__complex__ long double __clogl (__complex__ long double x) { __complex__ long double result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (rcls == FP_ZERO && icls == FP_ZERO) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PIl : 0.0; __imag__ result = __copysignl (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsl (__real__ x); } else if (rcls != FP_NAN && icls != FP_NAN) { /* Neither real nor imaginary part is NaN. */ __real__ result = __ieee754_logl (__ieee754_hypotl (__real__ x, __imag__ x)); __imag__ result = __ieee754_atan2l (__imag__ x, __real__ x); } else { __imag__ result = __nanl (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALL; else __real__ result = __nanl (""); } return result; }
long double __atan2l (long double y, long double x) { if (__builtin_expect (x == 0.0L && y == 0.0L, 0) && _LIB_VERSION == _SVID_) return __kernel_standard (y, x, 203); /* atan2(+-0,+-0) */ return __ieee754_atan2l (y, x); }
__complex__ long double __catanl (__complex__ long double x) { __complex__ long double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0)) { if (rcls == FP_INFINITE) { __real__ res = __copysignl (M_PI_2l, __real__ x); __imag__ res = __copysignl (0.0, __imag__ x); } else if (icls == FP_INFINITE) { if (rcls >= FP_ZERO) __real__ res = __copysignl (M_PI_2l, __real__ x); else __real__ res = __nanl (""); __imag__ res = __copysignl (0.0, __imag__ x); } else if (icls == FP_ZERO || icls == FP_INFINITE) { __real__ res = __nanl (""); __imag__ res = __copysignl (0.0, __imag__ x); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { res = x; } else { long double r2, num, den; r2 = __real__ x * __real__ x; den = 1 - r2 - __imag__ x * __imag__ x; __real__ res = 0.5 * __ieee754_atan2l (2.0 * __real__ x, den); num = __imag__ x + 1.0; num = r2 + num * num; den = __imag__ x - 1.0; den = r2 + den * den; __imag__ res = 0.25 * __ieee754_logl (num / den); } return res; }
__complex__ long double __clogl (__complex__ long double x) { __complex__ long double result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PIl : 0.0; __imag__ result = __copysignl (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsl (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ long double d; int scale = 0; if (fabsl (__real__ x) > LDBL_MAX / 2.0L || fabsl (__imag__ x) > LDBL_MAX / 2.0L) { scale = -1; __real__ x = __scalbnl (__real__ x, scale); __imag__ x = __scalbnl (__imag__ x, scale); } else if (fabsl (__real__ x) < LDBL_MIN && fabsl (__imag__ x) < LDBL_MIN) { scale = LDBL_MANT_DIG; __real__ x = __scalbnl (__real__ x, scale); __imag__ x = __scalbnl (__imag__ x, scale); } d = __ieee754_hypotl (__real__ x, __imag__ x); __real__ result = __ieee754_logl (d) - scale * M_LN2l; __imag__ result = __ieee754_atan2l (__imag__ x, __real__ x); } else { __imag__ result = __nanl (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALL; else __real__ result = __nanl (""); } return result; }
__complex__ long double __catanhl (__complex__ long double x) { __complex__ long double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0)) { if (icls == FP_INFINITE) { __real__ res = __copysignl (0.0, __real__ x); __imag__ res = __copysignl (M_PI_2l, __imag__ x); } else if (rcls == FP_INFINITE || rcls == FP_ZERO) { __real__ res = __copysignl (0.0, __real__ x); if (icls >= FP_ZERO) __imag__ res = __copysignl (M_PI_2l, __imag__ x); else __imag__ res = __nanl (""); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { res = x; } else { long double i2 = __imag__ x * __imag__ x; long double num = 1.0 + __real__ x; num = i2 + num * num; long