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-rw-r--r--Userland/Libraries/LibM/math.cpp446
-rw-r--r--Userland/Libraries/LibM/math.h39
2 files changed, 381 insertions, 104 deletions
diff --git a/Userland/Libraries/LibM/math.cpp b/Userland/Libraries/LibM/math.cpp
index 1bf898d7ae..3cab183d24 100644
--- a/Userland/Libraries/LibM/math.cpp
+++ b/Userland/Libraries/LibM/math.cpp
@@ -266,6 +266,17 @@ static int internal_ilogb(FloatT x) NOEXCEPT
}
template<typename FloatT>
+static FloatT internal_modf(FloatT x, FloatT* intpart) NOEXCEPT
+{
+ FloatT integer_part = internal_to_integer(x, RoundingMode::ToZero);
+ *intpart = integer_part;
+ auto fraction = x - integer_part;
+ if (signbit(fraction) != signbit(x))
+ fraction = -fraction;
+ return fraction;
+}
+
+template<typename FloatT>
static FloatT internal_scalbn(FloatT x, int exponent) NOEXCEPT
{
if (x == 0 || !isfinite(x) || isnan(x) || exponent == 0)
@@ -333,6 +344,11 @@ long double truncl(long double x) NOEXCEPT
return internal_to_integer(x, RoundingMode::ToZero);
}
+long double cosl(long double angle) NOEXCEPT
+{
+ return sinl(angle + M_PI_2);
+}
+
double cos(double angle) NOEXCEPT
{
return sin(angle + M_PI_2);
@@ -343,6 +359,17 @@ float cosf(float angle) NOEXCEPT
return sinf(angle + M_PI_2);
}
+long double sinl(long double angle) NOEXCEPT
+{
+ long double ret = 0.0;
+ __asm__(
+ "fsin"
+ : "=t"(ret)
+ : "0"(angle));
+
+ return ret;
+}
+
// This can also be done with a taylor expansion, but for
// now this works pretty well (and doesn't mess anything up
// in quake in particular, which is very Floating-Point precision
@@ -368,7 +395,7 @@ float sinf(float angle) NOEXCEPT
return ret;
}
-double pow(double x, double y) NOEXCEPT
+long double powl(long double x, long double y) NOEXCEPT
{
// FIXME: Please fix me. I am naive.
if (isnan(y))
@@ -380,20 +407,25 @@ double pow(double x, double y) NOEXCEPT
if (y == 1)
return x;
int y_as_int = (int)y;
- if (y == (double)y_as_int) {
- double result = x;
- for (int i = 0; i < fabs(y) - 1; ++i)
+ if (y == (long double)y_as_int) {
+ long double result = x;
+ for (int i = 0; i < fabsl(y) - 1; ++i)
result *= x;
if (y < 0)
- result = 1.0 / result;
+ result = 1.0l / result;
return result;
}
- return exp2(y * log2(x));
+ return exp2l(y * log2l(x));
+}
+
+double pow(double x, double y) NOEXCEPT
+{
+ return (double)powl(x, y);
}
float powf(float x, float y) NOEXCEPT
{
- return (float)pow(x, y);
+ return (float)powl(x, y);
}
// On systems where FLT_RADIX == 2, ldexp is equivalent to scalbn
@@ -412,42 +444,66 @@ float ldexpf(float x, int exp) NOEXCEPT
return internal_scalbn(x, exp);
}
-double tanh(double x) NOEXCEPT
+long double tanhl(long double x) NOEXCEPT
{
if (x > 0) {
- double exponentiated = exp(2 * x);
+ long double exponentiated = expl(2 * x);
return (exponentiated - 1) / (exponentiated + 1);
}
- double plusX = exp(x);
- double minusX = 1 / plusX;
+ long double plusX = expl(x);
+ long double minusX = 1 / plusX;
return (plusX - minusX) / (plusX + minusX);
}
-static double ampsin(double angle) NOEXCEPT
+double tanh(double x) NOEXCEPT
{
- double looped_angle = fmod(M_PI + angle, M_TAU) - M_PI;
- double looped_angle_squared = looped_angle * looped_angle;
+ return (double)tanhl(x);
