s_erfl.c

glibc 库, 不仅可以学习使用库函数,还可以学习函数的具体实现,是提高功力的好资料

-2.206127630303621521950193783894598987033E2L,
-1.861800338758066696514480386180875607204E3L,
-8.889048775872605708249140016201753255599E3L,
-2.465888106627948210478692168261494857089E4L,
-3.934642211710774494879042116768390014289E4L,
-3.455077258242252974937480623730228841003E4L,
-1.524083977439690284820586063729912653196E4L,
-2.810541887397984804237552337349093953857E3L,
-1.343929553541159933824901621702567066156E2L
 /* 1.0E0 */
};

/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
   1/4 <= 1/x < 3/8
   Peak relative error 8.4e-37  */
#define NRNr3 11
static const long double RNr3[NRNr3 + 1] =
{
-1.952401126551202208698629992497306292987E-6L,
-2.130881743066372952515162564941682716125E-4L,
-8.376493958090190943737529486107282224387E-3L,
-1.650592646560987700661598877522831234791E-1L,
-1.839290818933317338111364667708678163199E0L,
-1.216278715570882422410442318517814388470E1L,
-4.818759344462360427612133632533779091386E1L,
-1.120994661297476876804405329172164436784E2L,
-1.452850765662319264191141091859300126931E2L,
-9.485207851128957108648038238656777241333E1L,
-2.563663855025796641216191848818620020073E1L,
-1.787995944187565676837847610706317833247E0L
};
#define NRDr3 10
static const long double RDr3[NRDr3 + 1] =
{
 1.979130686770349481460559711878399476903E-4L,
 1.156941716128488266238105813374635099057E-2L,
 2.752657634309886336431266395637285974292E-1L,
 3.482245457248318787349778336603569327521E0L,
 2.569347069372696358578399521203959253162E1L,
 1.142279000180457419740314694631879921561E2L,
 3.056503977190564294341422623108332700840E2L,
 4.780844020923794821656358157128719184422E2L,
 4.105972727212554277496256802312730410518E2L,
 1.724072188063746970865027817017067646246E2L,
 2.815939183464818198705278118326590370435E1L
 /* 1.0E0 */
};

/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
   1/8 <= 1/x < 1/4
   Peak relative error 1.5e-36  */
#define NRNr2 11
static const long double RNr2[NRNr2 + 1] =
{
-2.638914383420287212401687401284326363787E-8L,
-3.479198370260633977258201271399116766619E-6L,
-1.783985295335697686382487087502222519983E-4L,
-4.777876933122576014266349277217559356276E-3L,
-7.450634738987325004070761301045014986520E-2L,
-7.068318854874733315971973707247467326619E-1L,
-4.113919921935944795764071670806867038732E0L,
-1.440447573226906222417767283691888875082E1L,
-2.883484031530718428417168042141288943905E1L,
-2.990886974328476387277797361464279931446E1L,
-1.325283914915104866248279787536128997331E1L,
-1.572436106228070195510230310658206154374E0L
};
#define NRDr2 10
static const long double RDr2[NRDr2 + 1] =
{
 2.675042728136731923554119302571867799673E-6L,
 2.170997868451812708585443282998329996268E-4L,
 7.249969752687540289422684951196241427445E-3L,
 1.302040375859768674620410563307838448508E-1L,
 1.380202483082910888897654537144485285549E0L,
 8.926594113174165352623847870299170069350E0L,
 3.521089584782616472372909095331572607185E1L,
 8.233547427533181375185259050330809105570E1L,
 1.072971579885803033079469639073292840135E2L,
 6.943803113337964469736022094105143158033E1L,
 1.775695341031607738233608307835017282662E1L
 /* 1.0E0 */
};

/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
   1/128 <= 1/x < 1/8
   Peak relative error 2.2e-36  */
#define NRNr1 9
static const long double RNr1[NRNr1 + 1] =
{
-4.250780883202361946697751475473042685782E-8L,
-5.375777053288612282487696975623206383019E-6L,
-2.573645949220896816208565944117382460452E-4L,
-6.199032928113542080263152610799113086319E-3L,
-8.262721198693404060380104048479916247786E-2L,
-6.242615227257324746371284637695778043982E-1L,
-2.609874739199595400225113299437099626386E0L,
-5.581967563336676737146358534602770006970E0L,
-5.124398923356022609707490956634280573882E0L,
-1.290865243944292370661544030414667556649E0L
};
#define NRDr1 8
static const long double RDr1[NRDr1 + 1] =
{
 4.308976661749509034845251315983612976224E-6L,
 3.265390126432780184125233455960049294580E-4L,
 9.811328839187040701901866531796570418691E-3L,
 1.511222515036021033410078631914783519649E-1L,
 1.289264341917429958858379585970225092274E0L,
 6.147640356182230769548007536914983522270E0L,
 1.573966871337739784518246317003956180750E1L,
 1.955534123435095067199574045529218238263E1L,
 9.472613121363135472247929109615785855865E0L
  /* 1.0E0 */
};


