void SinCos(float angle, float& sin, float& cos)
{
float angleRadians = angle * M_DEGTORAD;
#if defined(HAVE_SINCOSF)
sincosf(angleRadians, &sin, &cos);
#elif defined(HAVE_UNDERSCORE_SINCOSF)
__sincosf(angleRadians, &sin, &cos);
#else
sin = sinf(angleRadians);
cos = cosf(angleRadians);
#endif
}
float
__ieee754_y1f(float x)
{
float z, s,c,ss,cc,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(__builtin_expect(ix>=0x7f800000, 0)) return one/(x+x*x);
if(__builtin_expect(ix==0, 0))
return -HUGE_VALF+x; /* -inf and overflow exception. */
if(__builtin_expect(hx<0, 0)) return zero/(zero*x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
SET_RESTORE_ROUNDF (FE_TONEAREST);
__sincosf (x, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) { /* make sure x+x not overflow */
z = __cosf(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_sqrtf(x);
else {
u = ponef(x); v = qonef(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
}
return z;
}
if(__builtin_expect(ix<=0x33000000, 0)) { /* x < 2**-25 */
z = -tpi / x;
if (__isinff (z))
__set_errno (ERANGE);
return z;
}
z = x*x;
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]))));
return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
}
float
__ieee754_y0f(float x)
{
float z, s,c,ss,cc,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */
if(ix>=0x7f800000) return one/(x+x*x);
if(ix==0) return -HUGE_VALF+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.
*/
__sincosf (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<0x7f000000) { /* make sure x+x not overflow */
z = -__cosf(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<=0x32000000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_logf(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
}
__device__ void single_precision_intrinsics()
{
float fX, fY;
__cosf(0.0f);
__exp10f(0.0f);
__expf(0.0f);
__fadd_rd(0.0f, 1.0f);
__fadd_rn(0.0f, 1.0f);
__fadd_ru(0.0f, 1.0f);
__fadd_rz(0.0f, 1.0f);
__fdiv_rd(4.0f, 2.0f);
__fdiv_rn(4.0f, 2.0f);
__fdiv_ru(4.0f, 2.0f);
__fdiv_rz(4.0f, 2.0f);
__fdividef(4.0f, 2.0f);
__fmaf_rd(1.0f, 2.0f, 3.0f);
__fmaf_rn(1.0f, 2.0f, 3.0f);
__fmaf_ru(1.0f, 2.0f, 3.0f);
__fmaf_rz(1.0f, 2.0f, 3.0f);
__fmul_rd(1.0f, 2.0f);
__fmul_rn(1.0f, 2.0f);
__fmul_ru(1.0f, 2.0f);
__fmul_rz(1.0f, 2.0f);
__frcp_rd(2.0f);
__frcp_rn(2.0f);
__frcp_ru(2.0f);
__frcp_rz(2.0f);
__frsqrt_rn(4.0f);
__fsqrt_rd(4.0f);
__fsqrt_rn(4.0f);
__fsqrt_ru(4.0f);
__fsqrt_rz(4.0f);
__fsub_rd(2.0f, 1.0f);
__fsub_rn(2.0f, 1.0f);
__fsub_ru(2.0f, 1.0f);
__fsub_rz(2.0f, 1.0f);
__log10f(1.0f);
__log2f(1.0f);
__logf(1.0f);
__powf(1.0f, 0.0f);
__saturatef(0.1f);
__sincosf(0.0f, &fX, &fY);
__sinf(0.0f);
__tanf(0.0f);
}
float
__ieee754_j0f(float x)
{
float z, s,c,ss,cc,r,u,v;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return one/(x*x);
x = fabsf(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincosf (x, &s, &c);
ss = s-c;
cc = s+c;
if(ix<0x7f000000) { /* make sure x+x not overflow */
z = -__cosf(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_sqrtf(x);
else {
u = pzerof(x); v = qzerof(x);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x);
}
return z;
}
if(ix<0x39000000) { /* |x| < 2**-13 */
math_force_eval(huge+x); /* raise inexact if x != 0 */
if(ix<0x32000000) return one; /* |x|<2**-27 */
else return one - (float)0.25*x*x;
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3F800000) { /* |x| < 1.00 */
return one + z*((float)-0.25+(r/s));
} else {
u = (float)0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
__complex__ float
__ctanf (__complex__ float x)
{
__complex__ float res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinff (__imag__ x))
{
__real__ res = __copysignf (0.0, __real__ x);
__imag__ res = __copysignf (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
#ifdef FE_INVALID
if (__isinff (__real__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
float sin2rx, cos2rx;
float den;
__sincosf (2.0 * __real__ x, &sin2rx, &cos2rx);
den = cos2rx + __ieee754_coshf (2.0 * __imag__ x);
__real__ res = sin2rx / den;
__imag__ res = __ieee754_sinhf (2.0 * __imag__ x) / den;
}
return res;
}
float
__ieee754_j1f(float x)
{
float z, s,c,ss,cc,r,u,v,y;
int32_t hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(__builtin_expect(ix>=0x7f800000, 0)) return one/x;
y = fabsf(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
__sincosf (y, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) { /* make sure y+y not overflow */
z = __cosf(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_sqrtf(y);
else {
u = ponef(y); v = qonef(y);
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
}
if(hx<0) return -z;
else return z;
}
