double __modf (double x, double *iptr) { if (__builtin_isinf (x)) { *iptr = x; return __copysign (0.0, x); } else if (__builtin_isnan (x)) { *iptr = NAN; return NAN; } if (x >= 0.0) { *iptr = __floor (x); return __copysign (x - *iptr, x); } else { *iptr = __ceil (x); return __copysign (x - *iptr, x); } }
__complex__ double __kernel_casinh (__complex__ double x, int adj) { __complex__ double res; double rx, ix; __complex__ double y; /* Avoid cancellation by reducing to the first quadrant. */ rx = fabs (__real__ x); ix = fabs (__imag__ x); if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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) { double t = __real__ y; __real__ y = __copysign (__imag__ y, __imag__ x); __imag__ y = t; } res = __clog (y); __real__ res += M_LN2; } else { __real__ y = (rx - ix) * (rx + ix) + 1.0; __imag__ y = 2.0 * rx * ix; y = __csqrt (y); __real__ y += rx; __imag__ y += ix; if (adj) { double t = __real__ y; __real__ y = copysign (__imag__ y, __imag__ x); __imag__ y = t; } res = __clog (y); } /* Give results the correct sign for the original argument. */ __real__ res = __copysign (__real__ res, __real__ x); __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x)); return res; }
__complex__ double __ctanh (__complex__ double x) { __complex__ double res; if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0)) { if (__isinf_ns (__real__ x)) { __real__ res = __copysign (1.0, __real__ x); __imag__ res = __copysign (0.0, __imag__ x); } else if (__imag__ x == 0.0) { res = x; } else { __real__ res = __nan (""); __imag__ res = __nan (""); if (__isinf_ns (__imag__ x)) feraiseexcept (FE_INVALID); } } else { double sin2ix, cos2ix; double den; __sincos (2.0 * __imag__ x, &sin2ix, &cos2ix); den = (__ieee754_cosh (2.0 * __real__ x) + cos2ix); if (den == 0.0) { __complex__ double ez = __cexp (x); __complex__ double emz = __cexp (-x); res = (ez - emz) / (ez + emz); } else { __real__ res = __ieee754_sinh (2.0 * __real__ x) / den; __imag__ res = sin2ix / den; } } return res; }
double __ieee754_atanh (double x) { double xa = fabs (x); double t; if (isless (xa, 0.5)) { if (__glibc_unlikely (xa < 0x1.0p-28)) { math_force_eval (huge + x); math_check_force_underflow (x); return x; } t = xa + xa; t = 0.5 * __log1p (t + t * xa / (1.0 - xa)); } else if (__glibc_likely (isless (xa, 1.0))) t = 0.5 * __log1p ((xa + xa) / (1.0 - xa)); else { if (isgreater (xa, 1.0)) return (x - x) / (x - x); return x / 0.0; } return __copysign (t, x); }
__complex__ double __clog10 (__complex__ double x) { __complex__ 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_PI : 0.0; __imag__ result = __copysign (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabs (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ __real__ result = __ieee754_log10 (__ieee754_hypot (__real__ x, __imag__ x)); __imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x); } else { __imag__ result = __nan (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VAL; else __real__ result = __nan (""); } return result; }
double __ieee754_atanh (double x) { double xa = fabs (x); double t; if (isless (xa, 0.5)) { if (__builtin_expect (xa < 0x1.0p-28, 0)) { math_force_eval (huge + x); return x; } t = xa + xa; t = 0.5 * __log1p (t + t * xa / (1.0 - xa)); } else if (__builtin_expect (isless (xa, 1.0), 1)) t = 0.5 * __log1p ((xa + xa) / (1.0 - xa)); else { if (isgreater (xa, 1.0)) return (x - x) / (x - x); return x / 0.0; } return __copysign (t, x); }
double __asinh (double x) { double w; int32_t hx, ix; GET_HIGH_WORD (hx, x); ix = hx & 0x7fffffff; if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */ { if (huge + x > one) return x; /* return x inexact except 0 */ } if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */ { if (ix >= 0x7ff00000) return x + x; /* x is inf or NaN */ w = __ieee754_log (fabs (x)) + ln2; } else { double xa = fabs (x); if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */ { w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) + xa)); } else /* 2.0 > |x| > 2**-28 */ { double t = xa * xa; w = __log1p (xa + t / (one + __ieee754_sqrt (one + t))); } } return __copysign (w, x); }
__complex__ double __casinh (__complex__ double x) { __complex__ 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 = __copysign (HUGE_VAL, __real__ x); if (rcls == FP_NAN) __imag__ res = __nan (""); else __imag__ res = __copysign (rcls >= FP_ZERO ? M_PI_2 : M_PI_4, __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 = __copysign (0.0, __imag__ x); else __imag__ res = __nan (""); } else { __real__ res = __nan (""); __imag__ res = __nan (""); } } else if (rcls == FP_ZERO && icls == FP_ZERO) { res = x; } else { res = __kernel_casinh (x, 0); } return res; }
__complex__ double __ctanh (__complex__ double x) { __complex__ double res; if (!isfinite (__real__ x) || !isfinite (__imag__ x)) { if (__isinf (__real__ x)) { __real__ res = __copysign (1.0, __real__ x); __imag__ res = __copysign (0.0, __imag__ x); } else if (__imag__ x == 0.0) { res = x; } else { __real__ res = __nan (""); __imag__ res = __nan (""); #ifdef FE_INVALID if (__isinf (__imag__ x)) feraiseexcept (FE_INVALID); #endif } } else { double sin2ix, cos2ix; double den; __sincos (2.0 * __imag__ x, &sin2ix, &cos2ix); den = (__ieee754_cosh (2.0 * __real__ x) + cos2ix); __real__ res = __ieee754_sinh (2.0 * __real__ x) / den; __imag__ res = sin2ix / den; } return res; }
__complex__ double __clog (__complex__ double x) { __complex__ 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_PI : 0.0; __imag__ result = __copysign (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabs (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ double d; int scale = 0; if (fabs (__real__ x) > DBL_MAX / 2.0 || fabs (__imag__ x) > DBL_MAX / 2.0) { scale = -1; __real__ x = __scalbn (__real__ x, scale); __imag__ x = __scalbn (__imag__ x, scale); } else if (fabs (__real__ x) < DBL_MIN && fabs (__imag__ x) < DBL_MIN) { scale = DBL_MANT_DIG; __real__ x = __scalbn (__real__ x, scale); __imag__ x = __scalbn (__imag__ x, scale); } d = __ieee754_hypot (__real__ x, __imag__ x); __real__ result = __ieee754_log (d) - scale * M_LN2; __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x); } else { __imag__ result = __nan (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VAL; else __real__ result = __nan (""); } return result; }
__complex__ double __cproj (__complex__ double x) { if (isinf (__real__ x) || isinf (__imag__ x)) { __complex__ double res; __real__ res = INFINITY; __imag__ res = __copysign (0.0, __imag__ x); return res; } return x; }
__complex__ double __casin (__complex__ double x) { __complex__ double res; if (isnan (__real__ x) || isnan (__imag__ x)) { if (__real__ x == 0.0) { res = x; } else if (isinf (__real__ x) || isinf (__imag__ x)) { __real__ res = __nan (""); __imag__ res = __copysign (HUGE_VAL, __imag__ x); } else { __real__ res = __nan (""); __imag__ res = __nan (""); } } else { __complex__ double y; __real__ y = -__imag__ x; __imag__ y = __real__ x; y = __casinh (y); __real__ res = __imag__ y; __imag__ res = -__real__ y; } return res; }
Err mathlib_copysign(UInt16 refnum, double x, double y, double *result) { #pragma unused(refnum) *result = __copysign(x, y); return mlErrNone; }
__complex__ double __kernel_casinh (__complex__ double x, int adj) { __complex__ double res; double rx, ix; __complex__ double y; /* Avoid cancellation by reducing to the first quadrant. */ rx = fabs (__real__ x); ix = fabs (__imag__ x); if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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) { double t = __real__ y; __real__ y = __copysign (__imag__ y, __imag__ x); __imag__ y = t; } res = __clog (y); __real__ res += M_LN2; } else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0) { double s = __ieee754_hypot (1.0, rx); __real__ res = __ieee754_log (rx + s); if (adj) __imag__ res = __ieee754_atan2 (s, __imag__ x); else __imag__ res = __ieee754_atan2 (ix, s); } else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5) { double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0)); __real__ res = __ieee754_log (ix + s); if (adj) __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x)); else __imag__ res = __ieee754_atan2 (s, rx); } else if (ix > 1.0 && ix < 1.5 && rx < 0.5) { if (rx < DBL_EPSILON * DBL_EPSILON) { double ix2m1 = (ix + 1.0) * (ix - 1.0); double s = __ieee754_sqrt (ix2m1); __real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x)); else __imag__ res = __ieee754_atan2 (s, rx); } else { double ix2m1 = (ix + 1.0) * (ix - 1.0); double rx2 = rx * rx; double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix); double d = __ieee754_sqrt (ix2m1 * ix2m1 + f); double dp = d + ix2m1; double dm = f / dp; double r1 = __ieee754_sqrt ((dm + rx2) / 2.0); double r2 = rx * ix / r1; __real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2, __imag__ x)); else __imag__ res = __ieee754_atan2 (ix + r2, rx + r1); } } else if (ix == 1.0 && rx < 0.5) { if (rx < DBL_EPSILON / 8.0) { __real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx), __copysign (1.0, __imag__ x)); else __imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx)); } else { double d = rx * __ieee754_sqrt (4.0 + rx * rx); double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0); double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0); __real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2, __imag__ x)); else __imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1); } } else if (ix < 1.0 && rx < 0.5) { if (ix >= DBL_EPSILON) { if (rx < DBL_EPSILON * DBL_EPSILON) { double onemix2 = (1.0 + ix) * (1.0 - ix); double s = __ieee754_sqrt (onemix2); __real__ res = __log1p (2.0 * rx / s) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (s, __imag__ x); else __imag__ res = __ieee754_atan2 (ix, s); } else { double onemix2 = (1.0 + ix) * (1.0 - ix); double rx2 = rx * rx; double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix); double d = __ieee754_sqrt (onemix2 * onemix2 + f); double dp = d + onemix2; double dm = f / dp; double r1 = __ieee754_sqrt ((dp + rx2) / 2.0); double r2 = rx * ix / r1; __real__ res = __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2, __imag__ x)); else __imag__ res = __ieee754_atan2 (ix + r2, rx + r1); } } else { double s = __ieee754_hypot (1.0, rx); __real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0; if (adj) __imag__ res = __ieee754_atan2 (s, __imag__ x); else __imag__ res = __ieee754_atan2 (ix, s); } math_check_force_underflow_nonneg (__real__ res); } else { __real__ y = (rx - ix) * (rx + ix) + 1.0; __imag__ y = 2.0 * rx * ix; y = __csqrt (y); __real__ y += rx; __imag__ y += ix; if (adj) { double t = __real__ y; __real__ y = __copysign (__imag__ y, __imag__ x); __imag__ y = t; } res = __clog (y); } /* Give results the correct sign for the original argument. */ __real__ res = __copysign (__real__ res, __real__ x); __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x)); return res; }
__complex__ double __cacosh (__complex__ double x) { __complex__ 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_VAL; if (rcls == FP_NAN) __imag__ res = __nan (""); else __imag__ res = __copysign ((rcls == FP_INFINITE ? (__real__ x < 0.0 ? M_PI - M_PI_4 : M_PI_4) : M_PI_2), __imag__ x); } else if (rcls == FP_INFINITE) { __real__ res = HUGE_VAL; if (icls >= FP_ZERO) __imag__ res = __copysign (signbit (__real__ x) ? M_PI : 0.0, __imag__ x); else __imag__ res = __nan (""); } else { __real__ res = __nan (""); __imag__ res = __nan (""); } } else if (rcls == FP_ZERO && icls == FP_ZERO) { __real__ res = 0.0; __imag__ res = __copysign (M_PI_2, __imag__ x); } else { __complex__ double y; __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0; __imag__ y = 2.0 * __real__ x * __imag__ x; y = __csqrt (y); if (__real__ x < 0.0) y = -y; __real__ y += __real__ x; __imag__ y += __imag__ x; res = __clog (y); /* We have to use the positive branch. */ if (__real__ res < 0.0) res = -res; } return res; }
/* Fix the sign and return after stage 1 or stage 2 */ static double signArctan2 (double y, double z) { return __copysign (z, y); }
