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#######################################################################
## ##
## Compiling and installing libinum. ##
## ##
#######################################################################
* libinum should work on any POSIX compliant system, such as GNU/Linux or OSX.
* libinum is linked against the GNU MPFR, GNU GMP and pthread libraries.
* Compiling:
Run
make
The default paths can be modified by passing the appropriate arguments to
make, as specified in the following table
compiler : CC=/usr/bin/gcc
linker : LD=/usr/bin/gcc
archive : AR=/usr/bin/ar
include : INCLUDE=
lib paths : LIB=
optimize : OPT=-O3
For example,
make CC=/usr/local/bin/gcc INCLUDE=/usr/local/include LIBDIR=-L/usr/local/lib
In addition, libinum can be compiled as dynamic or static library, which is
controlled by the STATIC option of the makefile.
If STATIC=0 (default) then compile both
If STATIC=1 then compile the static library
If STATIC=2 then compile the dynamic library
* Installing:
Run
make install
The default install prefix (/usr) can be changed by changing the PREFIX
variable.
For example
make install PREFIX=/usr/local

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GNU LESSER GENERAL PUBLIC LICENSE
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Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
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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.
# whether to compile only the static library, only the dynamic library, or both
# if static=0 then compile both
# if static=2 then compile the dynamic library
# if static=1 then compile the static library
STATIC=0
VERSION=1.0
# products of the compilation
PROJECT_SO=libinum.so.$(VERSION)
PROJECT_LIBS=libinum.a
PROJECT_DOCS=libinum-doc.html
# debug and optimization flags
#DB= -ggdb
OPT= -O3
# warning flags
WARNINGS= -Wall -Wextra -Wno-strict-overflow -std=c99 -pedantic
# installation dirs
PREFIX=/usr
LIBDIR=$(PREFIX)/lib
INCLUDEDIR=$(PREFIX)/include
DOCDIR=$(PREFIX)/share/doc/libinum
# compiler
CC=/usr/bin/gcc
LD=$(CC)
AR=/usr/bin/ar
# directories
INCLUDE =
LIB =
# flags
override LDFLAGS +=$(LIB)
override CFLAGS +=$(INCLUDE)$(DB) $(OPT) $(WARNINGS)
# build directories
BUILDDIR=./build
SRCDIR=./src
OBJDIR=./objs
# objects
LIBINUM_OBJS = $(addprefix $(OBJDIR)/, array.o integral.o utils.o polynomial.o polynomialMV.o root.o)
ifeq ($(STATIC),1)
# compile libinum.a
PREREQ=static
# install static lib
INSTALLLIB=install-static
else ifeq ($(STATIC),2)
# compile libinum.so.$(VERSION)
PREREQ=shared
# install shared lib
INSTALLLIB=install-shared
else
# compile both
PREREQ=shared static
# install both
INSTALLLIB=install-shared install-static
endif
all: init $(PREREQ)
# create dirs
init:
@[ -d $(OBJDIR) ] || /bin/mkdir $(OBJDIR)
@[ -d $(BUILDDIR) ] || /bin/mkdir $(BUILDDIR)
# static library
static: $(PROJECT_LIBS)
# shared library
shared: $(PROJECT_SO)
libinum.a: $(LIBINUM_OBJS)
$(AR) -rc $(BUILDDIR)/$@ $^
libinum.so.$(VERSION): $(LIBINUM_OBJS)
$(LD) -shared -lm -lmpfr -lgmp -lpthread $(LDFLAGS) -o $(BUILDDIR)/$@ $^
ln -fs ./libinum.so.$(VERSION) $(BUILDDIR)/libinum.so
%.o : ../$(SRCDIR)/%.c
$(CC) -c $(CFLAGS) -fPIC $< -o $@
install: $(INSTALLLIB) all
mkdir -p $(MANDIR) $(DOCDIR) $(INCLUDEDIR)/libinum
cp -rL include/libinum/* $(INCLUDEDIR)/libinum/
install -Dm644 include/libinum.h $(INCLUDEDIR)/
cp -r doc/libinum-examples $(DOCDIR)/
install -Dm644 $(addprefix doc/,$(PROJECT_DOCS)) $(DOCDIR)/
install-static: all
mkdir -p $(LIBDIR)
install -Dm755 $(addprefix $(BUILDDIR)/,$(PROJECT_LIBS)) $(LIBDIR)/
install-shared: all
mkdir -p $(LIBDIR)
install -Dm755 $(addprefix $(BUILDDIR)/,$(PROJECT_SO)) $(LIBDIR)/
for lib in $(PROJECT_SO); do ln -fs ./$$lib $(LIBDIR)/$${lib%.so.*}.so; done
clean:
@rm -rf $(OBJDIR)
@rm -rf $(BUILDDIR)

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libinum
Copyright 2016 Ian Jauslin
Numerical values may be represented as multi-precision floats using
the GNU MPFR library, which is licensed under the GNU Lesser General
Public License (LGPL) version 3 (see LGPL3 for a copy of the license).
See
http://www.mpfr.org/
for details.
The GNU MPFR library is based on the GNU GMP library, which is licensed
under the GNU Lesser General Public License (LGPL) version 3 (see LGPL3
for a copy of the license). See
http://www.gmplib.org/
for details.

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# whether to link dynamically
# if static=0 then link dynamically
# if static=2 then link statically
# if static=1 then link libkondo statically but other libraries dynamically
STATIC=1
VERSION=0.3.1
# products of the compilation
PROJECT_BINS= root_newton integral_gauss-legendre
# debug and optimization flags
#DB= -ggdb
OPT= -O3
# warning flags
WARNINGS= -Wall -Wextra -Wno-strict-overflow -std=c99 -pedantic -Wno-unused-parameter
# compiler
CC=/usr/bin/gcc
LD=$(CC)
# directories
INCLUDE =
LIB =
#INCLUDE = -I../../include
#LIB = -L../../build
# flags
override LDFLAGS +=$(LIB)
override CFLAGS +=$(INCLUDE) $(DB) $(OPT) $(WARNINGS)
# build directories
BUILDDIR=./build
SRCDIR=./src
OBJDIR=./objs
# objects
OBJS = $(addprefix $(OBJDIR)/, root_newton.o integral_gauss-legendre.o)
# flags which depend on whether to link statically or dynamically
# lib flag
LIBINUM_FLAG=-linum
# additional library required for static linking
XTRA_LIBS=
ifeq ($(STATIC),1)
# libinum is linked against libm, libmpfr, libgmp and libpthread
XTRA_LIBS=-lm -lmpfr -lgmp -lpthread
# link binaries using the static library
LIBINUM_FLAG=-l:libinum.a
else ifeq ($(STATIC),2)
# libinum is linked against libm, libmpfr, libgmp and libpthread
XTRA_LIBS=-lm -lmpfr -lgmp -lpthread
# link binaries statically
override LDFLAGS += -static
else
# required flag for subsequent dynamic linking
override CFLAGS += -fPIC
endif
all: init $(PROJECT_BINS)
# create dirs
init:
@[ -d $(OBJDIR) ] || /bin/mkdir $(OBJDIR)
@[ -d $(BUILDDIR) ] || /bin/mkdir $(BUILDDIR)
root_newton:
$(CC) -c $(CFLAGS) src/$@.c -o objs/$@.o
$(LD) $(LDFLAGS) -o $(BUILDDIR)/$@ objs/$@.o $(LIBINUM_FLAG) $(XTRA_LIBS)
integral_gauss-legendre:
$(CC) -c $(CFLAGS) src/$@.c -o objs/$@.o
$(LD) $(LDFLAGS) -o $(BUILDDIR)/$@ objs/$@.o $(LIBINUM_FLAG) $(XTRA_LIBS)
clean:
@rm -rf $(OBJDIR)
@rm -rf $(BUILDDIR)

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#include <stdio.h>
#include <stdarg.h>
// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
#define MPFR_USE_VA_LIST
#include <mpfr.h>
#include <libinum.h>
int func(mpfr_t* out, mpfr_t in, void* extra_args);
int main(int argc, const char* argv[]){
int ret;
mpfr_t tolerance, val, lower, upper;
array_mpfr abcissa, weights;
// precision of MPFR floats
mpfr_set_default_prec(53);
// tolerance for computing weights
mpfr_init(tolerance);
mpfr_set_d(tolerance, 1.e-11, MPFR_RNDN);
// compute weights
ret=gauss_legendre_weights_mpfr(10, tolerance, 10000, &abcissa, &weights);
// return codes
if(ret==LIBINUM_ERROR_MAXITER){
printf("error: maximum number of iterations reached when computing the integration abcissa\n");
mpfr_clear(tolerance);
return(ret);
}
else if(ret==LIBINUM_ERROR_NAN){
printf("error: infinity encountered when computing the integration abcissa\n");
mpfr_clear(tolerance);
return(ret);
}
else{
printf("abcissa:\n");
array_mpfr_print(abcissa);
printf("\nweights:\n");
array_mpfr_print(weights);
printf("\n");
}
mpfr_clear(tolerance);
mpfr_inits(val, lower, upper, NULL);
mpfr_set_ui(lower, 0, MPFR_RNDN);
mpfr_set_ui(upper, 2, MPFR_RNDN);
ret=integrate_gauss_mpfr(&val, &func, lower, upper, abcissa, weights, NULL);
// return codes
if(ret==LIBINUM_ERROR_SIZE_MISMATCH){
printf("error: the mpfr_arrays 'abcissa' and 'weights' must have the same length\n");
mpfr_clears(val, upper, lower, NULL);
array_mpfr_free(abcissa);
array_mpfr_free(weights);
return(ret);
}
else if(ret==LIBINUM_ERROR_NAN){
printf("error: the integrand is singular\n");
array_mpfr_free(abcissa);
array_mpfr_free(weights);
mpfr_clears(val, upper, lower, NULL);
return(ret);
}
else{
printf("\\int_0^2 x/sin(x) dx = ");
fprint_mpfr(stdout, val);
printf("\n");
}
mpfr_clears(val, upper, lower, NULL);
array_mpfr_free(abcissa);
array_mpfr_free(weights);
return(0);
}
/*
// e^x
int func(mpfr_t* out, mpfr_t in, void* extra_args){
mpfr_exp(*out, in, MPFR_RNDN);
return(0);
}
*/
// x/sin(x)
int func(mpfr_t* out, mpfr_t in, void* extra_args){
mpfr_sin(*out, in, MPFR_RNDN);
mpfr_div(*out, in, *out, MPFR_RNDN);
return(0);
}

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#include <stdio.h>
#include <stdarg.h>
// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
#define MPFR_USE_VA_LIST
#include <mpfr.h>
#include <libinum.h>
int func(mpfr_t* out, mpfr_t in, void* extra_args);
int dfunc(mpfr_t* out, mpfr_t in, void* extra_args);
int main(int argc, const char* argv[]){
int ret;
mpfr_t init, prec, x;
unsigned int maxiter;
int extra_arg;
mpfr_inits(init, prec, x, NULL);
// start at 2
mpfr_set_ui(init, 2, MPFR_RNDN);
// precision
mpfr_set_d(prec, 1.e-30, MPFR_RNDN);
// maximum number of iterations before error
maxiter=10000;
// extra argument
extra_arg=4;
// compute root
ret=root_newton_mpfr(&x, &func, &dfunc, init, prec, maxiter, &extra_arg);
// return codes
if(ret==LIBINUM_ERROR_MAXITER){
printf("error: maximum number of iterations reached\n");
}
else if(ret==LIBINUM_ERROR_NAN){
printf("error: infinity encountered\n");
}
else{
mpfr_printf("% 14.7Re\n", x);
}
mpfr_clears(init, prec, x, NULL);
return(0);
}
// x^2-1
int func(mpfr_t* out, mpfr_t in, void* extra_args){
mpfr_pow_ui(*out, in, 2, MPFR_RNDN);
mpfr_add_d(*out, *out, -1./ *((int*)extra_args), MPFR_RNDN);
return(0);
}
// 2*x
int dfunc(mpfr_t* out, mpfr_t in, void* extra_args){
mpfr_mul_ui(*out, in, 2, MPFR_RNDN);
return(0);
}

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#ifndef LIBINUM_H
#define LIBINUM_H
#define LIBINUM_VERSION "1.0"
#include <libinum/types.h>
#include <libinum/errors.h>
#include <libinum/integral.h>
#include <libinum/root.h>
#include <libinum/utils.h>
#include <libinum/array.h>
#include <libinum/polynomial.h>
#include <libinum/polynomialMV.h>
#endif

