/*
Given an array of doubles, return the skewness
'df' is degrees-of-freedom. Use DF_POPULATION or DF_SAMPLE (see above).
*/
long double
skewness_value (const long double * const values, size_t n, int df)
{
long double moment2=0;
long double moment3=0;
long double mean;
long double skewness;
if (n<=1)
return nanl ("");
mean = arithmetic_mean_value (values, n);
for (size_t i = 0; i < n; i++)
{
const long double t = (values[i] - mean);
moment2 += t*t;
moment3 += t*t*t;
}
moment2 /= n;
moment3 /= n;
/* can't use 'powl (moment2,3.0/2.0)' - not all systems have powl */
skewness = moment3 / sqrtl (moment2*moment2*moment2);
if ( df == DF_SAMPLE )
{
if (n<=2)
return nanl ("");
skewness = ( sqrtl (n*(n-1)) / (n-2) ) * skewness;
}
return skewness;
}
/*
Given an array of doubles, return the excess kurtosis
'df' is degrees-of-freedom. Use DF_POPULATION or DF_SAMPLE (see above).
*/
long double _GL_ATTRIBUTE_PURE
excess_kurtosis_value (const long double * const values, size_t n, int df)
{
long double moment2=0;
long double moment4=0;
long double mean;
long double excess_kurtosis;
if (n<=1)
return nanl ("");
mean = arithmetic_mean_value (values, n);
for (size_t i = 0; i < n; i++)
{
const long double t = (values[i] - mean);
moment2 += t*t;
moment4 += t*t*t*t;
}
moment2 /= n;
moment4 /= n;
excess_kurtosis = moment4 / (moment2*moment2) - 3;
if ( df == DF_SAMPLE )
{
if (n<=3)
return nanl ("");
excess_kurtosis = ( ((long double)n-1)
/ (((long double)n-2)*((long double)n-3)) ) *
( (n+1)*excess_kurtosis + 6 ) ;
}
return excess_kurtosis;
}
TEST(math, logbl) {
ASSERT_EQ(-HUGE_VAL, logbl(0.0L));
ASSERT_TRUE(isnan(logbl(nanl(""))));
ASSERT_TRUE(isinf(logbl(HUGE_VALL)));
ASSERT_EQ(0.0L, logbl(1.0L));
ASSERT_EQ(3.0L, logbl(10.0L));
}
TEST(math, ilogbl) {
ASSERT_EQ(FP_ILOGB0, ilogbl(0.0L));
ASSERT_EQ(FP_ILOGBNAN, ilogbl(nanl("")));
ASSERT_EQ(INT_MAX, ilogbl(HUGE_VALL));
ASSERT_EQ(0L, ilogbl(1.0L));
ASSERT_EQ(3L, ilogbl(10.0L));
}
TEST(math, __fpclassifyl) {
EXPECT_EQ(FP_INFINITE, __fpclassifyl(HUGE_VALL));
EXPECT_EQ(FP_NAN, __fpclassifyl(nanl("")));
EXPECT_EQ(FP_NORMAL, __fpclassifyl(1.0L));
EXPECT_EQ(FP_SUBNORMAL, __fpclassifyl(ldouble_subnormal()));
EXPECT_EQ(FP_ZERO, __fpclassifyl(0.0L));
}
TEST(math, isnan) {
ASSERT_FALSE(test_capture_isnan(123.0f));
ASSERT_FALSE(test_capture_isnan(123.0));
ASSERT_FALSE(test_capture_isnan(123.0L));
ASSERT_TRUE(test_capture_isnan(nanf("")));
ASSERT_TRUE(test_capture_isnan(nan("")));
ASSERT_TRUE(test_capture_isnan(nanl("")));
}
/* Standard error of skewness (SES), given the sample size 'n' */
long double
SES_value (size_t n)
{
if (n<=2)
return nanl ("");
return sqrtl ( (long double)(6.0*n*(n-1))
/ ((long double)(n-2)*(n+1)*(n+3)) );
}
/* Skewness Test statistics Z = ( sample skewness / SES ) */
long double
skewnessZ_value (const long double * const values, size_t n)
{
const long double skew = skewness_value (values,n,DF_SAMPLE);
const long double SES = SES_value (n);
if (isnan (skew) || isnan (SES) )
return nanl ("");
return skew/SES;
}
TEST(math, roundl) {
fesetround(FE_TOWARDZERO); // roundl ignores the rounding mode and always rounds away from zero.
