示例#1
0
invalid_fn (double x, double fn)
{
  if (__rint (fn) != fn)
    return (fn - fn) / (fn - fn);
  else if (fn > 65000.0)
    return __scalbn (x, 65000);
  else
    return __scalbn (x,-65000);
}
示例#2
0
文件: s_clog.c 项目: AdvancedC/glibc
__complex__ double
__clog (__complex__ double x)
{
  __complex__ double 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 = __copysign (__imag__ result, __imag__ x);
      /* Yes, the following line raises an exception.  */
      __real__ result = -1.0 / fabs (__real__ x);
    }
  else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
    {
      /* Neither real nor imaginary part is NaN.  */
      double d;
      int scale = 0;

      if (fabs (__real__ x) > DBL_MAX / 2.0
	  || fabs (__imag__ x) > DBL_MAX / 2.0)
	{
	  scale = -1;
	  __real__ x = __scalbn (__real__ x, scale);
	  __imag__ x = __scalbn (__imag__ x, scale);
	}
      else if (fabs (__real__ x) < DBL_MIN
	       && fabs (__imag__ x) < DBL_MIN)
	{
	  scale = DBL_MANT_DIG;
	  __real__ x = __scalbn (__real__ x, scale);
	  __imag__ x = __scalbn (__imag__ x, scale);
	}

      d = __ieee754_hypot (__real__ x, __imag__ x);

      __real__ result = __ieee754_log (d) - scale * M_LN2;
      __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
    }
  else
    {
      __imag__ result = __nan ("");
      if (rcls == FP_INFINITE || icls == FP_INFINITE)
	/* Real or imaginary part is infinite.  */
	__real__ result = HUGE_VAL;
      else
	__real__ result = __nan ("");
    }

  return result;
}
示例#3
0
double __ldexp(double value, int exp)
{
	if(!isfinite(value)||value==0.0) return value;
	value = __scalbn(value,exp);
	if(!isfinite(value)||value==0.0) __set_errno (ERANGE);
	return value;
}
示例#4
0
int
__kernel_rem_pio2 (double *x, double *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;
  double 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) / 24; if (jv < 0)
    jv = 0;
  q0 = e0 - 24 * (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 : (double) 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 = (double) ((int32_t) (twon24 * z));
      iq[i] = (int32_t) (z - two24 * fw);
      z = q[j - 1] + fw;
    }

  /* compute n */
  z = __scalbn (z, q0);                 /* actual value of z */
  z -= 8.0 * floor (z * 0.125);               /* trim off integer >= 8 */
  n = (int32_t) z;
  z -= (double) n;
  ih = 0;
  if (q0 > 0)           /* need iq[jz-1] to determine n */
    {
      i = (iq[jz - 1] >> (24 - q0)); n += i;
      iq[jz - 1] -= i << (24 - q0);
      ih = iq[jz - 1] >> (23 - q0);
    }
示例#5
0
double
__ieee754_scalb (double x, double fn)
{
  if (__glibc_unlikely (isnan (x)))
    return x * fn;
  if (__glibc_unlikely (!isfinite (fn)))
    {
      if (isnan (fn) || fn > 0.0)
	return x * fn;
      if (x == 0.0)
	return x;
      return x / -fn;
    }
  if (__glibc_unlikely (fabs (fn) >= 0x1p31 || (double) (int) fn != fn))
    return invalid_fn (x, fn);

  return __scalbn (x, (int) fn);
}
示例#6
0
double jumpto__scalbn(double x, int n) {
	return __scalbn(x, n);
}
示例#7
0
Err mathlib_scalbn(UInt16 refnum, double x, Int16 exponent, double *result) {
#pragma unused(refnum)
	*result = __scalbn(x, exponent);
	return mlErrNone;
}
示例#8
0
double remquo ( double x, double y, int *quo)
{
      int			iclx,icly;						  /* classify results of x,y */
      int32_t		iquo;                             /* low 32 bits of integral quotient */
      int32_t		iscx, iscy, idiff;                /* logb values and difference */
      int			i;                                /* loop variable */
      double        absy,x1,y1,z;                     /* local floating-point variables */
      double        rslt;
      fenv_t        OldEnv;
      hexdouble     OldEnvironment;
      int           newexc;

      FEGETENVD ( OldEnvironment.d );
      FESETENVD ( 0.0 );
	  __NOOP;
	  __NOOP;

      OldEnv = OldEnvironment.i.lo;
      
