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c7b758f536
Because of the limitations of the floating-point representation, e^x is null for x <= 710, causing the nextRoot functions to find roots for it. To prevent this, we looking for places where a function changes sign, we actually require the function to take two non-null values of different signs.
294 lines
12 KiB
C++
294 lines
12 KiB
C++
#include <apps/shared/global_context.h>
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#include "helper.h"
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using namespace Poincare;
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enum class PointOfInterestType {
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Maximum,
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Minimum,
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Root,
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Intersection,
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};
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bool doubles_are_approximately_equal(double d1, double d2) {
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bool d2IsNaN = std::isnan(d2);
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if (std::isnan(d1)) {
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return d2IsNaN;
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}
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if (d2IsNaN) {
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return false;
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}
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return std::abs(d1-d2) < 0.00001;
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}
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void assert_points_of_interest_are(
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PointOfInterestType type,
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int numberOfPointsOfInterest,
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Coordinate2D<double> * pointsOfInterest,
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const char * expression1,
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const char * expression2,
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const char * symbol,
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double start,
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double step,
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double max,
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Preferences::ComplexFormat complexFormat = Preferences::ComplexFormat::Real,
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Preferences::AngleUnit angleUnit = Preferences::AngleUnit::Degree)
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{
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Shared::GlobalContext context;
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Poincare::Expression e1 = parse_expression(expression1, &context, false);
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Poincare::Expression e2;
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if (expression2) {
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assert(type == PointOfInterestType::Intersection);
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e2 = parse_expression(expression2, &context, false);
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}
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for (int i = 0; i < numberOfPointsOfInterest; i++) {
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quiz_assert_log_if_failure(!std::isnan(start), e1);
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Coordinate2D<double> nextPointOfInterest;
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if (type == PointOfInterestType::Maximum) {
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nextPointOfInterest = e1.nextMaximum(symbol, start, step, max, &context, complexFormat, angleUnit);
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} else if (type == PointOfInterestType::Minimum) {
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nextPointOfInterest = e1.nextMinimum(symbol, start, step, max, &context, complexFormat, angleUnit);
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} else if (type == PointOfInterestType::Root) {
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nextPointOfInterest = Coordinate2D<double>(e1.nextRoot(symbol, start, step, max, &context, complexFormat, angleUnit), 0.0);
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} else if (type == PointOfInterestType::Intersection) {
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nextPointOfInterest = e1.nextIntersection(symbol, start, step, max, &context, complexFormat, angleUnit, e2);
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}
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quiz_assert_log_if_failure(
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doubles_are_approximately_equal(pointsOfInterest[i].x1(), nextPointOfInterest.x1()) &&
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doubles_are_approximately_equal(pointsOfInterest[i].x2(), nextPointOfInterest.x2()),
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e1);
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start = nextPointOfInterest.x1() + step;
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}
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}
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QUIZ_CASE(poincare_function_extremum) {
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{
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{
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constexpr int numberOfMaxima = 3;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(0.0, 1.0),
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Coordinate2D<double>(360.0, 1.0),
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Coordinate2D<double>(NAN, NAN)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "cos(a)", nullptr, "a", -1.0, 0.1, 500.0);
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}
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{
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constexpr int numberOfMaxima = 3;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(360.0, 1.0),
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Coordinate2D<double>(0.0, 1.0),
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Coordinate2D<double>(NAN, NAN)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "cos(a)", nullptr, "a", 500.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(180.0, -1.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "cos(a)", nullptr, "a", 0.0, 0.1, 300.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(180.0, -1.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "cos(a)", nullptr, "a", 300.0, -0.1, 0.0);
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}
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}
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{
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{
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constexpr int numberOfMaxima = 1;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(NAN, NAN)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "a^2", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfMaxima = 1;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(NAN, NAN)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "a^2", nullptr, "a", 100.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(0.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "a^2", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(0.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "a^2", nullptr, "a", 100.0, -0.1, -1.0);
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}
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}
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{
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{
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constexpr int numberOfMaxima = 1;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(NAN, 3.0)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "3", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfMaxima = 1;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(NAN, 3.0)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "3", nullptr, "a", 100.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(NAN, 3.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "3", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(NAN, 3.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "3", nullptr, "a", 100.0, -0.1, -1.0);
