__complex__ long double
__ctanl (__complex__ long double x)
{
__complex__ long double res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinfl (__imag__ x))
{
__real__ res = __copysignl (0.0, __real__ x);
__imag__ res = __copysignl (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
#ifdef FE_INVALID
if (__isinfl (__real__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
long double sin2rx, cos2rx;
long double den;
__sincosl (2.0 * __real__ x, &sin2rx, &cos2rx);
den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
__real__ res = sin2rx / den;
__imag__ res = __ieee754_sinhl (2.0 * __imag__ x) / den;
}
return res;
}
__complex__ long double
__ccoshl (__complex__ long double x)
{
__complex__ long double retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
if (__glibc_likely (fabsl (__imag__ x) > LDBL_MIN))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
if (fabsl (__real__ x) > t)
{
long double exp_t = __ieee754_expl (t);
long double rx = fabsl (__real__ x);
if (signbit (__real__ x))
sinix = -sinix;
rx -= t;
sinix *= exp_t / 2.0L;
cosix *= exp_t / 2.0L;
if (rx > t)
{
rx -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (rx > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = LDBL_MAX * cosix;
__imag__ retval = LDBL_MAX * sinix;
}
else
{
long double exp_val = __ieee754_expl (rx);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
__real__ retval = __ieee754_coshl (__real__ x) * cosix;
__imag__ retval = __ieee754_sinhl (__real__ x) * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
__imag__ retval = __real__ x == 0.0 ? 0.0 : __nanl ("");
__real__ retval = __nanl ("") + __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else if (rcls == FP_INFINITE)
{
/* Real part is infinite. */
if (__glibc_likely (icls > FP_ZERO))
{
/* Imaginary part is finite. */
long double sinix, cosix;
if (__glibc_likely (fabsl (__imag__ x) > LDBL_MIN))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
__real__ retval = __copysignl (HUGE_VALL, cosix);
__imag__ retval = (__copysignl (HUGE_VALL, sinix)
* __copysignl (1.0, __real__ x));
}
else if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = HUGE_VALL;
__imag__ retval = __imag__ x * __copysignl (1.0, __real__ x);
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALL;
__imag__ retval = __nanl ("") + __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else
{
__real__ retval = __nanl ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanl ("");
}
return retval;
}
__complex__ long double
__cexpl (__complex__ long double x)
{
__complex__ long double retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls >= FP_ZERO, 1))
{
/* Real part is finite. */
if (__builtin_expect (icls >= FP_ZERO, 1))
{
/* Imaginary part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
__sincosl (__imag__ x, &sinix, &cosix);
if (__real__ x > t)
{
long double exp_t = __ieee754_expl (t);
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
if (__real__ x > t)
{
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
}
}
if (__real__ x > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = LDBL_MAX * cosix;
__imag__ retval = LDBL_MAX * sinix;
}
else
{
long double exp_val = __ieee754_expl (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
/* If the imaginary part is +-inf or NaN and the real part
is not +-inf the result is NaN + iNaN. */
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
feraiseexcept (FE_INVALID);
}
}
else if (__builtin_expect (rcls == FP_INFINITE, 1))
{
/* Real part is infinite. */
if (__builtin_expect (icls >= FP_ZERO, 1))
{
/* Imaginary part is finite. */
long double value = signbit (__real__ x) ? 0.0 : HUGE_VALL;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
long double sinix, cosix;
__sincosl (__imag__ x, &sinix, &cosix);
__real__ retval = __copysignl (value, cosix);
__imag__ retval = __copysignl (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = HUGE_VALL;
__imag__ retval = __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = 0.0;
__imag__ retval = __copysignl (0.0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN. */
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
return retval;
}
long double
__ieee754_y1l (long double x)
{
long double xx, xinv, z, p, q, c, s, cc, ss;
if (! __finitel (x))
{
if (x != x)
return x;
else
return 0.0L;
}
if (x <= 0.0L)
{
if (x < 0.0L)
return (zero / (zero * x));
return -HUGE_VALL + x;
}
xx = fabsl (x);
if (xx <= 2.0L)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
p = -TWOOPI / xx + p;
p = TWOOPI * __ieee754_logl (x) * __ieee754_j1l (x) + p;
return p;
}
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0L + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
return z;
}
_Float128
__ieee754_y0l(_Float128 x)
{
_Float128 xx, xinv, z, p, q, c, s, cc, ss;
if (! isfinite (x))
{
if (x != x)
return x + x;
else
return 0;
}
if (x <= 0)
{
if (x < 0)
return (zero / (zero * x));
return -HUGE_VALL + x;
}