      *quo = 0;                                       /* initialize quotient result */
      iclx = ___fpclassifyd(x);
      icly = ___fpclassifyd(y);
      if (likely((iclx & icly) >= FP_NORMAL))    {    /* x,y both nonzero finite case */
         x1 = __FABS(x);                              /* work with absolute values */
         absy = __FABS(y);
         iquo = 0;                                    /* zero local quotient */
         iscx = (int32_t) __logb(x1);                  /* get binary exponents */
         iscy = (int32_t) __logb(absy);
         idiff = iscx - iscy;                         /* exponent difference */
         if (idiff >= 0) {                            /* exponent of x1 >= exponent of y1 */
              if (idiff != 0) {                       /* exponent of x1 > exponent of y1 */
                   y1 = __scalbn(absy,-iscy);         /* scale |y| to unit binade */
                   x1 = __scalbn(x1,-iscx);           /* ditto for |x| */
                   for (i = idiff; i != 0; i--) {     /* begin remainder loop */
                        if ((z = x1 - y1) >= 0) {     /* nonzero remainder step result */
                            x1 = z;                   /* update remainder (x1) */
                            iquo += 1;                /* increment quotient */
                        }
                        iquo += iquo;                 /* shift quotient left one bit */
                        x1 += x1;                     /* shift (double) remainder */
                   }                                  /* end of remainder loop */
                   x1 = __scalbn(x1,iscy);            /* scale remainder to binade of |y| */
              }                                       /* remainder has exponent <= exponent of y */
              if (x1 >= absy) {                       /* last remainder step */
                   x1 -= absy;
                   iquo +=1;
              }                                       /* end of last remainder step */
         }                                            /* remainder (x1) has smaller exponent than y */
         if (likely( x1 < HugeHalved.d ))
            z = x1 + x1;                              /* double remainder, without overflow */
         else
            z = Huge.d;
         if ((z > absy) || ((z == absy) && ((iquo & 1) != 0))) {
              x1 -= absy;                             /* final remainder correction */
              iquo += 1;
         }
         if (x < 0.0)
              x1 = -x1;                               /* remainder if x is negative */
         iquo &= 0x0000007f;                          /* retain low 7 bits of integer quotient */
         if ((___signbitd(x) ^ ___signbitd(y)) != 0)    /* take care of sign of quotient */
              iquo = -iquo;
         *quo = iquo;                                 /* deliver quotient result */
         rslt = x1;
         goto ret;
    }                                                 /* end of x,y both nonzero finite case */
    else if ((iclx <= FP_QNAN) || (icly <= FP_QNAN)) {
         rslt = x+y;                                  /* at least one NaN operand */
         goto ret;
    }
    else if ((iclx == FP_INFINITE)||(icly == FP_ZERO)) {    /* invalid result */
         rslt = nan(REM_NAN);
            OldEnvironment.i.lo |= SET_INVALID;
            FESETENVD_GRP( OldEnvironment.d );
         goto ret;
    }
    else                                              /* trivial cases (finite REM infinite   */
         rslt = x;                                    /*  or  zero REM nonzero) with *quo = 0 */
  ret:
      FEGETENVD_GRP( OldEnvironment.d );
      newexc = OldEnvironment.i.lo & FE_ALL_EXCEPT;
      OldEnvironment.i.lo = OldEnv;
      if ((newexc & FE_INVALID) != 0)
            OldEnvironment.i.lo |= SET_INVALID;
      OldEnvironment.i.lo |=  newexc & ( FE_INEXACT | FE_DIVBYZERO | FE_UNDERFLOW | FE_OVERFLOW );
      FESETENVD_GRP( OldEnvironment.d );
      return rslt;
}
示例#9
0
__complex__ double
__csqrt (__complex__ double x)
{
  __complex__ double 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_VAL;
	  __imag__ res = __imag__ x;
	}
      else if (rcls == FP_INFINITE)
	{
	  if (__real__ x < 0.0)
	    {
	      __real__ res = icls == FP_NAN ? __nan ("") : 0;
	      __imag__ res = __copysign (HUGE_VAL, __imag__ x);
	    }
	  else
	    {
	      __real__ res = __real__ x;
	      __imag__ res = (icls == FP_NAN
			      ? __nan ("") : __copysign (0.0, __imag__ x));
	    }
	}
      else
	{
	  __real__ res = __nan ("");
	  __imag__ res = __nan ("");
	}
    }
  else
    {
      if (__builtin_expect (icls == FP_ZERO, 0))
	{
	  if (__real__ x < 0.0)
	    {
	      __real__ res = 0.0;
	      __imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
					 __imag__ x);
	    }
	  else
	    {
	      __real__ res = fabs (__ieee754_sqrt (__real__ x));
	      __imag__ res = __copysign (0.0, __imag__ x);
	    }
	}
      else if (__builtin_expect (rcls == FP_ZERO, 0))
	{
	  double r;
	  if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
	    r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
	  else
	    r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));

