__complex__ float __clog10f (__complex__ float x) { __complex__ float result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (rcls == FP_ZERO && icls == FP_ZERO) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PI : 0.0; __imag__ result = __copysignf (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsf (__real__ x); } else if (rcls != FP_NAN && icls != FP_NAN) { /* Neither real nor imaginary part is NaN. */ __real__ result = __ieee754_log10f (__ieee754_hypotf (__real__ x, __imag__ x)); __imag__ result = M_LOG10E * __ieee754_atan2f (__imag__ x, __real__ x); } else { __imag__ result = __nanf (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALF; else __real__ result = __nanf (""); } return result; }
float hypotf(float x, float y) /* wrapper hypotf */ { #ifdef _IEEE_LIBM return __ieee754_hypotf(x,y); #else float z; z = __ieee754_hypotf(x,y); if(_LIB_VERSION == _IEEE_) return z; if((!finitef(z))&&finitef(x)&&finitef(y)) /* hypot overflow */ return (float)__kernel_standard((double)x,(double)y,104); else return z; #endif }
float __hypotf(float x, float y) { float z = __ieee754_hypotf(x,y); if(__builtin_expect(!__finitef(z), 0) && __finitef(x) && __finitef(y) && _LIB_VERSION != _IEEE_) /* hypot overflow */ return __kernel_standard_f(x, y, 104); return z; }
__complex__ float __clog10f (__complex__ float x) { __complex__ float result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PI : 0.0; __imag__ result = __copysignf (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsf (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ float d; int scale = 0; if (fabsf (__real__ x) > FLT_MAX / 2.0f || fabsf (__imag__ x) > FLT_MAX / 2.0f) { scale = -1; __real__ x = __scalbnf (__real__ x, scale); __imag__ x = __scalbnf (__imag__ x, scale); } else if (fabsf (__real__ x) < FLT_MIN && fabsf (__imag__ x) < FLT_MIN) { scale = FLT_MANT_DIG; __real__ x = __scalbnf (__real__ x, scale); __imag__ x = __scalbnf (__imag__ x, scale); } d = __ieee754_hypotf (__real__ x, __imag__ x); __real__ result = __ieee754_log10f (d) - scale * M_LOG10_2f; __imag__ result = M_LOG10E * __ieee754_atan2f (__imag__ x, __real__ x); } else { __imag__ result = __nanf (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALF; else __real__ result = __nanf (""); } return result; }
//------------------------------------------------------------------------------ float Cmath::hypotf( float x, float y ) // wrapper hypotf { float z; struct fexception exc; z = __ieee754_hypotf( x, y ); if( m_fdlib_version == _IEEE_ ) { return z; } if( ( !finitef( z ) ) && finitef( x ) && finitef( y ) ) { // hypotf(finite,finite) overflow exc.type = EX_OVERFLOW; exc.name = "hypotf"; exc.err = 0; exc.arg1 = (double)x; exc.arg2 = (double)y; if( m_fdlib_version == _SVID_ ) { exc.retval = Huge(); } else { exc.retval = HUGE_VAL; } if( m_fdlib_version == _POSIX_ ) { errno = ERANGE; } else if( !matherr( &exc ) ) { errno = ERANGE; } if( exc.err != 0 ) { errno = exc.err; } return (float)exc.retval; } else { return z; } }
