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Reduce the argument of sin, cos and tan exactly and round once #1475

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Merged
mborland merged 1 commit into from
Sep 29, 2026
Merged

Reduce the argument of sin, cos and tan exactly and round once #1475

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96 changes: 16 additions & 80 deletions include/boost/decimal/detail/cmath/cos.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -7,18 +7,17 @@
#define BOOST_DECIMAL_DETAIL_CMATH_COS_HPP

#include <boost/decimal/fwd.hpp>
#include <boost/decimal/numbers.hpp>
#include <boost/decimal/detail/type_traits.hpp>
#include <boost/decimal/detail/concepts.hpp>
#include <boost/decimal/detail/config.hpp>
#include <boost/decimal/detail/cmath/cos.hpp>
#include <boost/decimal/detail/cmath/remquo.hpp>
#include <boost/decimal/detail/promotion.hpp>
#include <boost/decimal/detail/cmath/impl/trig_reduce.hpp>
#include <boost/decimal/detail/cmath/impl/sin_impl.hpp>
#include <boost/decimal/detail/cmath/impl/cos_impl.hpp>

#ifndef BOOST_DECIMAL_BUILD_MODULE
#include <limits>
#include <type_traits>
#include <cstdint>
#endif

namespace boost {
Expand All @@ -30,90 +29,27 @@ template <typename T>
constexpr auto cos_impl(const T x) noexcept
BOOST_DECIMAL_REQUIRES(detail::is_decimal_floating_point_v, T)
{
T result { };

#ifndef BOOST_DECIMAL_FAST_MATH
const auto fpc = fpclassify(x);

// First check non-finite values and small angles

if ((fpc == FP_INFINITE) || (fpc == FP_NAN))
if (isnan(x))
{
result = x;
return x;
}
else
#endif
if (signbit(x))
if (isinf(x))
{
result = cos(-x);
return std::numeric_limits<T>::quiet_NaN();
}
else
{
if (x > std::numeric_limits<T>::epsilon())
{
// Perform argument reduction and subsequent scaling of the result.

// Given x = k * (pi/2) + r, compute n = (k % 4).

// | n | sin(x) | cos(x) | sin(x)/cos(x) |
// |----------------------------------------|
// | 0 | sin(r) | cos(r) | sin(r)/cos(r) |
// | 1 | cos(r) | -sin(r) | -cos(r)/sin(r) |
// | 2 | -sin(r) | -cos(r) | sin(r)/cos(r) |
// | 3 | -cos(r) | sin(r) | -cos(r)/sin(r) |

const T two_x = x * 2;

const auto k = static_cast<unsigned>(two_x / numbers::pi_v<T>);
const auto n = k % static_cast<unsigned>(UINT8_C(4));

const T two_r { two_x - (numbers::pi_v<T> * k) };

T r { two_r / 2 };

constexpr T half { 5, -1 };

const bool do_scaling { r > half };

if(do_scaling)
{
// Reduce the argument with factors of three.
r /= static_cast<unsigned>(UINT8_C(3));
}

switch(n)
{
case static_cast<unsigned>(UINT8_C(1)):
case static_cast<unsigned>(UINT8_C(3)):
result = detail::sin_series_expansion(r);
break;
case static_cast<unsigned>(UINT8_C(0)):
case static_cast<unsigned>(UINT8_C(2)):
default:
result = detail::cos_series_expansion(r);
break;
}

if(do_scaling)
{
result *= (((result * result) * static_cast<unsigned>(UINT8_C(4))) - static_cast<unsigned>(UINT8_C(3)));
}

if(signbit(result)) { result = -result; }

const auto b_neg = ((n == static_cast<unsigned>(UINT8_C(1))) || (n == static_cast<unsigned>(UINT8_C(2))));

if(b_neg) { result = -result; }
}
else
{
constexpr T one { 1 };
#endif

result = one;
}
// x = n*pi/2 + r: cos(x) is cos(r), -sin(r), -cos(r) or sin(r) for n = 0 to 3.
const auto r {trig::trig_prepare(x)};
if (r.zero)
{
return T {1};
}

return result;
// The sign of sin(r) is r.neg, and cos(r) > 0.
return (r.n & 1U) == 0U ? trig::cos_of<T>(r, r.n == 2U)
: trig::sin_of<T>(r, r.neg != (r.n == 1U));
}

} // namespace detail
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