double
__ieee754_y1(double x)
{
double z, s,c,ss,cc,u,v,u1,u2,v1,v2,v3,z2,z4;
int32_t hx,ix,lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(__builtin_expect(ix>=0x7ff00000, 0)) return one/(x+x*x);
if(__builtin_expect((ix|lx)==0, 0))
return -HUGE_VAL+x; /* -inf and overflow exception. */;
if(__builtin_expect(hx<0, 0)) return zero/(zero*x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincos (x, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = __cos(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
}
return z;
}
if(__builtin_expect(ix<=0x3c900000, 0)) { /* x < 2**-54 */
return(-tpi/x);
}
z = x*x;
#ifdef DO_NOT_USE_THIS
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
#else
u1 = U0[0]+z*U0[1];z2=z*z;
u2 = U0[2]+z*U0[3];z4=z2*z2;
u = u1 + z2*u2 + z4*U0[4];
v1 = one+z*V0[0];
v2 = V0[1]+z*V0[2];
v3 = V0[3]+z*V0[4];
v = v1 + z2*v2 + z4*v3;
#endif
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}
double
__ieee754_j0(double x)
{
double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4;
int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/(x*x);
x = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincos (x, &s, &c);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -__cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x);
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
math_force_eval(huge+x); /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return one - 0.25*x*x;
}
z = x*x;
#ifdef DO_NOT_USE_THIS
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
#else
r1 = z*R[2]; z2=z*z;
r2 = R[3]+z*R[4]; z4=z2*z2;
r = r1 + z2*r2 + z4*R[5];
s1 = one+z*S[1];
s2 = S[2]+z*S[3];
s = s1 + z2*s2 + z4*S[4];
#endif
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return one + z*(-0.25+(r/s));
} else {
u = 0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
double
__ieee754_j1(double x)
{
double z, s,c,ss,cc,r,u,v,y,r1,r2,s1,s2,s3,z2,z4;
int32_t hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(__builtin_expect(ix>=0x7ff00000, 0)) return one/x;
y = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincos (y, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure y+y not overflow */
z = __cos(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
else {
u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
}
if(hx<0) return -z;
else return z;
}
if(__builtin_expect(ix<0x3e400000, 0)) { /* |x|<2**-27 */
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
#ifdef DO_NOT_USE_THIS
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
#else
r1 = z*R[0]; z2=z*z;
r2 = R[1]+z*R[2]; z4=z2*z2;
r = r1 + z2*r2 + z4*R[3];
r *= x;
s1 = one+z*S[1];
s2 = S[2]+z*S[3];
s3 = S[4]+z*S[5];
s = s1 + z2*s2 + z4*s3;
#endif
return(x*0.5+r/s);
}
__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;
}
__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
__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;
}
Err mathlib_sincos(UInt16 refnum, double x, double *sinx, double *cosx) {
#pragma unused(refnum)
__sincos(x, sinx, cosx);
return mlErrNone;
}
double
__ieee754_j1 (double x)
{
double z, s, c, ss, cc, r, u, v, y, r1, r2, s1, s2, s3, z2, z4;
int32_t hx, ix;
GET_HIGH_WORD (hx, x);
ix = hx & 0x7fffffff;
if (__glibc_unlikely (ix >= 0x7ff00000))
return one / x;
y = fabs (x);
if (ix >= 0x40000000) /* |x| >= 2.0 */
{
__sincos (y, &s, &c);
ss = -s - c;
cc = s - c;
if (ix < 0x7fe00000) /* make sure y+y not overflow */
{
z = __cos (y + y);
if ((s * c) > zero)
cc = z / ss;
else
ss = z / cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if (ix > 0x48000000)
z = (invsqrtpi * cc) / sqrt (y);
else
{
u = pone (y); v = qone (y);
z = invsqrtpi * (u * cc - v * ss) / sqrt (y);
}
if (hx < 0)
return -z;
else
return z;
}
if (__glibc_unlikely (ix < 0x3e400000)) /* |x|<2**-27 */
{
if (huge + x > one) /* inexact if x!=0 necessary */
{
double ret = math_narrow_eval (0.5 * x);
math_check_force_underflow (ret);
if (ret == 0 && x != 0)
__set_errno (ERANGE);
return ret;
}
}
z = x * x;
r1 = z * R[0]; z2 = z * z;
r2 = R[1] + z * R[2]; z4 = z2 * z2;
r = r1 + z2 * r2 + z4 * R[3];
r *= x;
s1 = one + z * S[1];
s2 = S[2] + z * S[3];
s3 = S[4] + z * S[5];
s = s1 + z2 * s2 + z4 * s3;
return (x * 0.5 + r / s);
}
double
__ieee754_y1 (double x)
{
double z, s, c, ss, cc, u, v, u1, u2, v1, v2, v3, z2, z4;
int32_t hx, ix, lx;
EXTRACT_WORDS (hx, lx, x);
ix = 0x7fffffff & hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if (__glibc_unlikely (ix >= 0x7ff00000))
return one / (x + x * x);
if (__glibc_unlikely ((ix | lx) == 0))
return -1 / zero; /* -inf and divide by zero exception. */
/* -inf and overflow exception. */;
if (__glibc_unlikely (hx < 0))
return zero / (zero * x);
if (ix >= 0x40000000) /* |x| >= 2.0 */
{
__sincos (x, &s, &c);
ss = -s - c;
cc = s - c;
if (ix < 0x7fe00000) /* make sure x+x not overflow */
{
z = __cos (x + x);
if ((s * c) > zero)
cc = z / ss;
else
ss = z / cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if (ix > 0x48000000)
z = (invsqrtpi * ss) / sqrt (x);
else
{
u = pone (x); v = qone (x);
z = invsqrtpi * (u * ss + v * cc) / sqrt (x);
}
return z;
}
if (__glibc_unlikely (ix <= 0x3c900000)) /* x < 2**-54 */
{
z = -tpi / x;
if (isinf (z))
__set_errno (ERANGE);
return z;
}
z = x * x;
u1 = U0[0] + z * U0[1]; z2 = z * z;
u2 = U0[2] + z * U0[3]; z4 = z2 * z2;
u = u1 + z2 * u2 + z4 * U0[4];
v1 = one + z * V0[0];
v2 = V0[1] + z * V0[2];
v3 = V0[3] + z * V0[4];
v = v1 + z2 * v2 + z4 * v3;
return (x * (u / v) + tpi * (__ieee754_j1 (x) * __ieee754_log (x) - one / x));
}
double
__ieee754_y0(double x)
{
double z, s,c,ss,cc,u,v,z2,z4,z6,u1,u2,u3,v1,v2;
int32_t hx,ix,lx;
EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */
if(hx<0) return zero/(zero*x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
__sincos (x, &s, &c);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -__cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return(U[0] + tpi*__ieee754_log(x));
}
z = x*x;
#ifdef DO_NOT_USE_THIS
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
#else
u1 = U[0]+z*U[1]; z2=z*z;
u2 = U[2]+z*U[3]; z4=z2*z2;
u3 = U[4]+z*U[5]; z6=z4*z2;
u = u1 + z2*u2 + z4*u3 + z6*U[6];
v1 = one+z*V[0];
v2 = V[1]+z*V[2];
v = v1 + z2*v2 + z4*V[3];
#endif
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
}
__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;
}
__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
__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;
}
