Skip to content

Increased precision for trigonometric functions #22

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
GYuvanShankar wants to merge 2 commits into
base: master
Choose a base branch
from
Open

Increased precision for trigonometric functions #22

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
0f63a2b
Changed initial guess of Newtons Square Root Method
GYuvanShankar Dec 25, 2021
3a3b491
Increased precision, other minor changes
GYuvanShankar Jan 17, 2022
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
66 changes: 34 additions & 32 deletions include/real/real_data.hpp
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -422,8 +422,9 @@ namespace boost {
* will change once, so we will different signs of derivative on upper and lower bound. If there are both minima and maxima,
* sign of derivative will change twice, so at the end, sign of derivative in both upper and lower bound will remain same.
**/
auto [sin_lower, cos_lower] = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
auto [sin_upper, cos_upper] = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
exact_number<T> sin_lower,sin_upper,cos_lower,cos_upper;
std::tie(sin_lower, cos_lower) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
std::tie(sin_upper, cos_upper) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
if(ro.get_lhs_itr().get_interval().upper_bound - ro.get_lhs_itr().get_interval().lower_bound >= literals::four_exact<T>){
/**
* If sign of derivative, which cos(x), if it is same for both upper and lower bound. Then we will return
Expand Down Expand Up @@ -537,8 +538,9 @@ namespace boost {
* will change once, so we will different signs of derivative on upper and lower bound. If there are both minima and maxima,
* sign of derivative will change twice, so at the end, sign of derivative in both upper and lower bound will remain same.
**/
auto [sin_lower, cos_lower] = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
auto [sin_upper, cos_upper] = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
exact_number<T> sin_lower,sin_upper,cos_lower,cos_upper;
std::tie(sin_lower, cos_lower) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
std::tie(sin_upper, cos_upper) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
if(ro.get_lhs_itr().get_interval().upper_bound - ro.get_lhs_itr().get_interval().lower_bound >= literals::four_exact<T>){
/**
* If sign of derivative, which -sin(x), if it is same for both upper and lower bound. Then we will return
Expand Down Expand Up @@ -641,8 +643,8 @@ namespace boost {
iterate_again = true;
}
else{
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
/**
* Now if difference between lower and upper bounds of interval is less than 4, then there can exist 0,1 or 2 minima/maxima points.
* First we will check whether the sign of cos(x) from lower to upper bound is changed or not, if it is, then we have one point
Expand Down Expand Up @@ -700,8 +702,8 @@ namespace boost {
iterate_again = true;
}
else{
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
/**
* Now if difference between lower and upper bounds of interval is less than 4, then there can exist 0,1 or 2 minima/maxima points.
* First we will check whether the sign of sin(x) from lower to upper bound is changed or not, if it is, then we have one point
Expand Down Expand Up @@ -761,8 +763,8 @@ namespace boost {
iterate_again = true;
}
else{
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
/**
* Now if difference between lower and upper bounds of interval is less than 4, then there can exist 0,1 or 2 minima/maxima points.
* First we will check whether the sign of cos(x) from lower to upper bound is changed or not, if it is, then we have one point
Expand Down Expand Up @@ -862,8 +864,8 @@ namespace boost {
iterate_again = true;
}
else{
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
std::tie(sin_lower_tmp, cos_lower_tmp) = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
std::tie(sin_upper_tmp, cos_upper_tmp) = sin_cos(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
/**
* Now if difference between lower and upper bounds of interval is less than 4, then there can exist 0,1 or 2 minima/maxima points.
* First we will check whether the sign of sin(x) from lower to upper bound is changed or not, if it is, then we have one point
Expand Down Expand Up @@ -975,9 +977,9 @@ namespace boost {

// asin is an increasing function in its domain
this->_approximation_interval.lower_bound =
sin_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
sin_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
this->_approximation_interval.upper_bound =
sin_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
sin_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
break;
}