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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.
*/
#include "array.h"
#include <stdlib.h>
#include <stdarg.h>
#include <stdio.h>
#include "errors.h"
#include "polynomial.h"
#include "utils.h"
//--------------------------------------------------
//
// integer array (array_int)
//
//--------------------------------------------------
#include "array_int.h"
#include "array_base.c"
//--------------------------------------------------
//
// unsigned integer array (array_uint)
//
//--------------------------------------------------
#include "array_uint.h"
#include "array_base.c"
//--------------------------------------------------
//
// double array (array_double)
//
//--------------------------------------------------
#include "array_double.h"
#include "array_base.c"
//--------------------------------------------------
//
// long double array (array_ldouble)
//
//--------------------------------------------------
#include "array_ldouble.h"
#include "array_base.c"
//--------------------------------------------------
//
// MPFR array (array_mpfr)
//
//--------------------------------------------------
#include "array_mpfr.h"
#include "array_base.c"
//--------------------------------------------------
//
// array of MPFR arrays (array_2_mpfr)
//
//--------------------------------------------------
#include "array_2_mpfr.h"
#include "array_base.c"
//--------------------------------------------------
//
// character array (array_char)
//
//--------------------------------------------------
#include "array_char.h"
#include "array_base.c"
// append a char*
int array_char_append_str(char* str, array_char* output){
char* ptr;
for (ptr=str;*ptr!='\0';ptr++){
array_char_append(*ptr, output);
}
return(0);
}
// convert to char*
int array_char_to_str(array_char input, char** output){
unsigned int i;
(*output)=calloc(input.length+1,sizeof(char));
for(i=0;i<input.length;i++){
(*output)[i]=input.values[i];
}
if((*output)[input.length-1]!='\0'){
(*output)[input.length]='\0';
}
return(0);
}
// noinit (changes the size of input if needed)
char* array_char_to_str_noinit(array_char* input){
if(input->values[input->length-1]!='\0'){
if(input->length==input->memory){
array_char_resize(input,input->length+1);
}
// add final '\0'
input->values[input->length]='\0';
}
return(input->values);
}
// convert from char*
int str_to_array_char(char* str, array_char* output){
char* ptr;
unsigned int str_len=0;
for(ptr=str;*ptr!='\0';ptr++){
str_len++;
}
array_char_init(output, str_len);
for(ptr=str;*ptr!='\0';ptr++){
array_char_append(*ptr,output);
}
return(0);
}
// compare an array_char and a char*
int array_char_cmp_str(array_char array_char, char* str){
unsigned int j;
for(j=0;j<array_char.length && str[j]!='\0';j++){
if(array_char.values[j]!=str[j]){
return(0);
}
}
if(j==array_char.length && str[j]=='\0'){
return(1);
}
return(0);
}
// format strings
int array_char_snprintf(array_char* output, char* fmt, ...){
size_t size=100;
unsigned int extra_size;
char* out_str=calloc(size,sizeof(char));
char* ptr;
va_list vaptr;
// initialize argument list starting after fmt
va_start(vaptr, fmt);
// print format
extra_size=vsnprintf(out_str, size, fmt, vaptr);
va_end(vaptr);
// if too large
if(extra_size>size){
// resize
free(out_str);
// +1 for '\0'
size=extra_size+1;
out_str=calloc(size,sizeof(char));
// read format again
va_start(vaptr, fmt);
vsnprintf(out_str,size,fmt,vaptr);
va_end(vaptr);
}
// write to char array
for(ptr=out_str;*ptr!='\0';ptr++){
array_char_append(*ptr, output);
}
free(out_str);
return(0);
}
//--------------------------------------------------
//
// string array (array_str)
//
//--------------------------------------------------
#include "array_str.h"
#include "array_base.c"
//--------------------------------------------------
//
// mpfr polynomial array (array_polynomial_mpfr)
//
//--------------------------------------------------
#include "array_polynomial_mpfr.h"
#include "array_base.c"
//--------------------------------------------------
//
// double polynomial array (array_polynomial_double)
//
//--------------------------------------------------
#include "array_polynomial_double.h"
#include "array_base.c"
//--------------------------------------------------
//
// long double polynomial array (array_polynomial_ldouble)
//
//--------------------------------------------------
#include "array_polynomial_ldouble.h"
#include "array_base.c"
//--------------------------------------------------
//
// pthread_t array (array_pthread_t)
//
//--------------------------------------------------
#include "array_pthread_t.h"
#include "array_base.c"

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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.
*/
/*
Mutable arrays
*/
#ifndef LIBINUM_ARRAY_H
#define LIBINUM_ARRAY_H
#include "types.h"
//--------------------------------------------------
//
// integer array (array_int)
//
//--------------------------------------------------
#include "array_int.h"
#include "array_base.h"
//--------------------------------------------------
//
// unsigned integer array (array_uint)
//
//--------------------------------------------------
#include "array_uint.h"
#include "array_base.h"
//--------------------------------------------------
//
// double array (array_double)
//
//--------------------------------------------------
#include "array_double.h"
#include "array_base.h"
//--------------------------------------------------
//
// long double array (array_ldouble)
//
//--------------------------------------------------
#include "array_ldouble.h"
#include "array_base.h"
//--------------------------------------------------
//
// MPFR array (array_mpfr)
//
//--------------------------------------------------
#include "array_mpfr.h"
#include "array_base.h"
//--------------------------------------------------
//
// array of MPFR arrays (array_2_mpfr)
//
//--------------------------------------------------
#include "array_2_mpfr.h"
#include "array_base.h"
//--------------------------------------------------
//
// character array (array_char)
//
//--------------------------------------------------
#include "array_char.h"
#include "array_base.h"
// append a char*
int array_char_append_str(char* str, array_char* output);
// convert to char*
int array_char_to_str(array_char input, char** output);
// noinit (changes the size of input if needed)
char* array_char_to_str_noinit(array_char* input);
// convert from char*
int str_to_array_char(char* str, array_char* output);
// compare an array_char and a char*
int array_char_cmp_str(array_char array_char, char* str);
// format strings
int array_char_snprintf(array_char* output, char* fmt, ...);
//--------------------------------------------------
//
// string array (array_str)
//
//--------------------------------------------------
#include "array_str.h"
#include "array_base.h"
//--------------------------------------------------
//
// mpfr polynomial array (array_polynomial_mpfr)
//
//--------------------------------------------------
#include "array_polynomial_mpfr.h"
#include "array_base.h"
//--------------------------------------------------
//
// double polynomial array (array_polynomial_double)
//
//--------------------------------------------------
#include "array_polynomial_double.h"
#include "array_base.h"
//--------------------------------------------------
//
// long double polynomial array (array_polynomial_ldouble)
//
//--------------------------------------------------
#include "array_polynomial_ldouble.h"
#include "array_base.h"
//--------------------------------------------------
//
// pthread_t array (array_pthread_t)
//
//--------------------------------------------------
#include "array_pthread_t.h"
#include "array_base.h"
#endif

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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.
*/
/*
Preprocessor macros for arrays of MPFR float arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_2_mpfr
// prefix of function names
#define ARRAY_FUNC(NAME) array_2_mpfr_ ## NAME
// type of values
#define ARRAY_VAL_TYPE array_mpfr
// free
#define ARRAY_VAL_FREE(VAL) array_mpfr_free(VAL)
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL=NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) array_mpfr_cpy(FROMVAL, &TOVAL);
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) array_mpfr_cmp(VAL1, VAL2)==0
#define ARRAY_VAL_IFLT(VAL1, VAL2) array_mpfr_cmp(VAL1, VAL2)<0
#define ARRAY_VAL_IFGT(VAL1, VAL2) array_mpfr_cmp(VAL1, VAL2)>0
// print values
#define ARRAY_VAL_PRINT(VAL) array_mpfr_print(VAL)

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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 arrays
see polynomial_*.h for the values taken by ARRAY_FUNC, etc...
*/
// init
int ARRAY_FUNC(init) (ARRAY_TYPENAME* array, unsigned int memory){
array->values=calloc(memory,sizeof(ARRAY_VAL_TYPE));
array->memory=memory;
array->length=0;
return(0);
}
int ARRAY_FUNC(free) (ARRAY_TYPENAME array){
#ifdef ARRAY_VAL_FREE
unsigned int i;
for(i=0;i<array.length;i++){
ARRAY_VAL_FREE(array.values[i]);
}
#endif
free(array.values);
return(0);
}
// do not free values, only free calloc'ed memory
int ARRAY_FUNC(free_vects) (ARRAY_TYPENAME array){
free(array.values);
return(0);
}
// resize memory
int ARRAY_FUNC(resize) (ARRAY_TYPENAME* array, unsigned int newsize){
unsigned int i;
ARRAY_TYPENAME new_array;
ARRAY_FUNC(init) (&new_array, newsize);
for(i=0;i<array->length;i++){
ARRAY_VAL_SET(new_array.values[i], array->values[i]);
}
free(array->values);
*array=new_array;
return(0);
}
// add a value
int ARRAY_FUNC(append) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME* output){
if(output->length >= output->memory){
ARRAY_FUNC(resize) (output,2*output->memory+1);
}
ARRAY_VAL_CPY(val, output->values[output->length]);
output->length++;
return(0);
}
// do not copy the value, instead let the last element of the array point to 'val'
// only if the value requires initializing
#ifdef ARRAY_VAL_FREE
int ARRAY_FUNC(append_noinit) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME* output){
if(output->length >= output->memory){
ARRAY_FUNC(resize) (output,2*output->memory+1);
}
ARRAY_VAL_SET(output->values[output->length], val);
output->length++;
return(0);
}
#endif
// add a value only if it is not already present
#ifdef ARRAY_VAL_IFEQ
int ARRAY_FUNC(append_unique) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME* output){
if(ARRAY_FUNC(find) (val, *output)<0){
ARRAY_FUNC(append) (val, output);
}
return(0);
}
#endif
// copy
int ARRAY_FUNC(cpy) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output){
ARRAY_FUNC(init) (output, input.length);
ARRAY_FUNC(cpy_noinit) (input, output);
return(0);
}
// do not init output array
int ARRAY_FUNC(cpy_noinit) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output){
unsigned int i;
if(output->memory<input.length){
return(LIBINUM_ERROR_SIZE_MISMATCH);
}
for(i=0;i<input.length;i++){
ARRAY_VAL_CPY(input.values[i], output->values[i]);
}
output->length=input.length;
return(0);
}
// concatenate
int ARRAY_FUNC(concat) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output){
unsigned int i;
for(i=0;i<input.length;i++){
ARRAY_FUNC(append) (input.values[i], output);
}
return(0);
}
// concat but only add values that are not already present in the array
#ifdef ARRAY_VAL_IFEQ
int ARRAY_FUNC(concat_unique) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output){
unsigned int i;
for(i=0;i<input.length;i++){
ARRAY_FUNC(append_unique) (input.values[i], output);
}
return(0);
}
#endif
// sub-array
int ARRAY_FUNC(subarray) (ARRAY_TYPENAME array, unsigned int begin, unsigned int end, ARRAY_TYPENAME* subarray){
unsigned int i;
if(begin>end || end>=array.length){
return(LIBINUM_ERROR_ILLEGAL_MEMORY_ACCESS);
}
ARRAY_FUNC(init) (subarray,end-begin);
for(i=begin;i<=end;i++){
ARRAY_FUNC(append) (array.values[i], subarray);
}
return(0);
}
// find (does not assume the array is sorted)
#ifdef ARRAY_VAL_IFEQ
int ARRAY_FUNC(find) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME array){
unsigned int i;
for(i=0;i<array.length;i++){
if(ARRAY_VAL_IFEQ(array.values[i], val)){
return(i);
}
}
return(-1);
}
#endif
// sort (quicksort)
#ifdef ARRAY_VAL_IFLT
int ARRAY_FUNC(sort) (ARRAY_TYPENAME array){
if(array.length>1){
ARRAY_FUNC(sort_sub) (array, 0, array.length-1);
}
return(0);
}
// sort a sub-array
int ARRAY_FUNC(sort_sub) (ARRAY_TYPENAME array, unsigned int begin, unsigned int end){
unsigned int i;
unsigned int index;
ARRAY_VAL_TYPE tmp;
// the pivot: middle of the array
unsigned int pivot=(begin+end)/2;
// if the array is non trivial
if(begin<end){
// send pivot to the end
ARRAY_VAL_SET(tmp, array.values[pivot]);
ARRAY_VAL_SET(array.values[pivot], array.values[end]);
ARRAY_VAL_SET(array.values[end], tmp);
// loop over the others
for(i=begin, index=begin;i<end;i++){
// compare with pivot
if(ARRAY_VAL_IFLT(array.values[i], array.values[end])){
// if smaller, exchange with reference index
ARRAY_VAL_SET(tmp, array.values[index]);
ARRAY_VAL_SET(array.values[index], array.values[i]);
ARRAY_VAL_SET(array.values[i], tmp);
// move reference index
index++;
}
}
// put pivot (which we had sent to the end) in the right place
ARRAY_VAL_SET(tmp, array.values[end]);
ARRAY_VAL_SET(array.values[end], array.values[index]);
ARRAY_VAL_SET(array.values[index], tmp);
// recurse
if(index>0){
ARRAY_FUNC(sort_sub) (array, begin, index-1);
}
ARRAY_FUNC(sort_sub) (array, index+1, end);
}
return(0);
}
#endif
// compare arrays
#if defined ARRAY_VAL_IFLT && defined ARRAY_VAL_IFGT
int ARRAY_FUNC(cmp) (ARRAY_TYPENAME array1, ARRAY_TYPENAME array2){
unsigned int i;
// compare lengths
if(array1.length<array2.length){
return(-1);
}
if(array1.length>array2.length){
return(1);
}
// compare terms
for(i=0;i<array1.length;i++){
if(ARRAY_VAL_IFLT(array1.values[i], array2.values[i])){
return(-1);
}
if(ARRAY_VAL_IFGT(array1.values[i], array2.values[i])){
return(1);
}
}
// if equal
return(0);
}
#endif
// print array
#ifdef ARRAY_VAL_PRINT
int ARRAY_FUNC(print) (ARRAY_TYPENAME array){
unsigned int i;
printf("(");
for(i=0;i<array.length;i++){
ARRAY_VAL_PRINT(array.values[i]);
if(i<array.length-1){
printf(", ");
}
}
printf(")");
return(0);
}
#endif