ASSERT_FLOAT_EQ(1.0, roundl(0.5));
ASSERT_FLOAT_EQ(-1.0, roundl(-0.5));
ASSERT_FLOAT_EQ(0.0, roundl(0.0));
ASSERT_FLOAT_EQ(-0.0, roundl(-0.0));
ASSERT_TRUE(isnan(roundl(nanl(""))));
ASSERT_FLOAT_EQ(HUGE_VALL, roundl(HUGE_VALL));
}
/* Kurtosis Test statistics Z = ( sample kurtosis / SEK ) */
long double
kurtosisZ_value (const long double * const values, size_t n)
{
const long double kurt = excess_kurtosis_value (values,n,DF_SAMPLE);
const long double SEK = SEK_value (n);
if (isnan (kurt) || isnan (SEK) )
return nanl ("");
return kurt/SEK;
}
long double acoshl(long double x)
{
if(x < 1.0)
{
errno = EDOM;
return nanl(NULL);
}
/* FIXME implement */
return 0.0;
}
long double atanhl(long double x)
{
if(abs(x) >= 1.0)
{
errno = EDOM;
return nanl(NULL);
}
/* FIXME implement */
return 0.0;
}
void testValues() {
f = 2;
long double result;
result = nanl(NULL);
// assert result == 0 || \is_NaN(result);
//@ assert f == 2;
//@ assert vacuous: \false;
}
/*
Given an array of doubles, return the p-Value
Of the Jarque-Bera Test for normality
http://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test
Equivalent to R's "jarque.test ()" function in the "moments" library.
*/
long double
jarque_bera_pvalue (const long double * const values, size_t n )
{
const long double k = excess_kurtosis_value (values,n,DF_POPULATION);
const long double s = skewness_value (values,n,DF_POPULATION);
const long double jb = (long double)(n*(s*s + k*k/4))/6.0 ;
const long double pval = 1.0 - pchisq_df2 (jb);
if (n<=1 || isnan (k) || isnan (s))
return nanl ("");
return pval;
}
/* Standard error of kurtisos (SEK), given the sample size 'n' */
long double
SEK_value (size_t n)
{
const long double ses = SES_value (n);
if (n<=3)
return nanl ("");
return 2 * ses * sqrtl ( (long double)(n*n-1)
/ ((long double)((n-3)*(n+5))) );
}
TEST(math, __fpclassifyl) {
#if defined(__BIONIC__)
EXPECT_EQ(FP_INFINITE, __fpclassifyl(HUGE_VALL));
EXPECT_EQ(FP_NAN, __fpclassifyl(nanl("")));
EXPECT_EQ(FP_NORMAL, __fpclassifyl(1.0));
EXPECT_EQ(FP_SUBNORMAL, __fpclassifyl(double_subnormal()));
EXPECT_EQ(FP_ZERO, __fpclassifyl(0.0));
#else // __BIONIC__
GTEST_LOG_(INFO) << "This test does nothing.\n";
#endif // __BIONIC__
}
TEST(math, roundl) {
auto guard = make_scope_guard([]() {
fesetenv(FE_DFL_ENV);
});
fesetround(FE_TOWARDZERO); // roundl ignores the rounding mode and always rounds away from zero.
ASSERT_DOUBLE_EQ(1.0L, roundl(0.5L));
ASSERT_DOUBLE_EQ(-1.0L, roundl(-0.5L));
ASSERT_DOUBLE_EQ(0.0L, roundl(0.0L));
ASSERT_DOUBLE_EQ(-0.0L, roundl(-0.0L));
ASSERT_TRUE(isnan(roundl(nanl(""))));
ASSERT_DOUBLE_EQ(HUGE_VALL, roundl(HUGE_VALL));
}
/*
D'Agostino-Perason omnibus test for normality.
returns the p-value,
where the null-hypothesis is normal distribution.
