6663b6c9
 adorian
projet complet av...
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extern "C" {
#include <assert.h>
#include <string.h>
#include <float.h>
}
#include <poincare/division.h>
#include <poincare/power.h>
#include <poincare/rational.h>
#include <poincare/tangent.h>
#include <poincare/multiplication.h>
#include <poincare/opposite.h>
#include "layout/fraction_layout.h"
#include <cmath>
namespace Poincare {
Expression::Type Division::type() const {
return Type::Division;
}
Expression * Division::clone() const {
return new Division(m_operands, true);
}
bool Division::needParenthesisWithParent(const Expression * e) const {
Type types[] = {Type::Division, Type::Power, Type::Factorial};
return e->isOfType(types, 3);
}
Expression * Division::shallowReduce(Context& context, AngleUnit angleUnit) {
Expression * e = Expression::shallowReduce(context, angleUnit);
if (e != this) {
return e;
}
Power * p = new Power(operand(1), new Rational(-1), false);
Multiplication * m = new Multiplication(operand(0), p, false);
detachOperands();
p->shallowReduce(context, angleUnit);
replaceWith(m, true);
return m->shallowReduce(context, angleUnit);
}
template<typename T>
Complex<T> Division::compute(const Complex<T> c, const Complex<T> d) {
/* We want to avoid multiplies in the middle of the calculation that could
* overflow.
* aa, ab, ba, bb, min, max = |d.a| <= |d.b| ? (c.a, c.b, -c.a, c.b, d.a, d.b)
* : (c.b, c.a, c.b, -c.a, d.b, d.a)
* c c.a+c.b*i d.a-d.b*i 1/max (c.a+c.b*i) * (d.a-d.b*i) / max
* - == --------- * --------- * ----- == -------------------------------
* d d.a+d.b*i d.a-d.b*i 1/max (d.a+d.b*i) * (d.a-d.b*i) / max
* (c.a*d.a - c.a*d.b*i + c.b*i*d.a - c.b*i*d.b*i) / max
* == -----------------------------------------------------
* (d.a*d.a - d.a*d.b*i + d.b*i*d.a - d.b*i*d.b*i) / max
* (c.a*d.a - c.b*d.b*i^2 + c.b*d.b*i - c.a*d.a*i) / max
* == -----------------------------------------------------
* (d.a*d.a - d.b*d.b*i^2) / max
* (c.a*d.a/max + c.b*d.b/max) + (c.b*d.b/max - c.a*d.a/max)*i
* == -----------------------------------------------------------
* d.a^2/max + d.b^2/max
* aa*min/max + ab*max/max bb*min/max + ba*max/max
* == ----------------------- + -----------------------*i
* min^2/max + max^2/max min^2/max + max^2/max
* min/max*aa + ab min/max*bb + ba
* == ----------------- + -----------------*i
* min/max*min + max min/max*min + max
* |min| <= |max| => |min/max| <= 1
* => |min/max*x| <= |x|
* => |min/max*x+y| <= |x|+|y|
* So the calculation is guaranteed to not overflow until the last divides as
* long as none of the input values have the representation's maximum exponent.
* Plus, the method does not propagate any error on real inputs: temp = 0,
* norm = d.a and then result = c.a/d.a. */
T aa = c.a(), ab = c.b(), ba = -aa, bb = ab;
T min = d.a(), max = d.b();
if (std::fabs(max) < std::fabs(min)) {
T temp = min;
min = max;
max = temp;
temp = aa;
aa = ab;
ab = temp;
temp = ba;
ba = bb;
bb = temp;
}
T temp = min/max;
T norm = temp*min + max;
return Complex<T>::Cartesian((temp*aa + ab) / norm, (temp*bb + ba) / norm);
}
ExpressionLayout * Division::privateCreateLayout(FloatDisplayMode floatDisplayMode, ComplexFormat complexFormat) const {
assert(floatDisplayMode != FloatDisplayMode::Default);
assert(complexFormat != ComplexFormat::Default);
const Expression * numerator = operand(0)->type() == Type::Parenthesis ? operand(0)->operand(0) : operand(0);
const Expression * denominator = operand(1)->type() == Type::Parenthesis ? operand(1)->operand(0) : operand(1);
return new FractionLayout(numerator->createLayout(floatDisplayMode, complexFormat), denominator->createLayout(floatDisplayMode, complexFormat));
}
template<typename T> Matrix * Division::computeOnComplexAndMatrix(const Complex<T> * c, const Matrix * n) {
Matrix * inverse = n->createInverse<T>();
if (inverse == nullptr) {
return nullptr;
}
Matrix * result = Multiplication::computeOnComplexAndMatrix<T>(c, inverse);
delete inverse;
return result;
}
template<typename T> Matrix * Division::computeOnMatrices(const Matrix * m, const Matrix * n) {
if (m->numberOfColumns() != n->numberOfColumns()) {
return nullptr;
}
Matrix * inverse = n->createInverse<T>();
if (inverse == nullptr) {
return nullptr;
}
Matrix * result = Multiplication::computeOnMatrices<T>(m, inverse);
delete inverse;
return result;
}
}
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