	  __real__ res = r;
	  __imag__ res = __copysign (r, __imag__ x);
	}
      else
	{
	  double d, r, s;
	  int scale = 0;

	  if (fabs (__real__ x) > DBL_MAX / 4.0)
	    {
	      scale = 1;
	      __real__ x = __scalbn (__real__ x, -2 * scale);
	      __imag__ x = __scalbn (__imag__ x, -2 * scale);
	    }
	  else if (fabs (__imag__ x) > DBL_MAX / 4.0)
	    {
	      scale = 1;
	      if (fabs (__real__ x) >= 4.0 * DBL_MIN)
		__real__ x = __scalbn (__real__ x, -2 * scale);
	      else
		__real__ x = 0.0;
	      __imag__ x = __scalbn (__imag__ x, -2 * scale);
	    }
	  else if (fabs (__real__ x) < DBL_MIN
		   && fabs (__imag__ x) < DBL_MIN)
	    {
	      scale = -(DBL_MANT_DIG / 2);
	      __real__ x = __scalbn (__real__ x, -2 * scale);
	      __imag__ x = __scalbn (__imag__ x, -2 * scale);
	    }

	  d = __ieee754_hypot (__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_sqrt (0.5 * (d + __real__ x));
	      s = 0.5 * (__imag__ x / r);
	    }
	  else
	    {
	      s = __ieee754_sqrt (0.5 * (d - __real__ x));
	      r = fabs (0.5 * (__imag__ x / s));
	    }

	  if (scale)
	    {
	      r = __scalbn (r, scale);
	      s = __scalbn (s, scale);
	    }

	  __real__ res = r;
	  __imag__ res = __copysign (s, __imag__ x);
	}
    }

  return res;
}
示例#10
0
double
__ieee754_gamma_r (double x, int *signgamp)
{
  int32_t hx;
  u_int32_t lx;

  EXTRACT_WORDS (hx, lx, x);

  if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 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 < 0xfff00000 && __rint (x) == x)
    {
      /* Return value for integer x < 0 is NaN with invalid exception.  */
      *signgamp = 0;
      return (x - x) / (x - x);
    }
  if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0))
    {
      /* x == -Inf.  According to ISO this is NaN.  */
      *signgamp = 0;
      return x - x;
    }
  if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000))
    {
      /* Positive infinity (return positive infinity) or NaN (return
	 NaN).  */
      *signgamp = 0;
      return x + x;
    }

  if (x >= 172.0)
    {
      /* Overflow.  */
      *signgamp = 0;
      return DBL_MAX * DBL_MAX;
    }
  else if (x > 0.0)
    {
      *signgamp = 0;
      int exp2_adj;
      double ret = gamma_positive (x, &exp2_adj);
      return __scalbn (ret, exp2_adj);
    }
  else if (x >= -DBL_EPSILON / 4.0)
    {
      *signgamp = 0;
      return 1.0 / x;
    }
  else
    {
      double tx = __trunc (x);
      *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1;
      if (x <= -184.0)
	/* Underflow.  */
	return DBL_MIN * DBL_MIN;
      double frac = tx - x;
      if (frac > 0.5)
	frac = 1.0 - frac;
      double sinpix = (frac <= 0.25
		       ? __sin (M_PI * frac)
		       : __cos (M_PI * (0.5 - frac)));
      int exp2_adj;
      double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj));
      return __scalbn (ret, -exp2_adj);
    }
}
示例#11
0
__complex__ double
__clog (__complex__ double x)
{
  __complex__ double 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 : 0.0;
      __imag__ result = __copysign (__imag__ result, __imag__ x);
      /* Yes, the following line raises an exception.  */
      __real__ result = -1.0 / fabs (__real__ x);
    }
  else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
    {
      /* Neither real nor imaginary part is NaN.  */
      double absx = fabs (__real__ x), absy = fabs (__imag__ x);
      int scale = 0;

