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LibM: Make the gamma family of functions more accurate and conformant

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This patch makes tgamma use an approximation that is more accurate with
regards to floating point arithmetic, and fixes some issues when tgamma
was called with positive integer values.

It also makes lgamma set signgam to the correct value, and makes its
return value be more inline with what the C standard defines.
This commit is contained in:
Mițca Dumitru 2021-03-15 16:27:14 +02:00 committed by Andreas Kling
parent 2d0f334e5d
commit 987cc904c2
2 changed files with 56 additions and 15 deletions
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44
Userland/Libraries/LibM/math.cpp
View file

@ -318,26 +318,28 @@ static FloatT internal_gamma(FloatT x) NOEXCEPT
if (isnan(x))
return (FloatT)NAN;
if (x < (FloatT)0 && (((long long)x == x) || isinf(x)))
if (x == (FloatT)0.0)
return signbit(x) ? (FloatT)-INFINITY : (FloatT)INFINITY;
if (x < (FloatT)0 && (rintl(x) == x || isinf(x)))
return (FloatT)NAN;
if (isinf(x))
return INFINITY;
return (FloatT)INFINITY;
using Extractor = FloatExtractor<FloatT>;
if ((long long)x == x) {
// These constants were obtained through use of WolframAlpha, they are (in order): 20!, 18!, 10!
constexpr auto max_factorial_that_fits = (Extractor::mantissa_bits == FloatExtractor<long double>::mantissa_bits ? 2'432'902'008'176'640'000ull : (Extractor::mantissa_bits == FloatExtractor<double>::mantissa_bits ? 6'402'373'705'728'000ull : (Extractor::mantissa_bits == FloatExtractor<float>::mantissa_bits ? 3'628'800ull : 0ull)));
static_assert(max_factorial_that_fits != 0, "internal_gamma needs to be aware of the integer factorial that fits in this floating point type.");
unsigned long long result = 1;
for (; result < max_factorial_that_fits; result++)
result *= result + 1;
// These constants were obtained through use of WolframAlpha
constexpr long long max_integer_whose_factorial_fits = (Extractor::mantissa_bits == FloatExtractor<long double>::mantissa_bits ? 20 : (Extractor::mantissa_bits == FloatExtractor<double>::mantissa_bits ? 18 : (Extractor::mantissa_bits == FloatExtractor<float>::mantissa_bits ? 10 : 0)));
static_assert(max_integer_whose_factorial_fits != 0, "internal_gamma needs to be aware of the integer factorial that fits in this floating point type.");
if (rintl(x) == (long double)x && x <= max_integer_whose_factorial_fits) {
long long result = 1;
for (long long cursor = 1; cursor <= min(max_integer_whose_factorial_fits, (long long)x); cursor++)
result *= cursor;
return (FloatT)result;
}
// Approximation taken from: <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5840229/>
// Web archive link: <https://web.archive.org/web/20210314174210/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5840229/>
return sqrtl(M_TAU * x) * powl(x / M_E, x) * powl(x * sinhl(1.0l / x), x / 2.0l) * expl((7.0l / 324.0l) * (1.0l / (powl(x, 3.0l) * (35.0l * powl(x, 2.0l) + 33.0l)))) - 1.0l;
// Stirling approximation
return sqrtl(2.0 * M_PI / x) * powl(x / M_E, x);
}
extern "C" {
@ -1072,22 +1074,34 @@ float lgammaf(float value) NOEXCEPT
long double lgammal_r(long double value, int* sign) NOEXCEPT
{
if (value == 1.0 || value == 2.0)
return 0.0;
if (isinf(value) || value == 0.0)
return INFINITY;
long double result = logl(internal_gamma(value));
*sign = signbit(result);
*sign = signbit(result) ? -1 : 1;
return result;
}
double lgamma_r(double value, int* sign) NOEXCEPT
{
if (value == 1.0 || value == 2.0)
return 0.0;
if (isinf(value) || value == 0.0)
return INFINITY;
double result = log(internal_gamma(value));
*sign = signbit(result);
*sign = signbit(result) ? -1 : 1;
return result;
}
float lgammaf_r(float value, int* sign) NOEXCEPT
{
if (value == 1.0 || value == 2.0)
return 0.0;
if (isinf(value) || value == 0.0)
return INFINITY;
float result = logf(internal_gamma(value));
*sign = signbit(result);
*sign = signbit(result) ? -1 : 1;
return result;
}

27
Userland/Tests/LibM/test-math.cpp
View file

@ -220,4 +220,31 @@ TEST_CASE(scalbn)
EXPECT_EQ(scalbn(2.0, 4), 32.0);
}
TEST_CASE(gamma)
{
EXPECT(isinf(tgamma(+0.0)) && !signbit(tgamma(+0.0)));
EXPECT(isinf(tgamma(-0.0)) && signbit(tgamma(-0.0)));
EXPECT(isinf(tgamma(INFINITY)) && !signbit(tgamma(INFINITY)));
EXPECT(isnan(tgamma(NAN)));
EXPECT(isnan(tgamma(-INFINITY)));
EXPECT(isnan(tgamma(-5)));
EXPECT_APPROXIMATE(tgamma(0.5), sqrt(M_PI));
EXPECT_EQ(tgammal(21.0l), 2'432'902'008'176'640'000.0l);
EXPECT_EQ(tgamma(19.0), 6'402'373'705'728'000.0);
EXPECT_EQ(tgammaf(11.0f), 3628800.0f);
EXPECT_EQ(tgamma(4.0), 6);
EXPECT_EQ(lgamma(1.0), 0.0);
EXPECT_EQ(lgamma(2.0), 0.0);
EXPECT(isinf(lgamma(0.0)));
EXPECT(!signbit(lgamma(-0.0)));
EXPECT(isnan(lgamma(NAN)));
EXPECT(isinf(lgamma(INFINITY)));
EXPECT(isinf(lgamma(-INFINITY)));
EXPECT_EQ(signgam, 1);
lgamma(-2.5);
EXPECT_EQ(signgam, -1);
}
TEST_MAIN(Math)