__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; }