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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 arrays
see polynomial_*.h for the values taken by ARRAY_FUNC, etc...
*/
// init
int ARRAY_FUNC(init) (ARRAY_TYPENAME* array, unsigned int memory);
int ARRAY_FUNC(free) (ARRAY_TYPENAME array);
// do not free values, only free calloc'ed memory
int ARRAY_FUNC(free_vects) (ARRAY_TYPENAME array);
// resize memory
int ARRAY_FUNC(resize) (ARRAY_TYPENAME* array, unsigned int newsize);
// add a value
int ARRAY_FUNC(append) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME* output);
#ifdef ARRAY_VAL_FREE
// do not copy the value, instead let the last element of the array point to 'val'
int ARRAY_FUNC(append_noinit) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME* output);
#endif
// add a value only if it is not already present
#ifdef ARRAY_VAL_IFEQ
int ARRAY_FUNC(append_unique) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME* output);
#endif
// copy
int ARRAY_FUNC(cpy) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output);
int ARRAY_FUNC(cpy_noinit) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output);
// concatenate
int ARRAY_FUNC(concat) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output);
// concat but only add values that are not already present in the array
#ifdef ARRAY_VAL_IFEQ
int ARRAY_FUNC(concat_unique) (ARRAY_TYPENAME input, ARRAY_TYPENAME* output);
#endif
// sub-array
int ARRAY_FUNC(subarray) (ARRAY_TYPENAME array, unsigned int begin, unsigned int end, ARRAY_TYPENAME* subarray);
// find (does not assume the array is sorted)
#ifdef ARRAY_VAL_IFEQ
int ARRAY_FUNC(find) (ARRAY_VAL_TYPE val, ARRAY_TYPENAME array);
#endif
// sort (quicksort)
#ifdef ARRAY_VAL_IFLT
int ARRAY_FUNC(sort) (ARRAY_TYPENAME array);
// sort a sub-array
int ARRAY_FUNC(sort_sub) (ARRAY_TYPENAME array, unsigned int begin, unsigned int end);
#endif
// compare arrays
#if defined ARRAY_VAL_IFLT && defined ARRAY_VAL_IFGT
int ARRAY_FUNC(cmp) (ARRAY_TYPENAME array1, ARRAY_TYPENAME array2);
#endif
// print array
#ifdef ARRAY_VAL_PRINT
int ARRAY_FUNC(print) (ARRAY_TYPENAME array);
#endif

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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.
*/
/*
Preprocessor macros for char arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_char
// prefix of function names
#define ARRAY_FUNC(NAME) array_char_ ## NAME
// type of values
#define ARRAY_VAL_TYPE char
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) TOVAL = FROMVAL
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) VAL1==VAL2
#define ARRAY_VAL_IFLT(VAL1, VAL2) VAL1<VAL2
#define ARRAY_VAL_IFGT(VAL1, VAL2) VAL1>VAL2
// print values
#define ARRAY_VAL_PRINT(VAL) printf("%c",VAL)

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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.
*/
/*
Preprocessor macros for double arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_double
// prefix of function names
#define ARRAY_FUNC(NAME) array_double_ ## NAME
// type of values
#define ARRAY_VAL_TYPE double
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) TOVAL = FROMVAL
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) VAL1==VAL2
#define ARRAY_VAL_IFLT(VAL1, VAL2) VAL1<VAL2
#define ARRAY_VAL_IFGT(VAL1, VAL2) VAL1>VAL2
// print values
#define ARRAY_VAL_PRINT(VAL) fprint_double(stdout, VAL)

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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.
*/
/*
Preprocessor macros for integer arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_int
// prefix of function names
#define ARRAY_FUNC(NAME) array_int_ ## NAME
// type of values
#define ARRAY_VAL_TYPE int
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) TOVAL = FROMVAL
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) VAL1==VAL2
#define ARRAY_VAL_IFLT(VAL1, VAL2) VAL1<VAL2
#define ARRAY_VAL_IFGT(VAL1, VAL2) VAL1>VAL2
// print values
#define ARRAY_VAL_PRINT(VAL) printf("%d",VAL)

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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.
*/
/*
Preprocessor macros for long double arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_ldouble
// prefix of function names
#define ARRAY_FUNC(NAME) array_ldouble_ ## NAME
// type of values
#define ARRAY_VAL_TYPE long double
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) TOVAL = FROMVAL
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) VAL1==VAL2
#define ARRAY_VAL_IFLT(VAL1, VAL2) VAL1<VAL2
#define ARRAY_VAL_IFGT(VAL1, VAL2) VAL1>VAL2
// print values
#define ARRAY_VAL_PRINT(VAL) fprint_ldouble(stdout, VAL)

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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.
*/
/*
Preprocessor macros for MPFR float arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_mpfr
// prefix of function names
#define ARRAY_FUNC(NAME) array_mpfr_ ## NAME
// type of values
#define ARRAY_VAL_TYPE mpfr_t
// free
#define ARRAY_VAL_FREE(VAL) mpfr_clear(VAL)
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL[0]=NEWVAL[0]
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) mpfr_init(TOVAL); mpfr_set(TOVAL, FROMVAL, MPFR_RNDN)
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) mpfr_cmp(VAL1, VAL2)==0
#define ARRAY_VAL_IFLT(VAL1, VAL2) mpfr_cmp(VAL1, VAL2)<0
#define ARRAY_VAL_IFGT(VAL1, VAL2) mpfr_cmp(VAL1, VAL2)>0
// print values
#define ARRAY_VAL_PRINT(VAL) fprint_mpfr(stdout, VAL)

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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.
*/
/*
Preprocessor macros for arrays of polynomials with double coefficients
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_polynomial_double
// prefix of function names
#define ARRAY_FUNC(NAME) array_polynomial_double_ ## NAME
// type of values
#define ARRAY_VAL_TYPE polynomial_double
// free
#define ARRAY_VAL_FREE(VAL) polynomial_double_free(VAL)
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) polynomial_double_cpy(FROMVAL, &TOVAL)
// print values
#define ARRAY_VAL_PRINT(VAL) polynomial_double_print(VAL)

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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.
*/
/*
Preprocessor macros for arrays of polynomials with long double coefficients
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_polynomial_ldouble
// prefix of function names
#define ARRAY_FUNC(NAME) array_polynomial_ldouble_ ## NAME
// type of values
#define ARRAY_VAL_TYPE polynomial_ldouble
// free
#define ARRAY_VAL_FREE(VAL) polynomial_ldouble_free(VAL)
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) polynomial_ldouble_cpy(FROMVAL, &TOVAL)
// print values
#define ARRAY_VAL_PRINT(VAL) polynomial_ldouble_print(VAL)

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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.
*/
/*
Preprocessor macros for arrays of polynomials with mpfr coefficients
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_polynomial_mpfr
// prefix of function names
#define ARRAY_FUNC(NAME) array_polynomial_mpfr_ ## NAME
// type of values
#define ARRAY_VAL_TYPE polynomial_mpfr
// free
#define ARRAY_VAL_FREE(VAL) polynomial_mpfr_free(VAL)
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) polynomial_mpfr_cpy(FROMVAL, &TOVAL)
// print values
#define ARRAY_VAL_PRINT(VAL) polynomial_mpfr_print(VAL)

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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.
*/
/*
Preprocessor macros for pthread_t arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_pthread_t
// prefix of function names
#define ARRAY_FUNC(NAME) array_pthread_t_ ## NAME
// type of values
#define ARRAY_VAL_TYPE pthread_t
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) TOVAL = FROMVAL
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) VAL1==VAL2
#define ARRAY_VAL_IFLT(VAL1, VAL2) VAL1<VAL2
#define ARRAY_VAL_IFGT(VAL1, VAL2) VAL1>VAL2

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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.
*/
/*
Preprocessor macros for string arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_str
// prefix of function names
#define ARRAY_FUNC(NAME) array_str_ ## NAME
// type of values
#define ARRAY_VAL_TYPE array_char
// free
#define ARRAY_VAL_FREE(VAL) array_char_free(VAL)
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) array_char_cpy(FROMVAL, &TOVAL)
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) array_char_cmp(VAL1, VAL2)==0
#define ARRAY_VAL_IFLT(VAL1, VAL2) array_char_cmp(VAL1, VAL2)<0
#define ARRAY_VAL_IFGT(VAL1, VAL2) array_char_cmp(VAL1, VAL2)>0
// print values
#define ARRAY_VAL_PRINT(VAL) array_char_print(VAL)

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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.
*/
/*
Structure definition for arrays
see array_*.h for the values taken by ARRAY_TYPENAME, etc...
*/
typedef struct ARRAY_TYPENAME {
ARRAY_VAL_TYPE* values;
unsigned int length;
unsigned int memory;
} ARRAY_TYPENAME;

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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.
*/
/*
Preprocessor macros for unsigned int arrays
*/
// reset CPP macros
#undef ARRAY_TYPENAME
#undef ARRAY_FUNC
#undef ARRAY_VAL_TYPE
#undef ARRAY_VAL_FREE
#undef ARRAY_VAL_SET
#undef ARRAY_VAL_CPY
#undef ARRAY_VAL_IFEQ
#undef ARRAY_VAL_IFLT
#undef ARRAY_VAL_IFGT
#undef ARRAY_VAL_PRINT
// name of the polynomial type
#define ARRAY_TYPENAME array_uint
// prefix of function names
#define ARRAY_FUNC(NAME) array_uint_ ## NAME
// type of values
#define ARRAY_VAL_TYPE unsigned int
// set values
#define ARRAY_VAL_SET(VAL, NEWVAL) VAL = NEWVAL
// copy values
#define ARRAY_VAL_CPY(FROMVAL, TOVAL) TOVAL = FROMVAL
// compare values
#define ARRAY_VAL_IFEQ(VAL1, VAL2) VAL1==VAL2
#define ARRAY_VAL_IFLT(VAL1, VAL2) VAL1<VAL2
#define ARRAY_VAL_IFGT(VAL1, VAL2) VAL1>VAL2
// print values
#define ARRAY_VAL_PRINT(VAL) printf("%u",VAL)

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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.
*/
#ifndef LIBINUM_ERRORS_H
#define LIBINUM_ERRORS_H
// maximal number of iterations reached
#define LIBINUM_ERROR_MAXITER -1
// illegal memoru access
#define LIBINUM_ERROR_ILLEGAL_MEMORY_ACCESS -2
// size incompatibilities
#define LIBINUM_ERROR_SIZE_MISMATCH -3
// NaN or Inf
#define LIBINUM_ERROR_NAN -4
#endif

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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.
*/
#include "integral.h"
#include <mpfr.h>
#include <math.h>
#include <stdlib.h>
#include "root.h"
#include "array.h"
#include "polynomial.h"
#include "errors.h"
//--------------------------------------------------
//
// using doubles
//
//--------------------------------------------------
#include "integral_double.h"
#include "integral_base.c"
//--------------------------------------------------
//
// using long doubles
//
//--------------------------------------------------
#include "integral_ldouble.h"
#include "integral_base.c"
//--------------------------------------------------
//
// using mpfr floats
//
//--------------------------------------------------
#include "integral_mpfr.h"
#include "integral_base.c"

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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.
*/
/*
Integration of real functions
*/
#ifndef LIBINUM_INTEGRAL_H
#define LIBINUM_INTEGRAL_H
#include "types.h"
//--------------------------------------------------
//
// using doubles
//
//--------------------------------------------------
#include "integral_double.h"
#include "integral_base.h"
//--------------------------------------------------
//
// using long doubles
//
//--------------------------------------------------
#include "integral_ldouble.h"
#include "integral_base.h"
//--------------------------------------------------
//
// using mpfr floats
//
//--------------------------------------------------
#include "integral_mpfr.h"
#include "integral_base.h"
#endif

