fix modf error
This commit is contained in:
10
README.md
10
README.md
@@ -89,11 +89,15 @@ finding the square root of x
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## dichotomy method
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## dichotomy method
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the dichotomie method, or binary search, consist on dividing the range of research by 2 each time, and choosing the right one for the next iteration.
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Ex :
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```
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```
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solution
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solution
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↓
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↓
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|------------------------------ 1. define range bound_1 : 0
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|------------------------------ 1. define range bound_1 : 0
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|-----------------------------| 2. choose range bound_2 : x
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|-----------------------------| 2. define range bound_2 : x
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|--------------+--------------| 3. take mid : (bound_1 + bound_2) / 2
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|--------------+--------------| 3. take mid : (bound_1 + bound_2) / 2
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|--------------|-------ø------| 4. choose range bound : bound_1 or bound_2
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|--------------|-------ø------| 4. choose range bound : bound_1 or bound_2
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@@ -123,7 +127,9 @@ finding the square root of x
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## Newton–Raphson method
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## Newton–Raphson method
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it's like a self-correcting binary search, we get rid of the step "choose range" :
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it's like a self-correcting binary search, we get rid of the step "choose range", we use the formulae `x/v` to find the next range, with `x` being the number we are trying to get the sqaure root from, and `v` the value found at the previous step.
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Ex :
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```
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```
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solution
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solution
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@@ -122,6 +122,8 @@ typedef enum
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typedef struct
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typedef struct
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{
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{
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double a; // a in "ax + b"
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double b; // b in "ax + b"
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int solution_gcd; // gcd(b, a)
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int solution_gcd; // gcd(b, a)
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int solution_numerator; // -b / gcd
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int solution_numerator; // -b / gcd
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int solution_denominator; // a / gcd
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int solution_denominator; // a / gcd
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@@ -130,6 +132,9 @@ typedef struct
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typedef struct
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typedef struct
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{
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{
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double a; // a in "ax² + bx + c"
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double b; // b in "ax² + bx + c"
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double c; // c in "ax² + bx + c"
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e_delta_sign delta_sign; // DELTA_PLUS or DELTA_MINUS or DELTA_ZERO
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e_delta_sign delta_sign; // DELTA_PLUS or DELTA_MINUS or DELTA_ZERO
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double delta_absolute; // |Δ| == |b² - 4ac|
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double delta_absolute; // |Δ| == |b² - 4ac|
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double delta_sqrt; // √|Δ|
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double delta_sqrt; // √|Δ|
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2
libft
2
libft
Submodule libft updated: ae9787ba6d...60c72d7560
@@ -103,6 +103,10 @@ static void solve_degree_2(s_solution_degree_2 *solution, double a, double b, do
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{
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{
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double delta;
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double delta;
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solution->a = a;
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solution->b = b;
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solution->c = c;
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delta = b * b - 4 * a * c;
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delta = b * b - 4 * a * c;
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solution->delta_sign = ft_fsign(delta);
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solution->delta_sign = ft_fsign(delta);
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solution->delta_absolute = ft_fabs(delta);
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solution->delta_absolute = ft_fabs(delta);
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@@ -115,7 +119,7 @@ static void solve_degree_2(s_solution_degree_2 *solution, double a, double b, do
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solution->first_term = -b / (2 * a);
