double __ieee754_exp10 (double arg) { int32_t lx; double arg_high, arg_low; double exp_high, exp_low; if (!isfinite (arg)) return __ieee754_exp (arg); if (arg < DBL_MIN_10_EXP - DBL_DIG - 10) return DBL_MIN * DBL_MIN; else if (arg > DBL_MAX_10_EXP + 1) return DBL_MAX * DBL_MAX; else if (fabs (arg) < 0x1p-56) return 1.0; GET_LOW_WORD (lx, arg); lx &= 0xf8000000; arg_high = arg; SET_LOW_WORD (arg_high, lx); arg_low = arg - arg_high; exp_high = arg_high * log10_high; exp_low = arg_high * log10_low + arg_low * M_LN10; return __ieee754_exp (exp_high) * __ieee754_exp (exp_low); }
double __ieee754_cosh (double x) { double t, w; int32_t ix; u_int32_t lx; /* High word of |x|. */ GET_HIGH_WORD (ix, x); ix &= 0x7fffffff; /* |x| in [0,22] */ if (ix < 0x40360000) { /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if (ix < 0x3fd62e43) { if (ix < 0x3c800000) return one; /* cosh(tiny) = 1 */ t = __expm1 (fabs (x)); w = one + t; return one + (t * t) / (w + w); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ t = __ieee754_exp (fabs (x)); return half * t + half / t; } /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ if (ix < 0x40862e42) return half * __ieee754_exp (fabs (x)); /* |x| in [log(maxdouble), overflowthresold] */ GET_LOW_WORD (lx, x); if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d))) { w = __ieee754_exp (half * fabs (x)); t = half * w; return t * w; } /* x is INF or NaN */ if (ix >= 0x7ff00000) return x * x; /* |x| > overflowthresold, cosh(x) overflow */ return huge * huge; }
double __ieee754_gamma_r (double x, int *signgamp) { /* We don't have a real gamma implementation now. We'll use lgamma and the exp function. But due to the required boundary conditions we must check some values separately. */ int32_t hx; u_int32_t lx; EXTRACT_WORDS (hx, lx, x); if (((hx & 0x7fffffff) | lx) == 0) { /* Return value for x == 0 is NaN with invalid exception. */ *signgamp = 0; return x / x; } if (hx < 0 && (u_int32_t) hx < 0xfff00000 && __rint (x) == x) { /* Return value for integer x < 0 is NaN with invalid exception. */ *signgamp = 0; return (x - x) / (x - x); } if ((unsigned int) hx == 0xfff00000 && lx==0) { /* x == -Inf. According to ISO this is NaN. */ *signgamp = 0; return x - x; } /* XXX FIXME. */ return __ieee754_exp (__ieee754_lgamma_r (x, signgamp)); }
double __ieee754_sinh(double x) { double t,h; int32_t ix,jx; /* High word of |x|. */ GET_HIGH_WORD(jx,x); ix = jx&0x7fffffff; /* x is INF or NaN */ if(ix>=0x7ff00000) return x+x; h = 0.5; if (jx<0) h = -h; /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ if (ix < 0x40360000) { /* |x|<22 */ if (ix<0x3e300000) /* |x|<2**-28 */ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ t = expm1(fabs(x)); if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); return h*(t+t/(t+one)); } /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ if (ix<=0x408633CE) return h*2.0*__ldexp_exp(fabs(x), -1); /* |x| > overflowthresold, sinh(x) overflow */ return x*shuge; }
float __ieee754_exp10f (float arg) { /* The argument to exp needs to be calculated in enough precision that the fractional part has as much precision as float, in addition to the bits in the integer part; using double ensures this. */ return __ieee754_exp (M_LN10 * arg); }
void Math_exp(void *fp) { F_Math_exp *f; f = fp; *f->ret = __ieee754_exp(f->x); }
double __ieee754_exp10 (double arg) { if (isfinite (arg) && arg < DBL_MIN_10_EXP - DBL_DIG - 10) return DBL_MIN * DBL_MIN; else /* This is a very stupid and inprecise implementation. It'll get replaced sometime (soon?). */ return __ieee754_exp (M_LN10 * arg); }
double exp(double x) /* wrapper exp */ { #ifdef _IEEE_LIBM return __ieee754_exp(x); #else double z; z = __ieee754_exp(x); if(_LIB_VERSION == _IEEE_) return z; if(finite(x)) { if(x>o_threshold) return __kernel_standard(x,x,6); /* exp overflow */ else if(x<u_threshold) return __kernel_standard(x,x,7); /* exp underflow */ } return z; #endif }
/* wrapper exp */ double __exp (double x) { double z = __ieee754_exp (x); if (__builtin_expect (!isfinite (z) || z == 0, 0) && isfinite (x) && _LIB_VERSION != _IEEE_) return __kernel_standard (x, x, 6 + !!signbit (x)); return z; }