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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 integration
see integral_*.h for the values taken by INTEGRAL_FUNC, etc...
*/
// compute the integral of a real function of 1 variable using the Gauss-Legendre scheme
int INTEGRAL_FUNC(integrate_gauss) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, void* extra_args){
unsigned int i;
INTEGRAL_FLOAT_TYPE valf, delta, avg, x;
int ret;
// check arguments
if(abcissa.length != weights.length){
return(LIBINUM_ERROR_SIZE_MISMATCH);
}
#ifdef INTEGRAL_FLOAT_INIT
INTEGRAL_FLOAT_INIT(valf);
INTEGRAL_FLOAT_INIT(delta);
INTEGRAL_FLOAT_INIT(avg);
INTEGRAL_FLOAT_INIT(x);
#endif
// init to 0
INTEGRAL_FLOAT_SET_UI(*out, 0);
// half length of interval
INTEGRAL_FLOAT_SUB(delta, upper, lower);
INTEGRAL_FLOAT_DIV_UI(delta, delta, 2);
// average of interval
INTEGRAL_FLOAT_ADD(avg, upper, lower);
INTEGRAL_FLOAT_DIV_UI(avg, avg, 2);
for(i=0;i<abcissa.length;i++){
// evaluate at x
INTEGRAL_FLOAT_MUL(x, delta, abcissa.values[i]);
INTEGRAL_FLOAT_ADD(x, x, avg);
ret=(*func)(&valf, x, extra_args);
if(ret<0){
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(valf);
INTEGRAL_FLOAT_FREE(delta);
INTEGRAL_FLOAT_FREE(avg);
INTEGRAL_FLOAT_FREE(x);
#endif
return(ret);
}
// check whether valf is a number
if(! INTEGRAL_FLOAT_ISNUMBER(valf)){
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(valf);
INTEGRAL_FLOAT_FREE(delta);
INTEGRAL_FLOAT_FREE(avg);
INTEGRAL_FLOAT_FREE(x);
#endif
return(LIBINUM_ERROR_NAN);
}
INTEGRAL_FLOAT_MUL(valf, valf, weights.values[i]);
INTEGRAL_FLOAT_ADD(*out, *out, valf);
}
INTEGRAL_FLOAT_MUL(*out, *out, delta);
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(valf);
INTEGRAL_FLOAT_FREE(delta);
INTEGRAL_FLOAT_FREE(avg);
INTEGRAL_FLOAT_FREE(x);
#endif
return(0);
}
// multithreaded version
// arguments to pass to each thread
struct INTEGRAL_FUNC(pthread_integrate_gauss_args) {
// partial sum of the values assigned to the thread
INTEGRAL_FLOAT_TYPE out;
// abcissa
INTEGRAL_FLOATARRAY_TYPE x;
// weights
INTEGRAL_FLOATARRAY_TYPE weights;
// pointer to the function to evaluate
int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*);
// extra arguments passed to func
void* extra_args;
// return value
int ret;
};
int INTEGRAL_FUNC(integrate_gauss_multithread) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, void* extra_args, unsigned int threads, array_pthread_t* thread_ids){
unsigned int i;
INTEGRAL_FLOAT_TYPE x, delta, avg;
struct INTEGRAL_FUNC(pthread_integrate_gauss_args) args[threads];
int ret=0;
unsigned int thread_nr;
array_pthread_t_init(thread_ids, threads);
thread_ids->length=threads;
// check arguments
if(abcissa.length != weights.length){
return(LIBINUM_ERROR_SIZE_MISMATCH);
}
#ifdef INTEGRAL_FLOAT_INIT
INTEGRAL_FLOAT_INIT(delta);
INTEGRAL_FLOAT_INIT(avg);
INTEGRAL_FLOAT_INIT(x);
#endif
// init to 0
INTEGRAL_FLOAT_SET_UI(*out, 0);
// half length of interval
INTEGRAL_FLOAT_SUB(delta, upper, lower);
INTEGRAL_FLOAT_DIV_UI(delta, delta, 2);
// average of interval
INTEGRAL_FLOAT_ADD(avg, upper, lower);
INTEGRAL_FLOAT_DIV_UI(avg, avg, 2);
// inits
for(thread_nr=0;thread_nr<threads;thread_nr++){
INTEGRAL_FLOATARRAY_FUNC(init) (&(args[thread_nr].x),abcissa.length/threads+1);
INTEGRAL_FLOATARRAY_FUNC(init) (&(args[thread_nr].weights),abcissa.length/threads+1);
#ifdef INTEGRAL_FLOAT_INIT
INTEGRAL_FLOAT_INIT(args[thread_nr].out);
#endif
}
// set abcissa and weights
for(i=0,thread_nr=0;i<abcissa.length;i++,thread_nr=(thread_nr+1)%threads){
INTEGRAL_FLOAT_MUL(x, delta, abcissa.values[i]);
INTEGRAL_FLOAT_ADD(x, x, avg);
INTEGRAL_FLOATARRAY_FUNC(append) (x, &(args[thread_nr].x));
INTEGRAL_FLOATARRAY_FUNC(append) (weights.values[i], &(args[thread_nr].weights));
}
for(thread_nr=0;thread_nr<threads;thread_nr++){
// set func
args[thread_nr].func=func;
// set extra_args
args[thread_nr].extra_args=extra_args;
// init ret
args[thread_nr].ret=0;
// run threads
pthread_create(thread_ids->values+thread_nr, NULL, INTEGRAL_FUNC(integrate_gauss_thread), (void*)(args+thread_nr));
}
// wait for completion and join
for(thread_nr=0;thread_nr<threads;thread_nr++){
pthread_join(thread_ids->values[thread_nr], NULL);
if(args[thread_nr].ret<0){
ret=args[thread_nr].ret;
}
else{
INTEGRAL_FLOAT_ADD(*out, *out, args[thread_nr].out);
}
}
// multiply by size of interval
INTEGRAL_FLOAT_MUL(*out, *out, delta);
for(thread_nr=0;thread_nr<threads;thread_nr++){
INTEGRAL_FLOATARRAY_FUNC(free) (args[thread_nr].x);
INTEGRAL_FLOATARRAY_FUNC(free) (args[thread_nr].weights);
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(args[thread_nr].out);
#endif
}
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(delta);
INTEGRAL_FLOAT_FREE(avg);
INTEGRAL_FLOAT_FREE(x);
#endif
return(ret);
}
// per-thread function
void* INTEGRAL_FUNC(integrate_gauss_thread) (void* args){
unsigned int i;
INTEGRAL_FLOAT_TYPE valf;
int ret;
struct INTEGRAL_FUNC(pthread_integrate_gauss_args)* argument=((struct INTEGRAL_FUNC(pthread_integrate_gauss_args)*)args);
#ifdef INTEGRAL_FLOAT_INIT
INTEGRAL_FLOAT_INIT(valf);
#endif
INTEGRAL_FLOAT_SET_UI(argument->out, 0);
for(i=0;i<argument->x.length;i++){
// evaluate
ret=(*(argument->func))(&valf, argument->x.values[i], argument->extra_args);
if(ret<0){
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(valf);
#endif
argument->ret=ret;
return(NULL);
}
// check whether valf is a number
if(! INTEGRAL_FLOAT_ISNUMBER(valf)){
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(valf);
#endif
argument->ret=LIBINUM_ERROR_NAN;
return(NULL);
}
INTEGRAL_FLOAT_MUL(valf, valf, argument->weights.values[i]);
INTEGRAL_FLOAT_ADD(argument->out, argument->out, valf);
}
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(valf);
#endif
return(NULL);
}
// smart management of temporary variables: initialize as many as needed but allow them to be re-used instead of freeing them
#ifdef INTEGRAL_FLOAT_INIT
int INTEGRAL_FUNC(integrate_gauss_smarttmp) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, INTEGRAL_FLOATARRAY_TYPE* tmps, void* extra_args){
unsigned int i;
int ret;
// check arguments
if(abcissa.length != weights.length){
return(LIBINUM_ERROR_SIZE_MISMATCH);
}
// allocate tmps if needed
if(tmps->memory<4){
// no need to resize since the values should not be kept
INTEGRAL_FLOATARRAY_FUNC(free)(*tmps);
INTEGRAL_FLOATARRAY_FUNC(init)(tmps, 4);
}
for (i=tmps->length;i<4;i++){
INTEGRAL_FLOAT_INIT(tmps->values[i]);
(tmps->length)++;
}
// init to 0
INTEGRAL_FLOAT_SET_UI(*out, 0);
// half length of interval
INTEGRAL_FLOAT_SUB(tmps->values[0], upper, lower);
INTEGRAL_FLOAT_DIV_UI(tmps->values[0], tmps->values[0], 2);
// average of interval
INTEGRAL_FLOAT_ADD(tmps->values[1], upper, lower);
INTEGRAL_FLOAT_DIV_UI(tmps->values[1], tmps->values[1], 2);
for(i=0;i<abcissa.length;i++){
// evaluation point
INTEGRAL_FLOAT_MUL(tmps->values[2], tmps->values[0], abcissa.values[i]);
INTEGRAL_FLOAT_ADD(tmps->values[2], tmps->values[2], tmps->values[1]);
ret=(*func)(tmps->values+3, tmps->values[2], extra_args);
if(ret<0){
return(ret);
}
// check whether tmps->values[3] is a number
if(! INTEGRAL_FLOAT_ISNUMBER(tmps->values[3])){
return(LIBINUM_ERROR_NAN);
}
INTEGRAL_FLOAT_MUL(tmps->values[3], tmps->values[3], weights.values[i]);
INTEGRAL_FLOAT_ADD(*out, *out, tmps->values[3]);
}
INTEGRAL_FLOAT_MUL(*out, *out, tmps->values[0]);
return(0);
}
#endif
// multithreaded version with smart management of temporary variables (only for datatypes that need to be initialized)
#ifdef INTEGRAL_FLOAT_INIT
// arguments to pass to each thread
struct INTEGRAL_FUNC(pthread_integrate_gauss_smarttmp_args) {
// partial sum of the values assigned to the thread
INTEGRAL_FLOAT_TYPE* out;
// abcissa
INTEGRAL_FLOATARRAY_TYPE x;
// weights
INTEGRAL_FLOATARRAY_TYPE weights;
// tmp
INTEGRAL_FLOAT_TYPE* tmp;
// pointer to the function to evaluate
int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*);
// extra arguments passed to func
void* extra_args;
// return value
int ret;
};
int INTEGRAL_FUNC(integrate_gauss_smarttmp_multithread) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, INTEGRAL_FLOATARRAY_TYPE* tmps, void* extra_args, unsigned int threads, array_pthread_t* thread_ids){
unsigned int i;
struct INTEGRAL_FUNC(pthread_integrate_gauss_smarttmp_args) args[threads];
int ret=0;
unsigned int thread_nr;
array_pthread_t_init(thread_ids, threads);
thread_ids->length=threads;
// check arguments
if(abcissa.length != weights.length){
return(LIBINUM_ERROR_SIZE_MISMATCH);
}
// allocate tmps if needed
if(tmps->memory<2+2*threads+abcissa.length){
// no need to resize since the values should not be kept
INTEGRAL_FLOATARRAY_FUNC(free)(*tmps);
INTEGRAL_FLOATARRAY_FUNC(init)(tmps, 2+2*threads+abcissa.length);
}
for (i=tmps->length;i<2+2*threads+abcissa.length;i++){
INTEGRAL_FLOAT_INIT(tmps->values[i]);
(tmps->length)++;
}
// init to 0
INTEGRAL_FLOAT_SET_UI(*out, 0);
// half length of interval
INTEGRAL_FLOAT_SUB(tmps->values[0], upper, lower);
INTEGRAL_FLOAT_DIV_UI(tmps->values[0], tmps->values[0], 2);
// average of interval
INTEGRAL_FLOAT_ADD(tmps->values[1], upper, lower);
INTEGRAL_FLOAT_DIV_UI(tmps->values[1], tmps->values[1], 2);
// inits
for(thread_nr=0;thread_nr<threads;thread_nr++){
INTEGRAL_FLOATARRAY_FUNC(init) (&(args[thread_nr].x),abcissa.length/threads+1);
INTEGRAL_FLOATARRAY_FUNC(init) (&(args[thread_nr].weights),abcissa.length/threads+1);
args[thread_nr].out=tmps->values+2+thread_nr;
args[thread_nr].tmp=tmps->values+2+threads+thread_nr;
}
// set abcissa and weights
for(i=0,thread_nr=0;i<abcissa.length;i++,thread_nr=(thread_nr+1)%threads){
INTEGRAL_FLOAT_MUL(tmps->values[2+2*threads+i], tmps->values[0], abcissa.values[i]);
INTEGRAL_FLOAT_ADD(tmps->values[2+2*threads+i], tmps->values[2+2*threads+i], tmps->values[1]);
INTEGRAL_FLOATARRAY_FUNC(append_noinit) (tmps->values[2+2*threads+i], &(args[thread_nr].x));
INTEGRAL_FLOATARRAY_FUNC(append_noinit) (weights.values[i], &(args[thread_nr].weights));
}
for(thread_nr=0;thread_nr<threads;thread_nr++){
// set func
args[thread_nr].func=func;
// set extra_args
args[thread_nr].extra_args=extra_args;
// init ret
args[thread_nr].ret=0;
// run threads
pthread_create(thread_ids->values+thread_nr, NULL, INTEGRAL_FUNC(integrate_gauss_smarttmp_thread), (void*)(args+thread_nr));
}
// wait for completion and join
for(thread_nr=0;thread_nr<threads;thread_nr++){
pthread_join(thread_ids->values[thread_nr], NULL);
if(args[thread_nr].ret<0){
ret=args[thread_nr].ret;
}
else{
INTEGRAL_FLOAT_ADD(*out, *out, *(args[thread_nr].out));
}
}
// multiply by size of interval
INTEGRAL_FLOAT_MUL(*out, *out, tmps->values[0]);
// free x and weights
for(thread_nr=0;thread_nr<threads;thread_nr++){
INTEGRAL_FLOATARRAY_FUNC(free_vects)(args[thread_nr].x);
INTEGRAL_FLOATARRAY_FUNC(free_vects)(args[thread_nr].weights);
}
return(ret);
}
// per-thread function
void* INTEGRAL_FUNC(integrate_gauss_smarttmp_thread) (void* args){
unsigned int i;
int ret;
struct INTEGRAL_FUNC(pthread_integrate_gauss_smarttmp_args)* argument=((struct INTEGRAL_FUNC(pthread_integrate_gauss_smarttmp_args)*)args);
INTEGRAL_FLOAT_SET_UI(*(argument->out), 0);
for(i=0;i<argument->x.length;i++){
// evaluate
ret=(*(argument->func))(argument->tmp, argument->x.values[i], argument->extra_args);
if(ret<0){
argument->ret=ret;
return(NULL);
}
// check whether argument->tmp is a number
if(! INTEGRAL_FLOAT_ISNUMBER(*(argument->tmp))){
argument->ret=LIBINUM_ERROR_NAN;
return(NULL);
}
INTEGRAL_FLOAT_MUL(*(argument->tmp), *(argument->tmp), argument->weights.values[i]);
INTEGRAL_FLOAT_ADD(*(argument->out), *(argument->out), *(argument->tmp));
}
return(NULL);
}
#endif
// compute the abcissa and weights for the Gauss-Legendre numerical integration scheme
int INTEGRAL_FUNC(gauss_legendre_weights) (unsigned int order, INTEGRAL_FLOAT_TYPE tolerance, unsigned int maxiter, INTEGRAL_FLOATARRAY_TYPE* abcissa, INTEGRAL_FLOATARRAY_TYPE* weights){
unsigned int i;
INTEGRAL_FLOAT_TYPE x, tmp;
INTEGRAL_POLYNOMIALARRAY_TYPE legendre;
int ret;
INTEGRAL_FLOATARRAY_FUNC(init) (abcissa, order);
INTEGRAL_FLOATARRAY_FUNC(init) (weights, order);
#ifdef INTEGRAL_FLOAT_INIT
INTEGRAL_FLOAT_INIT(x);
INTEGRAL_FLOAT_INIT(tmp);
#endif
INTEGRAL_POLYNOMIALARRAY_FUNC(init) (&legendre, 2);
// compute the roots of the 'order'-th Legendre polynomial
INTEGRAL_POLYNOMIAL_FUNC(legendre) (order, legendre.values);
INTEGRAL_POLYNOMIAL_FUNC(derive) (legendre.values[0], legendre.values+1);
legendre.length=2;
for(i=0;i<order;i++){
// initial guess
INTEGRAL_FLOAT_SET_D(x, cos(3.1415926*(i+0.75)/(order+0.5)));
ret=INTEGRAL_FUNC(root_newton_inplace) (&x, &INTEGRAL_FUNC(legendre_wrapper), &INTEGRAL_FUNC(deriv_legendre_wrapper), tolerance, maxiter, &legendre);
if(ret<0){
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(x);
INTEGRAL_FLOAT_FREE(tmp);
#endif
INTEGRAL_POLYNOMIALARRAY_FUNC(free) (legendre);
INTEGRAL_FLOATARRAY_FUNC(free) (*abcissa);
INTEGRAL_FLOATARRAY_FUNC(free) (*weights);
return(ret);
}
INTEGRAL_FLOATARRAY_FUNC(append) (x, abcissa);
// weight: 2/((1-x^2)*(deriv_Legendre(x)))^2
INTEGRAL_POLYNOMIAL_FUNC(evaluate) (&tmp, x, legendre.values[1]);
INTEGRAL_FLOAT_POW_UI(tmp, tmp, 2);
INTEGRAL_FLOAT_POW_UI(x, x, 2);
INTEGRAL_FLOAT_UI_SUB(x, 1, x);
INTEGRAL_FLOAT_MUL(x, x, tmp);
INTEGRAL_FLOAT_SET_UI(tmp, 2);
INTEGRAL_FLOAT_DIV(x, tmp, x);
INTEGRAL_FLOATARRAY_FUNC(append) (x, weights);
}
#ifdef INTEGRAL_FLOAT_FREE
INTEGRAL_FLOAT_FREE(x);
INTEGRAL_FLOAT_FREE(tmp);
#endif
INTEGRAL_POLYNOMIALARRAY_FUNC(free) (legendre);
return(0);
}
// wrapper functions to evaluate the legendre polynomial and its derivative
int INTEGRAL_FUNC(legendre_wrapper) (INTEGRAL_FLOAT_TYPE* out, INTEGRAL_FLOAT_TYPE in, void* legendre){
INTEGRAL_POLYNOMIAL_FUNC(evaluate) (out, in, ((INTEGRAL_POLYNOMIALARRAY_TYPE*)legendre)->values[0]);
return(0);
}
int INTEGRAL_FUNC(deriv_legendre_wrapper) (INTEGRAL_FLOAT_TYPE* out, INTEGRAL_FLOAT_TYPE in, void* legendre){
INTEGRAL_POLYNOMIAL_FUNC(evaluate) (out, in, ((INTEGRAL_POLYNOMIALARRAY_TYPE*)legendre)->values[1]);
return(0);
}