+}
- double quadratic_term;
+float tanhf(float x) NOEXCEPT
+{
+ return (float)tanhl(x);
+}
+
+static long double ampsin(long double angle) NOEXCEPT
+{
+ long double looped_angle = fmodl(M_PI + angle, M_TAU) - M_PI;
+ long double looped_angle_squared = looped_angle * looped_angle;
+
+ long double quadratic_term;
if (looped_angle > 0) {
quadratic_term = -looped_angle_squared;
} else {
quadratic_term = looped_angle_squared;
}
- double linear_term = M_PI * looped_angle;
+ long double linear_term = M_PI * looped_angle;
return quadratic_term + linear_term;
}
-double tan(double angle) NOEXCEPT
+long double tanl(long double angle) NOEXCEPT
{
return ampsin(angle) / ampsin(M_PI_2 + angle);
}
+double tan(double angle) NOEXCEPT
+{
+ return (double)tanl(angle);
+}
+
float tanf(float angle) NOEXCEPT
{
- return (float)tan((double)angle);
+ return (float)tanl(angle);
+}
+
+long double sqrtl(long double x) NOEXCEPT
+{
+ long double res;
+ asm("fsqrt"
+ : "=t"(res)
+ : "0"(x));
+ return res;
}
double sqrt(double x) NOEXCEPT
@@ -468,17 +524,27 @@ float sqrtf(float x) NOEXCEPT
return res;
}
-double sinh(double x) NOEXCEPT
+long double sinhl(long double x) NOEXCEPT
{
- double exponentiated = exp(x);
+ long double exponentiated = expl(x);
if (x > 0)
return (exponentiated * exponentiated - 1) / 2 / exponentiated;
return (exponentiated - 1 / exponentiated) / 2;
}
-double log10(double x) NOEXCEPT
+double sinh(double x) NOEXCEPT
{
- double ret = 0.0;
+ return (double)sinhl(x);
+}
+
+float sinhf(float x) NOEXCEPT
+{
+ return (float)sinhl(x);
+}
+
+long double log10l(long double x) NOEXCEPT
+{
+ long double ret = 0.0l;
__asm__(
"fldlg2\n"
"fld %%st(1)\n"
@@ -489,10 +555,20 @@ double log10(double x) NOEXCEPT
return ret;
}
-double log(double x) NOEXCEPT
+double log10(double x) NOEXCEPT
{
- double ret = 0.0;
- __asm__(
+ return (double)log10l(x);
+}
+
+float log10f(float x) NOEXCEPT
+{
+ return (float)log10l(x);
+}
+
+long double logl(long double x) NOEXCEPT
+{
+ long double ret = 0.0l;
+ asm(
"fldln2\n"
"fld %%st(1)\n"
"fyl2x\n"
@@ -502,9 +578,19 @@ double log(double x) NOEXCEPT
return ret;
}
+double log(double x) NOEXCEPT
+{
+ return (double)logl(x);
+}
+
float logf(float x) NOEXCEPT
{
- return (float)log(x);
+ return (float)logl(x);
+}
+
+long double fmodl(long double index, long double period) NOEXCEPT
+{
+ return index - truncl(index / period) * period;
}
double fmod(double index, double period) NOEXCEPT
@@ -517,60 +603,80 @@ float fmodf(float index, float period) NOEXCEPT
return index - trunc(index / period) * period;
}
-double exp(double exponent) NOEXCEPT
+long double expl(long double exponent) NOEXCEPT
{
- double res = 0;
- __asm__("fldl2e\n"
- "fmulp\n"
- "fld1\n"
- "fld %%st(1)\n"
- "fprem\n"
- "f2xm1\n"
- "faddp\n"
- "fscale\n"
- "fstp %%st(1)"
- : "=t"(res)
- : "0"(exponent));
+ long double res = 0;
+ asm("fldl2e\n"
+ "fmulp\n"
+ "fld1\n"
+ "fld %%st(1)\n"
+ "fprem\n"
+ "f2xm1\n"
+ "faddp\n"
+ "fscale\n"
+ "fstp %%st(1)"
+ : "=t"(res)
+ : "0"(exponent));
return res;
}
+double exp(double exponent) NOEXCEPT
+{
+ return (double)expl(exponent);
+}
+
float expf(float exponent) NOEXCEPT
{
- return (float)exp(exponent);
+ return (float)expl(exponent);
}