if(__builtin_expect(ix<0x32000000, 0)) { /* |x|<2**-27 */
if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*(float)0.5+r/s);
}
__complex__ float
__csinhf (__complex__ float x)
{
__complex__ float retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = fabsf (__real__ x);
if (rcls >= FP_ZERO)
{
/* Real part is finite. */
if (icls >= FP_ZERO)
{
/* Imaginary part is finite. */
float sinh_val = __ieee754_sinhf (__real__ x);
float cosh_val = __ieee754_coshf (__real__ x);
float sinix, cosix;
__sincosf (__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 = __copysignf (0.0, negate ? -1.0 : 1.0);
__imag__ retval = __nanf ("") + __nanf ("");
#ifdef FE_INVALID
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __nanf ("");
#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_VALF : HUGE_VALF;
__imag__ retval = __imag__ x;
}
else if (icls > FP_ZERO)
{
/* Imaginary part is finite. */
float sinix, cosix;
__sincosf (__imag__ x, &sinix, &cosix);
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = __copysignf (HUGE_VALF, sinix);
if (negate)
__real__ retval = -__real__ retval;
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("") + __nanf ("");
#ifdef FE_INVALID
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanf ("");
}
return retval;
}
__complex__ float
__csinhf (__complex__ float x)
{
__complex__ float retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = fabsf (__real__ 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) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
if (__builtin_expect (icls != FP_SUBNORMAL, 1))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (fabsf (__real__ x) > t)
{
float exp_t = __ieee754_expf (t);
float rx = fabsf (__real__ x);
if (signbit (__real__ x))
cosix = -cosix;
rx -= t;
sinix *= exp_t / 2.0f;
cosix *= exp_t / 2.0f;
if (rx > t)
{
rx -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (rx > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = FLT_MAX * cosix;
__imag__ retval = FLT_MAX * sinix;
}
else
{
float exp_val = __ieee754_expf (rx);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
__real__ retval = __ieee754_sinhf (__real__ x) * cosix;
__imag__ retval = __ieee754_coshf (__real__ x) * sinix;
}
if (negate)
__real__ retval = -__real__ retval;
if (fabsf (__real__ retval) < FLT_MIN)
{
volatile float force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsf (__imag__ retval) < FLT_MIN)
{
volatile float force_underflow
= __imag__ retval * __imag__ retval;
(void) force_underflow;
}
}
else
{
if (rcls == FP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = __copysignf (0.0, negate ? -1.0 : 1.0);
__imag__ retval = __nanf ("") + __nanf ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __nanf ("");
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. */
float sinix, cosix;
if (__builtin_expect (icls != FP_SUBNORMAL, 1))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = __copysignf (HUGE_VALF, sinix);
if (negate)
__real__ retval = -__real__ retval;
}
else if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = negate ? -HUGE_VALF : HUGE_VALF;
__imag__ retval = __imag__ x;
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("") + __nanf ("");
#ifdef FE_INVALID
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanf ("");
}
return retval;
}
__complex__ float
__ctanf (__complex__ float x)
{
__complex__ float res;
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
{
if (isinf (__imag__ x))
{
if (isfinite (__real__ x) && fabsf (__real__ x) > 1.0f)
{
float sinrx, cosrx;
__sincosf (__real__ x, &sinrx, &cosrx);
__real__ res = __copysignf (0.0f, sinrx * cosrx);
}
else
__real__ res = __copysignf (0.0, __real__ x);
__imag__ res = __copysignf (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
if (isinf (__real__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
float sinrx, cosrx;
float den;
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
if (__glibc_likely (fabsf (__real__ x) > FLT_MIN))
{
__sincosf (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0f;
}
if (fabsf (__imag__ x) > t)
{
/* Avoid intermediate overflow when the real part of the
result may be subnormal. Ignoring negligible terms, the
imaginary part is +/- 1, the real part is
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
float exp_2t = __ieee754_expf (2 * t);
__imag__ res = __copysignf (1.0, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsf (__imag__ x);
__imag__ x -= t;
__real__ res /= exp_2t;
if (__imag__ x > t)
{
/* Underflow (original imaginary part of x has absolute
value > 2t). */
__real__ res /= exp_2t;
}
else
__real__ res /= __ieee754_expf (2 * __imag__ x);
}
else
{
float sinhix, coshix;