xx = fabsl (x);
if (xx <= 0x1p-57)
return U0 + TWOOPI * __ieee754_logl (x);
if (xx <= 2)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
p = TWOOPI * __ieee754_logl (x) * __ieee754_j0l (x) + p;
return p;
}
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (x, &s, &c);
ss = s - c;
cc = s + c;
if (xx <= LDBL_MAX / 2)
{
z = -__cosl (x + x);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
}
if (xx > L(0x1p256))
return ONEOSQPI * ss / __ieee754_sqrtl (x);
xinv = 1 / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1 + z * p;
q = z * xinv * q;
q = q - L(0.125) * xinv;
z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x);
return z;
}
__complex__ long double
__ctanl (__complex__ long double x)
{
__complex__ long double res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_nsl (__imag__ x))
{
__real__ res = __copysignl (0.0, __real__ x);
__imag__ res = __copysignl (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
if (__isinf_nsl (__real__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
long double sinrx, cosrx;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
int rcls = fpclassify (__real__ x);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincosl (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0;
}
if (fabsl (__imag__ x) > t)
{
/* Avoid intermediate overflow when the real part of the
result may be subnormal. Ignoring negligible terms, the
imaginary part is +/- 1, the real part is
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
long double exp_2t = __ieee754_expl (2 * t);
__imag__ res = __copysignl (1.0, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsl (__imag__ x);
__imag__ x -= t;
__real__ res /= exp_2t;
if (__imag__ x > t)
{
/* Underflow (original imaginary part of x has absolute
value > 2t). */
__real__ res /= exp_2t;
}
else
__real__ res /= __ieee754_expl (2 * __imag__ x);
}
else
{
long double sinhix, coshix;
if (fabsl (__imag__ x) > LDBL_MIN)
{
sinhix = __ieee754_sinhl (__imag__ x);
coshix = __ieee754_coshl (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0L;
}
if (fabsl (sinhix) > fabsl (cosrx) * LDBL_EPSILON)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
}
return res;
}
__complex__ long double
__ctanhl (__complex__ long double x)
{
__complex__ long double res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinfl (__real__ x))
{
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = __copysignl (0.0L, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
#ifdef FE_INVALID
if (__isinfl (__imag__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
long double sinix, cosix;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
__sincosl (__imag__ x, &sinix, &cosix);
if (fabsl (__real__ x) > t)
{
/* Avoid intermediate overflow when the imaginary part of
the result may be subnormal. Ignoring negligible terms,
the real part is +/- 1, the imaginary part is
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
long double exp_2t = __ieee754_expl (2 * t);
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsl (__real__ x);
__real__ x -= t;
__imag__ res /= exp_2t;
if (__real__ x > t)
{
/* Underflow (original real part of x has absolute value
> 2t). */
__imag__ res /= exp_2t;
}
else
__imag__ res /= __ieee754_expl (2.0L * __real__ x);
}
else
{
long double sinhrx, coshrx;
if (fabs (__real__ x) > LDBL_MIN)
{
sinhrx = __ieee754_sinhl (__real__ x);
coshrx = __ieee754_coshl (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0L;
}
if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * (coshrx / den);
__imag__ res = sinix * (cosix / den);
}
/* __gcc_qmul does not respect -0.0 so we need the following fixup. */
if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
__real__ res = __real__ x;
if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
__imag__ res = __imag__ x;
}
return res;
}
long double
__ieee754_j0l (long double x)
{
long double xx, xinv, z, p, q, c, s, cc, ss;
if (! isfinite (x))
{
if (x != x)
return x;
else
return 0.0L;
}
if (x == 0.0L)
return 1.0L;
xx = fabsl (x);
if (xx <= 2.0L)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = z * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
p -= 0.25L * z;
p += 1.0L;
return p;
}
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = s - c;
cc = s + c;
if (xx <= LDBL_MAX / 2.0L)
{
z = -__cosl (xx + xx);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
}
if (xx > 0x1p256L)
return ONEOSQPI * cc / __ieee754_sqrtl (xx);
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0L + z * p;
q = z * xinv * q;
q = q - 0.125L * xinv;
z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
return z;
}
__complex__ long double
__cexpl (__complex__ long double x)
{
__complex__ long double retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
if (__glibc_likely (icls != FP_SUBNORMAL))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
if (__real__ x > t)
{
long double exp_t = __ieee754_expl (t);