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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 integration
see integral_*.h for the values taken by INTEGRAL_FUNC, etc...
*/
#include <pthread.h>
// compute the integral of a real function of 1 variable using the Gauss-Legendre scheme
int INTEGRAL_FUNC(integrate_gauss) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, void* extra_args);
// multithreaded version
int INTEGRAL_FUNC(integrate_gauss_multithread) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, void* extra_args, unsigned int threads, array_pthread_t* thread_ids);
// per-thread function
void* INTEGRAL_FUNC(integrate_gauss_thread) (void* args);
// smart management of temporary variables: initialize as many as needed but allow them to be re-used instead of freeing them
#ifdef INTEGRAL_FLOAT_INIT
int INTEGRAL_FUNC(integrate_gauss_smarttmp) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, INTEGRAL_FLOATARRAY_TYPE* tmps, void* extra_args);
// multithreaded version with smart management of temporary variables (only for datatypes that need to be initialized)
int INTEGRAL_FUNC(integrate_gauss_smarttmp_multithread) (INTEGRAL_FLOAT_TYPE* out, int (*func)(INTEGRAL_FLOAT_TYPE*, INTEGRAL_FLOAT_TYPE, void*), INTEGRAL_FLOAT_TYPE lower, INTEGRAL_FLOAT_TYPE upper, INTEGRAL_FLOATARRAY_TYPE abcissa, INTEGRAL_FLOATARRAY_TYPE weights, INTEGRAL_FLOATARRAY_TYPE* tmps, void* extra_args, unsigned int threads, array_pthread_t* thread_ids);
// per-thread function
void* INTEGRAL_FUNC(integrate_gauss_smarttmp_thread) (void* args);
#endif
// compute the abcissa and weights for the Gauss-Legendre numerical integration scheme
int INTEGRAL_FUNC(gauss_legendre_weights) (unsigned int order, INTEGRAL_FLOAT_TYPE tolerance, unsigned int maxiter, INTEGRAL_FLOATARRAY_TYPE* abcissa, INTEGRAL_FLOATARRAY_TYPE* weights);
// wrapper functions to evaluate the legendre polynomial and its derivative
int INTEGRAL_FUNC(legendre_wrapper) (INTEGRAL_FLOAT_TYPE* out, INTEGRAL_FLOAT_TYPE in, void* legendre);
int INTEGRAL_FUNC(deriv_legendre_wrapper) (INTEGRAL_FLOAT_TYPE* out, INTEGRAL_FLOAT_TYPE in, void* legendre);

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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.
*/
/*
Preprocessor macros for integration using with doubles
*/
// reset CPP macros
#undef INTEGRAL_FUNC
#undef INTEGRAL_FLOAT_TYPE
#undef INTEGRAL_FLOAT_INIT
#undef INTEGRAL_FLOAT_FREE
#undef INTEGRAL_FLOAT_SET_D
#undef INTEGRAL_FLOAT_SET_UI
#undef INTEGRAL_FLOAT_ADD
#undef INTEGRAL_FLOAT_SUB
#undef INTEGRAL_FLOAT_UI_SUB
#undef INTEGRAL_FLOAT_MUL
#undef INTEGRAL_FLOAT_POW_UI
#undef INTEGRAL_FLOAT_DIV
#undef INTEGRAL_FLOAT_DIV_UI
#undef INTEGRAL_FLOAT_ISNUMBER
#undef INTEGRAL_FLOATARRAY_TYPE
#undef INTEGRAL_FLOATARRAY_FUNC
#undef INTEGRAL_POLYNOMIAL_FUNC
#undef INTEGRAL_POLYNOMIALARRAY_TYPE
#undef INTEGRAL_POLYNOMIALARRAY_FUNC
// suffix of function names
#define INTEGRAL_FUNC(NAME) NAME ## _double
// type of floats
#define INTEGRAL_FLOAT_TYPE double
// set float from double
#define INTEGRAL_FLOAT_SET_D(FLOAT, VAL) FLOAT=VAL
// set float from unsigned int
#define INTEGRAL_FLOAT_SET_UI(FLOAT, VAL) FLOAT=(double)VAL
// add floats
#define INTEGRAL_FLOAT_ADD(FLOAT, VAL1, VAL2) FLOAT=VAL1+VAL2
// subtract floats
#define INTEGRAL_FLOAT_SUB(FLOAT, VAL1, VAL2) FLOAT=VAL1-VAL2
// subtract floats in which the first is specified as an unsigned int
#define INTEGRAL_FLOAT_UI_SUB(FLOAT, VAL1, VAL2) FLOAT=(double)VAL1-VAL2
// multiply floats
#define INTEGRAL_FLOAT_MUL(FLOAT, VAL1, VAL2) FLOAT=VAL1*VAL2
// power of a float, specified as an unsigned int
#define INTEGRAL_FLOAT_POW_UI(FLOAT, VAL1, VAL2) FLOAT=pow(VAL1, (double)VAL2)
// divide floats
#define INTEGRAL_FLOAT_DIV(FLOAT, VAL1, VAL2) FLOAT=VAL1/VAL2
// divide floats, one of which is specified as an unsigned int
#define INTEGRAL_FLOAT_DIV_UI(FLOAT, VAL1, VAL2) FLOAT=VAL1/(double)VAL2
// check whether a float is a regular number
#define INTEGRAL_FLOAT_ISNUMBER(FLOAT) (fpclassify(FLOAT)>=FP_ZERO)
// type of float arrays
#define INTEGRAL_FLOATARRAY_TYPE array_double
// prefix of float array function names
#define INTEGRAL_FLOATARRAY_FUNC(NAME) array_double_ ## NAME
// prefix of polynomial function names
#define INTEGRAL_POLYNOMIAL_FUNC(NAME) polynomial_double_ ## NAME
// type of polynomial arrays
#define INTEGRAL_POLYNOMIALARRAY_TYPE array_polynomial_double
// prefix of polynomial array function names
#define INTEGRAL_POLYNOMIALARRAY_FUNC(NAME) array_polynomial_double_ ## NAME

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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.
*/
/*
Preprocessor macros for integration using with long doubles
*/
// reset CPP macros
#undef INTEGRAL_FUNC
#undef INTEGRAL_FLOAT_TYPE
#undef INTEGRAL_FLOAT_INIT
#undef INTEGRAL_FLOAT_FREE
#undef INTEGRAL_FLOAT_SET_D
#undef INTEGRAL_FLOAT_SET_UI
#undef INTEGRAL_FLOAT_ADD
#undef INTEGRAL_FLOAT_SUB
#undef INTEGRAL_FLOAT_UI_SUB
#undef INTEGRAL_FLOAT_MUL
#undef INTEGRAL_FLOAT_POW_UI
#undef INTEGRAL_FLOAT_DIV
#undef INTEGRAL_FLOAT_DIV_UI
#undef INTEGRAL_FLOAT_ISNUMBER
#undef INTEGRAL_FLOATARRAY_TYPE
#undef INTEGRAL_FLOATARRAY_FUNC
#undef INTEGRAL_POLYNOMIAL_FUNC
#undef INTEGRAL_POLYNOMIALARRAY_TYPE
#undef INTEGRAL_POLYNOMIALARRAY_FUNC
// suffix of function names
#define INTEGRAL_FUNC(NAME) NAME ## _ldouble
// type of floats
#define INTEGRAL_FLOAT_TYPE long double
// set float from double
#define INTEGRAL_FLOAT_SET_D(FLOAT, VAL) FLOAT=(long double)VAL
// set float from unsigned int
#define INTEGRAL_FLOAT_SET_UI(FLOAT, VAL) FLOAT=(long double)VAL
// add floats
#define INTEGRAL_FLOAT_ADD(FLOAT, VAL1, VAL2) FLOAT=VAL1+VAL2
// subtract floats
#define INTEGRAL_FLOAT_SUB(FLOAT, VAL1, VAL2) FLOAT=VAL1-VAL2
// subtract floats in which the first is specified as an unsigned int
#define INTEGRAL_FLOAT_UI_SUB(FLOAT, VAL1, VAL2) FLOAT=(long double)VAL1-VAL2
// multiply floats
#define INTEGRAL_FLOAT_MUL(FLOAT, VAL1, VAL2) FLOAT=VAL1*VAL2
// power of a float, specified as an unsigned int
#define INTEGRAL_FLOAT_POW_UI(FLOAT, VAL1, VAL2) FLOAT=powl(VAL1, (long double)VAL2)
// divide floats
#define INTEGRAL_FLOAT_DIV(FLOAT, VAL1, VAL2) FLOAT=VAL1/VAL2
// divide floats, one of which is specified as an unsigned int
#define INTEGRAL_FLOAT_DIV_UI(FLOAT, VAL1, VAL2) FLOAT=VAL1/(long double)VAL2
// check whether a float is a regular number
#define INTEGRAL_FLOAT_ISNUMBER(FLOAT) (fpclassify(FLOAT)>=FP_ZERO)
// type of float arrays
#define INTEGRAL_FLOATARRAY_TYPE array_ldouble
// prefix of float array function names
#define INTEGRAL_FLOATARRAY_FUNC(NAME) array_ldouble_ ## NAME
// prefix of polynomial function names
#define INTEGRAL_POLYNOMIAL_FUNC(NAME) polynomial_ldouble_ ## NAME
// type of polynomial arrays
#define INTEGRAL_POLYNOMIALARRAY_TYPE array_polynomial_ldouble
// prefix of polynomial array function names
#define INTEGRAL_POLYNOMIALARRAY_FUNC(NAME) array_polynomial_ldouble_ ## NAME