__complex__ double __clog10 (__complex__ double x) { __complex__ 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_PI : 0.0; __imag__ result = __copysign (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabs (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ double absx = fabs (__real__ x), absy = fabs (__imag__ x); int scale = 0; if (absx < absy) { double t = absx; absx = absy; absy = t; } if (absx > DBL_MAX / 2.0) { scale = -1; absx = __scalbn (absx, scale); absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0); } else if (absx < DBL_MIN && absy < DBL_MIN) { scale = DBL_MANT_DIG; absx = __scalbn (absx, scale); absy = __scalbn (absy, scale); } if (absx == 1.0 && scale == 0) { double absy2 = absy * absy; if (absy2 <= DBL_MIN * 2.0 * M_LN10) { #if __FLT_EVAL_METHOD__ == 0 __real__ result = (absy2 / 2.0 - absy2 * absy2 / 4.0) * M_LOG10E; #else volatile double force_underflow = absy2 * absy2 / 4.0; __real__ result = (absy2 / 2.0 - force_underflow) * M_LOG10E; #endif } else __real__ result = __log1p (absy2) * (M_LOG10E / 2.0); } else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0) { double d2m1 = (absx - 1.0) * (absx + 1.0); if (absy >= DBL_EPSILON) d2m1 += absy * absy; __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0); } else if (absx < 1.0 && absx >= 0.75 && absy < DBL_EPSILON / 2.0 && scale == 0) { double d2m1 = (absx - 1.0) * (absx + 1.0); __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0); } else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0) { double d2m1 = __x2y2m1 (absx, absy); __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0); } else { double d = __ieee754_hypot (absx, absy); __real__ result = __ieee754_log10 (d) - scale * M_LOG10_2; } __imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x); } else { __imag__ result = __nan (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VAL; else __real__ result = __nan (""); } return result; }
long double __copysignl(long double x, long double y) { return ( (long double)__copysign((double)x, (double)y) ); }
__complex__ double __csin (__complex__ double x) { __complex__ double retval; int negate = signbit (__real__ x); int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); __real__ x = fabs (__real__ x); if (__glibc_likely (icls >= FP_ZERO)) { /* Imaginary part is finite. */ if (__glibc_likely (rcls >= FP_ZERO)) { /* Real part is finite. */ const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2); double sinix, cosix; if (__glibc_likely (rcls != FP_SUBNORMAL)) { __sincos (__real__ x, &sinix, &cosix); } else { sinix = __real__ x; cosix = 1.0; } if (fabs (__imag__ x) > t) { double exp_t = __ieee754_exp (t); double ix = fabs (__imag__ x); if (signbit (__imag__ x)) cosix = -cosix; ix -= t; sinix *= exp_t / 2.0; cosix *= exp_t / 2.0; if (ix > t) { ix -= t; sinix *= exp_t; cosix *= exp_t; } if (ix > t) { /* Overflow (original imaginary part of x > 3t). */ __real__ retval = DBL_MAX * sinix; __imag__ retval = DBL_MAX * cosix; } else { double exp_val = __ieee754_exp (ix); __real__ retval = exp_val * sinix; __imag__ retval = exp_val * cosix; } } else { __real__ retval = __ieee754_cosh (__imag__ x) * sinix; __imag__ retval = __ieee754_sinh (__imag__ x) * cosix; } if (negate) __real__ retval = -__real__ retval; if (fabs (__real__ retval) < DBL_MIN) { volatile double force_underflow = __real__ retval * __real__ retval; (void) force_underflow; } if (fabs (__imag__ retval) < DBL_MIN) { volatile double force_underflow = __imag__ retval * __imag__ retval; (void) force_underflow; } } else { if (icls == FP_ZERO) { /* Imaginary part is 0.0. */ __real__ retval = __nan (""); __imag__ retval = __imag__ x; if (rcls == FP_INFINITE) feraiseexcept (FE_INVALID); } else { __real__ retval = __nan (""); __imag__ retval = __nan (""); feraiseexcept (FE_INVALID); } } } else if (icls == FP_INFINITE) { /* Imaginary part is infinite. */ if (rcls == FP_ZERO) { /* Real part is 0.0. */ __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0); __imag__ retval = __imag__ x; } else if (rcls > FP_ZERO) { /* Real part is finite. */ double sinix, cosix; if (__glibc_likely (rcls != FP_SUBNORMAL)) { __sincos (__real__ x, &sinix, &cosix); } else { sinix = __real__ x; cosix = 1.0; } __real__ retval = __copysign (HUGE_VAL, sinix); __imag__ retval = __copysign (HUGE_VAL, cosix); if (negate) __real__ retval = -__real__ retval; if (signbit (__imag__ x)) __imag__ retval = -__imag__ retval; } else { /* The addition raises the invalid exception. */ __real__ retval = __nan (""); __imag__ retval = HUGE_VAL; if (rcls == FP_INFINITE) feraiseexcept (FE_INVALID); } } else { if (rcls == FP_ZERO) __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0); else __real__ retval = __nan (""); __imag__ retval = __nan (""); } return retval; }
/* Fix the sign of y and return */ static double __signArctan (double x, double y) { return __copysign (y, x); }
