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Cover the rest of the sin, cos and tan reduction #1481

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Merged
ckormanyos merged 1 commit into from
Oct 1, 2026
Merged

Cover the rest of the sin, cos and tan reduction #1481

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22 changes: 4 additions & 18 deletions include/boost/decimal/detail/cmath/impl/trig_reduce.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -248,12 +248,8 @@ constexpr auto to_words(const boost::int128::uint128_t& m, std::uint64_t* out) n
out[1] = lo / word_base;
out[2] = hi % word_base;
out[3] = hi / word_base;
int n {4};
while (n > 0 && out[n - 1] == 0U)
{
--n;
}
return n;
// Zero high words do not change the product.
return 4;
}

// m * 10^shift in words of 9 digits, low word first, for 0 <= shift < 9; returns the count of words.
Expand Down Expand Up @@ -436,17 +432,12 @@ constexpr auto trig_reduce(const Significand m, const int e, const bool xneg) no
out.n = n;
out.neg = rneg;

// The fraction is not zero: its worst case has 9, 19 and 37 leading zero digits (see trig_traits).
int lead {};
while (lead < window - 1 && f[lead] == 0U)
{
++lead;
}
if (lead == window - 1)
{
// Only for an exact multiple of pi/2, which no nonzero x is.
out.zero = true;
return out;
}

std::uint64_t r[static_cast<std::size_t>(2 * frac + 1)] {};
times_half_pi<frac, window - 1>(f, lead, r);
Expand Down Expand Up @@ -573,17 +564,12 @@ constexpr auto trig_reduce_binary(const Significand m, const int e, const bool x
out.n = n;
out.neg = rneg;

// The fraction is not zero: its worst case has 27, 58 and 117 leading zero bits (see trig_traits).
int lead {};
while (lead < frac && f[lead] == 0U)
{
++lead;
}
if (lead == frac)
{
// Only for an exact multiple of pi/2, which no nonzero x is.
out.zero = true;
return out;
}

// r = (rw words of f from word lead) * pi/2 = (s from word rw) * 2^-64(lead + rw). The four spare
// words take the scale by 10^k below.
Expand Down
14 changes: 13 additions & 1 deletion test/test_trig_rounding.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -15,7 +15,7 @@ using namespace boost::decimal;
using namespace boost::decimal::literals;

// Each type has inputs near pi/2, pi and 1000*pi/2, the value nearest to a multiple of pi/2 in its exponent
// range (4.327189e+48 for decimal32_t) and below 10^19 (76.96902), and the inputs on each side of 10^19.
// range (4.327189e+48 for decimal32_t) and below 10^19 (76.96902), the inputs on each side of 10^19, -10^19 and 10^-80.
template <typename T>
void check(const T x, const T s, const T c, const T t)
{
Expand All @@ -41,6 +41,8 @@ void test_nearest_decimal32_t()
check(7.696902e+01_DF, 1.000000e0_DF, 1.294993e-8_DF, 7.722047e7_DF);
check(9.999999e+18_DF, -9.628773e-1_DF, 2.699396e-1_DF, -3.567010e0_DF);
check(1.000000e+19_DF, -9.270632e-1_DF, -3.749052e-1_DF, 2.472794e0_DF);
check(-1.000000e+19_DF, 9.270632e-1_DF, -3.749052e-1_DF, -2.472794e0_DF);
check(1.000000e-80_DF, 1.000000e-80_DF, 1.000000e0_DF, 1.000000e-80_DF);
}

void test_nearest_decimal_fast32_t()
Expand All @@ -60,6 +62,8 @@ void test_nearest_decimal_fast32_t()
check(7.696902e+01_DFF, 1.000000e0_DFF, 1.294993e-8_DFF, 7.722047e7_DFF);
check(9.999999e+18_DFF, -9.628773e-1_DFF, 2.699396e-1_DFF, -3.567010e0_DFF);
check(1.000000e+19_DFF, -9.270632e-1_DFF, -3.749052e-1_DFF, 2.472794e0_DFF);
check(-1.000000e+19_DFF, 9.270632e-1_DFF, -3.749052e-1_DFF, -2.472794e0_DFF);
check(1.000000e-80_DFF, 1.000000e-80_DFF, 1.000000e0_DFF, 1.000000e-80_DFF);
}

