOR_FUNC(sort) (out_factor);
      // multiply coefficient
      POLYNOMIALMV_COEF_MUL(out_num, input1.coefficients[pos1], input2.coefficients[pos2]);

      // write factor and coef
      POLYNOMIALMV_FUNC(append_noinit_inplace) (out_factor, out_num, output);
    }
  }

  #ifdef POLYNOMIALMV_COEF_FREE
    POLYNOMIALMV_COEF_FREE(out_num);
  #endif
  return(0);
}

// order factors
int POLYNOMIALMV_FUNC(order) (POLYNOMIALMV_TYPENAME polynomial){
  unsigned int i,j;
  for(i=0;i<polynomial.length;i++){
    for(j=0;j<polynomial.factors[i].length-1;j++){
      if(polynomial.factors[i].values[j] > polynomial.factors[i].values[j+1]){
	POLYNOMIALMV_FACTOR_FUNC(sort) (polynomial.factors[i]);
	break;
      }
    }
  }
  return(0);
}

// print
int POLYNOMIALMV_FUNC(print) (POLYNOMIALMV_TYPENAME polynomial){
  unsigned int i,j;

  // for each monomial
  for(i=0;i<polynomial.length;i++){
    if(i==0){
      printf("  ");
    }
    else{
      printf("+ ");
    }

    // print num
    POLYNOMIALMV_COEF_PRINT(polynomial.coefficients[i]);

    // print factors
    for(j=0;j<polynomial.factors[i].length;j++){
      POLYNOMIALMV_FACTOR_ELT_PRINT(polynomial.factors[i].values[j]);
    }

    printf("\n");
  }
  return(0);
}