double __ieee754_sinh(double x) { double t,w,h; int ix,jx; unsigned lx; /* High word of |x|. */ jx = CYG_LIBM_HI(x); ix = jx&0x7fffffff; /* x is INF or NaN */ if(ix>=0x7ff00000) return x+x; h = 0.5; if (jx<0) h = -h; /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ if (ix < 0x40360000) { /* |x|<22 */ if (ix<0x3e300000) /* |x|<2**-28 */ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ t = expm1(fabs(x)); if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); return h*(t+t/(t+one)); } /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ lx = CYG_LIBM_LO(x); if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) { w = __ieee754_exp(0.5*fabs(x)); t = h*w; return t*w; } /* |x| > overflowthresold, sinh(x) overflow */ return x*shuge; }
double __ieee754_cosh(double x) { double t,w; int32_t ix; /* High word of |x|. */ GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; /* x is INF or NaN */ if(ix>=0x7ff00000) return x*x; /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if(ix<0x3fd62e43) { t = expm1(fabs(x)); w = one+t; if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ return one+(t*t)/(w+w); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ if (ix < 0x40360000) { t = __ieee754_exp(fabs(x)); return half*t+half/t; } /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ if (ix<=0x408633CE) return __ldexp_exp(fabs(x), -1); /* |x| > overflowthresold, cosh(x) overflow */ return huge*huge; }
EXPORT(sqInt) primitiveExp(void) { double rcvr; double result; rcvr = interpreterProxy->stackFloatValue(0); if (interpreterProxy->failed()) { return null; } result = __ieee754_exp(rcvr); if (isnan(result)) { return interpreterProxy->primitiveFail(); } interpreterProxy->pop((interpreterProxy->methodArgumentCount()) + 1); interpreterProxy->pushFloat(result); }
primitiveExp(void) { // FloatMathPlugin>>#primitiveExp double rcvr; double result; rcvr = stackFloatValue(0); if (failed()) { return null; } result = __ieee754_exp(rcvr); if (isnan(result)) { return primitiveFail(); } pop((methodArgumentCount()) + 1); pushFloat(result); }
__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 __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 __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; }
Err mathlib_exp(UInt16 refnum, double x, double *result) { #pragma unused(refnum) *result = __ieee754_exp(x); return mlErrNone; }
static double gamma_positive (double x, int *exp2_adj) { int local_signgam; if (x < 0.5) { *exp2_adj = 0; return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x; } else if (x <= 1.5) { *exp2_adj = 0; return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam)); } else if (x < 6.5) { /* Adjust into the range for using exp (lgamma). */ *exp2_adj = 0; double n = __ceil (x - 1.5); double x_adj = x - n; double eps; double prod = __gamma_product (x_adj, 0, n, &eps); return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam)) * prod * (1.0 + eps)); } else { double eps = 0; double x_eps = 0; double x_adj = x; double prod = 1; if (x < 12.0) { /* Adjust into the range for applying Stirling's approximation. */ double n = __ceil (12.0 - x); #if FLT_EVAL_METHOD != 0 volatile #endif double x_tmp = x + n; x_adj = x_tmp; x_eps = (x - (x_adj - n)); prod = __gamma_product (x_adj - n, x_eps, n, &eps); } /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, starting by computing pow (X_ADJ, X_ADJ) with a power of 2 factored out. */ double exp_adj = -eps; double x_adj_int = __round (x_adj); double x_adj_frac = x_adj - x_adj_int; int x_adj_log2; double x_adj_mant = __frexp (x_adj, &x_adj_log2); if (x_adj_mant < M_SQRT1_2) { x_adj_log2--; x_adj_mant *= 2.0; } *exp2_adj = x_adj_log2 * (int) x_adj_int; double ret = (__ieee754_pow (x_adj_mant, x_adj) * __ieee754_exp2 (x_adj_log2 * x_adj_frac) * __ieee754_exp (-x_adj) * __ieee754_sqrt (2 * M_PI / x_adj) / prod); exp_adj += x_eps * __ieee754_log (x); double bsum = gamma_coeff[NCOEFF - 1]; double x_adj2 = x_adj * x_adj; for (size_t i = 1; i <= NCOEFF - 1; i++) bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; exp_adj += bsum / x_adj; return ret + ret * __expm1 (exp_adj); } }
__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 __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; }