-double exp2(double exponent) NOEXCEPT
+long double exp2l(long double exponent) NOEXCEPT
{
- double res = 0;
- __asm__("fld1\n"
- "fld %%st(1)\n"
- "fprem\n"
- "f2xm1\n"
- "faddp\n"
- "fscale\n"
- "fstp %%st(1)"
- : "=t"(res)
- : "0"(exponent));
+ long double res = 0;
+ asm("fld1\n"
+ "fld %%st(1)\n"
+ "fprem\n"
+ "f2xm1\n"
+ "faddp\n"
+ "fscale\n"
+ "fstp %%st(1)"
+ : "=t"(res)
+ : "0"(exponent));
return res;
}
+double exp2(double exponent) NOEXCEPT
+{
+ return (double)exp2l(exponent);
+}
+
float exp2f(float exponent) NOEXCEPT
{
- return (float)exp2(exponent);
+ return (float)exp2l(exponent);
}
-double cosh(double x) NOEXCEPT
+long double coshl(long double x) NOEXCEPT
{
- double exponentiated = exp(-x);
+ long double exponentiated = expl(-x);
if (x < 0)
return (1 + exponentiated * exponentiated) / 2 / exponentiated;
return (1 / exponentiated + exponentiated) / 2;
}
-double atan2(double y, double x) NOEXCEPT
+double cosh(double x) NOEXCEPT
+{
+ return (double)coshl(x);
+}
+
+float coshf(float x) NOEXCEPT
+{
+ return (float)coshl(x);
+}
+
+long double atan2l(long double y, long double x) NOEXCEPT
{
if (x > 0)
- return atan(y / x);
+ return atanl(y / x);
if (x == 0) {
if (y > 0)
return M_PI_2;
@@ -579,34 +685,49 @@ double atan2(double y, double x) NOEXCEPT
return 0;
}
if (y >= 0)
- return atan(y / x) + M_PI;
- return atan(y / x) - M_PI;
+ return atanl(y / x) + M_PI;
+ return atanl(y / x) - M_PI;
+}
+
+double atan2(double y, double x) NOEXCEPT
+{
+ return (double)atan2l(y, x);
}
float atan2f(float y, float x) NOEXCEPT
{
- return (float)atan2(y, x);
+ return (float)atan2l(y, x);
}
-double atan(double x) NOEXCEPT
+long double atanl(long double x) NOEXCEPT
{
if (x < 0)
- return -atan(-x);
+ return -atanl(-x);
if (x > 1)
- return M_PI_2 - atan(1 / x);
- double squared = x * x;
+ return M_PI_2 - atanl(1 / x);
+ long double squared = x * x;
return x / (1 + 1 * 1 * squared / (3 + 2 * 2 * squared / (5 + 3 * 3 * squared / (7 + 4 * 4 * squared / (9 + 5 * 5 * squared / (11 + 6 * 6 * squared / (13 + 7 * 7 * squared)))))));
}
-double asin(double x) NOEXCEPT
+double atan(double x) NOEXCEPT
+{
+ return (double)atanl(x);
+}
+
+float atanf(float x) NOEXCEPT
+{
+ return (float)atanl(x);
+}
+
+long double asinl(long double x) NOEXCEPT
{
if (x > 1 || x < -1)
return NAN;
if (x > 0.5 || x < -0.5)
- return 2 * atan(x / (1 + sqrt(1 - x * x)));
- double squared = x * x;
- double value = x;
- double i = x * squared;
+ return 2 * atanl(x / (1 + sqrtl(1 - x * x)));
+ long double squared = x * x;
+ long double value = x;
+ long double i = x * squared;
value += i * product_odd<1>() / product_even<2>() / 3;
i *= squared;
value += i * product_odd<3>() / product_even<4>() / 5;
@@ -621,9 +742,19 @@ double asin(double x) NOEXCEPT
return value;
}
+double asin(double x) NOEXCEPT
+{
+ return (double)asinl(x);
+}
+
float asinf(float x) NOEXCEPT
{
- return (float)asin(x);
+ return (float)asinl(x);
+}
+
+long double acosl(long double x) NOEXCEPT
+{
+ return M_PI_2 - asinl(x);
}
double acos(double x) NOEXCEPT
@@ -636,11 +767,21 @@ float acosf(float x) NOEXCEPT
return M_PI_2 - asinf(x);
}
+long double fabsl(long double value) NOEXCEPT
+{
+ return value < 0 ? -value : value;
+}
+
double fabs(double value) NOEXCEPT
{
