Ian Jauslin

Ian Jauslin

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+/*
+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);
+}
+
+
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