__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; }
__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 __casinhl (__complex__ long double x) { __complex__ long double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (rcls <= FP_INFINITE || icls <= FP_INFINITE) { if (icls == FP_INFINITE) { __real__ res = __copysignl (HUGE_VALL, __real__ x); if (rcls == FP_NAN) __imag__ res = __nanl (""); else __imag__ res = __copysignl (rcls >= FP_ZERO ? M_PI_2l : M_PI_4l, __imag__ x); } else if (rcls <= FP_INFINITE) { __real__ res = __real__ x; if ((rcls == FP_INFINITE && icls >= FP_ZERO) || (rcls == FP_NAN && icls == FP_ZERO)) __imag__ res = __copysignl (0.0, __imag__ x); else __imag__ res = __nanl (""); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else if (rcls == FP_ZERO && icls == FP_ZERO) { res = x; } else { res = __kernel_casinhl (x, 0); } return res; }
__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 __casinl (__complex__ long double x) { __complex__ long double res; if (isnan (__real__ x) || isnan (__imag__ x)) { if (__real__ x == 0.0) { res = x; } else if (__isinfl (__real__ x) || __isinfl (__imag__ x)) { __real__ res = __nanl (""); __imag__ res = __copysignl (HUGE_VALL, __imag__ x); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else { __complex__ long double y; __real__ y = -__imag__ x; __imag__ y = __real__ x; y = __casinhl (y); __real__ res = __imag__ y; __imag__ res = -__real__ y; } return res; }
__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 __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; }
__complex__ long double __cacoshl (__complex__ long double x) { __complex__ long double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (rcls <= FP_INFINITE || icls <= FP_INFINITE) { if (icls == FP_INFINITE) { __real__ res = HUGE_VALL; if (rcls == FP_NAN) __imag__ res = __nanl (""); else __imag__ res = __copysignl ((rcls == FP_INFINITE ? (__real__ x < 0.0 ? M_PIl - M_PI_4l : M_PI_4l) : M_PI_2l), __imag__ x); } else if (rcls == FP_INFINITE) { __real__ res = HUGE_VALL; if (icls >= FP_ZERO) __imag__ res = __copysignl (signbit (__real__ x) ? M_PIl : 0.0, __imag__ x); else __imag__ res = __nanl (""); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else if (rcls == FP_ZERO && icls == FP_ZERO) { __real__ res = 0.0; __imag__ res = __copysignl (M_PI_2l, __imag__ x); } /* The factor 16 is just a guess. */ else if (16.0L * fabsl (__imag__ x) < fabsl (__real__ x)) { /* Kahan's formula which avoid cancellation through subtraction in some cases. */ res = 2.0L * __clogl (__csqrtl ((x + 1.0L) / 2.0L) + __csqrtl ((x - 1.0L) / 2.0L)); if (signbit (__real__ res)) __real__ res = 0.0L; } else { __complex__ long double y; __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0; __imag__ y = 2.0 * __real__ x * __imag__ x; y = __csqrtl (y); if (signbit (__real__ x)) y = -y; __real__ y += __real__ x; __imag__ y += __imag__ x; res = __clogl (y); } return res; }
// // atanhl // long double atanhl(long double x) { if(fabsl(x) >= 1) {errno = EDOM; return __nanl();} return logl((1 + x) / (1 - x)) >> 1; }
__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; }
__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; }
__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 __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; }
// // nanl // long double nanl(char const *tagp) { return __nanl(); }
// // acoshl // long double acoshl(long double x) { if(x < 1) {errno = EDOM; return __nanl();} return logl(x + sqrtl(x * x - 1)); }
__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 __csqrtl (__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 = HUGE_VALL; __imag__ res = __imag__ x; } else if (rcls == FP_INFINITE) { if (__real__ x < 0.0) { __real__ res = icls == FP_NAN ? __nanl ("") : 0; __imag__ res = __copysignl (HUGE_VALL, __imag__ x); } else { __real__ res = __real__ x; __imag__ res = (icls == FP_NAN ? __nanl ("") : __copysignl (0.0, __imag__ x)); } } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else { if (__builtin_expect (icls == FP_ZERO, 0)) { if (__real__ x < 0.0) { __real__ res = 0.0; __imag__ res = __copysignl (__ieee754_sqrtl (-__real__ x), __imag__ x); } else { __real__ res = fabsl (__ieee754_sqrtl (__real__ x)); __imag__ res = __copysignl (0.0, __imag__ x); } } else if (__builtin_expect (rcls == FP_ZERO, 0)) { long double r = __ieee754_sqrtl (0.5 * fabsl (__imag__ x)); __real__ res = r; __imag__ res = __copysignl (r, __imag__ x); } else { long double d, r, s; d = __ieee754_hypotl (__real__ x, __imag__ x); /* Use the identity 2 Re res Im res = Im x to avoid cancellation error in d +/- Re x. */ if (__real__ x > 0) { r = __ieee754_sqrtl (0.5L * d + 0.5L * __real__ x); s = (0.5L * __imag__ x) / r; } else { s = __ieee754_sqrtl (0.5L * d - 0.5L * __real__ x); r = fabsl ((0.5L * __imag__ x) / s); } __real__ res = r; __imag__ res = __copysignl (s, __imag__ x); } } 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 __cacoshl (__complex__ long double x) { __complex__ long double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (rcls <= FP_INFINITE || icls <= FP_INFINITE) { if (icls == FP_INFINITE) { __real__ res = HUGE_VALL; if (rcls == FP_NAN) __imag__ res = __nanl (""); else __imag__ res = __copysignl ((rcls == FP_INFINITE ? (__real__ x < 0.0 ? M_PIl - M_PI_4l : M_PI_4l) : M_PI_2l), __imag__ x); } else if (rcls == FP_INFINITE) { __real__ res = HUGE_VALL; if (icls >= FP_ZERO) __imag__ res = __copysignl (signbit (__real__ x) ? M_PIl : 0.0, __imag__ x); else __imag__ res = __nanl (""); } else { __real__ res = __nanl (""); __imag__ res = __nanl (""); } } else if (rcls == FP_ZERO && icls == FP_ZERO) { __real__ res = 0.0; __imag__ res = __copysignl (M_PI_2l, __imag__ x); } else { __complex__ long double y; __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0; __imag__ y = 2.0 * __real__ x * __imag__ x; y = __csqrtl (y); if (__real__ x < 0.0) y = -y; __real__ y += __real__ x; __imag__ y += __imag__ x; res = __clogl (y); } return res; }