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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.
*/
/*
Preprocessor macros for integration using with multi-precision floats (mpfr)
*/
// reset CPP macros
#undef INTEGRAL_FUNC
#undef INTEGRAL_FLOAT_TYPE
#undef INTEGRAL_FLOAT_INIT
#undef INTEGRAL_FLOAT_FREE
#undef INTEGRAL_FLOAT_SET_D
#undef INTEGRAL_FLOAT_SET_UI
#undef INTEGRAL_FLOAT_ADD
#undef INTEGRAL_FLOAT_SUB
#undef INTEGRAL_FLOAT_UI_SUB
#undef INTEGRAL_FLOAT_MUL
#undef INTEGRAL_FLOAT_POW_UI
#undef INTEGRAL_FLOAT_DIV
#undef INTEGRAL_FLOAT_DIV_UI
#undef INTEGRAL_FLOAT_ISNUMBER
#undef INTEGRAL_FLOATARRAY_TYPE
#undef INTEGRAL_FLOATARRAY_FUNC
#undef INTEGRAL_POLYNOMIAL_FUNC
#undef INTEGRAL_POLYNOMIALARRAY_TYPE
#undef INTEGRAL_POLYNOMIALARRAY_FUNC
// suffix of function names
#define INTEGRAL_FUNC(NAME) NAME ## _mpfr
// type of floats
#define INTEGRAL_FLOAT_TYPE mpfr_t
// init float
#define INTEGRAL_FLOAT_INIT(VAR) mpfr_init(VAR)
// free float
#define INTEGRAL_FLOAT_FREE(VAR) mpfr_clear(VAR)
// set float from double
#define INTEGRAL_FLOAT_SET_D(FLOAT, VAL) mpfr_set_d(FLOAT, VAL, MPFR_RNDN)
// set float from unsigned int
#define INTEGRAL_FLOAT_SET_UI(FLOAT, VAL) mpfr_set_ui(FLOAT, VAL, MPFR_RNDN)
// add floats
#define INTEGRAL_FLOAT_ADD(FLOAT, VAL1, VAL2) mpfr_add(FLOAT, VAL1, VAL2, MPFR_RNDN)
// subtract floats
#define INTEGRAL_FLOAT_SUB(FLOAT, VAL1, VAL2) mpfr_sub(FLOAT, VAL1, VAL2, MPFR_RNDN)
// subtract floats in which the first is specified as an unsigned int
#define INTEGRAL_FLOAT_UI_SUB(FLOAT, VAL1, VAL2) mpfr_ui_sub(FLOAT, VAL1, VAL2, MPFR_RNDN)
// multiply floats
#define INTEGRAL_FLOAT_MUL(FLOAT, VAL1, VAL2) mpfr_mul(FLOAT, VAL1, VAL2, MPFR_RNDN)
// power of a float, specified as an unsigned int
#define INTEGRAL_FLOAT_POW_UI(FLOAT, VAL1, VAL2) mpfr_pow_ui(FLOAT, VAL1, VAL2, MPFR_RNDN)
// divide floats
#define INTEGRAL_FLOAT_DIV(FLOAT, VAL1, VAL2) mpfr_div(FLOAT, VAL1, VAL2, MPFR_RNDN)
// divide floats, one of which is specified as an unsigned int
#define INTEGRAL_FLOAT_DIV_UI(FLOAT, VAL1, VAL2) mpfr_div_ui(FLOAT, VAL1, VAL2, MPFR_RNDN)
// check whether a float is a regular number
#define INTEGRAL_FLOAT_ISNUMBER(FLOAT) mpfr_number_p(FLOAT)!=0
// type of float arrays
#define INTEGRAL_FLOATARRAY_TYPE array_mpfr
// prefix of float array function names
#define INTEGRAL_FLOATARRAY_FUNC(NAME) array_mpfr_ ## NAME
// prefix of polynomial function names
#define INTEGRAL_POLYNOMIAL_FUNC(NAME) polynomial_mpfr_ ## NAME
// type of polynomial arrays
#define INTEGRAL_POLYNOMIALARRAY_TYPE array_polynomial_mpfr
// prefix of polynomial array function names
#define INTEGRAL_POLYNOMIALARRAY_FUNC(NAME) array_polynomial_mpfr_ ## NAME

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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.
*/
#include "polynomial.h"
#include <stdlib.h>
#include <stdio.h>
#include <mpfr.h>
#include <math.h>
#include "array.h"
#include "utils.h"
#include "errors.h"
//--------------------------------------------------
//
// mpfr coefficients, unsigned int order (polynomial_mpfr)
//
//--------------------------------------------------
#include "polynomial_mpfr.h"
#include "polynomial_base.c"
//--------------------------------------------------
//
// double coefficients, unsigned int order (polynomial_mpfr)
//
//--------------------------------------------------
#include "polynomial_double.h"
#include "polynomial_base.c"
//--------------------------------------------------
//
// long double coefficients, unsigned int order (polynomial_mpfr)
//
//--------------------------------------------------
#include "polynomial_ldouble.h"
#include "polynomial_base.c"

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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.
*/
/*
Real polynomial
*/
#ifndef LIBINUM_POLYNOMIAL_H
#define LIBINUM_POLYNOMIAL_H
#include "types.h"
//--------------------------------------------------
//
// mpfr coefficients, unsigned int order (polynomial_mpfr)
//
//--------------------------------------------------
#include "polynomial_mpfr.h"
#include "polynomial_base.h"
//--------------------------------------------------
//
// double coefficients, unsigned int order (polynomial_mpfr)
//
//--------------------------------------------------
#include "polynomial_double.h"
#include "polynomial_base.h"
//--------------------------------------------------
//
// long double coefficients, unsigned int order (polynomial_mpfr)
//
//--------------------------------------------------
#include "polynomial_ldouble.h"
#include "polynomial_base.h"
#endif

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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.
*/
#include "polynomialMV.h"
#include <stdlib.h>
#include <stdio.h>
#include "array.h"
#include "errors.h"
// multi-precision integer coefficients
#include "polynomialMV_mpz.h"
#include "polynomialMV_base.c"
// integer coefficients
#include "polynomialMV_int.h"
#include "polynomialMV_base.c"

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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.
*/
/*
Multi-variable polynomials
*/
#ifndef LIBINUM_POLYNOMIAL_MV_H
#define LIBINUM_POLYNOMIAL_MV_H
#include "types.h"
// multi-precision integer coefficients
#include "polynomialMV_mpz.h"
#include "polynomialMV_base.h"
// integer coefficients
#include "polynomialMV_int.h"
#include "polynomialMV_base.h"
#endif

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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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/*
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
polynomialMV_*.h for the values taken by POLYNOMIALMV_FUNC, etc...
*/
// init
int POLYNOMIALMV_FUNC(init) (POLYNOMIALMV_TYPENAME* polynomial, int size);
int POLYNOMIALMV_FUNC(free) (POLYNOMIALMV_TYPENAME polynomial);
// resize the memory allocated to a polynomial
int POLYNOMIALMV_FUNC(resize) (POLYNOMIALMV_TYPENAME* polynomial, int new_size);
// copy a polynomial
int POLYNOMIALMV_FUNC(cpy) (POLYNOMIALMV_TYPENAME input, POLYNOMIALMV_TYPENAME* output);
int POLYNOMIALMV_FUNC(cpy_noinit) (POLYNOMIALMV_TYPENAME input, POLYNOMIALMV_TYPENAME* output);
// append an element to a polynomial
int POLYNOMIALMV_FUNC(append) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output);
// 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);
// do not allocate memory for factor or coefficient
int POLYNOMIALMV_FUNC(append_noinit) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output);
// noinit factor but init coefficient
int POLYNOMIALMV_FUNC(append_noinitfactor) (POLYNOMIALMV_FACTOR_TYPE factor, POLYNOMIALMV_COEF_TYPE coef, POLYNOMIALMV_TYPENAME* output);
// 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);
// noinit factors 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);
// add polynomials (inplace)
int POLYNOMIALMV_FUNC(add_inplace) (POLYNOMIALMV_TYPENAME input, POLYNOMIALMV_TYPENAME* inout);
// not inplace
int POLYNOMIALMV_FUNC(add) (POLYNOMIALMV_TYPENAME input1, POLYNOMIALMV_TYPENAME input2, POLYNOMIALMV_TYPENAME* output);
// multiply a polynomial by a scalar
int POLYNOMIALMV_FUNC(multiply_scalar) (POLYNOMIALMV_TYPENAME polynomial, POLYNOMIALMV_COEF_TYPE num);
// multiply polynomials
int POLYNOMIALMV_FUNC(prod) (POLYNOMIALMV_TYPENAME input1, POLYNOMIALMV_TYPENAME input2, POLYNOMIALMV_TYPENAME* output);
// order factors
int POLYNOMIALMV_FUNC(order) (POLYNOMIALMV_TYPENAME polynomial);
// print
int POLYNOMIALMV_FUNC(print) (POLYNOMIALMV_TYPENAME polynomial);

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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.
*/
/*
Preprocessor macros for multivariable polynomials with integer coefficients and integer-indexed variables
*/
// reset CPP macros
#undef POLYNOMIALMV_TYPENAME
#undef POLYNOMIALMV_FUNC
#undef POLYNOMIALMV_COEF_TYPE
#undef POLYNOMIALMV_COEF_INIT
#undef POLYNOMIALMV_COEF_FREE
#undef POLYNOMIALMV_COEF_SET
#undef POLYNOMIALMV_COEF_CPY
#undef POLYNOMIALMV_COEF_ADD
#undef POLYNOMIALMV_COEF_MUL
#undef POLYNOMIALMV_COEF_PRINT
#undef POLYNOMIALMV_FACTOR_TYPE
#undef POLYNOMIALMV_FACTOR_FUNC
#undef POLYNOMIALMV_FACTOR_ELT_PRINT
// name of the polynomial type
#define POLYNOMIALMV_TYPENAME polynomialMV_int
// prefix of function names
#define POLYNOMIALMV_FUNC(NAME) polynomialMV_int_ ## NAME
// type of the coefficient
#define POLYNOMIALMV_COEF_TYPE int
// set coefficient
#define POLYNOMIALMV_COEF_SET(COEF, VAL) COEF = VAL
// copy coefficient
#define POLYNOMIALMV_COEF_CPY(COEF, VAL) COEF = VAL
// add coefficients
#define POLYNOMIALMV_COEF_ADD(COEF, VAL1, VAL2) COEF = VAL1 + VAL2
// multiply coefficients
#define POLYNOMIALMV_COEF_MUL(COEF, VAL1, VAL2) COEF = VAL1 * VAL2
// print a coefficient
#define POLYNOMIALMV_COEF_PRINT(COEF) printf("%d", COEF)
// type of the factor (must be an array)
#define POLYNOMIALMV_FACTOR_TYPE array_int
// prefix of factor function names
#define POLYNOMIALMV_FACTOR_FUNC(NAME) array_int_ ## NAME
// print an element of a factor
#define POLYNOMIALMV_FACTOR_ELT_PRINT(ELT) printf("[x%d]", ELT)

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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.
*/
/*
Preprocessor macros for multivariable polynomials with multi-precision integer (mpz) coefficients and integer-indexed variables
*/
// reset CPP macros
#undef POLYNOMIALMV_TYPENAME
#undef POLYNOMIALMV_FUNC
#undef POLYNOMIALMV_COEF_TYPE
#undef POLYNOMIALMV_COEF_INIT
#undef POLYNOMIALMV_COEF_FREE
#undef POLYNOMIALMV_COEF_SET
#undef POLYNOMIALMV_COEF_CPY
#undef POLYNOMIALMV_COEF_ADD
#undef POLYNOMIALMV_COEF_MUL
#undef POLYNOMIALMV_COEF_PRINT
#undef POLYNOMIALMV_FACTOR_TYPE
#undef POLYNOMIALMV_FACTOR_FUNC
#undef POLYNOMIALMV_FACTOR_ELT_PRINT
// name of the polynomial type
#define POLYNOMIALMV_TYPENAME polynomialMV_mpz
// prefix of function names
#define POLYNOMIALMV_FUNC(NAME) polynomialMV_mpz_ ## NAME
// type of the coefficient
#define POLYNOMIALMV_COEF_TYPE mpz_t
// init coefficient
#define POLYNOMIALMV_COEF_INIT(VAR) mpz_init(VAR)
// free coefficient
#define POLYNOMIALMV_COEF_FREE(VAR) mpz_clear(VAR)
// set coefficient
#define POLYNOMIALMV_COEF_SET(COEF, VAL) COEF[0]=VAL[0]
// copy coefficient
#define POLYNOMIALMV_COEF_CPY(COEF, VAL) mpz_init(COEF); mpz_set(COEF, VAL)
// add coefficients
#define POLYNOMIALMV_COEF_ADD(COEF, VAL1, VAL2) mpz_add(COEF, VAL1, VAL2)
// multiply coefficients
#define POLYNOMIALMV_COEF_MUL(COEF, VAL1, VAL2) mpz_mul(COEF, VAL1, VAL2)
// print a coefficient
#define POLYNOMIALMV_COEF_PRINT(COEF) gmp_printf("%Zd", COEF)
// type of the factor (must be an array)
#define POLYNOMIALMV_FACTOR_TYPE array_int
// prefix of factor function names
#define POLYNOMIALMV_FACTOR_FUNC(NAME) array_int_ ## NAME
// print an element of a factor
#define POLYNOMIALMV_FACTOR_ELT_PRINT(ELT) printf("[x%d]", ELT)

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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.
*/
/*
Structure definition for multivariable polynomials
see polynomialMV_*.h for the values taken by POLYNOMIALMV_TYPENAME, etc...
*/
typedef struct POLYNOMIALMV_TYPENAME {
POLYNOMIALMV_COEF_TYPE* coefficients;
POLYNOMIALMV_FACTOR_TYPE* factors;
unsigned int length;
unsigned int memory;
} POLYNOMIALMV_TYPENAME;

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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 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);
}

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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 real polynomials
see polynomial_*.h for the values taken by POLYNOMIAL_FUNC, etc...
*/
// init
int POLYNOMIAL_FUNC(init) (POLYNOMIAL_TYPENAME* poly, unsigned int memory);
int POLYNOMIAL_FUNC(free) (POLYNOMIAL_TYPENAME poly);
// resize memory
int POLYNOMIAL_FUNC(resize) (POLYNOMIAL_TYPENAME* poly, unsigned int newsize);
// add a monomial
int POLYNOMIAL_FUNC(add_monomial) (POLYNOMIAL_COEF_TYPE val, POLYNOMIAL_ORDER_TYPE order, POLYNOMIAL_TYPENAME* output);
// from a double-valued coefficient and an unsigned int order
int POLYNOMIAL_FUNC(add_monomial_dui) (double val, unsigned int order, POLYNOMIAL_TYPENAME* output);
// copy
int POLYNOMIAL_FUNC(cpy) (POLYNOMIAL_TYPENAME input, POLYNOMIAL_TYPENAME* output);
int POLYNOMIAL_FUNC(cpy_noinit) (POLYNOMIAL_TYPENAME input, POLYNOMIAL_TYPENAME* output);
// add
int POLYNOMIAL_FUNC(add_inplace) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME* poly2);
int POLYNOMIAL_FUNC(add) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME poly2, POLYNOMIAL_TYPENAME* output);
// multiply by a scalar
int POLYNOMIAL_FUNC(mul_scalar_inplace) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_TYPENAME* poly);
int POLYNOMIAL_FUNC(mul_scalar) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_TYPENAME poly, POLYNOMIAL_TYPENAME* output);
// multiply by a monomial
int POLYNOMIAL_FUNC(mul_monomial_inplace) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_ORDER_TYPE order, POLYNOMIAL_TYPENAME* poly);
int POLYNOMIAL_FUNC(mul_monomial) (POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_ORDER_TYPE order, POLYNOMIAL_TYPENAME poly, POLYNOMIAL_TYPENAME* output);
// multiply two polynomials
int POLYNOMIAL_FUNC(mul_inplace) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME* poly2);
int POLYNOMIAL_FUNC(mul) (POLYNOMIAL_TYPENAME poly1, POLYNOMIAL_TYPENAME poly2, POLYNOMIAL_TYPENAME* output);
// derive
int POLYNOMIAL_FUNC(derive_inplace) (POLYNOMIAL_TYPENAME* poly);
int POLYNOMIAL_FUNC(derive) (POLYNOMIAL_TYPENAME poly, POLYNOMIAL_TYPENAME* output);
// evaluate
int POLYNOMIAL_FUNC(evaluate) (POLYNOMIAL_COEF_TYPE* out, POLYNOMIAL_COEF_TYPE x, POLYNOMIAL_TYPENAME poly);
// print
int POLYNOMIAL_FUNC(print) (POLYNOMIAL_TYPENAME poly);
// n-th Legendre polynomial
int POLYNOMIAL_FUNC(legendre) (unsigned int n, POLYNOMIAL_TYPENAME* output);