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solution->first_term = -b / (2 * a);
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// second term
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// second term
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// solution->second_term_gcd = find_gcd(b, 2 * a);
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solution->second_term_gcd = find_gcd(solution->delta_sqrt, 2 * a);
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// solution->second_term_numerator = ;
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// solution->second_term_numerator = ;
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// solution->second_term_denominator = ;
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// solution->second_term_denominator = ;
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// solution->second_term = ;
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// solution->second_term = ;
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@@ -76,22 +76,29 @@ static void print_context_solution()
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if (solution_g_err->degree == 2)
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if (solution_g_err->degree == 2)
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{
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{
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solution_2 = solution_g_err->solution_degree_2;
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solution_2 = solution_g_err->solution_degree_2;
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dprintf(STDERR_FILENO, "degree 2 : delta > 0 ( -b/2a +- √Δ/2a )\n");
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dprintf(STDERR_FILENO, "degree 2 : delta > 0 ( -b / 2a +- √Δ / 2a )\n");
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dprintf(STDERR_FILENO, " delta == 0 ( -b/2a )\n");
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dprintf(STDERR_FILENO, " delta == 0 ( -b / 2a )\n");
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dprintf(STDERR_FILENO, " delta < 0 ( -b/2a +- i√|Δ|/2a )\n");
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dprintf(STDERR_FILENO, " delta < 0 ( -b / 2a +- i√|Δ| / 2a )\n");
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dprintf(STDERR_FILENO, "delta_sign : %25s\n", delta_sign_to_str(solution_2.delta_sign));
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dprintf(STDERR_FILENO, "delta_absolute : %25g ( |Δ| == |b² - 4ac| )\n", solution_2.delta_absolute);
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dprintf(STDERR_FILENO, "a : %15g\n", solution_2.a);
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dprintf(STDERR_FILENO, "delta_sqrt : %25g (√|Δ| )\n", solution_2.delta_sqrt);
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dprintf(STDERR_FILENO, "b : %15g\n", solution_2.b);
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dprintf(STDERR_FILENO, "first_term_gcd : %25i\n", solution_2.first_term_gcd);
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dprintf(STDERR_FILENO, "c : %15g\n", solution_2.c);
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dprintf(STDERR_FILENO, "first_term_numerator : %25i (-b / gcd )\n", solution_2.first_term_numerator);
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dprintf(STDERR_FILENO, "first_term_denominator : %25i (2a / gcd )\n", solution_2.first_term_denominator);
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dprintf(STDERR_FILENO, "delta_sign : %15s\n", delta_sign_to_str(solution_2.delta_sign));
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dprintf(STDERR_FILENO, "first_term : %25g (-b / 2a )\n", solution_2.first_term);
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dprintf(STDERR_FILENO, "delta_absolute : %15g ( |Δ| == |b² - 4ac| )\n", solution_2.delta_absolute);
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// dprintf(STDERR_FILENO, "second_term_gcd : %25g\n", solution_2.second_term_gcd);
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dprintf(STDERR_FILENO, "delta_sqrt : %15g ( √|Δ| )\n", solution_2.delta_sqrt);
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// dprintf(STDERR_FILENO, "second_term_numerator : %25g\n", solution_2.second_term_numerator);
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// dprintf(STDERR_FILENO, "second_term_denominator: %25g\n", solution_2.second_term_denominator);
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dprintf(STDERR_FILENO, "first_term_gcd : %15i\n", solution_2.first_term_gcd);
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// dprintf(STDERR_FILENO, "second_term : %25g\n", solution_2.second_term);
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dprintf(STDERR_FILENO, "first_term_numerator : %15i ( -b / gcd )\n", solution_2.first_term_numerator);
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// dprintf(STDERR_FILENO, "solution1 : %25g\n", solution_2.solution1);
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dprintf(STDERR_FILENO, "first_term_denominator : %15i ( 2a / gcd )\n", solution_2.first_term_denominator);
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// dprintf(STDERR_FILENO, "solution2 : %25g\n", solution_2.solution2);
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dprintf(STDERR_FILENO, "first_term : %15g ( -b / 2a )\n", solution_2.first_term);
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dprintf(STDERR_FILENO, "second_term_gcd : %15i\n", solution_2.second_term_gcd);
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// dprintf(STDERR_FILENO, "second_term_numerator : %15g\n", solution_2.second_term_numerator);
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// dprintf(STDERR_FILENO, "second_term_denominator: %15g\n", solution_2.second_term_denominator);
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// dprintf(STDERR_FILENO, "second_term : %15g\n", solution_2.second_term);
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// dprintf(STDERR_FILENO, "solution1 : %15g\n", solution_2.solution1);
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// dprintf(STDERR_FILENO, "solution2 : %15g\n", solution_2.solution2);
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}
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}
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ft_putchar_fd('\n', STDERR_FILENO);
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ft_putchar_fd('\n', STDERR_FILENO);
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