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; }