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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.
*/
/*
Preprocessor macros for real polynomials with double coefficients and unsigned integer powers
*/
// reset CPP macros
#undef POLYNOMIAL_TYPENAME
#undef POLYNOMIAL_FUNC
#undef POLYNOMIAL_COEF_TYPE
#undef POLYNOMIAL_COEFSARRAY_TYPE
#undef POLYNOMIAL_COEFSARRAY_FUNC
#undef POLYNOMIAL_COEF_INIT
#undef POLYNOMIAL_COEF_FREE
#undef POLYNOMIAL_COEF_SET
#undef POLYNOMIAL_COEF_SET_SI
#undef POLYNOMIAL_COEF_SET_UI
#undef POLYNOMIAL_COEF_CPY
#undef POLYNOMIAL_COEF_CPY_D
#undef POLYNOMIAL_COEF_ADD
#undef POLYNOMIAL_COEF_ADD_D
#undef POLYNOMIAL_COEF_MUL
#undef POLYNOMIAL_COEF_MUL_ORDER
#undef POLYNOMIAL_COEF_DIV_UI
#undef POLYNOMIAL_COEF_POW_UI
#undef POLYNOMIAL_COEF_PRINT
#undef POLYNOMIAL_ORDER_TYPE
#undef POLYNOMIAL_ORDERSARRAY_TYPE
#undef POLYNOMIAL_ORDERSARRAY_FUNC
#undef POLYNOMIAL_ORDER_INIT
#undef POLYNOMIAL_ORDER_FREE
#undef POLYNOMIAL_ORDER_SET
#undef POLYNOMIAL_ORDER_SET_UI
#undef POLYNOMIAL_ORDER_CPY
#undef POLYNOMIAL_ORDER_CPY_UI
#undef POLYNOMIAL_ORDER_ADD
#undef POLYNOMIAL_ORDER_SUB_UI
#undef POLYNOMIAL_ORDER_CMP
#undef POLYNOMIAL_ORDER_CMP_UI
#undef POLYNOMIAL_ORDER_PRINT
// name of the polynomial type
#define POLYNOMIAL_TYPENAME polynomial_double
// prefix of function names
#define POLYNOMIAL_FUNC(NAME) polynomial_double_ ## NAME
// type of the coefficient
#define POLYNOMIAL_COEF_TYPE double
// type of coefficient arrays
#define POLYNOMIAL_COEFSARRAY_TYPE array_double
// prefix of coefficient array function names
#define POLYNOMIAL_COEFSARRAY_FUNC(NAME) array_double_ ## NAME
// set coefficient
#define POLYNOMIAL_COEF_SET(COEF, VAL) COEF=VAL
// set coefficient from signed int
#define POLYNOMIAL_COEF_SET_SI(COEF, VAL) COEF=(double)VAL
// set coefficient from unsigned int
#define POLYNOMIAL_COEF_SET_UI(COEF, VAL) COEF=(double)VAL
// copy coefficient
#define POLYNOMIAL_COEF_CPY(VAL, COEF) COEF=VAL
// copy coefficient from double
#define POLYNOMIAL_COEF_CPY_D(VAL, COEF) COEF=VAL
// add coefficients
#define POLYNOMIAL_COEF_ADD(COEF, VAL1, VAL2) COEF=VAL1+VAL2
// add coefficients, one of which is specified as a double
#define POLYNOMIAL_COEF_ADD_D(COEF, VAL1, VAL2) COEF=VAL1+VAL2
// multiply coefficients
#define POLYNOMIAL_COEF_MUL(COEF, VAL1, VAL2) COEF=VAL1*VAL2
// multiply coefficients, one of which is specified as a POLYNOMIAL_ORDER_TYPE
#define POLYNOMIAL_COEF_MUL_ORDER(COEF, VAL1, VAL2) COEF=VAL1*(double)VAL2
// divide coefficients, one of which is specified as an unsigned int
#define POLYNOMIAL_COEF_DIV_UI(COEF, VAL1, VAL2) COEF=VAL1/(double)VAL2
// power of a coefficient, specified as an unsigned int
#define POLYNOMIAL_COEF_POW_UI(COEF, VAL1, VAL2) COEF=pow(VAL1, (double)VAL2)
// print a coefficient
#define POLYNOMIAL_COEF_PRINT(COEF) fprint_double(stdout, COEF)
// type of the order
#define POLYNOMIAL_ORDER_TYPE unsigned int
// type of order arrays
#define POLYNOMIAL_ORDERSARRAY_TYPE array_uint
// prefix of order array function names
#define POLYNOMIAL_ORDERSARRAY_FUNC(NAME) array_uint_ ## NAME
// set order
#define POLYNOMIAL_ORDER_SET(ORDER, VAL) ORDER=VAL
// set order from unsigned int
#define POLYNOMIAL_ORDER_SET_UI(ORDER, VAL) ORDER=VAL
// copy order
#define POLYNOMIAL_ORDER_CPY(VAL, ORDER) ORDER=VAL
// copy order from unsigned int
#define POLYNOMIAL_ORDER_CPY_UI(VAL, ORDER) ORDER=VAL
// add orders
#define POLYNOMIAL_ORDER_ADD(ORDER, VAL1, VAL2) ORDER=VAL1+VAL2
// subtract an order and an unsigned integer
#define POLYNOMIAL_ORDER_SUB_UI(ORDER, VAL1, VAL2) ORDER=VAL1-VAL2
// compare orders (0 if equal, -1 if <, +1 if >)
#define POLYNOMIAL_ORDER_CMP(VAL1, VAL2) (int)VAL1-(int)VAL2
// compare orders, one of which is specified as an unsigned int (0 if equal, -1 if <, +1 if >)
#define POLYNOMIAL_ORDER_CMP_UI(VAL1, VAL2) (int)VAL1-(int)VAL2
// print orders
#define POLYNOMIAL_ORDER_PRINT(ORDER) printf("%u",ORDER)

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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.
*/
/*
Preprocessor macros for real polynomials with long double coefficients and unsigned integer powers
*/
// reset CPP macros
#undef POLYNOMIAL_TYPENAME
#undef POLYNOMIAL_FUNC
#undef POLYNOMIAL_COEF_TYPE
#undef POLYNOMIAL_COEFSARRAY_TYPE
#undef POLYNOMIAL_COEFSARRAY_FUNC
#undef POLYNOMIAL_COEF_INIT
#undef POLYNOMIAL_COEF_FREE
#undef POLYNOMIAL_COEF_SET
#undef POLYNOMIAL_COEF_SET_SI
#undef POLYNOMIAL_COEF_SET_UI
#undef POLYNOMIAL_COEF_CPY
#undef POLYNOMIAL_COEF_CPY_D
#undef POLYNOMIAL_COEF_ADD
#undef POLYNOMIAL_COEF_ADD_D
#undef POLYNOMIAL_COEF_MUL
#undef POLYNOMIAL_COEF_MUL_ORDER
#undef POLYNOMIAL_COEF_DIV_UI
#undef POLYNOMIAL_COEF_POW_UI
#undef POLYNOMIAL_COEF_PRINT
#undef POLYNOMIAL_ORDER_TYPE
#undef POLYNOMIAL_ORDERSARRAY_TYPE
#undef POLYNOMIAL_ORDERSARRAY_FUNC
#undef POLYNOMIAL_ORDER_INIT
#undef POLYNOMIAL_ORDER_FREE
#undef POLYNOMIAL_ORDER_SET
#undef POLYNOMIAL_ORDER_SET_UI
#undef POLYNOMIAL_ORDER_CPY
#undef POLYNOMIAL_ORDER_CPY_UI
#undef POLYNOMIAL_ORDER_ADD
#undef POLYNOMIAL_ORDER_SUB_UI
#undef POLYNOMIAL_ORDER_CMP
#undef POLYNOMIAL_ORDER_CMP_UI
#undef POLYNOMIAL_ORDER_PRINT
// name of the polynomial type
#define POLYNOMIAL_TYPENAME polynomial_ldouble
// prefix of function names
#define POLYNOMIAL_FUNC(NAME) polynomial_ldouble_ ## NAME
// type of the coefficient
#define POLYNOMIAL_COEF_TYPE long double
// type of coefficient arrays
#define POLYNOMIAL_COEFSARRAY_TYPE array_ldouble
// prefix of coefficient array function names
#define POLYNOMIAL_COEFSARRAY_FUNC(NAME) array_ldouble_ ## NAME
// set coefficient
#define POLYNOMIAL_COEF_SET(COEF, VAL) COEF=VAL
// set coefficient from signed int
#define POLYNOMIAL_COEF_SET_SI(COEF, VAL) COEF=(long double)VAL
// set coefficient from unsigned int
#define POLYNOMIAL_COEF_SET_UI(COEF, VAL) COEF=(long double)VAL
// copy coefficient
#define POLYNOMIAL_COEF_CPY(VAL, COEF) COEF=VAL
// copy coefficient from double
#define POLYNOMIAL_COEF_CPY_D(VAL, COEF) COEF=(long double)VAL
// add coefficients
#define POLYNOMIAL_COEF_ADD(COEF, VAL1, VAL2) COEF=VAL1+VAL2
// add coefficients, one of which is specified as a double
#define POLYNOMIAL_COEF_ADD_D(COEF, VAL1, VAL2) COEF=VAL1+(long double)VAL2
// multiply coefficients
#define POLYNOMIAL_COEF_MUL(COEF, VAL1, VAL2) COEF=VAL1*VAL2
// multiply coefficients, one of which is specified as a POLYNOMIAL_ORDER_TYPE
#define POLYNOMIAL_COEF_MUL_ORDER(COEF, VAL1, VAL2) COEF=VAL1*(long double)VAL2
// divide coefficients, one of which is specified as an unsigned int
#define POLYNOMIAL_COEF_DIV_UI(COEF, VAL1, VAL2) COEF=VAL1/(long double)VAL2
// power of a coefficient, specified as an unsigned int
#define POLYNOMIAL_COEF_POW_UI(COEF, VAL1, VAL2) COEF=powl(VAL1, (long double)VAL2)
// print a coefficient
#define POLYNOMIAL_COEF_PRINT(COEF) fprint_ldouble(stdout, COEF)
// type of the order
#define POLYNOMIAL_ORDER_TYPE unsigned int
// type of order arrays
#define POLYNOMIAL_ORDERSARRAY_TYPE array_uint
// prefix of order array function names
#define POLYNOMIAL_ORDERSARRAY_FUNC(NAME) array_uint_ ## NAME
// set order
#define POLYNOMIAL_ORDER_SET(ORDER, VAL) ORDER=VAL
// set order from unsigned int
#define POLYNOMIAL_ORDER_SET_UI(ORDER, VAL) ORDER=VAL
// copy order
#define POLYNOMIAL_ORDER_CPY(VAL, ORDER) ORDER=VAL
// copy order from unsigned int
#define POLYNOMIAL_ORDER_CPY_UI(VAL, ORDER) ORDER=VAL
// add orders
#define POLYNOMIAL_ORDER_ADD(ORDER, VAL1, VAL2) ORDER=VAL1+VAL2
// subtract an order and an unsigned integer
#define POLYNOMIAL_ORDER_SUB_UI(ORDER, VAL1, VAL2) ORDER=VAL1-VAL2
// compare orders (0 if equal, -1 if <, +1 if >)
#define POLYNOMIAL_ORDER_CMP(VAL1, VAL2) (int)VAL1-(int)VAL2
// compare orders, one of which is specified as an unsigned int (0 if equal, -1 if <, +1 if >)
#define POLYNOMIAL_ORDER_CMP_UI(VAL1, VAL2) (int)VAL1-(int)VAL2
// print orders
#define POLYNOMIAL_ORDER_PRINT(ORDER) printf("%u",ORDER)