double den = 1.0 - __real__ x; den = i2 + den * den; __real__ res = 0.25 * (__ieee754_logl (num) - __ieee754_logl (den)); den = 1 - __real__ x * __real__ x - i2; __imag__ res = 0.5 * __ieee754_atan2l (2.0 * __imag__ x, den); } return res; }
__complex__ long double __kernel_casinhl (__complex__ long double x, int adj) { __complex__ long double res; long double rx, ix; __complex__ long double y; /* Avoid cancellation by reducing to the first quadrant. */ rx = fabsl (__real__ x); ix = fabsl (__imag__ x); if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON) { /* For large x in the first quadrant, x + csqrt (1 + x * x) is sufficiently close to 2 * x to make no significant difference to the result; avoid possible overflow from the squaring and addition. */ __real__ y = rx; __imag__ y = ix; if (adj) { long double t = __real__ y; __real__ y = __copysignl (__imag__ y, __imag__ x); __imag__ y = t; } res = __clogl (y); __real__ res += M_LN2l; } else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L) { long double s = __ieee754_hypotl (1.0L, rx); __real__ res = __ieee754_logl (rx + s); if (adj) __imag__ res = __ieee754_atan2l (s, __imag__ x); else __imag__ res = __ieee754_atan2l (ix, s); } else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L) { long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L)); __real__ res = __ieee754_logl (ix + s); if (adj) __imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x)); else __imag__ res = __ieee754_atan2l (s, rx); } else if (ix > 1.0L && ix < 1.5L && rx < 0.5L) { if (rx < LDBL_EPSILON * LDBL_EPSILON) { long double ix2m1 = (ix + 1.0L) * (ix - 1.0L); long double s = __ieee754_sqrtl (ix2m1); __real__ res = __log1pl (2.0L * (ix2m1 + ix * s)) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x)); else __imag__ res = __ieee754_atan2l (s, rx); } else { long double ix2m1 = (ix + 1.0L) * (ix - 1.0L); long double rx2 = rx * rx; long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix); long double d = __ieee754_sqrtl (ix2m1 * ix2m1 + f); long double dp = d + ix2m1; long double dm = f / dp; long double r1 = __ieee754_sqrtl ((dm + rx2) / 2.0L); long double r2 = rx * ix / r1; __real__ res = __log1pl (rx2 + dp + 2.0L * (rx * r1 + ix * r2)) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2, __imag__ x)); else __imag__ res = __ieee754_atan2l (ix + r2, rx + r1); } } else if (ix == 1.0L && rx < 0.5L) { if (rx < LDBL_EPSILON / 8.0L) { __real__ res = __log1pl (2.0L * (rx + __ieee754_sqrtl (rx))) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (__ieee754_sqrtl (rx), __copysignl (1.0L, __imag__ x)); else __imag__ res = __ieee754_atan2l (1.0L, __ieee754_sqrtl (rx)); } else { long double d = rx * __ieee754_sqrtl (4.0L + rx * rx); long double s1 = __ieee754_sqrtl ((d + rx * rx) / 2.0L); long double s2 = __ieee754_sqrtl ((d - rx * rx) / 2.0L); __real__ res = __log1pl (rx * rx + d + 2.0L * (rx * s1 + s2)) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (rx + s1, __copysignl (1.0L + s2, __imag__ x)); else __imag__ res = __ieee754_atan2l (1.0L + s2, rx + s1); } } else if (ix < 1.0L && rx < 0.5L) { if (ix >= LDBL_EPSILON) { if (rx < LDBL_EPSILON * LDBL_EPSILON) { long double onemix2 = (1.0L + ix) * (1.0L - ix); long double s = __ieee754_sqrtl (onemix2); __real__ res = __log1pl (2.0L * rx / s) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (s, __imag__ x); else __imag__ res = __ieee754_atan2l (ix, s); } else { long double onemix2 = (1.0L + ix) * (1.0L - ix); long double rx2 = rx * rx; long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix); long double d = __ieee754_sqrtl (onemix2 * onemix2 + f); long double dp = d + onemix2; long double dm = f / dp; long double r1 = __ieee754_sqrtl ((dp + rx2) / 2.0L); long double r2 = rx * ix / r1; __real__ res = __log1pl (rx2 + dm + 2.0L * (rx * r1 + ix * r2)) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2, __imag__ x)); else __imag__ res = __ieee754_atan2l (ix + r2, rx + r1); } } else { long double s = __ieee754_hypotl (1.0L, rx); __real__ res = __log1pl (2.0L * rx * (rx + s)) / 2.0L; if (adj) __imag__ res = __ieee754_atan2l (s, __imag__ x); else __imag__ res = __ieee754_atan2l (ix, s); } if (__real__ res < LDBL_MIN) { volatile long double force_underflow = __real__ res * __real__ res; (void) force_underflow; } } else { __real__ y = (rx - ix) * (rx + ix) + 1.0L; __imag__ y = 2.0L * rx * ix; y = __csqrtl (y); __real__ y += rx; __imag__ y += ix; if (adj) { long double t = __real__ y; __real__ y = __copysignl (__imag__ y, __imag__ x); __imag__ y = t; } res = __clogl (y); } /* Give results the correct sign for the original argument. */ __real__ res = __copysignl (__real__ res, __real__ x); __imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x)); return res; }
__complex__ long double __clogl (__complex__ long double x) { __complex__ long double result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PIl : 0.0; __imag__ result = __copysignl (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsl (__real__ x); } else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN)) { /* Neither real nor imaginary part is NaN. */ long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x); int scale = 0; if (absx < absy) { long double t = absx; absx = absy; absy = t; } if (absx > LDBL_MAX / 2.0L) { scale = -1; absx = __scalbnl (absx, scale); absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L); } else if (absx < LDBL_MIN && absy < LDBL_MIN) { scale = LDBL_MANT_DIG; absx = __scalbnl (absx, scale); absy = __scalbnl (absy, scale); } if (absx == 1.0L && scale == 0) { __real__ result = __log1pl (absy * absy) / 2.0L; math_check_force_underflow_nonneg (__real__ result); } else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0) { long double d2m1 = (absx - 1.0L) * (absx + 1.0L); if (absy >= LDBL_EPSILON) d2m1 += absy * absy; __real__ result = __log1pl (d2m1) / 2.0L; } else if (absx < 1.0L && absx >= 0.5L && absy < LDBL_EPSILON / 2.0L && scale == 0) { long double d2m1 = (absx - 1.0L) * (absx + 1.0L); __real__ result = __log1pl (d2m1) / 2.0L; } else if (absx < 1.0L && absx >= 0.5L && scale == 0 && absx * absx + absy * absy >= 0.5L) { long double d2m1 = __x2y2m1l (absx, absy); __real__ result = __log1pl (d2m1) / 2.0L; } else { long double d = __ieee754_hypotl (absx, absy); __real__ result = __ieee754_logl (d) - scale * M_LN2l; } __imag__ result = __ieee754_atan2l (__imag__ x, __real__ x); } else { __imag__ result = __nanl (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALL; else __real__ result = __nanl (""); } return result; }
__complex__ long double __catanl (__complex__ long double x) { __complex__ long double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0)) { if (rcls == FP_INFINITE) { __real__ res = __copysignl (M_PI_2l, __real__ x); __imag__ res = __copysignl (0.0, __imag__ x); } else if (icls == FP_INFINITE) { if (rcls >= FP_ZERO) __real__ res = __copysignl (M_PI_2l, __real__ x); else __real__ res = __nanl (""); __imag__ res = __copysignl (0.0, __imag__ x); } else if (icls == FP_ZERO || icls == FP_INFINITE) { __real__ res = __nanl (""); __imag__ res = __copysignl (0.0, __imag__ x); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { res = x; } else { if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON) { __real__ res = __copysignl (M_PI_2l, __real__ x); if (fabsl (__real__ x) <= 1.0L) __imag__ res = 1.0L / __imag__ x; else if (fabsl (__imag__ x) <= 1.0L) __imag__ res = __imag__ x / __real__ x / __real__ x; else { long double h = __ieee754_hypotl (__real__ x / 2.0L, __imag__ x / 2.0L); __imag__ res = __imag__ x / h / h / 4.0L; } } else { long double den, absx, absy; absx = fabsl (__real__ x); absy = fabsl (__imag__ x); if (absx < absy) { long double t = absx; absx = absy; absy = t; } if (absy < LDBL_EPSILON / 2.0L) den = (1.0L - absx) * (1.0L + absx); else if (absx >= 1.0L) den = (1.0L - absx) * (1.0L + absx) - absy * absy; else if (absx >= 0.75L || absy >= 0.5L) den = -__x2y2m1l (absx, absy); else den = (1.0L - absx) * (1.0L + absx) - absy * absy; __real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den); if (fabsl (__imag__ x) == 1.0L && fabsl (__real__ x) < LDBL_EPSILON * LDBL_EPSILON) __imag__ res = (__copysignl (0.5L, __imag__ x) * (M_LN2l - __ieee754_logl (fabsl (__real__ x)))); else { long double r2 = 0.0L, num, f; if (fabsl (__real__ x) >= LDBL_EPSILON * LDBL_EPSILON) r2 = __real__ x * __real__ x; num = __imag__ x + 1.0L; num = r2 + num * num; den = __imag__ x - 1.0L; den = r2 + den * den; f = num / den; if (f < 0.5L) __imag__ res = 0.25L * __ieee754_logl (f); else { num = 4.0L * __imag__ x; __imag__ res = 0.25L * __log1pl (num / den); } } } if (fabsl (__real__ res) < LDBL_MIN) { volatile long double force_underflow = __real__ res * __real__ res; (void) force_underflow; } if (fabsl (__imag__ res) < LDBL_MIN) { volatile long double force_underflow = __imag__ res * __imag__ res; (void) force_underflow; } } return res; }
__complex__ long double __clog10l (__complex__ long double x) { __complex__ long double result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PIl : 0.0; __imag__ result = __copysignl (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsl (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x); int scale = 0; if (absx < absy) { long double t = absx; absx = absy; absy = t; } if (absx > LDBL_MAX / 2.0L) { scale = -1; absx = __scalbnl (absx, scale); absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L); } else if (absx < LDBL_MIN && absy < LDBL_MIN) { scale = LDBL_MANT_DIG; absx = __scalbnl (absx, scale); absy = __scalbnl (absy, scale); } if (absx == 1.0L && scale == 0) { long double absy2 = absy * absy; if (absy2 <= LDBL_MIN * 2.0L * M_LN10l) __real__ result = (absy2 / 2.0L - absy2 * absy2 / 4.0L) * M_LOG10El; else __real__ result = __log1pl (absy2) * (M_LOG10El / 2.0L); } else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0) { long double d2m1 = (absx - 1.0L) * (absx + 1.0L); if (absy >= LDBL_EPSILON) d2m1 += absy * absy; __real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L); } else if (absx < 1.0L && absx >= 0.75L && absy < LDBL_EPSILON / 2.0L && scale == 0) { long double d2m1 = (absx - 1.0L) * (absx + 1.0L); __real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L); } else if (absx < 1.0L && (absx >= 0.75L || absy >= 0.5L) && scale == 0) { long double d2m1 = __x2y2m1l (absx, absy); __real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L); } else { long double d = __ieee754_hypotl (absx, absy); __real__ result = __ieee754_log10l (d) - scale * M_LOG10_2l; } __imag__ result = M_LOG10El * __ieee754_atan2l (__imag__ x, __real__ x); } else { __imag__ result = __nanl (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALL; else __real__ result = __nanl (""); } return result; }