double __kernel_standard(double x, double y, int type) { struct exception exc; #ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ #define HUGE_VAL inf double inf = 0.0; SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ #endif #ifdef _USE_WRITE (void) fflush(stdout); #endif exc.arg1 = x; exc.arg2 = y; switch(type) { case 1: case 101: case 201: /* acos(|x|>1) */ exc.type = DOMAIN; exc.name = type < 100 ? "acos" : (type < 200 ? "acosf" : "acosl");; if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = NAN; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if(_LIB_VERSION == _SVID_) { (void) WRITE2("acos: DOMAIN error\n", 19); } __set_errno (EDOM); } break; case 2: case 102: case 202: /* asin(|x|>1) */ exc.type = DOMAIN; exc.name = type < 100 ? "asin" : (type < 200 ? "asinf" : "asinl"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = NAN; if(_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if(_LIB_VERSION == _SVID_) { (void) WRITE2("asin: DOMAIN error\n", 19); } __set_errno (EDOM); } break; case 3: case 103: case 203: /* atan2(+-0,+-0) */ exc.arg1 = y; exc.arg2 = x; exc.type = DOMAIN; exc.name = type < 100 ? "atan2" : (type < 200 ? "atan2f" : "atan2l"); assert (_LIB_VERSION == _SVID_); exc.retval = HUGE; if(_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if(_LIB_VERSION == _SVID_) { (void) WRITE2("atan2: DOMAIN error\n", 20); } __set_errno (EDOM); } break; case 4: case 104: case 204: /* hypot(finite,finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "hypot" : (type < 200 ? "hypotf" : "hypotl"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 5: case 105: case 205: /* cosh(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "cosh" : (type < 200 ? "coshf" : "coshl"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 6: case 106: case 206: /* exp(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "exp" : (type < 200 ? "expf" : "expl"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 7: case 107: case 207: /* exp(finite) underflow */ exc.type = UNDERFLOW; exc.name = type < 100 ? "exp" : (type < 200 ? "expf" : "expl"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 8: case 108: case 208: /* y0(0) = -inf */ exc.type = DOMAIN; /* should be SING for IEEE */ exc.name = type < 100 ? "y0" : (type < 200 ? "y0f" : "y0l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("y0: DOMAIN error\n", 17); } __set_errno (EDOM); } break; case 9: case 109: case 209: /* y0(x<0) = NaN */ exc.type = DOMAIN; exc.name = type < 100 ? "y0" : (type < 200 ? "y0f" : "y0l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("y0: DOMAIN error\n", 17); } __set_errno (EDOM); } break; case 10: case 110: case 210: /* y1(0) = -inf */ exc.type = DOMAIN; /* should be SING for IEEE */ exc.name = type < 100 ? "y1" : (type < 200 ? "y1f" : "y1l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("y1: DOMAIN error\n", 17); } __set_errno (EDOM); } break; case 11: case 111: case 211: /* y1(x<0) = NaN */ exc.type = DOMAIN; exc.name = type < 100 ? "y1" : (type < 200 ? "y1f" : "y1l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("y1: DOMAIN error\n", 17); } __set_errno (EDOM); } break; case 12: case 112: case 212: /* yn(n,0) = -inf */ exc.type = DOMAIN; /* should be SING for IEEE */ exc.name = type < 100 ? "yn" : (type < 200 ? "ynf" : "ynl"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("yn: DOMAIN error\n", 17); } __set_errno (EDOM); } break; case 13: case 113: case 213: /* yn(x<0) = NaN */ exc.type = DOMAIN; exc.name = type < 100 ? "yn" : (type < 200 ? "ynf" : "ynl"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("yn: DOMAIN error\n", 17); } __set_errno (EDOM); } break; case 14: case 114: case 214: /* lgamma(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "lgamma" : (type < 200 ? "lgammaf" : "lgammal"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 15: case 115: case 215: /* lgamma(-integer) or lgamma(0) */ exc.type = SING; exc.name = type < 100 ? "lgamma" : (type < 200 ? "lgammaf" : "lgammal"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("lgamma: SING error\n", 19); } __set_errno (EDOM); } break; case 16: case 116: case 216: /* log(0) */ exc.type = SING; exc.name = type < 100 ? "log" : (type < 200 ? "logf" : "logl"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("log: SING error\n", 16); } __set_errno (EDOM); } break; case 17: case 117: case 217: /* log(x<0) */ exc.type = DOMAIN; exc.name = type < 100 ? "log" : (type < 200 ? "logf" : "logl"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = NAN; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("log: DOMAIN error\n", 18); } __set_errno (EDOM); } break; case 18: case 118: case 218: /* log10(0) */ exc.type = SING; exc.name = type < 100 ? "log10" : (type < 200 ? "log10f" : "log10l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("log10: SING error\n", 18); } __set_errno (EDOM); } break; case 19: case 119: case 219: /* log10(x<0) */ exc.type = DOMAIN; exc.name = type < 100 ? "log10" : (type < 200 ? "log10f" : "log10l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = NAN; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("log10: DOMAIN error\n", 20); } __set_errno (EDOM); } break; case 20: case 120: case 220: /* pow(0.0,0.0) */ /* error only if _LIB_VERSION == _SVID_ */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); exc.retval = zero; if (_LIB_VERSION != _SVID_) exc.retval = 1.0; else if (!matherr(&exc)) { (void) WRITE2("pow(0,0): DOMAIN error\n", 23); __set_errno (EDOM); } break; case 21: case 121: case 221: /* pow(x,y) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); if (_LIB_VERSION == _SVID_) { exc.retval = HUGE; y *= 0.5; if(x<zero&&__rint(y)!=y) exc.retval = -HUGE; } else { exc.retval = HUGE_VAL; y *= 0.5; if(x<zero&&__rint(y)!