      if (absx < absy)
	{
	  double t = absx;
	  absx = absy;
	  absy = t;
	}

      if (absx > DBL_MAX / 2.0)
	{
	  scale = -1;
	  absx = __scalbn (absx, scale);
	  absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
	}
      else if (absx < DBL_MIN && absy < DBL_MIN)
	{
	  scale = DBL_MANT_DIG;
	  absx = __scalbn (absx, scale);
	  absy = __scalbn (absy, scale);
	}

      if (absx == 1.0 && scale == 0)
	{
	  __real__ result = __log1p (absy * absy) / 2.0;
	  math_check_force_underflow_nonneg (__real__ result);
	}
      else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
	{
	  double d2m1 = (absx - 1.0) * (absx + 1.0);
	  if (absy >= DBL_EPSILON)
	    d2m1 += absy * absy;
	  __real__ result = __log1p (d2m1) / 2.0;
	}
      else if (absx < 1.0
	       && absx >= 0.5
	       && absy < DBL_EPSILON / 2.0
	       && scale == 0)
	{
	  double d2m1 = (absx - 1.0) * (absx + 1.0);
	  __real__ result = __log1p (d2m1) / 2.0;
	}
      else if (absx < 1.0
	       && absx >= 0.5
	       && scale == 0
	       && absx * absx + absy * absy >= 0.5)
	{
	  double d2m1 = __x2y2m1 (absx, absy);
	  __real__ result = __log1p (d2m1) / 2.0;
	}
      else
	{
	  double d = __ieee754_hypot (absx, absy);
	  __real__ result = __ieee754_log (d) - scale * M_LN2;
	}

      __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
    }
  else
    {
      __imag__ result = __nan ("");
      if (rcls == FP_INFINITE || icls == FP_INFINITE)
	/* Real or imaginary part is infinite.  */
	__real__ result = HUGE_VAL;
      else
	__real__ result = __nan ("");
    }

  return result;
}
示例#12
0
__complex__ double
__clog10 (__complex__ double x)
{
  __complex__ double 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 = __copysign (__imag__ result, __imag__ x);
      /* Yes, the following line raises an exception.  */
      __real__ result = -1.0 / fabs (__real__ x);
    }
  else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
    {
      /* Neither real nor imaginary part is NaN.  */
      double absx = fabs (__real__ x), absy = fabs (__imag__ x);
      int scale = 0;

      if (absx < absy)
	{
	  double t = absx;
	  absx = absy;
	  absy = t;
	}

      if (absx > DBL_MAX / 2.0)
	{
	  scale = -1;
	  absx = __scalbn (absx, scale);
	  absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
	}
      else if (absx < DBL_MIN && absy < DBL_MIN)
	{
	  scale = DBL_MANT_DIG;
	  absx = __scalbn (absx, scale);
	  absy = __scalbn (absy, scale);
	}

      if (absx == 1.0 && scale == 0)
	{
	  double absy2 = absy * absy;
	  if (absy2 <= DBL_MIN * 2.0 * M_LN10)
	    {
#if __FLT_EVAL_METHOD__ == 0
	      __real__ result = (absy2 / 2.0 - absy2 * absy2 / 4.0) * M_LOG10E;
#else
	      volatile double force_underflow = absy2 * absy2 / 4.0;
	      __real__ result = (absy2 / 2.0 - force_underflow) * M_LOG10E;
#endif
	    }
	  else
	    __real__ result = __log1p (absy2) * (M_LOG10E / 2.0);
	}
      else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
	{
	  double d2m1 = (absx - 1.0) * (absx + 1.0);
	  if (absy >= DBL_EPSILON)
	    d2m1 += absy * absy;
	  __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
	}
      else if (absx < 1.0
	       && absx >= 0.75
	       && absy < DBL_EPSILON / 2.0
	       && scale == 0)
	{
	  double d2m1 = (absx - 1.0) * (absx + 1.0);
	  __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
	}
      else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0)
	{
	  double d2m1 = __x2y2m1 (absx, absy);
	  __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
	}
      else
	{
	  double d = __ieee754_hypot (absx, absy);
	  __real__ result = __ieee754_log10 (d) - scale * M_LOG10_2;
	}

      __imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x);
    }
  else
    {
      __imag__ result = __nan ("");
      if (rcls == FP_INFINITE || icls == FP_INFINITE)
	/* Real or imaginary part is infinite.  */
	__real__ result = HUGE_VAL;
      else
	__real__ result = __nan ("");
    }

  return result;
}