*/
long double
dagostino_pearson_omnibus_pvalue (const long double * const values, size_t n)
{
const long double z_skew = skewnessZ_value (values, n);
const long double z_kurt = kurtosisZ_value (values, n);
const long double DP = z_skew*z_skew + z_kurt*z_kurt;
const long double pval = 1.0 - pchisq_df2 (DP);
if (isnan (z_skew) || isnan (z_kurt))
return nanl ("");
return pval;
}
long double _GL_ATTRIBUTE_PURE
variance_value (const long double * const values, size_t n, int df)
{
long double sum=0;
long double mean;
long double variance;
assert (df>=0); /* LCOV_EXCL_LINE */
if ( (size_t)df == n )
return nanl ("");
mean = arithmetic_mean_value (values, n);
sum = 0 ;
for (size_t i = 0; i < n; i++)
sum += (values[i] - mean) * (values[i] - mean);
variance = sum / ( n - df );
return variance;
}
/* acosh(x) = log (x + sqrt(x * x - 1)) */
long double acoshl (long double x)
{
if (isnan (x))
return x;
if (x < 1.0L)
{
errno = EDOM;
return nanl("");
}
if (x > 0x1p32L)
/* Avoid overflow (and unnecessary calculation when
sqrt (x * x - 1) == x).
The M_LN2 define doesn't have enough precison for
long double so use this one. GCC optimizes by replacing
the const with a fldln2 insn. */
return __fast_logl (x) + 6.9314718055994530941723E-1L;
/* Since x >= 1, the arg to log will always be greater than
the fyl2xp1 limit (approx 0.29) so just use logl. */
return __fast_logl (x + __fast_sqrtl((x + 1.0L) * (x - 1.0L)));
}
TEST(math, fpclassify) {
ASSERT_EQ(FP_INFINITE, fpclassify(INFINITY));
ASSERT_EQ(FP_INFINITE, fpclassify(HUGE_VALF));
ASSERT_EQ(FP_INFINITE, fpclassify(HUGE_VAL));
ASSERT_EQ(FP_INFINITE, fpclassify(HUGE_VALL));
ASSERT_EQ(FP_NAN, fpclassify(nanf("")));
ASSERT_EQ(FP_NAN, fpclassify(nan("")));
ASSERT_EQ(FP_NAN, fpclassify(nanl("")));
ASSERT_EQ(FP_NORMAL, fpclassify(1.0f));
ASSERT_EQ(FP_NORMAL, fpclassify(1.0));
ASSERT_EQ(FP_NORMAL, fpclassify(1.0L));
ASSERT_EQ(FP_SUBNORMAL, fpclassify(float_subnormal()));
ASSERT_EQ(FP_SUBNORMAL, fpclassify(double_subnormal()));
ASSERT_EQ(FP_SUBNORMAL, fpclassify(ldouble_subnormal()));
ASSERT_EQ(FP_ZERO, fpclassify(0.0f));
ASSERT_EQ(FP_ZERO, fpclassify(0.0));
ASSERT_EQ(FP_ZERO, fpclassify(0.0L));
}
/* atanh (x) = 0.5 * log ((1.0 + x)/(1.0 - x)) */
long double atanhl (long double x)
{
long double z;
if (isnan (x))
return x;
z = fabsl (x);
if (z == 1.0L)
{
errno = ERANGE;
return (x > 0 ? INFINITY : -INFINITY);
}
if ( z > 1.0L)
{
errno = EDOM;
return nanl("");
}
/* Rearrange formula to avoid precision loss for small x.
atanh(x) = 0.5 * log ((1.0 + x)/(1.0 - x))
= 0.5 * log1p ((1.0 + x)/(1.0 - x) - 1.0)
= 0.5 * log1p ((1.0 + x - 1.0 + x) /(1.0 - x))
= 0.5 * log1p ((2.0 * x ) / (1.0 - x)) */
z = 0.5L * __fast_log1pl ((z + z) / (1.0L - z));
return x >= 0 ? z : -z;
}
void
testnan(const char *nan_format)
{
char nan_str[128];
char *end;
long double ald[4];
double ad[4];
float af[4];
int i;
snprintf(nan_str, sizeof(nan_str), "nan(%s)", nan_format);
for (i = 0; i < 4; i++) {
/*
* x86 has an 80-bit long double stored in 96 bits,
* so we need to initialize the memory for the memcmp()
* checks below to work.