=y) exc.retval = -HUGE_VAL; } if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 22: case 122: case 222: /* pow(x,y) underflow */ exc.type = UNDERFLOW; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); exc.retval = zero; y *= 0.5; if (x < zero && __rint (y) != y) exc.retval = -zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 23: case 123: case 223: /* -0**neg */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); if (_LIB_VERSION == _SVID_) exc.retval = zero; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); } __set_errno (EDOM); } break; case 43: case 143: case 243: /* +0**neg */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); if (_LIB_VERSION == _SVID_) exc.retval = zero; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); } __set_errno (EDOM); } break; case 24: case 124: case 224: /* neg**non-integral */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); if (_LIB_VERSION == _SVID_) exc.retval = zero; else exc.retval = zero/zero; /* X/Open allow NaN */ if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("neg**non-integral: DOMAIN error\n", 32); } __set_errno (EDOM); } break; case 25: case 125: case 225: /* sinh(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "sinh" : (type < 200 ? "sinhf" : "sinhl"); if (_LIB_VERSION == _SVID_) exc.retval = ( (x>zero) ? HUGE : -HUGE); else exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 26: case 126: case 226: /* sqrt(x<0) */ exc.type = DOMAIN; exc.name = type < 100 ? "sqrt" : (type < 200 ? "sqrtf" : "sqrtl"); if (_LIB_VERSION == _SVID_) exc.retval = zero; else exc.retval = zero/zero; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("sqrt: DOMAIN error\n", 19); } __set_errno (EDOM); } break; case 27: case 127: case 227: /* fmod(x,0) */ exc.type = DOMAIN; exc.name = type < 100 ? "fmod" : (type < 200 ? "fmodf" : "fmodl"); if (_LIB_VERSION == _SVID_) exc.retval = x; else exc.retval = zero/zero; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("fmod: DOMAIN error\n", 20); } __set_errno (EDOM); } break; case 28: case 128: case 228: /* remainder(x,0) */ exc.type = DOMAIN; exc.name = type < 100 ? "remainder" : (type < 200 ? "remainderf" : "remainderl"); exc.retval = zero/zero; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("remainder: DOMAIN error\n", 24); } __set_errno (EDOM); } break; case 29: case 129: case 229: /* acosh(x<1) */ exc.type = DOMAIN; exc.name = type < 100 ? "acosh" : (type < 200 ? "acoshf" : "acoshl"); exc.retval = zero/zero; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("acosh: DOMAIN error\n", 20); } __set_errno (EDOM); } break; case 30: case 130: case 230: /* atanh(|x|>1) */ exc.type = DOMAIN; exc.name = type < 100 ? "atanh" : (type < 200 ? "atanhf" : "atanhl"); exc.retval = zero/zero; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("atanh: DOMAIN error\n", 20); } __set_errno (EDOM); } break; case 31: case 131: case 231: /* atanh(|x|=1) */ exc.type = SING; exc.name = type < 100 ? "atanh" : (type < 200 ? "atanhf" : "atanhl"); exc.retval = x/zero; /* sign(x)*inf */ if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("atanh: SING error\n", 18); } __set_errno (EDOM); } break; case 32: case 132: case 232: /* scalb overflow; SVID also returns +-HUGE_VAL */ exc.type = OVERFLOW; exc.name = type < 100 ? "scalb" : (type < 200 ? "scalbf" : "scalbl"); exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 33: case 133: case 233: /* scalb underflow */ exc.type = UNDERFLOW; exc.name = type < 100 ? "scalb" : (type < 200 ? "scalbf" : "scalbl"); exc.retval = __copysign(zero,x); if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 34: case 134: case 234: /* j0(|x|>X_TLOSS) */ exc.type = TLOSS; exc.name = type < 100 ? "j0" : (type < 200 ? "j0f" : "j0l"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2(exc.name, 2); (void) WRITE2(": TLOSS error\n", 14); } __set_errno (ERANGE); } break; case 35: case 135: case 235: /* y0(x>X_TLOSS) */ exc.type = TLOSS; exc.name = type < 100 ? "y0" : (type < 200 ? "y0f" : "y0l"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2(exc.name, 2); (void) WRITE2(": TLOSS error\n", 14); } __set_errno (ERANGE); } break; case 36: case 136: case 236: /* j1(|x|>X_TLOSS) */ exc.type = TLOSS; exc.name = type < 100 ? "j1" : (type < 200 ? "j1f" : "j1l"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2(exc.name, 2); (void) WRITE2(": TLOSS error\n", 14); } __set_errno (ERANGE); } break; case 37: case 137: case 237: /* y1(x>X_TLOSS) */ exc.type = TLOSS; exc.name = type < 100 ? "y1" : (type < 200 ? "y1f" : "y1l"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2(exc.name, 2); (void) WRITE2(": TLOSS error\n", 14); } __set_errno (ERANGE); } break; case 38: case 138: case 238: /* jn(|x|>X_TLOSS) */ exc.type = TLOSS; exc.name = type < 100 ? "jn" : (type < 200 ? "jnf" : "jnl"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2(exc.name, 2); (void) WRITE2(": TLOSS error\n", 14); } __set_errno (ERANGE); } break; case 39: case 139: case 239: /* yn(x>X_TLOSS) */ exc.type = TLOSS; exc.name = type < 100 ? "yn" : (type < 200 ? "ynf" : "ynl"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2(exc.name, 2); (void) WRITE2(": TLOSS error\n", 14); } __set_errno (ERANGE); } break; case 40: case 140: case 240: /* tgamma(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "tgamma" : (type < 200 ? "tgammaf" : "tgammal"); exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 41: case 141: case 241: /* tgamma(-integer) */ exc.type = SING; exc.name = type < 100 ? "tgamma" : (type < 200 ? "tgammaf" : "tgammal"); exc.retval = NAN; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { (void) WRITE2("tgamma: SING error\n", 18); exc.retval = HUGE_VAL; } __set_errno (EDOM); } break; case 42: case 142: case 242: /* pow(NaN,0.0) */ /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : (type < 200 ? "powf" : "powl"); exc.retval = x; if (_LIB_VERSION == _IEEE_ || _LIB_VERSION == _POSIX_) exc.retval = 1.0; else if (!matherr(&exc)) { __set_errno (EDOM); } break; case 44: case 144: case 244: /* exp(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "exp2" : (type < 200 ? "exp2f" : "exp2l"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 45: case 145: case 245: /* exp(finite) underflow */ exc.type = UNDERFLOW; exc.name = type < 100 ? "exp2" : (type < 200 ? "exp2f" : "exp2l"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 46: case 146: case 246: /* exp(finite) overflow */ exc.type = OVERFLOW; exc.name = type < 100 ? "exp10" : (type < 200 ? "exp10f" : "exp10l"); if (_LIB_VERSION == _SVID_) exc.retval = HUGE; else exc.retval = HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 47: case 147: case 247: /* exp(finite) underflow */ exc.type = UNDERFLOW; exc.name = type < 100 ? "exp10" : (type < 200 ? "exp10f" : "exp10l"); exc.retval = zero; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (ERANGE); } break; case 48: case 148: case 248: /* log2(0) */ exc.type = SING; exc.name = type < 100 ? "log2" : (type < 200 ? "log2f" : "log2l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { __set_errno (EDOM); } break; case 49: case 149: case 249: /* log2(x<0) */ exc.type = DOMAIN; exc.name = type < 100 ? "log2" : (type < 200 ? "log2f" : "log2l"); if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = NAN; if (_LIB_VERSION == _POSIX_) __set_errno (EDOM); else if (!matherr(&exc)) { __set_errno (EDOM); } break; case 50: case 150: case 250: /* tgamma(+-0) */ exc.type = SING; exc.name = type < 100 ? "tgamma" : (type < 200 ? "tgammaf" : "tgammal"); exc.retval = __copysign (HUGE_VAL, x); if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) (void) WRITE2("tgamma: SING error\n", 18); __set_errno (ERANGE); } break; /* #### Last used is 50/150/250 ### */ } return exc.retval; }
__complex__ double __ctanh (__complex__ double x) { __complex__ double res; if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) { if (isinf (__real__ x)) { __real__ res = __copysign (1.0, __real__ x); if (isfinite (__imag__ x) && fabs (__imag__ x) > 1.0) { double sinix, cosix; __sincos (__imag__ x, &sinix, &cosix); __imag__ res = __copysign (0.0, sinix * cosix); } else __imag__ res = __copysign (0.0, __imag__ x); } else if (__imag__ x == 0.0) { res = x; } else { __real__ res = __nan (""); __imag__ res = __nan (""); if (isinf (__imag__ x)) feraiseexcept (FE_INVALID); } } else { double sinix, cosix; double den; const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); /* 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). */ if (__glibc_likely (fabs (__imag__ x) > DBL_MIN)) { __sincos (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1.0; } if (fabs (__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). */ double exp_2t = __ieee754_exp (2 * t); __real__ res = __copysign (1.0, __real__ x); __imag__ res = 4 * sinix * cosix; __real__ x = fabs (__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_exp (2 * __real__ x); } else { double sinhrx, coshrx; if (fabs (__real__ x) > DBL_MIN) { sinhrx = __ieee754_sinh (__real__ x); coshrx = __ieee754_cosh (__real__ x); } else { sinhrx = __real__ x; coshrx = 1.0; } if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON) den = sinhrx * sinhrx + cosix * cosix; else den = cosix * cosix; __real__ res = sinhrx * coshrx / den; __imag__ res = sinix * cosix / den; } math_check_force_underflow_complex (res); } return res; }
__complex__ double __clog (__complex__ double x) { __complex__ 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_PI : 0.0; __imag__ result = __copysign (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabs (__real__ x); } else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN)) { /* Neither real nor imaginary part is NaN. */ double absx = fabs (__real__ x), absy = fabs (__imag__ x); int scale = 0; if (absx < absy) { double t = absx; absx = absy; absy = t; } if (absx > DBL_MAX / 2.0) { scale = -1; absx = __scalbn (absx, scale); absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0); } else if (absx < DBL_MIN && absy < DBL_MIN) { scale = DBL_MANT_DIG; absx = __scalbn (absx, scale); absy = __scalbn (absy, scale); } if (absx == 1.0 && scale == 0) { __real__ result = __log1p (absy * absy) / 2.0; math_check_force_underflow_nonneg (__real__ result); } else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0) { double d2m1 = (absx - 1.0) * (absx + 1.0); if (absy >= DBL_EPSILON) d2m1 += absy * absy; __real__ result = __log1p (d2m1) / 2.0; } else if (absx < 1.0 && absx >= 0.5 && absy < DBL_EPSILON / 2.0 && scale == 0) { double d2m1 = (absx - 1.0) * (absx + 1.0); __real__ result = __log1p (d2m1) / 2.0; } else if (absx < 1.0 && absx >= 0.5 && scale == 0 && absx * absx + absy * absy >= 0.5) { double d2m1 = __x2y2m1 (absx, absy); __real__ result = __log1p (d2m1) / 2.0; } else { double d = __ieee754_hypot (absx, absy); __real__ result = __ieee754_log (d) - scale * M_LN2; } __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x); } else { __imag__ result = __nan (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VAL; else __real__ result = __nan (""); } return result; }
__complex__ double __csinh (__complex__ double x) { __complex__ double retval; int negate = signbit (__real__ x); int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); __real__ x = fabs (__real__ x); if (rcls >= FP_ZERO) { /* Real part is finite. */ if (icls >= FP_ZERO) { /* Imaginary part is finite. */ double sinh_val = __ieee754_sinh (__real__ x); double cosh_val = __ieee754_cosh (__real__ x); double sinix, cosix; __sincos (__imag__ x, &sinix, &cosix); __real__ retval = sinh_val * cosix; __imag__ retval = cosh_val * sinix; if (negate) __real__ retval = -__real__ retval; } else { if (rcls == FP_ZERO) { /* Real