return value < 0 ? -value : value;
}
+float fabsf(float value) NOEXCEPT
+{
+ return value < 0 ? -value : value;
+}
+
int ilogbl(long double x) NOEXCEPT
{
return internal_ilogb(x);
@@ -671,10 +812,10 @@ float logbf(float x) NOEXCEPT
return ilogbf(x);
}
-double log2(double x) NOEXCEPT
+long double log2l(long double x) NOEXCEPT
{
- double ret = 0.0;
- __asm__(
+ long double ret = 0.0;
+ asm(
"fld1\n"
"fld %%st(1)\n"
"fyl2x\n"
@@ -684,14 +825,14 @@ double log2(double x) NOEXCEPT
return ret;
}
-float log2f(float x) NOEXCEPT
+double log2(double x) NOEXCEPT
{
- return log2(x);
+ return (double)log2l(x);
}
-long double log2l(long double x) NOEXCEPT
+float log2f(float x) NOEXCEPT
{
- return log2(x);
+ return (float)log2l(x);
}
double frexp(double x, int* exp) NOEXCEPT
@@ -802,14 +943,19 @@ long double ceill(long double value) NOEXCEPT
return internal_to_integer(value, RoundingMode::Up);
}
+long double modfl(long double x, long double* intpart) NOEXCEPT
+{
+ return internal_modf(x, intpart);
+}
+
double modf(double x, double* intpart) NOEXCEPT
{
- double integer_part = internal_to_integer(x, RoundingMode::ToZero);
- *intpart = integer_part;
- auto fraction = x - integer_part;
- if (signbit(fraction) != signbit(x))
- fraction = -fraction;
- return fraction;
+ return internal_modf(x, intpart);
+}
+
+float modff(float x, float* intpart) NOEXCEPT
+{
+ return internal_modf(x, intpart);
}
double gamma(double x) NOEXCEPT
@@ -818,91 +964,181 @@ double gamma(double x) NOEXCEPT
return sqrt(2.0 * M_PI / x) * pow(x / M_E, x);
}
+long double expm1l(long double x) NOEXCEPT
+{
+ return expl(x) - 1;
+}
+
double expm1(double x) NOEXCEPT
{
return exp(x) - 1;
}
-double cbrt(double x) NOEXCEPT
+float expm1f(float x) NOEXCEPT
+{
+ return expf(x) - 1;
+}
+
+long double cbrtl(long double x) NOEXCEPT
{
if (isinf(x) || x == 0)
return x;
if (x < 0)
- return -cbrt(-x);
+ return -cbrtl(-x);
- double r = x;
- double ex = 0;
+ long double r = x;
+ long double ex = 0;
- while (r < 0.125) {
+ while (r < 0.125l) {
r *= 8;
ex--;
}
- while (r > 1.0) {
- r *= 0.125;
+ while (r > 1.0l) {
+ r *= 0.125l;
ex++;
}
- r = (-0.46946116 * r + 1.072302) * r + 0.3812513;
+ r = (-0.46946116l * r + 1.072302l) * r + 0.3812513l;
while (ex < 0) {
- r *= 0.5;
+ r *= 0.5l;
ex++;
}
while (ex > 0) {
- r *= 2;
+ r *= 2.0l;
ex--;
}
- r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
- r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
- r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
- r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
+ r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
+ r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
+ r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
+ r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
return r;
}
+double cbrt(double x) NOEXCEPT
+{
+ return (double)cbrtl(x);
+}
+
+float cbrtf(float x) NOEXCEPT
+{
+ return (float)cbrtl(x);
+}
+
+long double log1pl(long double x) NOEXCEPT
+{
+ return logl(1 + x);
+}
+
double log1p(double x) NOEXCEPT
{
return log(1 + x);
}
+float log1pf(float x) NOEXCEPT
+{
+ return logf(1 + x);
+}
+
+long double acoshl(long double x) NOEXCEPT
+{
+ return logl(x + sqrtl(x * x - 1));
+}
+
double acosh(double x) NOEXCEPT
