static TACommandVerdict exp2l_cmd(TAThread thread,TAInputStream stream)
{
long double x, res;
// Prepare
x = readLongDouble(&stream);
errno = 0;
START_TARGET_OPERATION(thread);
// Execute
res = exp2l(x);
END_TARGET_OPERATION(thread);
// Response
writeLongDouble(thread, res);
writeInt(thread, errno);
sendResponse(thread);
return taDefaultVerdict;
}
void test_exp2()
{
static_assert((std::is_same<decltype(exp2((double)0)), double>::value), "");
static_assert((std::is_same<decltype(exp2f(0)), float>::value), "");
static_assert((std::is_same<decltype(exp2l(0)), long double>::value), "");
assert(exp2(1) == 2);
}
TEST(math, exp2_STRICT_ALIGN_OpenBSD_bug) {
// OpenBSD/x86's libm had a bug here, but it was already fixed in FreeBSD:
// http://svnweb.FreeBSD.org/base/head/lib/msun/src/math_private.h?revision=240827&view=markup
ASSERT_DOUBLE_EQ(5.0, exp2(log2(5)));
ASSERT_FLOAT_EQ(5.0f, exp2f(log2f(5)));
ASSERT_DOUBLE_EQ(5.0L, exp2l(log2l(5)));
}
//
// powl
//
long double powl(long double x, long double y)
{
if(isnan(x)) return x;
if(isnan(y)) return y;
return exp2l(y * log2l(x));
}
void testValues() {
f = 2;
long double result;
//result = exp2l(2.0L);
// assert result == \pow(2, 2.0);
result = exp2l(1.0L);
//@ assert result == 2;
result = exp2l(0.0L);
//@ assert result == 1;
result = exp2l(-1.0L);
//@ assert result == 0.5L;
result = exp2(LDBL_MAX);
//@ assert result == HUGE_VALL;
//@ assert (math_errhandling & MATH_ERRNO) ==> (errno == ERANGE);
//@ assert f == 2;
//@ assert vacuous: \false;
}
long double exp10l(long double x)
{
static const long double p10[] = {
1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10,
1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15
};
long double n, y = modfl(x, &n);
if (fabsl(n) < 16) {
if (!y) return p10[(int)n+15];
y = exp2l(3.32192809488736234787031942948939L * y);
return y * p10[(int)n+15];
}
return powl(10.0, x);
}
long double exp10l(long double x)
{
static const long double p10[] = {
1e-15L, 1e-14L, 1e-13L, 1e-12L, 1e-11L, 1e-10L,
1e-9L, 1e-8L, 1e-7L, 1e-6L, 1e-5L, 1e-4L, 1e-3L, 1e-2L, 1e-1L,
1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15
};
long double n, y = modfl(x, &n);
union ldshape u = {n};
/* fabsl(n) < 16 without raising invalid on nan */
if ((u.i.se & 0x7fff) < 0x3fff+4) {
if (!y) return p10[(int)n+15];
y = exp2l(3.32192809488736234787031942948939L * y);
return y * p10[(int)n+15];
}
return powl(10.0, x);
}
void
run_exp2_tests(void)
{
int i;
/*
* We should insist that exp2() return exactly the correct
* result and not raise an inexact exception for integer
* arguments.