part is 0.0. */ __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0); __imag__ retval = __nan ("") + __nan (""); #ifdef FE_INVALID if (icls == FP_INFINITE) feraiseexcept (FE_INVALID); #endif } else { __real__ retval = __nan (""); __imag__ retval = __nan (""); #ifdef FE_INVALID feraiseexcept (FE_INVALID); #endif } } } else if (rcls == FP_INFINITE) { /* Real part is infinite. */ if (icls == FP_ZERO) { /* Imaginary part is 0.0. */ __real__ retval = negate ? -HUGE_VAL : HUGE_VAL; __imag__ retval = __imag__ x; } else if (icls > FP_ZERO) { /* Imaginary part is finite. */ double sinix, cosix; __sincos (__imag__ x, &sinix, &cosix); __real__ retval = __copysign (HUGE_VAL, cosix); __imag__ retval = __copysign (HUGE_VAL, sinix); if (negate) __real__ retval = -__real__ retval; } else { /* The addition raises the invalid exception. */ __real__ retval = HUGE_VAL; __imag__ retval = __nan ("") + __nan (""); #ifdef FE_INVALID if (icls == FP_INFINITE) feraiseexcept (FE_INVALID); #endif } } else { __real__ retval = __nan (""); __imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nan (""); } return retval; }
__complex__ double __cexp (__complex__ double x) { __complex__ 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) ((DBL_MAX_EXP - 1) * M_LN2); double sinix, cosix; if (__builtin_expect (icls != FP_SUBNORMAL, 1)) { __sincos (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1.0; } if (__real__ x > t) { double exp_t = __ieee754_exp (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 = DBL_MAX * cosix; __imag__ retval = DBL_MAX * sinix; } else { double exp_val = __ieee754_exp (__real__ x); __real__ retval = exp_val * cosix; __imag__ retval = exp_val * sinix; } if (fabs (__real__ retval) < DBL_MIN) { volatile double force_underflow = __real__ retval * __real__ retval; (void) force_underflow; } if (fabs (__imag__ retval) < DBL_MIN) { volatile 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 = __nan (""); __imag__ retval = __nan (""); 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. */ double value = signbit (__real__ x) ? 0.0 : HUGE_VAL; if (icls == FP_ZERO) { /* Imaginary part is 0.0. */ __real__ retval = value; __imag__ retval = __imag__ x; } else { double sinix, cosix; if (__builtin_expect (icls != FP_SUBNORMAL, 1)) { __sincos (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1.0; } __real__ retval = __copysign (value, cosix); __imag__ retval = __copysign (value, sinix); } } else if (signbit (__real__ x) == 0) { __real__ retval = HUGE_VAL; __imag__ retval = __nan (""); if (icls == FP_INFINITE) feraiseexcept (FE_INVALID); } else { __real__ retval = 0.0; __imag__ retval = __copysign (0.0, __imag__ x); } } else { /* If the real part is NaN the result is NaN + iNaN. */ __real__ retval = __nan (""); __imag__ retval = __nan (""); if (rcls != FP_NAN || icls != FP_NAN) feraiseexcept (FE_INVALID); } return retval; }
__complex__ double __catanh (__complex__ double x) { __complex__ double res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) { if (icls == FP_INFINITE) { __real__ res = __copysign (0.0, __real__ x); __imag__ res = __copysign (M_PI_2, __imag__ x); } else if (rcls == FP_INFINITE || rcls == FP_ZERO) { __real__ res = __copysign (0.0, __real__ x); if (icls >= FP_ZERO) __imag__ res = __copysign (M_PI_2, __imag__ x); else __imag__ res = __nan (""); } else { __real__ res = __nan (""); __imag__ res = __nan (""); } } else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) { res = x; } else { if (fabs (__real__ x) >= 16.0 / DBL_EPSILON || fabs (__imag__ x) >= 16.0 / DBL_EPSILON) { __imag__ res = __copysign (M_PI_2, __imag__ x); if (fabs (__imag__ x) <= 1.0) __real__ res = 1.0 / __real__ x; else if (fabs (__real__ x) <= 1.0) __real__ res = __real__ x / __imag__ x / __imag__ x; else { double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0); __real__ res = __real__ x / h / h / 4.0; } } else { if (fabs (__real__ x) == 1.0 && fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON) __real__ res = (__copysign (0.5, __real__ x) * (M_LN2 - __ieee754_log (fabs (__imag__ x)))); else { double i2 = 0.0; if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON) i2 = __imag__ x * __imag__ x; double num = 1.0 + __real__ x; num = i2 + num * num; double den = 1.0 - __real__ x; den = i2 + den * den; double f = num / den; if (f < 0.5) __real__ res = 0.25 * __ieee754_log (f); else { num = 4.0 * __real__ x; __real__ res = 0.25 * __log1p (num / den); } } double absx, absy, den; absx = fabs (__real__ x); absy = fabs (__imag__ x); if (absx < absy) { double t = absx; absx = absy; absy = t; } if (absy < DBL_EPSILON / 2.0) { den = (1.0 - absx) * (1.0 + absx); if (den == -0.0) den = 0.0; } else if (absx >= 1.0) den = (1.0 - absx) * (1.0 + absx) - absy * absy; else if (absx >= 0.75 || absy >= 0.5) den = -__x2y2m1 (absx, absy); else den = (1.0 - absx) * (1.0 + absx) - absy * absy; __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den); } math_check_force_underflow_complex (res); } return res; }
__complex__ double __cexp (__complex__ double x) { __complex__ 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. */ double exp_val = __ieee754_exp (__real__ x); double sinix, cosix; __sincos (__imag__ x, &sinix, &cosix); if (isfinite (exp_val)) { __real__ retval = exp_val * cosix; __imag__ retval = exp_val * sinix; } else { __real__ retval = __copysign (exp_val, cosix); __imag__ retval = __copysign (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 = __nan (""); __imag__ retval = __nan (""); 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. */ double value = signbit (__real__ x) ? 