__complex__ float __clog10f (__complex__ float x) { __complex__ float result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PI_LOG10Ef : 0.0; __imag__ result = __copysignf (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsf (__real__ x); } else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN)) { /* Neither real nor imaginary part is NaN. */ float absx = fabsf (__real__ x), absy = fabsf (__imag__ x); int scale = 0; if (absx < absy) { float t = absx; absx = absy; absy = t; } if (absx > FLT_MAX / 2.0f) { scale = -1; absx = __scalbnf (absx, scale); absy = (absy >= FLT_MIN * 2.0f ? __scalbnf (absy, scale) : 0.0f); } else if (absx < FLT_MIN && absy < FLT_MIN) { scale = FLT_MANT_DIG; absx = __scalbnf (absx, scale); absy = __scalbnf (absy, scale); } if (absx == 1.0f && scale == 0) { float absy2 = absy * absy; if (absy2 <= FLT_MIN * 2.0f * (float) M_LN10) { float force_underflow = absy2 * absy2; __real__ result = absy2 * ((float) M_LOG10E / 2.0f); math_force_eval (force_underflow); } else __real__ result = __log1pf (absy2) * ((float) M_LOG10E / 2.0f); } else if (absx > 1.0f && absx < 2.0f && absy < 1.0f && scale == 0) { float d2m1 = (absx - 1.0f) * (absx + 1.0f); if (absy >= FLT_EPSILON) d2m1 += absy * absy; __real__ result = __log1pf (d2m1) * ((float) M_LOG10E / 2.0f); } else if (absx < 1.0f && absx >= 0.75f && absy < FLT_EPSILON / 2.0f && scale == 0) { float d2m1 = (absx - 1.0f) * (absx + 1.0f); __real__ result = __log1pf (d2m1) * ((float) M_LOG10E / 2.0f); } else if (absx < 1.0f && (absx >= 0.75f || absy >= 0.5f) && scale == 0) { float d2m1 = __x2y2m1f (absx, absy); __real__ result = __log1pf (d2m1) * ((float) M_LOG10E / 2.0f); } else { float d = __ieee754_hypotf (absx, absy); __real__ result = __ieee754_log10f (d) - scale * M_LOG10_2f; } __imag__ result = M_LOG10E * __ieee754_atan2f (__imag__ x, __real__ x); } else { __imag__ result = __nanf (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALF; else __real__ result = __nanf (""); } return result; }
__complex__ float __clogf (__complex__ float x) { __complex__ float result; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0)) { /* Real and imaginary part are 0.0. */ __imag__ result = signbit (__real__ x) ? M_PI : 0.0; __imag__ result = __copysignf (__imag__ result, __imag__ x); /* Yes, the following line raises an exception. */ __real__ result = -1.0 / fabsf (__real__ x); } else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1)) { /* Neither real nor imaginary part is NaN. */ float absx = fabsf (__real__ x), absy = fabsf (__imag__ x); int scale = 0; if (absx < absy) { float t = absx; absx = absy; absy = t; } if (absx > FLT_MAX / 2.0f) { scale = -1; absx = __scalbnf (absx, scale); absy = (absy >= FLT_MIN * 2.0f ? __scalbnf (absy, scale) : 0.0f); } else if (absx < FLT_MIN && absy < FLT_MIN) { scale = FLT_MANT_DIG; absx = __scalbnf (absx, scale); absy = __scalbnf (absy, scale); } if (absx == 1.0f && scale == 0) { float absy2 = absy * absy; if (absy2 <= FLT_MIN * 2.0f) { #if __FLT_EVAL_METHOD__ == 0 __real__ result = absy2 / 2.0f - absy2 * absy2 / 4.0f; #else volatile float force_underflow = absy2 * absy2 / 4.0f; __real__ result = absy2 / 2.0f - force_underflow; #endif } else __real__ result = __log1pf (absy2) / 2.0f; } else if (absx > 1.0f && absx < 2.0f && absy < 1.0f && scale == 0) { float d2m1 = (absx - 1.0f) * (absx + 1.0f); if (absy >= FLT_EPSILON) d2m1 += absy * absy; __real__ result = __log1pf (d2m1) / 2.0f; } else if (absx < 1.0f && absx >= 0.75f && absy < FLT_EPSILON / 2.0f && scale == 0) { float d2m1 = (absx - 1.0f) * (absx + 1.0f); __real__ result = __log1pf (d2m1) / 2.0f; } else if (absx < 1.0f && (absx >= 0.75f || absy >= 0.5f) && scale == 0) { float d2m1 = __x2y2m1f (absx, absy); __real__ result = __log1pf (d2m1) / 2.0f; } else { float d = __ieee754_hypotf (absx, absy); __real__ result = __ieee754_logf (d) - scale * (float) M_LN2; } __imag__ result = __ieee754_atan2f (__imag__ x, __real__ x); } else { __imag__ result = __nanf (""); if (rcls == FP_INFINITE || icls == FP_INFINITE) /* Real or imaginary part is infinite. */ __real__ result = HUGE_VALF; else __real__ result = __nanf (""); } return result; }
__complex__ float __csqrtf (__complex__ float x) { __complex__ float res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0)) { if (icls == FP_INFINITE) { __real__ res = HUGE_VALF; __imag__ res = __imag__ x; } else if (rcls == FP_INFINITE) { if (__real__ x < 0.0) { __real__ res = icls == FP_NAN ? __nanf ("") : 0; __imag__ res = __copysignf (HUGE_VALF, __imag__ x); } else { __real__ res = __real__ x; __imag__ res = (icls == FP_NAN ? __nanf ("") : __copysignf (0.0, __imag__ x)); } } else { __real__ res = __nanf (""); __imag__ res = __nanf (""); } } else { if (__builtin_expect (icls == FP_ZERO, 0)) { if (__real__ x < 0.0) { __real__ res = 0.0; __imag__ res = __copysignf (__ieee754_sqrtf (-__real__ x), __imag__ x); } else { __real__ res = fabsf (__ieee754_sqrtf (__real__ x)); __imag__ res = __copysignf (0.0, __imag__ x); } } else if (__builtin_expect (rcls == FP_ZERO, 0)) { float r; if (fabsf (__imag__ x) >= 2.0f * FLT_MIN) r = __ieee754_sqrtf (0.5f * fabsf (__imag__ x)); else r = 0.5f * __ieee754_sqrtf (2.0f * fabsf (__imag__ x)); __real__ res = r; __imag__ res = __copysignf (r, __imag__ x); } else { float d, r, s; int scale = 0; if (fabsf (__real__ x) > FLT_MAX / 4.0f) { scale = 1; __real__ x = __scalbnf (__real__ x, -2 * scale); __imag__ x = __scalbnf (__imag__ x, -2 * scale); } else if (fabsf (__imag__ x) > FLT_MAX / 4.0f) { scale = 1; if (fabsf (__real__ x) >= 4.0f * FLT_MIN) __real__ x = __scalbnf (__real__ x, -2 * scale); else __real__ x = 0.0f; __imag__ x = __scalbnf (__imag__ x, -2 * scale); } else if (fabsf (__real__ x) < FLT_MIN && fabsf (__imag__ x) < FLT_MIN) { scale = -(FLT_MANT_DIG / 2); __real__ x = __scalbnf (__real__ x, -2 * scale); __imag__ x = __scalbnf (__imag__ x, -2 * scale); } d = __ieee754_hypotf (__real__ x, __imag__ x); /* Use the identity 2 Re res Im res = Im x to avoid cancellation error in d +/- Re x. */ if (__real__ x > 0) { r = __ieee754_sqrtf (0.5f * (d + __real__ x)); s = 0.5f * (__imag__ x / r); } else { s = __ieee754_sqrtf (0.5f * (d - __real__ x)); r = fabsf (0.5f * (__imag__ x / s)); } if (scale) { r = __scalbnf (r, scale); s = __scalbnf (s, scale); } __real__ res = r; __imag__ res = __copysignf (s, __imag__ x); } } return res; }
__complex__ float __catanf (__complex__ float x) { __complex__ float res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) { if (rcls == FP_INFINITE) { __real__ res = __copysignf (M_PI_2, __real__ x); __imag__ res = __copysignf (0.0, __imag__ x); } else if (icls == FP_INFINITE) { if (rcls >= FP_ZERO) __real__ res = __copysignf (M_PI_2, __real__ x); else __real__ res = __nanf (""); __imag__ res = __copysignf (0.0, __imag__ x); } else if (icls == FP_ZERO || icls == FP_INFINITE) { __real__ res = __nanf (""); __imag__ res = __copysignf (0.0, __imag__ x); } else { __real__ res = __nanf (""); __imag__ res = __nanf (""); } } else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) { res = x; } else { if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON || fabsf (__imag__ x) >= 16.0f / FLT_EPSILON) { __real__ res = __copysignf ((float) M_PI_2, __real__ x); if (fabsf (__real__ x) <= 1.0f) __imag__ res = 1.0f / __imag__ x; else if (fabsf (__imag__ x) <= 1.0f) __imag__ res = __imag__ x / __real__ x / __real__ x; else { float h = __ieee754_hypotf (__real__ x / 2.0f, __imag__ x / 2.0f); __imag__ res = __imag__ x / h / h / 4.0f; } } else { float den, absx, absy; absx = fabsf (__real__ x); absy = fabsf (__imag__ x); if (absx < absy) { float t = absx; absx = absy; absy = t; } if (absy < FLT_EPSILON / 2.0f) { den = (1.0f - absx) * (1.0f + absx); if (den == -0.0f) den = 0.0f; } else if (absx >= 1.0f) den = (1.0f - absx) * (1.0f + absx) - absy * absy; else if (absx >= 0.75f || absy >= 0.5f) den = -__x2y2m1f (absx, absy); else den = (1.0f - absx) * (1.0f + absx) - absy * absy; __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den); if (fabsf (__imag__ x) == 1.0f && fabsf (__real__ x) < FLT_EPSILON * FLT_EPSILON) __imag__ res = (__copysignf (0.5f, __imag__ x) * ((float) M_LN2 - __ieee754_logf (fabsf (__real__ x)))); else { float r2 = 0.0f, num, f; if (fabsf (__real__ x) >= FLT_EPSILON * FLT_EPSILON) r2 = __real__ x * __real__ x; num = __imag__ x + 1.0f; num = r2 + num * num; den = __imag__ x - 1.0f; den = r2 + den * den; f = num / den; if (f < 0.5f) __imag__ res = 0.25f * __ieee754_logf (f); else { num = 4.0f * __imag__ x; __imag__ res = 0.25f * __log1pf (num / den); } } } if (fabsf (__real__ res) < FLT_MIN) { volatile float force_underflow = __real__ res * __real__ res; (void) force_underflow; } if (fabsf (__imag__ res) < FLT_MIN) { volatile float force_underflow = __imag__ res * __imag__ res; (void) force_underflow; } } return res; }
__complex__ float __kernel_casinhf (__complex__ float x, int adj) { __complex__ float res; float rx, ix; __complex__ float y; /* Avoid cancellation by reducing to the first quadrant. */ rx = fabsf (__real__ x); ix = fabsf (__imag__ x); if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON) { /* For large x in the first quadrant, x + csqrt (1 + x * x) is sufficiently close to 2 * x to make no significant difference to the result; avoid possible overflow from the squaring and addition. */ __real__ y = rx; __imag__ y = ix; if (adj) { float t = __real__ y; __real__ y = __copysignf (__imag__ y, __imag__ x); __imag__ y = t; } res = __clogf (y); __real__ res += (float) M_LN2; } else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f) { float s = __ieee754_hypotf (1.0f, rx); __real__ res = __ieee754_logf (rx + s); if (adj) __imag__ res = __ieee754_atan2f (s, __imag__ x); else __imag__ res = __ieee754_atan2f (ix, s); } else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f) { float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f)); __real__ res = __ieee754_logf (ix + s); if (adj) __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x)); else __imag__ res = __ieee754_atan2f (s, rx); } else if (ix > 1.0f && ix < 1.5f && rx < 0.5f) { if (rx < FLT_EPSILON * FLT_EPSILON) { float ix2m1 = (ix + 1.0f) * (ix - 1.0f); float s = __ieee754_sqrtf (ix2m1); __real__ res = __log1pf (2.0f * (ix2m1 + ix * s)) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x)); else __imag__ res = __ieee754_atan2f (s, rx); } else { float ix2m1 = (ix + 1.0f) * (ix - 1.0f); float rx2 = rx * rx; float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix); float d = __ieee754_sqrtf (ix2m1 * ix2m1 + f); float dp = d + ix2m1; float dm = f / dp; float r1 = __ieee754_sqrtf ((dm + rx2) / 2.0f); float r2 = rx * ix / r1; __real__ res = __log1pf (rx2 + dp + 2.0f * (rx * r1 + ix * r2)) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2, __imag__ x)); else __imag__ res = __ieee754_atan2f (ix + r2, rx + r1); } } else if (ix == 1.0f && rx < 0.5f) { if (rx < FLT_EPSILON / 8.0f) { __real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx), __copysignf (1.0f, __imag__ x)); else __imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx)); } else { float d = rx * __ieee754_sqrtf (4.0f + rx * rx); float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f); float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f); __real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (rx + s1, __copysignf (1.0f + s2, __imag__ x)); else __imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1); } } else if (ix < 1.0f && rx < 0.5f) { if (ix >= FLT_EPSILON) { if (rx < FLT_EPSILON * FLT_EPSILON) { float onemix2 = (1.0f + ix) * (1.0f - ix); float s = __ieee754_sqrtf (onemix2); __real__ res = __log1pf (2.0f * rx / s) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (s, __imag__ x); else __imag__ res = __ieee754_atan2f (ix, s); } else { float onemix2 = (1.0f + ix) * (1.0f - ix); float rx2 = rx * rx; float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix); float d = __ieee754_sqrtf (onemix2 * onemix2 + f); float dp = d + onemix2; float dm = f / dp; float r1 = __ieee754_sqrtf ((dp + rx2) / 2.0f); float r2 = rx * ix / r1; __real__ res = __log1pf (rx2 + dm + 2.0f * (rx * r1 + ix * r2)) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2, __imag__ x)); else __imag__ res = __ieee754_atan2f (ix + r2, rx + r1); } } else { float s = __ieee754_hypotf (1.0f, rx); __real__ res = __log1pf (2.0f * rx * (rx + s)) / 2.0f; if (adj) __imag__ res = __ieee754_atan2f (s, __imag__ x); else __imag__ res = __ieee754_atan2f (ix, s); } if (__real__ res < FLT_MIN) { volatile float force_underflow = __real__ res * __real__ res; (void) force_underflow; } } else { __real__ y = (rx - ix) * (rx + ix) + 1.0f; __imag__ y = 2.0f * rx * ix; y = __csqrtf (y); __real__ y += rx; __imag__ y += ix; if (adj) { float t = __real__ y; __real__ y = __copysignf (__imag__ y, __imag__ x); __imag__ y = t; } res = __clogf (y); } /* Give results the correct sign for the original argument. */ __real__ res = __copysignf (__real__ res, __real__ x); __imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x)); return res; }
__complex__ float __csqrtf (__complex__ float x) { __complex__ float res; int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); if (rcls <= FP_INFINITE || icls <= FP_INFINITE) { if (icls == FP_INFINITE) { __real__ res = HUGE_VALF; __imag__ res = __imag__ x; } else if (rcls == FP_INFINITE) { if (__real__ x < 0.0) { __real__ res = icls == FP_NAN ? __nanf ("") : 0; __imag__ res = __copysignf (HUGE_VALF, __imag__ x); } else { __real__ res = __real__ x; __imag__ res = (icls == FP_NAN ? __nanf ("") : __copysignf (0.0, __imag__ x)); } } else { __real__ res = __nanf (""); __imag__ res = __nanf (""); } } else { if (icls == FP_ZERO) { if (__real__ x < 0.0) { __real__ res = 0.0; __imag__ res = __copysignf (__ieee754_sqrtf (-__real__ x), __imag__ x); } else { __real__ res = fabsf (__ieee754_sqrtf (__real__ x)); __imag__ res = __copysignf (0.0, __imag__ x); } } else if (rcls == FP_ZERO) { float r = __ieee754_sqrtf (0.5 * fabsf (__imag__ x)); __real__ res = __copysignf (r, __imag__ x); __imag__ res = r; } else { float d, r, s; d = __ieee754_hypotf (__real__ x, __imag__ x); /* Use the identity 2 Re res Im res = Im x to avoid cancellation error in d +/- Re x. */ if (__real__ x > 0) { r = __ieee754_sqrtf (0.5f * d + 0.5f * __real__ x); s = (0.5f * __imag__ x) / r; } else { s = __ieee754_sqrtf (0.5f * d - 0.5f * __real__ x); r = fabsf ((0.5f * __imag__ x) / s); } __real__ res = r; __imag__ res = __copysignf (s, __imag__ x); } } return res; }