float sinhf(float x) /* wrapper sinhf */ { #ifdef _IEEE_LIBM return __ieee754_sinhf(x); #else float z; z = __ieee754_sinhf(x); if(_LIB_VERSION == _IEEE_) return z; if(!finitef(z)&&finitef(x)) { /* sinhf overflow */ return (float)__kernel_standard((double)x,(double)x,125); } else return z; #endif }
__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; }
__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 __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; }