*/
bzero(&af[i], sizeof(float));
bzero(&ad[i], sizeof(double));
bzero(&ald[i], sizeof(long double));
}
af[0] = nanf(nan_format);
assert(isnan(af[0]));
af[1] = strtof(nan_str, &end);
assert(end == nan_str + strlen(nan_str));
assert(sscanf(nan_str, "%e", &af[2]) == 1);
assert(memcmp(&af[0], &af[1], sizeof(float)) == 0);
#if !__gnu_linux__
assert(memcmp(&af[1], &af[2], sizeof(float)) == 0);
#endif /* !__gnu_linux__ */
if (*nan_format == '\0') {
/* nanf("") == strtof("nan") */
af[3] = strtof("nan", NULL);
assert(memcmp(&af[2], &af[3], sizeof(float)) == 0);
}
ad[0] = nan(nan_format);
assert(isnan(ad[0]));
ad[1] = strtod(nan_str, &end);
assert(end == nan_str + strlen(nan_str));
assert(sscanf(nan_str, "%le", &ad[2]) == 1);
assert(memcmp(&ad[0], &ad[1], sizeof(double)) == 0);
#if !__gnu_linux__
assert(memcmp(&ad[1], &ad[2], sizeof(double)) == 0);
#endif /* !__gnu_linux__ */
if (*nan_format == '\0') {
/* nan("") == strtod("nan") */
ad[3] = strtod("nan", NULL);
assert(memcmp(&ad[2], &ad[3], sizeof(double)) == 0);
}
ald[0] = nanl(nan_format);
assert(isnan(ald[0]));
ald[1] = strtold(nan_str, &end);
assert(end == nan_str + strlen(nan_str));
assert(sscanf(nan_str, "%Le", &ald[2]) == 1);
assert(memcmp(&ald[0], &ald[1], sizeof(long double)) == 0);
#if 0
assert(memcmp(&ald[1], &ald[2], sizeof(long double)) == 0);
if (*nan_format == '\0') {
/* nanl("") == strtold("nan") */
ald[3] = strtold("nan", NULL);
assert(memcmp(&ald[2], &ald[3], sizeof(long double)) == 0);
}
#endif
}
void
domathl (void)
{
#ifndef NO_LONG_DOUBLE
long double f1;
long double f2;
int i1;
f1 = acosl(0.0);
fprintf( stdout, "acosl : %Lf\n", f1);
f1 = acoshl(0.0);
fprintf( stdout, "acoshl : %Lf\n", f1);
f1 = asinl(1.0);
fprintf( stdout, "asinl : %Lf\n", f1);
f1 = asinhl(1.0);
fprintf( stdout, "asinhl : %Lf\n", f1);
f1 = atanl(M_PI_4);
fprintf( stdout, "atanl : %Lf\n", f1);
f1 = atan2l(2.3, 2.3);
fprintf( stdout, "atan2l : %Lf\n", f1);
f1 = atanhl(1.0);
fprintf( stdout, "atanhl : %Lf\n", f1);
f1 = cbrtl(27.0);
fprintf( stdout, "cbrtl : %Lf\n", f1);
f1 = ceill(3.5);
fprintf( stdout, "ceill : %Lf\n", f1);
f1 = copysignl(3.5, -2.5);
fprintf( stdout, "copysignl : %Lf\n", f1);
f1 = cosl(M_PI_2);
fprintf( stdout, "cosl : %Lf\n", f1);
f1 = coshl(M_PI_2);
fprintf( stdout, "coshl : %Lf\n", f1);
f1 = erfl(42.0);
fprintf( stdout, "erfl : %Lf\n", f1);
f1 = erfcl(42.0);
fprintf( stdout, "erfcl : %Lf\n", f1);
f1 = expl(0.42);
fprintf( stdout, "expl : %Lf\n", f1);
f1 = exp2l(0.42);
fprintf( stdout, "exp2l : %Lf\n", f1);
f1 = expm1l(0.00042);
fprintf( stdout, "expm1l : %Lf\n", f1);
f1 = fabsl(-1.123);
