__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;
}
int32_t
__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
{
int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
float z, fw, f[20], fq[20], q[20];
/* initialize jk */
jp = jk = 9;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx - 1;
exp = __float_get_exp (e0) - 127;
jv = (exp - 3) / 8;
if (jv < 0)
jv = 0;
q0 = exp - 8 * (jv + 1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
j = jv - jx;
m = jx + jk;
for (i = 0; i <= m; i++, j++)
f[i] = (j < 0) ? zero : two_over_pi[j];
/* compute q[0],q[1],...q[jk] */
for (i = 0; i <= jk; i++)
{
for (j = 0, fw = 0.0; j <= jx; j++)
fw += x[j] * f[jx + i - j];
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
{
fw = __truncf (twon8 * z);
iq[i] = (int32_t) (z - two8 * fw);
z = q[j - 1] + fw;
}
/* compute n */
z = __scalbnf (z, q0); /* actual value of z */
z -= 8.0 * __floorf (z * 0.125); /* trim off integer >= 8 */
n = (int32_t) z;
z -= __truncf (z);
ih = 0;
if (q0 > 0)
{ /* need iq[jz-1] to determine n */
i = (iq[jz - 1] >> (8 - q0));
n += i;
iq[jz - 1] -= i << (8 - q0);
ih = iq[jz - 1] >> (7 - q0);
}
int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
{
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
float z,fw,f[20],fq[20],q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/8; if(jv<0) jv=0;
q0 = e0-8*(jv+1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
/* compute q[0],q[1],...q[jk] */
for (i=0;i<=jk;i++) {
for(j=0,fw=0.0;j<=jx;j++)
fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
fw = (float)((int32_t)(twon8* z));
iq[i] = (int32_t)(z-two8*fw);
z = q[j-1]+fw;
}
/* compute n */
z = __scalbnf(z,q0); /* actual value of z */
z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */
n = (int32_t) z;
z -= (float)n;
ih = 0;
if(q0>0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1]>>(8-q0)); n += i;
iq[jz-1] -= i<<(8-q0);
ih = iq[jz-1]>>(7-q0);
}
__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;
}
float
__ieee754_gammaf_r (float x, int *signgamp)
{
int32_t hx;
float ret;
GET_FLOAT_WORD (hx, x);
if (__glibc_unlikely ((hx & 0x7fffffff) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__builtin_expect (hx < 0, 0)
&& (u_int32_t) hx < 0xff800000 && __rintf (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (__glibc_unlikely (hx == 0xff800000))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (x >= 36.0f)
{
/* Overflow. */
*signgamp = 0;
ret = math_narrow_eval (FLT_MAX * FLT_MAX);
return ret;
}
else
{
SET_RESTORE_ROUNDF (FE_TONEAREST);
if (x > 0.0f)
{
*signgamp = 0;
int exp2_adj;
float tret = gammaf_positive (x, &exp2_adj);
ret = __scalbnf (tret, exp2_adj);
}
else if (x >= -FLT_EPSILON / 4.0f)
{
*signgamp = 0;
ret = 1.0f / x;
}
else
{
float tx = __truncf (x);
*signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1;
if (x <= -42.0f)
/* Underflow. */
ret = FLT_MIN * FLT_MIN;
else
{
float frac = tx - x;
if (frac > 0.5f)
frac = 1.0f - frac;
float sinpix = (frac <= 0.25f
? __sinf ((float) M_PI * frac)
: __cosf ((float) M_PI * (0.5f - frac)));
int exp2_adj;
float tret = (float) M_PI / (-x * sinpix
* gammaf_positive (-x, &exp2_adj));
ret = __scalbnf (tret, -exp2_adj);
math_check_force_underflow_nonneg (ret);
}
}
ret = math_narrow_eval (ret);
}
if (isinf (ret) && x != 0)
{
if (*signgamp < 0)
{
ret = math_narrow_eval (-__copysignf (FLT_MAX, ret) * FLT_MAX);
ret = -ret;
}
else
ret = math_narrow_eval (__copysignf (FLT_MAX, ret) * FLT_MAX);
return ret;
}
else if (ret == 0)
{
if (*signgamp < 0)
{
ret = math_narrow_eval (-__copysignf (FLT_MIN, ret) * FLT_MIN);
ret = -ret;
}
else
ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN);
return ret;
}
else
return ret;
}
__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;
}