0.0 : HUGE_VAL; if (icls == FP_ZERO) { /* Imaginary part is 0.0. */ __real__ retval = value; __imag__ retval = __imag__ x; } else { double sinix, cosix; __sincos (__imag__ x, &sinix, &cosix); __real__ retval = __copysign (value, cosix); __imag__ retval = __copysign (value, sinix); } } else if (signbit (__real__ x) == 0) { __real__ retval = HUGE_VAL; __imag__ retval = __nan (""); if (icls == FP_INFINITE) feraiseexcept (FE_INVALID); } else { __real__ retval = 0.0; __imag__ retval = __copysign (0.0, __imag__ x); } } else { /* If the real part is NaN the result is NaN + iNaN. */ __real__ retval = __nan (""); __imag__ retval = __nan (""); if (rcls != FP_NAN || icls != FP_NAN) feraiseexcept (FE_INVALID); } return retval; }
__complex__ double __csqrt (__complex__ double x) { __complex__ 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_VAL; __imag__ res = __imag__ x; } else if (rcls == FP_INFINITE) { if (__real__ x < 0.0) { __real__ res = icls == FP_NAN ? __nan ("") : 0; __imag__ res = __copysign (HUGE_VAL, __imag__ x); } else { __real__ res = __real__ x; __imag__ res = (icls == FP_NAN ? __nan ("") : __copysign (0.0, __imag__ x)); } } else { __real__ res = __nan (""); __imag__ res = __nan (""); } } else { if (__builtin_expect (icls == FP_ZERO, 0)) { if (__real__ x < 0.0) { __real__ res = 0.0; __imag__ res = __copysign (__ieee754_sqrt (-__real__ x), __imag__ x); } else { __real__ res = fabs (__ieee754_sqrt (__real__ x)); __imag__ res = __copysign (0.0, __imag__ x); } } else if (__builtin_expect (rcls == FP_ZERO, 0)) { double r; if (fabs (__imag__ x) >= 2.0 * DBL_MIN) r = __ieee754_sqrt (0.5 * fabs (__imag__ x)); else r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x)); __real__ res = r; __imag__ res = __copysign (r, __imag__ x); } else { double d, r, s; int scale = 0; if (fabs (__real__ x) > DBL_MAX / 4.0) { scale = 1; __real__ x = __scalbn (__real__ x, -2 * scale); __imag__ x = __scalbn (__imag__ x, -2 * scale); } else if (fabs (__imag__ x) > DBL_MAX / 4.0) { scale = 1; if (fabs (__real__ x) >= 4.0 * DBL_MIN) __real__ x = __scalbn (__real__ x, -2 * scale); else __real__ x = 0.0; __imag__ x = __scalbn (__imag__ x, -2 * scale); } else if (fabs (__real__ x) < DBL_MIN && fabs (__imag__ x) < DBL_MIN) { scale = -(DBL_MANT_DIG / 2); __real__ x = __scalbn (__real__ x, -2 * scale); __imag__ x = __scalbn (__imag__ x, -2 * scale); } d = __ieee754_hypot (__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_sqrt (0.5 * (d + __real__ x)); s = 0.5 * (__imag__ x / r); } else { s = __ieee754_sqrt (0.5 * (d - __real__ x)); r = fabs (0.5 * (__imag__ x / s)); } if (scale) { r = __scalbn (r, scale); s = __scalbn (s, scale); } __real__ res = r; __imag__ res = __copysign (s, __imag__ x); } } return res; }
__complex__ double __ccosh (__complex__ double x) { __complex__ 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) ((DBL_MAX_EXP - 1) * M_LN2); double sinix, cosix; if (__builtin_expect (icls != FP_SUBNORMAL, 1)) { __sincos (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1.0; } if (fabs (__real__ x) > t) { double exp_t = __ieee754_exp (t); double rx = fabs (__real__ x); if (signbit (__real__ x)) sinix = -sinix; rx -= t; sinix *= exp_t / 2.0; cosix *= exp_t / 2.0; if (rx > t) { rx -= t; sinix *= exp_t; cosix *= exp_t; } if (rx > t) { /* Overflow (original real part of x > 3t). */ __real__ retval = DBL_MAX * cosix; __imag__ retval = DBL_MAX * sinix; } else { double exp_val = __ieee754_exp (rx); __real__ retval = exp_val * cosix; __imag__ retval = exp_val * sinix; } } else { __real__ retval = __ieee754_cosh (__real__ x) * cosix; __imag__ retval = __ieee754_sinh (__real__ x) * sinix; } if (fabs (__real__ retval) < DBL_MIN) { volatile double force_underflow = __real__ retval * __real__ retval; (void) force_underflow; } if (fabs (__imag__ retval) < DBL_MIN) { volatile double force_underflow = __imag__ retval * __imag__ retval; (void) force_underflow; } } else { __imag__ retval = __real__ x == 0.0 ? 0.0 : __nan (""); __real__ retval = __nan ("") + __nan (""); if (icls == FP_INFINITE) feraiseexcept (FE_INVALID); } } else if (rcls == FP_INFINITE) { /* Real part is infinite. */ if (__builtin_expect (icls > FP_ZERO, 1)) { /* Imaginary part is finite. */ double sinix, cosix; if (__builtin_expect (icls != FP_SUBNORMAL, 1)) { __sincos (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1.0; } __real__ retval = __copysign (HUGE_VAL, cosix); __imag__ retval = (__copysign (HUGE_VAL, sinix) * __copysign (1.0, __real__ x)); } else if (icls == FP_ZERO) { /* Imaginary part is 0.0. */ __real__ retval = HUGE_VAL; __imag__ retval = __imag__ x * __copysign (1.0, __real__ x); } else { /* The addition raises the invalid exception. */ __real__ retval = HUGE_VAL; __imag__ retval = __nan ("") + __nan (""); if (icls == FP_INFINITE) feraiseexcept (FE_INVALID); } } else { __real__ retval = __nan (""); __imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nan (""); } return retval; }
__complex__ double __cacosh (__complex__ double x) { __complex__ 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_VAL; if (rcls == FP_NAN) __imag__ res = __nan (""); else __imag__ res = __copysign ((rcls == FP_INFINITE ? (__real__ x < 0.0 ? M_PI - M_PI_4 : M_PI_4) : M_PI_2), __imag__ x); } else if (rcls == FP_INFINITE) { __real__ res = HUGE_VAL; if (icls >= FP_ZERO) __imag__ res = __copysign (signbit (__real__ x) ? M_PI : 0.0, __imag__ x); else __imag__ res = __nan (""); } else { __real__ res = __nan (""); __imag__ res = __nan (""); } } else if (rcls == FP_ZERO && icls == FP_ZERO) { __real__ res = 0.0; __imag__ res = __copysign (M_PI_2, __imag__ x); } else { __complex__ double y; __real__ y = -__imag__ x; __imag__ y = __real__ x; y = __kernel_casinh (y, 1); if (signbit (__imag__ x)) { __real__ res = __real__ y; __imag__ res = -__imag__ y; } else { __real__ res = -__real__ y; __imag__ res = __imag__ y; } } return res; }