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
if (__real__ x > t)
{
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
}
}
if (__real__ x > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = LDBL_MAX * cosix;
__imag__ retval = LDBL_MAX * sinix;
}
else
{
long double exp_val = __ieee754_expl (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
if (fabsl (__real__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsl (__imag__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __imag__ retval * __imag__ retval;
(void) force_underflow;
}
}
else
{
/* If the imaginary part is +-inf or NaN and the real part
is not +-inf the result is NaN + iNaN. */
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
feraiseexcept (FE_INVALID);
}
}
else if (__glibc_likely (rcls == FP_INFINITE))
{
/* Real part is infinite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
long double value = signbit (__real__ x) ? 0.0 : HUGE_VALL;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
long double sinix, cosix;
if (__glibc_likely (icls != FP_SUBNORMAL))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
__real__ retval = __copysignl (value, cosix);
__imag__ retval = __copysignl (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = HUGE_VALL;
__imag__ retval = __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = 0.0;
__imag__ retval = __copysignl (0.0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN unless the
imaginary part is zero. */
__real__ retval = __nanl ("");
if (icls == FP_ZERO)
__imag__ retval = __imag__ x;
else
{
__imag__ retval = __nanl ("");
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
}
return retval;
}
__complex__ long double
__csinl (__complex__ long double x)
{
__complex__ long double retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = fabsl (__real__ x);
if (__builtin_expect (icls >= FP_ZERO, 1))
{
/* Imaginary part is finite. */
if (__builtin_expect (rcls >= FP_ZERO, 1))
{
/* Real part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincosl (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1.0;
}
if (fabsl (__imag__ x) > t)
{
long double exp_t = __ieee754_expl (t);
long double ix = fabsl (__imag__ x);
if (signbit (__imag__ x))
cosix = -cosix;
ix -= t;
sinix *= exp_t / 2.0L;
cosix *= exp_t / 2.0L;
if (ix > t)
{
ix -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (ix > t)
{
/* Overflow (original imaginary part of x > 3t). */
__real__ retval = LDBL_MAX * sinix;
__imag__ retval = LDBL_MAX * cosix;
}
else
{
long double exp_val = __ieee754_expl (ix);
__real__ retval = exp_val * sinix;
__imag__ retval = exp_val * cosix;
}
}
else
{
__real__ retval = __ieee754_coshl (__imag__ x) * sinix;
__imag__ retval = __ieee754_sinhl (__imag__ x) * cosix;
}
if (negate)
__real__ retval = -__real__ retval;
if (fabsl (__real__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsl (__imag__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __imag__ retval * __imag__ retval;
(void) force_underflow;
}
}
else
{
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = __nanl ("");
__imag__ retval = __imag__ x;
if (rcls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
feraiseexcept (FE_INVALID);
}
}
}
else if (icls == FP_INFINITE)
{
/* Imaginary part is infinite. */
if (rcls == FP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = __copysignl (0.0, negate ? -1.0 : 1.0);
__imag__ retval = __imag__ x;
}
else if (rcls > FP_ZERO)
{
/* Real part is finite. */
long double sinix, cosix;
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincosl (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1.0;
}
__real__ retval = __copysignl (HUGE_VALL, sinix);
__imag__ retval = __copysignl (HUGE_VALL, cosix);
if (negate)
__real__ retval = -__real__ retval;
if (signbit (__imag__ x))
__imag__ retval = -__imag__ retval;
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = __nanl ("");
__imag__ retval = HUGE_VALL;
if (rcls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else
{
if (rcls == FP_ZERO)
__real__ retval = __copysignl (0.0, negate ? -1.0 : 1.0);
else
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
}
return retval;
}
long double
__ieee754_j1l (long double x)
{
long double xx, xinv, z, p, q, c, s, cc, ss;
if (! isfinite (x))
{
if (x != x)
return x;
else
return 0.0L;
}
if (x == 0.0L)
return x;
xx = fabsl (x);
if (xx <= 0x1p-58L)
{
long double ret = x * 0.5L;
if (fabsl (ret) < LDBL_MIN)
{
long double force_underflow = ret * ret;
math_force_eval (force_underflow);
}
return ret;
}
if (xx <= 2.0L)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = xx * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
p += 0.5L * xx;
if (x < 0)
p = -p;
return p;
}
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
if (xx <= LDBL_MAX / 2.0L)
{
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
}
if (xx > 0x1p256L)
{
z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0L + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