*/
feclearexcept(FE_ALL_EXCEPT);
for (i = FLT_MIN_EXP - FLT_MANT_DIG; i < FLT_MAX_EXP; i++) {
assert(exp2f(i) == ldexpf(1.0, i));
assert(fetestexcept(ALL_STD_EXCEPT) == 0);
}
for (i = DBL_MIN_EXP - DBL_MANT_DIG; i < DBL_MAX_EXP; i++) {
assert(exp2(i) == ldexp(1.0, i));
assert(fetestexcept(ALL_STD_EXCEPT) == 0);
}
for (i = LDBL_MIN_EXP - LDBL_MANT_DIG; i < LDBL_MAX_EXP; i++) {
assert(exp2l(i) == ldexpl(1.0, i));
assert(fetestexcept(ALL_STD_EXCEPT) == 0);
}
}
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
}
long double t4(unsigned char x) {
return exp2l(x);
}
npy_longdouble npy_exp2l(npy_longdouble x)
{
return exp2l(x);
}
TEST(math, exp2l) {
ASSERT_DOUBLE_EQ(8.0L, exp2l(3.0L));
}
ldcomplex
cpowl(ldcomplex z, ldcomplex w) {
ldcomplex ans;
long double x, y, u, v, t, c, s, r;
long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2;
int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k;
x = LD_RE(z);
y = LD_IM(z);
u = LD_RE(w);
v = LD_IM(w);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
hu = HI_XWORD(u);
hv = HI_XWORD(v);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
iu = hu & 0x7fffffff;
iv = hv & 0x7fffffff;
j = 0;
if (v == zero) { /* z**(real) */
if (u == one) { /* (anything) ** 1 is itself */
LD_RE(ans) = x;
LD_IM(ans) = y;
} else if (u == zero) { /* (anything) ** 0 is 1 */
LD_RE(ans) = one;
LD_IM(ans) = zero;
} else if (y == zero) { /* real ** real */
LD_IM(ans) = zero;
if (hx < 0 && ix < hiinf && iu < hiinf) {
/* -x ** u is exp(i*pi*u)*pow(x,u) */
r = powl(-x, u);
sincospil(u, &s, &c);
LD_RE(ans) = (c == zero)? c: c * r;
LD_IM(ans) = (s == zero)? s: s * r;
} else
LD_RE(ans) = powl(x, u);
} else if (x == zero || ix >= hiinf || iy >= hiinf) {
if (isnanl(x) || isnanl(y) || isnanl(u))
LD_RE(ans) = LD_IM(ans) = x + y + u;
else {
if (x == zero)
r = fabsl(y);
else
r = fabsl(x) + fabsl(y);
t = atan2pil(y, x);
sincospil(t * u, &s, &c);
LD_RE(ans) = (c == zero)? c: c * r;
LD_IM(ans) = (s == zero)? s: s * r;
}
} else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */
if (hx >= 0) {
t = (hy >= 0)? 0.25L : -0.25L;
sincospil(t * u, &s, &c);
} else if ((LAST(u) & 3) == 0) {
t = (hy >= 0)? 0.75L : -0.75L;
sincospil(t * u, &s, &c);
} else {
r = (hy >= 0)? u : -u;
t = -0.25L * r;
w1 = r + t;
w2 = t - (w1 - r);
sincospil(w1, &t1, &t2);
sincospil(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
}
if (ix < 0x3ffe0000) /* |x| < 1/2 */
r = powl(fabsl(x + x), u) * exp2l(-0.5L * u);
else if (ix >= 0x3fff0000 || iu < 0x400cfff8)
/* |x| >= 1 or |u| < 16383 */
r = powl(fabsl(x), u) * exp2l(0.5L * u);
else /* special treatment */
j = 2;
if (j == 0) {
LD_RE(ans) = (c == zero)? c: c * r;
LD_IM(ans) = (s == zero)? s: s * r;
}
} else
j = 1;
if (j == 0)
return (ans);
}
if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
/*
* non-zero imag part(s) with inf component(s) yields NaN
*/
t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v);
LD_RE(ans) = LD_IM(ans) = t - t;
} else {
k = 0; /* no scaling */
if (iu > 0x7ffe0000 || iv > 0x7ffe0000) {
u *= 1.52587890625000000000e-05L;
v *= 1.52587890625000000000e-05L;
k = 1; /* scale u and v by 2**-16 */
}
/*
* Use similated higher precision arithmetic to compute:
* r = u * log(hypot(x, y)) - v * atan2(y, x)
* q = u * atan2(y, x) + v * log(hypot(x, y))
*/
t1 = __k_clog_rl(x, y, &t2);
t3 = __k_atan2l(y, x, &t4);
x1 = t1; HALF(x1);
y1 = t3; HALF(y1);
u1 = u; HALF(u1);
v1 = v; HALF(v1);
x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */
y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */
/* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
