Initial commit

doc/libinum-examples/Makefile

@@ -0,0 +1,80 @@
+# 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)

doc/libinum-examples/src/integral_gauss-legendre.c

@@ -0,0 +1,92 @@
+#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);
+}

doc/libinum-examples/src/root_newton.c

@@ -0,0 +1,58 @@
+#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);
+}