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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.
*/
/*
Preprocessor macros for real polynomials with multi-precision float (mpfr) coefficients and unsigned integer powers
*/
// reset CPP macros
#undef POLYNOMIAL_TYPENAME
#undef POLYNOMIAL_FUNC
#undef POLYNOMIAL_COEF_TYPE
#undef POLYNOMIAL_COEFSARRAY_TYPE
#undef POLYNOMIAL_COEFSARRAY_FUNC
#undef POLYNOMIAL_COEF_INIT
#undef POLYNOMIAL_COEF_FREE
#undef POLYNOMIAL_COEF_SET
#undef POLYNOMIAL_COEF_SET_SI
#undef POLYNOMIAL_COEF_SET_UI
#undef POLYNOMIAL_COEF_CPY
#undef POLYNOMIAL_COEF_CPY_D
#undef POLYNOMIAL_COEF_ADD
#undef POLYNOMIAL_COEF_ADD_D
#undef POLYNOMIAL_COEF_MUL
#undef POLYNOMIAL_COEF_MUL_ORDER
#undef POLYNOMIAL_COEF_DIV_UI
#undef POLYNOMIAL_COEF_POW_UI
#undef POLYNOMIAL_COEF_PRINT
#undef POLYNOMIAL_ORDER_TYPE
#undef POLYNOMIAL_ORDERSARRAY_TYPE
#undef POLYNOMIAL_ORDERSARRAY_FUNC
#undef POLYNOMIAL_ORDER_INIT
#undef POLYNOMIAL_ORDER_FREE
#undef POLYNOMIAL_ORDER_SET
#undef POLYNOMIAL_ORDER_SET_UI
#undef POLYNOMIAL_ORDER_CPY
#undef POLYNOMIAL_ORDER_CPY_UI
#undef POLYNOMIAL_ORDER_ADD
#undef POLYNOMIAL_ORDER_SUB_UI
#undef POLYNOMIAL_ORDER_CMP
#undef POLYNOMIAL_ORDER_CMP_UI
#undef POLYNOMIAL_ORDER_PRINT
// name of the polynomial type
#define POLYNOMIAL_TYPENAME polynomial_mpfr
// prefix of function names
#define POLYNOMIAL_FUNC(NAME) polynomial_mpfr_ ## NAME
// type of the coefficient
#define POLYNOMIAL_COEF_TYPE mpfr_t
// type of coefficient arrays
#define POLYNOMIAL_COEFSARRAY_TYPE array_mpfr
// prefix of coefficient array function names
#define POLYNOMIAL_COEFSARRAY_FUNC(NAME) array_mpfr_ ## NAME
// init coefficient
#define POLYNOMIAL_COEF_INIT(VAR) mpfr_init(VAR)
// free coefficient
#define POLYNOMIAL_COEF_FREE(VAR) mpfr_clear(VAR)
// set coefficient
#define POLYNOMIAL_COEF_SET(COEF, VAL) COEF[0]=VAL[0]
// set coefficient from signed int
#define POLYNOMIAL_COEF_SET_SI(COEF, VAL) mpfr_set_si(COEF, VAL, MPFR_RNDN)
// set coefficient from unsigned int
#define POLYNOMIAL_COEF_SET_UI(COEF, VAL) mpfr_set_ui(COEF, VAL, MPFR_RNDN)
// copy coefficient
#define POLYNOMIAL_COEF_CPY(VAL, COEF) mpfr_init(COEF); mpfr_set(COEF, VAL, MPFR_RNDN)
// copy coefficient from double
#define POLYNOMIAL_COEF_CPY_D(VAL, COEF) mpfr_init(COEF); mpfr_set_d(COEF, VAL, MPFR_RNDN)
// add coefficients
#define POLYNOMIAL_COEF_ADD(COEF, VAL1, VAL2) mpfr_add(COEF, VAL1, VAL2, MPFR_RNDN)
// add coefficients, one of which is specified as a double
#define POLYNOMIAL_COEF_ADD_D(COEF, VAL1, VAL2) mpfr_add_d(COEF, VAL1, VAL2, MPFR_RNDN)
// multiply coefficients
#define POLYNOMIAL_COEF_MUL(COEF, VAL1, VAL2) mpfr_mul(COEF, VAL1, VAL2, MPFR_RNDN)
// multiply coefficients, one of which is specified as a POLYNOMIAL_ORDER_TYPE
#define POLYNOMIAL_COEF_MUL_ORDER(COEF, VAL1, VAL2) mpfr_mul_ui(COEF, VAL1, VAL2, MPFR_RNDN)
// divide coefficients, one of which is specified as an unsigned int
#define POLYNOMIAL_COEF_DIV_UI(COEF, VAL1, VAL2) mpfr_div_ui(COEF, VAL1, VAL2, MPFR_RNDN)
// power of a coefficient, specified as an unsigned int
#define POLYNOMIAL_COEF_POW_UI(COEF, VAL1, VAL2) mpfr_pow_ui(COEF, VAL1, VAL2, MPFR_RNDN)
// print a coefficient
#define POLYNOMIAL_COEF_PRINT(COEF) fprint_mpfr(stdout, COEF)
// type of the order
#define POLYNOMIAL_ORDER_TYPE unsigned int
// type of order arrays
#define POLYNOMIAL_ORDERSARRAY_TYPE array_uint
// prefix of order array function names
#define POLYNOMIAL_ORDERSARRAY_FUNC(NAME) array_uint_ ## NAME
// set order
#define POLYNOMIAL_ORDER_SET(ORDER, VAL) ORDER=VAL
// set order from unsigned int
#define POLYNOMIAL_ORDER_SET_UI(ORDER, VAL) ORDER=VAL
// copy order
#define POLYNOMIAL_ORDER_CPY(VAL, ORDER) ORDER=VAL
// copy order from unsigned int
#define POLYNOMIAL_ORDER_CPY_UI(VAL, ORDER) ORDER=VAL
// add orders
#define POLYNOMIAL_ORDER_ADD(ORDER, VAL1, VAL2) ORDER=VAL1+VAL2
// subtract an order and an unsigned integer
#define POLYNOMIAL_ORDER_SUB_UI(ORDER, VAL1, VAL2) ORDER=VAL1-VAL2
// compare orders (0 if equal, -1 if <, +1 if >)
#define POLYNOMIAL_ORDER_CMP(VAL1, VAL2) (int)VAL1-(int)VAL2
// compare orders, one of which is specified as an unsigned int (0 if equal, -1 if <, +1 if >)
#define POLYNOMIAL_ORDER_CMP_UI(VAL1, VAL2) (int)VAL1-(int)VAL2
// print orders
#define POLYNOMIAL_ORDER_PRINT(ORDER) printf("%u",ORDER)

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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.
*/
/*
Structure definition for real polynomials
see polynomial_*.h for the values taken by POLYNOMIAL_TYPENAME, etc...
*/
typedef struct POLYNOMIAL_TYPENAME {
POLYNOMIAL_COEFSARRAY_TYPE coefficients;
POLYNOMIAL_ORDERSARRAY_TYPE orders;
} POLYNOMIAL_TYPENAME;

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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.
*/
#include "root.h"
#include <mpfr.h>
#include <math.h>
#include "errors.h"
//--------------------------------------------------
//
// using doubles
//
//--------------------------------------------------
#include "root_double.h"
#include "root_base.c"
//--------------------------------------------------
//
// using long doubles
//
//--------------------------------------------------
#include "root_ldouble.h"
#include "root_base.c"
//--------------------------------------------------
//
// using mpfr floats
//
//--------------------------------------------------
#include "root_mpfr.h"
#include "root_base.c"

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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.
*/
/*
Root finding
*/
#ifndef LIBINUM_ROOT_H
#define LIBINUM_ROOT_H
#include "types.h"
//--------------------------------------------------
//
// using doubles
//
//--------------------------------------------------
#include "root_double.h"
#include "root_base.h"
//--------------------------------------------------
//
// using long doubles
//
//--------------------------------------------------
#include "root_ldouble.h"
#include "root_base.h"
//--------------------------------------------------
//
// using mpfr floats
//
//--------------------------------------------------
#include "root_mpfr.h"
#include "root_base.h"
#endif

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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 root finding
see integral_*.h for the values taken by ROOT_FUNC, etc...
*/
// compute the root of a real function of 1 variable using the Newton method
int ROOT_FUNC(root_newton_inplace) (ROOT_FLOAT_TYPE* out, int (*func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), int (*deriv_func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), ROOT_FLOAT_TYPE tolerance, unsigned int maxiter, void* extra_args){
unsigned int count=0;
ROOT_FLOAT_TYPE valf, valdf, delta, tmp;
int ret;
#ifdef ROOT_FLOAT_INIT
ROOT_FLOAT_INIT(valf);
ROOT_FLOAT_INIT(valdf);
ROOT_FLOAT_INIT(delta);
ROOT_FLOAT_INIT(tmp);
#endif
// evaluate at guess
ret=(*func)(&valf, *out, extra_args);
if(ret<0){
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
return(ret);
}
// check that valf is a number
if(! ROOT_FLOAT_ISNUMBER(valf)){
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
return(LIBINUM_ERROR_NAN);
}
ROOT_FLOAT_ABS(delta, valf);
// loop until tolerance is reached
while(ROOT_FLOAT_CMP(delta, tolerance) > 0 && count < maxiter){
// new guess
(*deriv_func)(&valdf, *out, extra_args);
if(ret<0){
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
return(ret);
}
// check that valdf is a number that is not 0
if(! ROOT_FLOAT_ISNUMBER(valdf) || ROOT_FLOAT_ISZERO(valdf)){
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
return(LIBINUM_ERROR_NAN);
}
ROOT_FLOAT_DIV(tmp, valf, valdf);
ROOT_FLOAT_SUB(*out, *out, tmp);
// evaluate at new guess
(*func)(&valf, *out, extra_args);
if(ret<0){
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
return(ret);
}
// check that valf is a number
if(! ROOT_FLOAT_ISNUMBER(valf)){
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
return(LIBINUM_ERROR_NAN);
}
ROOT_FLOAT_ABS(delta, valf);
// increase counter
count++;
}
// free variables
#ifdef ROOT_FLOAT_FREE
ROOT_FLOAT_FREE(valf);
ROOT_FLOAT_FREE(valdf);
ROOT_FLOAT_FREE(delta);
ROOT_FLOAT_FREE(tmp);
#endif
// fail if maxiter was reached
if(count==maxiter){
return(LIBINUM_ERROR_MAXITER);
}
return(0);
}
int ROOT_FUNC(root_newton) (ROOT_FLOAT_TYPE* out, int (*func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), int (*deriv_func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), ROOT_FLOAT_TYPE init, ROOT_FLOAT_TYPE tolerance, unsigned int maxiter, void* extra_args){
ROOT_FLOAT_SET(*out, init);
ROOT_FUNC(root_newton_inplace) (out, func, deriv_func, tolerance, maxiter, extra_args);
return(0);
}

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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 root finding
see integral_*.h for the values taken by ROOT_FUNC, etc...
*/
// compute the root of a real function of 1 variable using the Newton method
int ROOT_FUNC(root_newton_inplace) (ROOT_FLOAT_TYPE* out, int (*func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), int (*deriv_func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), ROOT_FLOAT_TYPE tolerance, unsigned int maxiter, void* extra_args);
int ROOT_FUNC(root_newton) (ROOT_FLOAT_TYPE* out, int (*func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), int (*deriv_func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), ROOT_FLOAT_TYPE init, ROOT_FLOAT_TYPE tolerance, unsigned int maxiter, void* extra_args);

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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.
*/
/*
Preprocessor macros for root finding using doubles
*/
// reset CPP macros
#undef ROOT_FUNC
#undef ROOT_FLOAT_TYPE
#undef ROOT_FLOAT_INIT
#undef ROOT_FLOAT_FREE
#undef ROOT_FLOAT_SET
#undef ROOT_FLOAT_SUB
#undef ROOT_FLOAT_DIV
#undef ROOT_FLOAT_CMP
#undef ROOT_FLOAT_ABS
#undef ROOT_FLOAT_ISNUMBER
#undef ROOT_FLOAT_ISZERO
// suffix of function names
#define ROOT_FUNC(NAME) NAME ## _double
// type of floats
#define ROOT_FLOAT_TYPE double
// set float
#define ROOT_FLOAT_SET(FLOAT, VAL) FLOAT=VAL
// subtract floats
#define ROOT_FLOAT_SUB(FLOAT, VAL1, VAL2) FLOAT=VAL1-VAL2
// divide floats
#define ROOT_FLOAT_DIV(FLOAT, VAL1, VAL2) FLOAT=VAL1/VAL2
// compare floats (0 if equal, -1 if <, +1 if >)
#define ROOT_FLOAT_CMP(VAL1, VAL2) VAL1-VAL2
// abs of float
#define ROOT_FLOAT_ABS(FLOAT, VAL) FLOAT=fabs(VAL)
// check whether a float is a regular number
#define ROOT_FLOAT_ISNUMBER(FLOAT) (fpclassify(FLOAT)>=FP_ZERO)
// whether float is 0
#define ROOT_FLOAT_ISZERO(VAL) (VAL==0.)

55
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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.
*/
/*
Preprocessor macros for root finding using long doubles
*/
// reset CPP macros
#undef ROOT_FUNC
#undef ROOT_FLOAT_TYPE
#undef ROOT_FLOAT_INIT
#undef ROOT_FLOAT_FREE
#undef ROOT_FLOAT_SET
#undef ROOT_FLOAT_SUB
#undef ROOT_FLOAT_DIV
#undef ROOT_FLOAT_CMP
#undef ROOT_FLOAT_ABS
#undef ROOT_FLOAT_ISNUMBER
#undef ROOT_FLOAT_ISZERO
// suffix of function names
#define ROOT_FUNC(NAME) NAME ## _ldouble
// type of floats
#define ROOT_FLOAT_TYPE long double
// set float
#define ROOT_FLOAT_SET(FLOAT, VAL) FLOAT=VAL
// subtract floats
#define ROOT_FLOAT_SUB(FLOAT, VAL1, VAL2) FLOAT=VAL1-VAL2
// divide floats
#define ROOT_FLOAT_DIV(FLOAT, VAL1, VAL2) FLOAT=VAL1/VAL2
// compare floats (0 if equal, -1 if <, +1 if >)
#define ROOT_FLOAT_CMP(VAL1, VAL2) VAL1-VAL2
// abs of float
#define ROOT_FLOAT_ABS(FLOAT, VAL) FLOAT=fabsl(VAL)
// check whether a float is a regular number
#define ROOT_FLOAT_ISNUMBER(FLOAT) (fpclassify(FLOAT)>=FP_ZERO)
// whether float is 0
#define ROOT_FLOAT_ISZERO(VAL) (VAL==0.)

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