fprintf( stdout, "fabsl : %Lf\n", f1);
f1 = fdiml(1.123, 2.123);
fprintf( stdout, "fdiml : %Lf\n", f1);
f1 = floorl(0.5);
fprintf( stdout, "floorl : %Lf\n", f1);
f1 = floorl(-0.5);
fprintf( stdout, "floorl : %Lf\n", f1);
f1 = fmal(2.1, 2.2, 3.01);
fprintf( stdout, "fmal : %Lf\n", f1);
f1 = fmaxl(-0.42, 0.42);
fprintf( stdout, "fmaxl : %Lf\n", f1);
f1 = fminl(-0.42, 0.42);
fprintf( stdout, "fminl : %Lf\n", f1);
f1 = fmodl(42.0, 3.0);
fprintf( stdout, "fmodl : %Lf\n", f1);
/* no type-specific variant */
i1 = fpclassify(1.0);
fprintf( stdout, "fpclassify : %d\n", i1);
f1 = frexpl(42.0, &i1);
fprintf( stdout, "frexpl : %Lf\n", f1);
f1 = hypotl(42.0, 42.0);
fprintf( stdout, "hypotl : %Lf\n", f1);
i1 = ilogbl(42.0);
fprintf( stdout, "ilogbl : %d\n", i1);
/* no type-specific variant */
i1 = isfinite(3.0);
fprintf( stdout, "isfinite : %d\n", i1);
/* no type-specific variant */
i1 = isgreater(3.0, 3.1);
fprintf( stdout, "isgreater : %d\n", i1);
/* no type-specific variant */
i1 = isgreaterequal(3.0, 3.1);
fprintf( stdout, "isgreaterequal : %d\n", i1);
/* no type-specific variant */
i1 = isinf(3.0);
fprintf( stdout, "isinf : %d\n", i1);
/* no type-specific variant */
i1 = isless(3.0, 3.1);
fprintf( stdout, "isless : %d\n", i1);
/* no type-specific variant */
i1 = islessequal(3.0, 3.1);
fprintf( stdout, "islessequal : %d\n", i1);
/* no type-specific variant */
i1 = islessgreater(3.0, 3.1);
fprintf( stdout, "islessgreater : %d\n", i1);
/* no type-specific variant */
i1 = isnan(0.0);
fprintf( stdout, "isnan : %d\n", i1);
/* no type-specific variant */
i1 = isnormal(3.0);
fprintf( stdout, "isnormal : %d\n", i1);
/* no type-specific variant */
f1 = isunordered(1.0, 2.0);
fprintf( stdout, "isunordered : %d\n", i1);
f1 = j0l(1.2);
fprintf( stdout, "j0l : %Lf\n", f1);
f1 = j1l(1.2);
fprintf( stdout, "j1l : %Lf\n", f1);
f1 = jnl(2,1.2);
fprintf( stdout, "jnl : %Lf\n", f1);
f1 = ldexpl(1.2,3);
fprintf( stdout, "ldexpl : %Lf\n", f1);
f1 = lgammal(42.0);
fprintf( stdout, "lgammal : %Lf\n", f1);
f1 = llrintl(-0.5);
fprintf( stdout, "llrintl : %Lf\n", f1);
f1 = llrintl(0.5);
fprintf( stdout, "llrintl : %Lf\n", f1);
f1 = llroundl(-0.5);
fprintf( stdout, "lroundl : %Lf\n", f1);
f1 = llroundl(0.5);
fprintf( stdout, "lroundl : %Lf\n", f1);
f1 = logl(42.0);
fprintf( stdout, "logl : %Lf\n", f1);
f1 = log10l(42.0);
fprintf( stdout, "log10l : %Lf\n", f1);
f1 = log1pl(42.0);
fprintf( stdout, "log1pl : %Lf\n", f1);
f1 = log2l(42.0);
fprintf( stdout, "log2l : %Lf\n", f1);
f1 = logbl(42.0);
fprintf( stdout, "logbl : %Lf\n", f1);
f1 = lrintl(-0.5);
fprintf( stdout, "lrintl : %Lf\n", f1);
f1 = lrintl(0.5);