Expand All @@ -1003,27 +1005,27 @@ namespace boost {

// acos is a decreasing function in its domain
this->_approximation_interval.lower_bound =
cos_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, false);
cos_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, false);
this->_approximation_interval.upper_bound =
cos_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, true);
cos_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, true);
break;
}

case OPERATION::ATAN :{
// atan is an increasing function in its domain
this->_approximation_interval.lower_bound =
tan_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
tan_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
this->_approximation_interval.upper_bound =
tan_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
tan_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
break;
}

case OPERATION::ACOT :{
// acot is a decreasing function in its domain
this->_approximation_interval.lower_bound =
cot_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, false);
cot_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, false);
this->_approximation_interval.upper_bound =
cot_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, true);
cot_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, true);
break;
}

Expand All @@ -1049,9 +1051,9 @@ namespace boost {

// asec is an increasing function in its domain
this->_approximation_interval.lower_bound =
sec_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false);
sec_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, false);
this->_approximation_interval.upper_bound =
sec_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, true);
sec_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, true);
break;
}

Expand All @@ -1077,9 +1079,9 @@ namespace boost {

// acosec is a decreasing function in its domain
this->_approximation_interval.lower_bound =
cosec_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision, false);
cosec_inverse(ro.get_lhs_itr().get_interval().upper_bound.up_to(_precision, true), _precision+4, false);
this->_approximation_interval.upper_bound =
cosec_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, true);
cosec_inverse(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision+4, true);
break;
}

Expand Down Expand Up @@ -1133,7 +1135,7 @@ namespace boost {
numerator = ro.get_lhs_itr().get_interval().upper_bound;
denominator = ro.get_rhs_itr().get_interval().upper_bound;
}
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision, deviation_upper_boundary);
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_upper_boundary);

// Lower Boundary
if (ro.get_lhs_itr().get_interval().positive()) {
Expand All @@ -1145,7 +1147,7 @@ namespace boost {
numerator = ro.get_lhs_itr().get_interval().lower_bound;
denominator = ro.get_rhs_itr().get_interval().lower_bound;
}
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision, deviation_lower_boundary);
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_lower_boundary);
}
else {
// x < 0, atan2 is dicontinuous along negative x-axis
Expand Down Expand Up @@ -1174,19 +1176,19 @@ namespace boost {
deviation_upper_boundary = false;
numerator = ro.get_lhs_itr().get_interval().lower_bound;
denominator = ro.get_rhs_itr().get_interval().lower_bound;
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision, deviation_upper_boundary);
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_upper_boundary);

// Lower Boundary
if (ro.get_rhs_itr().get_interval().negative()) {
deviation_lower_boundary = true;
numerator = ro.get_lhs_itr().get_interval().upper_bound;
denominator = ro.get_rhs_itr().get_interval().upper_bound;
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision, deviation_lower_boundary);
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_lower_boundary);
} else {
deviation_lower_boundary = true;
numerator = ro.get_lhs_itr().get_interval().lower_bound;
denominator = ro.get_rhs_itr().get_interval().upper_bound;
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision, deviation_lower_boundary);
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_lower_boundary);
}
}
else {
Expand All @@ -1197,19 +1199,19 @@ namespace boost {
deviation_upper_boundary = true;
numerator = ro.get_lhs_itr().get_interval().lower_bound;
denominator = ro.get_rhs_itr().get_interval().upper_bound;
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision, deviation_upper_boundary);
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_upper_boundary);
} else {
deviation_upper_boundary = true;
numerator = ro.get_lhs_itr().get_interval().upper_bound;
denominator = ro.get_rhs_itr().get_interval().upper_bound;
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision, deviation_upper_boundary);
this->_approximation_interval.upper_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_upper_boundary);
}

// Lower Boundary
deviation_lower_boundary = false;
numerator = ro.get_lhs_itr().get_interval().upper_bound;
denominator = ro.get_rhs_itr().get_interval().lower_bound;
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision, deviation_lower_boundary);
this->_approximation_interval.lower_bound = tan2_inverse(numerator, denominator, _precision+4, deviation_lower_boundary);
}
}

Expand Down