void test_nearest_decimal64_t()
Expand All @@ -79,6 +83,8 @@ void test_nearest_decimal64_t()
check(9.538513039607291e+06_DD, -6.771756623504492e-18_DD, -1.000000000000000e0_DD, 6.771756623504492e-18_DD);
check(9.999999999999999e+18_DD, -2.113595126444045e-1_DD, -9.774083877349937e-1_DD, 2.162448320442599e-1_DD);
check(1.000000000000000e+19_DD, -9.270631660486504e-1_DD, -3.749051695507178e-1_DD, 2.472793765846527e0_DD);
check(-1.000000000000000e+19_DD, 9.270631660486504e-1_DD, -3.749051695507178e-1_DD, -2.472793765846527e0_DD);
check(1.000000000000000e-80_DD, 1.000000000000000e-80_DD, 1.000000000000000e0_DD, 1.000000000000000e-80_DD);
}

void test_nearest_decimal_fast64_t()
Expand All @@ -98,6 +104,8 @@ void test_nearest_decimal_fast64_t()
check(9.538513039607291e+06_DDF, -6.771756623504492e-18_DDF, -1.000000000000000e0_DDF, 6.771756623504492e-18_DDF);
check(9.999999999999999e+18_DDF, -2.113595126444045e-1_DDF, -9.774083877349937e-1_DDF, 2.162448320442599e-1_DDF);
check(1.000000000000000e+19_DDF, -9.270631660486504e-1_DDF, -3.749051695507178e-1_DDF, 2.472793765846527e0_DDF);
check(-1.000000000000000e+19_DDF, 9.270631660486504e-1_DDF, -3.749051695507178e-1_DDF, -2.472793765846527e0_DDF);
check(1.000000000000000e-80_DDF, 1.000000000000000e-80_DDF, 1.000000000000000e0_DDF, 1.000000000000000e-80_DDF);
}

void test_nearest_decimal128_t()
Expand All @@ -117,6 +125,8 @@ void test_nearest_decimal128_t()
check(2.589477332551582209163675623249625e+08_DL, -1.000000000000000000000000000000000e0_DL, 1.532138639232766081410107492878833e-35_DL, -6.526824494816997196224318392388852e34_DL);
check(9.999999999999999999999999999999999e+18_DL, -9.270631660486500103289527389466423e-1_DL, -3.749051695507187572163865946598085e-1_DL, 2.472793765846520245629178386203776e0_DL);
check(1.000000000000000000000000000000000e+19_DL, -9.270631660486503852341222896649360e-1_DL, -3.749051695507178301532205460096107e-1_DL, 2.472793765846527360338186795636566e0_DL);
check(-1.000000000000000000000000000000000e+19_DL, 9.270631660486503852341222896649360e-1_DL, -3.749051695507178301532205460096107e-1_DL, -2.472793765846527360338186795636566e0_DL);
check(1.000000000000000000000000000000000e-80_DL, 1.000000000000000000000000000000000e-80_DL, 1.000000000000000000000000000000000e0_DL, 1.000000000000000000000000000000000e-80_DL);
}

void test_nearest_decimal_fast128_t()
Expand All @@ -136,6 +146,8 @@ void test_nearest_decimal_fast128_t()
check(2.589477332551582209163675623249625e+08_DLF, -1.000000000000000000000000000000000e0_DLF, 1.532138639232766081410107492878833e-35_DLF, -6.526824494816997196224318392388852e34_DLF);
check(9.999999999999999999999999999999999e+18_DLF, -9.270631660486500103289527389466423e-1_DLF, -3.749051695507187572163865946598085e-1_DLF, 2.472793765846520245629178386203776e0_DLF);
check(1.000000000000000000000000000000000e+19_DLF, -9.270631660486503852341222896649360e-1_DLF, -3.749051695507178301532205460096107e-1_DLF, 2.472793765846527360338186795636566e0_DLF);
check(-1.000000000000000000000000000000000e+19_DLF, 9.270631660486503852341222896649360e-1_DLF, -3.749051695507178301532205460096107e-1_DLF, -2.472793765846527360338186795636566e0_DLF);
check(1.000000000000000000000000000000000e-80_DLF, 1.000000000000000000000000000000000e-80_DLF, 1.000000000000000000000000000000000e0_DLF, 1.000000000000000000000000000000000e-80_DLF);
}

void test_downward_decimal32_t()
Expand Down
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