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}
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}
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{
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{
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constexpr int numberOfMaxima = 1;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "0", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfMaxima = 1;
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Coordinate2D<double> maxima[numberOfMaxima] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Maximum, numberOfMaxima, maxima, "0", nullptr, "a", 100.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "0", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfMinima = 1;
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Coordinate2D<double> minima[numberOfMinima] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Minimum, numberOfMinima, minima, "0", nullptr, "a", 100.0, -0.1, -1.0);
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}
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}
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}
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QUIZ_CASE(poincare_function_root) {
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{
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constexpr int numberOfRoots = 3;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(90.0, 0.0),
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Coordinate2D<double>(270.0, 0.0),
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Coordinate2D<double>(450.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "cos(a)", nullptr, "a", 0.0, 0.1, 500.0);
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}
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{
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constexpr int numberOfRoots = 3;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(450.0, 0.0),
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Coordinate2D<double>(270.0, 0.0),
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Coordinate2D<double>(90.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "cos(a)", nullptr, "a", 500.0, -0.1, 0.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(0.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "a^2", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(0.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "a^2", nullptr, "a", 100.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfRoots = 2;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(-2.0, 0.0),
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Coordinate2D<double>(2.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "a^2-4", nullptr, "a", -5.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfRoots = 2;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(2.0, 0.0),
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Coordinate2D<double>(-2.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "a^2-4", nullptr, "a", 100.0, -0.1, -5.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "3", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "3", nullptr, "a", 100.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(-0.9, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "0", nullptr, "a", -1.0, 0.1, 100.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(99.9, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "0", nullptr, "a", 100.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfRoots = 1;
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Coordinate2D<double> roots[numberOfRoots] = {
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Coordinate2D<double>(NAN, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Root, numberOfRoots, roots, "ℯ^x", nullptr, "a", -1000.0, 0.1, -800);
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}
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}
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QUIZ_CASE(poincare_function_intersection) {
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{
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constexpr int numberOfIntersections = 1;
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Coordinate2D<double> intersections[numberOfIntersections] = {
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Coordinate2D<double>(NAN, NAN)};
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assert_points_of_interest_are(PointOfInterestType::Intersection, numberOfIntersections, intersections, "cos(a)", "2", "a", -1.0, 0.1, 500.0);
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}
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{
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constexpr int numberOfIntersections = 1;
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Coordinate2D<double> intersections[numberOfIntersections] = {
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Coordinate2D<double>(NAN, NAN)};
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assert_points_of_interest_are(PointOfInterestType::Intersection, numberOfIntersections, intersections, "cos(a)", "2", "a", 500.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfIntersections = 2;
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Coordinate2D<double> intersections[numberOfIntersections] = {
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Coordinate2D<double>(0.0, 1.0),
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Coordinate2D<double>(360.0, 1.0)};
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assert_points_of_interest_are(PointOfInterestType::Intersection, numberOfIntersections, intersections, "cos(a)", "1", "a", -1.0, 0.1, 500.0);
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}
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{
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constexpr int numberOfIntersections = 2;
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Coordinate2D<double> intersections[numberOfIntersections] = {
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Coordinate2D<double>(360.0, 1.0),
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Coordinate2D<double>(0.0, 1.0)};
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assert_points_of_interest_are(PointOfInterestType::Intersection, numberOfIntersections, intersections, "cos(a)", "1", "a", 500.0, -0.1, -1.0);
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}
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{
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constexpr int numberOfIntersections = 3;
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Coordinate2D<double> intersections[numberOfIntersections] = {
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Coordinate2D<double>(90.0, 0.0),
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Coordinate2D<double>(270.0, 0.0),
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Coordinate2D<double>(450.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Intersection, numberOfIntersections, intersections, "cos(a)", "0", "a", -1.0, 0.1, 500.0);
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}
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{
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constexpr int numberOfIntersections = 3;
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Coordinate2D<double> intersections[numberOfIntersections] = {
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Coordinate2D<double>(450.0, 0.0),
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Coordinate2D<double>(270.0, 0.0),
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Coordinate2D<double>(90.0, 0.0)};
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assert_points_of_interest_are(PointOfInterestType::Intersection, numberOfIntersections, intersections, "cos(a)", "0", "a", 500.0, -0.1, -1.0);
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}
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}
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