{
return log(x + sqrt(x * x - 1));
}
+float acoshf(float x) NOEXCEPT
+{
+ return logf(x + sqrtf(x * x - 1));
+}
+
+long double asinhl(long double x) NOEXCEPT
+{
+ return logl(x + sqrtl(x * x + 1));
+}
+
double asinh(double x) NOEXCEPT
{
return log(x + sqrt(x * x + 1));
}
+float asinhf(float x) NOEXCEPT
+{
+ return logf(x + sqrtf(x * x + 1));
+}
+
+long double atanhl(long double x) NOEXCEPT
+{
+ return logl((1 + x) / (1 - x)) / 2.0l;
+}
+
double atanh(double x) NOEXCEPT
{
return log((1 + x) / (1 - x)) / 2.0;
}
+float atanhf(float x) NOEXCEPT
+{
+ return logf((1 + x) / (1 - x)) / 2.0f;
+}
+
+long double hypotl(long double x, long double y) NOEXCEPT
+{
+ return sqrtl(x * x + y * y);
+}
+
double hypot(double x, double y) NOEXCEPT
{
return sqrt(x * x + y * y);
}
-double erf(double x) NOEXCEPT
+float hypotf(float x, float y) NOEXCEPT
+{
+ return sqrtf(x * x + y * y);
+}
+
+long double erfl(long double x) NOEXCEPT
{
// algorithm taken from Abramowitz and Stegun (no. 26.2.17)
- double t = 1 / (1 + 0.47047 * fabs(x));
- double poly = t * (0.3480242 + t * (-0.958798 + t * 0.7478556));
- double answer = 1 - poly * exp(-x * x);
+ long double t = 1 / (1 + 0.47047l * fabsl(x));
+ long double poly = t * (0.3480242l + t * (-0.958798l + t * 0.7478556l));
+ long double answer = 1 - poly * expl(-x * x);
if (x < 0)
return -answer;
return answer;
}
+double erf(double x) NOEXCEPT
+{
+ return (double)erfl(x);
+}
+
+float erff(float x) NOEXCEPT
+{
+ return (float)erf(x);
+}
+
+long double erfcl(long double x) NOEXCEPT
+{
+ return 1 - erfl(x);
+}
+
double erfc(double x) NOEXCEPT
{
return 1 - erf(x);
}
+float erfcf(float x) NOEXCEPT
+{
+ return 1 - erff(x);
+}
+
double nextafter(double x, double target) NOEXCEPT
{
if (x == target)
@@ -917,9 +1153,9 @@ float nextafterf(float x, float target) NOEXCEPT
return internal_nextafter(x, target >= x);
}
-long double nextafterl(long double, long double) NOEXCEPT
+long double nextafterl(long double x, long double target) NOEXCEPT
{
- TODO();
+ return internal_nextafter(x, target >= x);
}
double nexttoward(double x, long double target) NOEXCEPT
@@ -936,9 +1172,11 @@ float nexttowardf(float x, long double target) NOEXCEPT
return internal_nextafter(x, target >= x);
}
-long double nexttowardl(long double, long double) NOEXCEPT
+long double nexttowardl(long double x, long double target) NOEXCEPT
{
- TODO();
+ if (x == target)
+ return target;
+ return internal_nextafter(x, target >= x);
}
float copysignf(float x, float y) NOEXCEPT
diff --git a/Userland/Libraries/LibM/math.h b/Userland/Libraries/LibM/math.h
index 224eb283a9..c6ce9733cf 100644
--- a/Userland/Libraries/LibM/math.h
+++ b/Userland/Libraries/LibM/math.h
@@ -81,24 +81,34 @@ long double nanl(const char*) NOEXCEPT;
double nan(const char*) NOEXCEPT;
float nanf(const char*) NOEXCEPT;
+long double acosl(long double) NOEXCEPT;
double acos(double) NOEXCEPT;
float acosf(float) NOEXCEPT;
+long double asinl(long double) NOEXCEPT;
double asin(double) NOEXCEPT;
float asinf(float) NOEXCEPT;
+long double atanl(long double) NOEXCEPT;
double atan(double) NOEXCEPT;
float atanf(float) NOEXCEPT;
+long double atan2l(long double, long double) NOEXCEPT;
double atan2(double, double) NOEXCEPT;