fprintf( stdout, "lrintl : %Lf\n", f1);
f1 = lroundl(-0.5);
fprintf( stdout, "lroundl : %Lf\n", f1);
f1 = lroundl(0.5);
fprintf( stdout, "lroundl : %Lf\n", f1);
f1 = modfl(42.0,&f2);
fprintf( stdout, "lmodfl : %Lf\n", f1);
f1 = nanl("");
fprintf( stdout, "nanl : %Lf\n", f1);
f1 = nearbyintl(1.5);
fprintf( stdout, "nearbyintl : %Lf\n", f1);
f1 = nextafterl(1.5,2.0);
fprintf( stdout, "nextafterl : %Lf\n", f1);
f1 = powl(3.01, 2.0);
fprintf( stdout, "powl : %Lf\n", f1);
f1 = remainderl(3.01,2.0);
fprintf( stdout, "remainderl : %Lf\n", f1);
f1 = remquol(29.0,3.0,&i1);
fprintf( stdout, "remquol : %Lf\n", f1);
f1 = rintl(0.5);
fprintf( stdout, "rintl : %Lf\n", f1);
f1 = rintl(-0.5);
fprintf( stdout, "rintl : %Lf\n", f1);
f1 = roundl(0.5);
fprintf( stdout, "roundl : %Lf\n", f1);
f1 = roundl(-0.5);
fprintf( stdout, "roundl : %Lf\n", f1);
f1 = scalblnl(1.2,3);
fprintf( stdout, "scalblnl : %Lf\n", f1);
f1 = scalbnl(1.2,3);
fprintf( stdout, "scalbnl : %Lf\n", f1);
/* no type-specific variant */
i1 = signbit(1.0);
fprintf( stdout, "signbit : %i\n", i1);
f1 = sinl(M_PI_4);
fprintf( stdout, "sinl : %Lf\n", f1);
f1 = sinhl(M_PI_4);
fprintf( stdout, "sinhl : %Lf\n", f1);
f1 = sqrtl(9.0);
fprintf( stdout, "sqrtl : %Lf\n", f1);
f1 = tanl(M_PI_4);
fprintf( stdout, "tanl : %Lf\n", f1);
f1 = tanhl(M_PI_4);
fprintf( stdout, "tanhl : %Lf\n", f1);
f1 = tgammal(2.1);
fprintf( stdout, "tgammal : %Lf\n", f1);
f1 = truncl(3.5);
fprintf( stdout, "truncl : %Lf\n", f1);
f1 = y0l(1.2);
fprintf( stdout, "y0l : %Lf\n", f1);
f1 = y1l(1.2);
fprintf( stdout, "y1l : %Lf\n", f1);
f1 = ynl(3,1.2);
fprintf( stdout, "ynl : %Lf\n", f1);
#endif
}
void runSuccess() {
char buf[] = "";
//@ assert \valid(buf+(0..\block_length(buf)-1));
//@ assert \exists integer x; buf[x] == '\0';
nanl(buf);
}
void test_nan()
{
static_assert((std::is_same<decltype(nan("")), double>::value), "");
static_assert((std::is_same<decltype(nanf("")), float>::value), "");
static_assert((std::is_same<decltype(nanl("")), long double>::value), "");
}
void runSuccess1() {
nanl(NULL);
}
TEST(math, log1pl) {
ASSERT_EQ(-HUGE_VALL, log1pl(-1.0L));
ASSERT_TRUE(isnan(log1pl(nanl(""))));
ASSERT_TRUE(isinf(log1pl(HUGE_VALL)));
ASSERT_DOUBLE_EQ(1.0L, log1pl(M_E - 1.0L));
}
TEST(math, powl) {
ASSERT_TRUE(__isnanl(powl(nanl(""), 3.0L)));
ASSERT_DOUBLE_EQ(1.0L, (powl(1.0L, nanl(""))));
ASSERT_TRUE(__isnanl(powl(2.0L, nanl(""))));
ASSERT_DOUBLE_EQ(8.0L, powl(2.0L, 3.0L));
}
TEST(math, fminl) {
ASSERT_DOUBLE_EQ(10.0L, fminl(12.0L, 10.0L));
ASSERT_DOUBLE_EQ(12.0L, fminl(12.0L, nanl("")));
ASSERT_DOUBLE_EQ(12.0L, fminl(nanl(""), 12.0L));
}