if (j != 2) {
b[0] = u1 * y1;
b[1] = (u - u1) * y1 + u * y2;
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = v1 * x1;
b[3] = (v - v1) * x1 + v * x2;
w1 = sum4fpl(b, &w2);
}
sincosl(w1, &t1, &t2);
sincosl(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
if (k == 1) /* square j times */
for (i = 0; i < 10; i++) {
t1 = s * c;
c = (c + s) * (c - s);
s = t1 + t1;
}
}
/* compute r = u * (t1, t2) - v * (t3, t4) */
b[0] = u1 * x1;
b[1] = (u - u1) * x1 + u * x2;
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = -v1 * y1;
b[3] = (v1 - v) * y1 - v * y2;
w1 = sum4fpl(b, &w2);
}
/* scale back unless w1 is large enough to cause exception */
if (k != 0 && fabsl(w1) < 20000.0L) {
w1 *= 65536.0L; w2 *= 65536.0L;
}
hx = HI_XWORD(w1);
ix = hx & 0x7fffffff;
/* compute exp(w1 + w2) */
k = 0;
if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */
r = one;
else if (ix >= 0x400c6760) /* overflow/underflow */
r = (hx < 0)? tiny * tiny : huge * huge;
else { /* compute exp(w1 + w2) */
k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L));
t1 = (long double) k;
t2 = w1 - t1 * ln2hil;
t3 = w2 - t1 * ln2lol;
r = expl(t2 + t3);
}
if (c != zero) c *= r;
if (s != zero) s *= r;
if (k != 0) {
c = scalbnl(c, k);
s = scalbnl(s, k);
}
LD_RE(ans) = c;
LD_IM(ans) = s;
}
return (ans);
}
TEST(math, exp2l) {
ASSERT_FLOAT_EQ(8.0, exp2l(3.0));
}
static int testl(long double long_double_x, int int_x, long long_x)
{
int r = 0;
r += __finitel(long_double_x);
r += __fpclassifyl(long_double_x);
r += __isinfl(long_double_x);
r += __isnanl(long_double_x);
r += __signbitl(long_double_x);
r += acoshl(long_double_x);
r += acosl(long_double_x);
r += asinhl(long_double_x);
r += asinl(long_double_x);
r += atan2l(long_double_x, long_double_x);
r += atanhl(long_double_x);
r += atanl(long_double_x);
r += cbrtl(long_double_x);
r += ceill(long_double_x);
r += copysignl(long_double_x, long_double_x);
r += coshl(long_double_x);
r += cosl(long_double_x);
r += erfcl(long_double_x);
r += erfl(long_double_x);
r += exp2l(long_double_x);
r += expl(long_double_x);
r += expm1l(long_double_x);
r += fabsl(long_double_x);
r += fdiml(long_double_x, long_double_x);
r += floorl(long_double_x);
r += fmal(long_double_x, long_double_x, long_double_x);
r += fmaxl(long_double_x, long_double_x);
r += fminl(long_double_x, long_double_x);
r += fmodl(long_double_x, long_double_x);
r += frexpl(long_double_x, &int_x);
r += hypotl(long_double_x, long_double_x);
r += ilogbl(long_double_x);
r += ldexpl(long_double_x, int_x);
r += lgammal(long_double_x);
r += llrintl(long_double_x);
r += llroundl(long_double_x);
r += log10l(long_double_x);
r += log1pl(long_double_x);
r += log2l(long_double_x);
r += logbl(long_double_x);
r += logl(long_double_x);
r += lrintl(long_double_x);
r += lroundl(long_double_x);
r += modfl(long_double_x, &long_double_x);
r += nearbyintl(long_double_x);
r += nextafterl(long_double_x, long_double_x);
r += nexttowardl(long_double_x, long_double_x);
r += powl(long_double_x, long_double_x);
r += remainderl(long_double_x, long_double_x);
r += remquol(long_double_x, long_double_x, &int_x);
r += rintl(long_double_x);
r += roundl(long_double_x);
r += scalblnl(long_double_x, long_x);
r += scalbnl(long_double_x, int_x);
r += sinhl(long_double_x);
r += sinl(long_double_x);
r += sqrtl(long_double_x);
r += tanhl(long_double_x);
r += tanl(long_double_x);
r += tgammal(long_double_x);
r += truncl(long_double_x);
return r;
}
void runSuccess() {
exp2l(0.0L);
exp2l(1.0L);
exp2l(-1.0L);
exp2l(anylongdouble());
}
double exp2(double x)
{
return exp2l(x);
}