#ifdef __STDC__
long double
__erfl (long double x)
#else
double
__erfl (x)
     long double x;
#endif
{
  long double a, y, z;
  int32_t i, ix, sign;
  ieee854_long_double_shape_type u;

  u.value = x;
  sign = u.parts32.w0;
  ix = sign & 0x7fffffff;

  if (ix >= 0x7ff00000)
    {				/* erf(nan)=nan */
      i = ((sign & 0xfff00000) >> 31) << 1;
      return (long double) (1 - i) + one / x;	/* erf(+-inf)=+-1 */
    }

  if (ix >= 0x3ff00000) /* |x| >= 1.0 */
    {
      y = __erfcl (x);
      return (one - y);
      /*    return (one - __erfcl (x)); */
    }
  u.parts32.w0 = ix;
  a = u.value;
  z = x * x;
  if (ix < 0x3fec0000)  /* a < 0.875 */
    {
      if (ix < 0x3c600000) /* |x|<2**-57 */
	{
	  if (ix < 0x00800000)
	    {
	      /* erf (-0) = -0.  Unfortunately, for IBM extended double
		 0.125 * (8.0 * x + efx8 * x) for x = -0 evaluates to 0.  */
	      if (x == 0)
		return x;
	      return 0.125 * (8.0 * x + efx8 * x);	/*avoid underflow */
	    }
	  return x + efx * x;
	}
      y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1);
    }
  else
    {
      a = a - one;
      y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2);
    }

  if (sign & 0x80000000) /* x < 0 */
    y = -y;
  return( y );
}

long_double_symbol (libm, __erfl, erfl);
#ifdef __STDC__
     long double
     __erfcl (long double x)
#else
     long double
     __erfcl (x)
     double
       x;
#endif
{
  long double y, z, p, r;
  int32_t i, ix, sign;
  ieee854_long_double_shape_type u;

  u.value = x;
  sign = u.parts32.w0;
  ix = sign & 0x7fffffff;
  u.parts32.w0 = ix;

  if (ix >= 0x7ff00000)
    {				/* erfc(nan)=nan */
      /* erfc(+-inf)=0,2 */
      return (long double) (((u_int32_t) sign >> 31) << 1) + one / x;
    }

  if (ix < 0x3fd00000) /* |x| <1/4 */
    {
      if (ix < 0x38d00000) /* |x|<2**-114 */
	return one - x;
      return one - __erfl (x);
    }
  if (ix < 0x3ff40000) /* 1.25 */
    {
      x = u.value;
      i = 8.0 * x;
      switch (i)
	{
	case 2:
	  z = x - 0.25L;
	  y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13);
	  y += C13a;
	  break;
	case 3:
	  z = x - 0.375L;
	  y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14);
	  y += C14a;
	  break;
	case 4:
	  z = x - 0.5L;
	  y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15);
	  y += C15a;
	  break;
	case 5:
	  z = x - 0.625L;
	  y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16);
	  y += C16a;
	  break;
	case 6:
	  z = x - 0.75L;
	  y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17);
	  y += C17a;
	  break;
	case 7:
	  z = x - 0.875L;
	  y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18);
	  y += C18a;
	  break;
	case 8:
	  z = x - 1.0L;
	  y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19);
	  y += C19a;
	  break;
	case 9:
	  z = x - 1.125L;
	  y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20);
	  y += C20a;
	  break;
	}
      if (sign & 0x80000000)
	y = 2.0L - y;
      return y;
    }
  /* 1.25 < |x| < 107 */
  if (ix < 0x405ac000)
    {
      /* x < -9 */
      if ((ix >= 0x40220000) && (sign & 0x80000000))
	return two - tiny;

      x = fabsl (x);
      z = one / (x * x);
      i = 8.0 / x;
      switch (i)
	{
	default:
	case 0:
	  p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1);
	  break;
	case 1:
	  p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2);
	  break;
	case 2:
	  p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3);
	  break;
	case 3:
	  p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4);
	  break;
	case 4:
	  p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5);
	  break;
	case 5:
	  p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6);
	  break;
	case 6:
	  p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7);
	  break;
	case 7:
	  p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8);
	  break;
	}
      u.value = x;
      u.parts32.w3 = 0;
      u.parts32.w2 &= 0xffffe000;
      z = u.value;
      r = __ieee754_expl (-z * z - 0.5625) *
	__ieee754_expl ((z - x) * (z + x) + p);
      if ((sign & 0x80000000) == 0)
	return r / x;
      else
	return two - r / x;
    }
  else
    {
      if ((sign & 0x80000000) == 0)
	return tiny * tiny;
      else
	return two - tiny;
    }
}

long_double_symbol (libm, __erfcl, erfcl);