if (fabsf (__imag__ x) > FLT_MIN)
{
sinhix = __ieee754_sinhf (__imag__ x);
coshix = __ieee754_coshf (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0f;
}
if (fabsf (sinhix) > fabsf (cosrx) * FLT_EPSILON)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
math_check_force_underflow_complex (res);
}
return res;
}
__complex__ float
__cexpf (__complex__ float x)
{
__complex__ float retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
if (__glibc_likely (icls != FP_SUBNORMAL))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (__real__ x > t)
{
float exp_t = __ieee754_expf (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 = FLT_MAX * cosix;
__imag__ retval = FLT_MAX * sinix;
}
else
{
float exp_val = __ieee754_expf (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
if (fabsf (__real__ retval) < FLT_MIN)
{
volatile float force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsf (__imag__ retval) < FLT_MIN)
{
volatile float 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 = __nanf ("");
__imag__ retval = __nanf ("");
feraiseexcept (FE_INVALID);
}
}
else if (__glibc_likely (rcls == FP_INFINITE))
{
/* Real part is infinite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
float value = signbit (__real__ x) ? 0.0 : HUGE_VALF;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
float sinix, cosix;
if (__glibc_likely (icls != FP_SUBNORMAL))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
__real__ retval = __copysignf (value, cosix);
__imag__ retval = __copysignf (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = 0.0;
__imag__ retval = __copysignf (0.0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN unless the
imaginary part is zero. */
__real__ retval = __nanf ("");
if (icls == FP_ZERO)
__imag__ retval = __imag__ x;
else
{
__imag__ retval = __nanf ("");
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
}
return retval;
}
__complex__ float
__ccoshf (__complex__ float x)
{
__complex__ float retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
if (__glibc_likely (fabsf (__imag__ x) > FLT_MIN))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (fabsf (__real__ x) > t)
{
float exp_t = __ieee754_expf (t);
float rx = fabsf (__real__ x);
if (signbit (__real__ x))
sinix = -sinix;
rx -= t;
sinix *= exp_t / 2.0f;
cosix *= exp_t / 2.0f;
if (rx > t)
{
rx -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (rx > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = FLT_MAX * cosix;
__imag__ retval = FLT_MAX * sinix;
}
else
{
float exp_val = __ieee754_expf (rx);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
__real__ retval = __ieee754_coshf (__real__ x) * cosix;
__imag__ retval = __ieee754_sinhf (__real__ x) * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
__imag__ retval = __real__ x == 0.0 ? 0.0 : __nanf ("");
__real__ retval = __nanf ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else if (rcls == FP_INFINITE)
{
/* Real part is infinite. */
if (__glibc_likely (icls > FP_ZERO))
{
/* Imaginary part is finite. */
float sinix, cosix;
if (__glibc_likely (fabsf (__imag__ x) > FLT_MIN))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = (__copysignf (HUGE_VALF, sinix)
* __copysignf (1.0, __real__ x));
}
else if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = HUGE_VALF;
__imag__ retval = __imag__ x * __copysignf (1.0, __real__ x);
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("") + __nanf ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanf ("");
}
return retval;
}
__complex__ float
__ctanhf (__complex__ float x)
{
__complex__ float res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_nsf (__real__ x))
{
__real__ res = __copysignf (1.0, __real__ x);
__imag__ res = __copysignf (0.0, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
if (__isinf_nsf (__imag__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
float sinix, cosix;
float den;
const int t = (int) ((FLT_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 (__builtin_expect (fpclassify(__imag__ x) != FP_SUBNORMAL, 1))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (fabsf (__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). */
float exp_2t = __ieee754_expf (2 * t);
__real__ res = __copysignf (1.0, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsf (__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_expf (2 * __real__ x);
}
else
{
float sinhrx, coshrx;
if (fabsf (__real__ x) > FLT_MIN)
{
sinhrx = __ieee754_sinhf (__real__ x);
coshrx = __ieee754_coshf (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0f;
}
if (fabsf (sinhrx) > fabsf (cosix) * FLT_EPSILON)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
}
return res;
}