float atan2f(float, float) NOEXCEPT;
+long double cosl(long double) NOEXCEPT;
double cos(double) NOEXCEPT;
float cosf(float) NOEXCEPT;
+long double coshl(long double) NOEXCEPT;
double cosh(double) NOEXCEPT;
float coshf(float) NOEXCEPT;
+long double sinl(long double) NOEXCEPT;
double sin(double) NOEXCEPT;
float sinf(float) NOEXCEPT;
+long double sinhl(long double) NOEXCEPT;
double sinh(double) NOEXCEPT;
float sinhf(float) NOEXCEPT;
+long double tanl(long double) NOEXCEPT;
double tan(double) NOEXCEPT;
float tanf(float) NOEXCEPT;
+long double tanhl(long double) NOEXCEPT;
double tanh(double) NOEXCEPT;
float tanhf(float) NOEXCEPT;
double ceil(double) NOEXCEPT;
@@ -121,27 +131,38 @@ long lrintf(float) NOEXCEPT;
long long llrintl(long double) NOEXCEPT;
long long llrint(double) NOEXCEPT;
long long llrintf(float) NOEXCEPT;
+long double fabsl(long double) NOEXCEPT;
double fabs(double) NOEXCEPT;
float fabsf(float) NOEXCEPT;
+long double fmodl(long double, long double) NOEXCEPT;
double fmod(double, double) NOEXCEPT;
float fmodf(float, float) NOEXCEPT;
+long double expl(long double) NOEXCEPT;
double exp(double) NOEXCEPT;
float expf(float) NOEXCEPT;
+long double exp2l(long double) NOEXCEPT;
double exp2(double) NOEXCEPT;
float exp2f(float) NOEXCEPT;
+long double frexpl(long double, int* exp) NOEXCEPT;
double frexp(double, int* exp) NOEXCEPT;
float frexpf(float, int* exp) NOEXCEPT;
+long double logl(long double) NOEXCEPT;
double log(double) NOEXCEPT;
float logf(float) NOEXCEPT;
+long double log10l(long double) NOEXCEPT;
double log10(double) NOEXCEPT;
float log10f(float) NOEXCEPT;
+long double sqrtl(long double) NOEXCEPT;
double sqrt(double) NOEXCEPT;
float sqrtf(float) NOEXCEPT;
+
+long double modfl(long double, long double*) NOEXCEPT;
double modf(double, double*) NOEXCEPT;
float modff(float, float*) NOEXCEPT;
double ldexp(double, int exp) NOEXCEPT;
float ldexpf(float, int exp) NOEXCEPT;
+long double powl(long double x, long double y) NOEXCEPT;
double pow(double x, double y) NOEXCEPT;
float powf(float x, float y) NOEXCEPT;
@@ -162,15 +183,33 @@ float frexpf(float, int*) NOEXCEPT;
long double frexpl(long double, int*) NOEXCEPT;
double gamma(double) NOEXCEPT;
+long double expm1l(long double) NOEXCEPT;
double expm1(double) NOEXCEPT;
+float expm1f(float) NOEXCEPT;
+long double cbrtl(long double) NOEXCEPT;
double cbrt(double) NOEXCEPT;
+float cbrtf(float) NOEXCEPT;
+long double log1pl(long double) NOEXCEPT;
double log1p(double) NOEXCEPT;
+float log1pf(float) NOEXCEPT;
+long double acoshl(long double) NOEXCEPT;
double acosh(double) NOEXCEPT;
+float acoshf(float) NOEXCEPT;
+long double asinhl(long double) NOEXCEPT;
double asinh(double) NOEXCEPT;
+float asinhf(float) NOEXCEPT;
+long double atanhl(long double) NOEXCEPT;
double atanh(double) NOEXCEPT;
+float atanhf(float) NOEXCEPT;
+long double hypotl(long double, long double) NOEXCEPT;
double hypot(double, double) NOEXCEPT;
+float hypotf(float, float) NOEXCEPT;
+long double erfl(long double) NOEXCEPT;
double erf(double) NOEXCEPT;
+float erff(float) NOEXCEPT;
+long double erfcl(long double) NOEXCEPT;
double erfc(double) NOEXCEPT;
+float erfcf(float) NOEXCEPT;
double nextafter(double, double) NOEXCEPT;
float nextafterf(float, float) NOEXCEPT;