hypot.c

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MIT License
-----------
 
Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
 
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#include "libm.h"
#include "libm_util.h"
 
#define FAST_BUT_GREATER_THAN_ONE_ULP  /* Helps speed by trading off a little
                                          accuracy */
#define USE_SCALEDOUBLE_1
#define USE_INFINITY_WITH_FLAGS
#define USE_HANDLE_ERROR
#include "libm_inlines.h"
#undef USE_SCALEDOUBLE_1
#undef USE_INFINITY_WITH_FLAGS
#undef USE_HANDLE_ERROR
 
#include "libm_errno.h"
 
#if (_MSC_VER >= 1920) // VS 2019+ / Compiler version 14.20
#pragma function(_hypot)
#endif
 
double FN_PROTOTYPE(_hypot)(double x, double y)
{
  /* Returns sqrt(x*x + y*y) with no overflow or underflow unless
     the result warrants it */
 
  const double large = 1.79769313486231570815e+308; /* 0x7fefffffffffffff */
 
#ifdef FAST_BUT_GREATER_THAN_ONE_ULP
  double r, retval;
  unsigned long long xexp, yexp, ux, uy;
#else  
  double u, r, retval, hx, tx, x2, hy, ty, y2, hs, ts;
  unsigned long long xexp, yexp, ux, uy, ut;
#endif
  int dexp, expadjust;
 
  GET_BITS_DP64(x, ux);
  ux &= ~SIGNBIT_DP64;
  GET_BITS_DP64(y, uy);
  uy &= ~SIGNBIT_DP64;
  xexp = (ux >> EXPSHIFTBITS_DP64);
  yexp = (uy >> EXPSHIFTBITS_DP64);
 
  if (xexp == BIASEDEMAX_DP64 + 1 || yexp == BIASEDEMAX_DP64 + 1)
    {
      /* One or both of the arguments are NaN or infinity. The
         result will also be NaN or infinity. */
      retval = x*x + y*y;
      if (((xexp == BIASEDEMAX_DP64 + 1) && !(ux & MANTBITS_DP64)) ||
          ((yexp == BIASEDEMAX_DP64 + 1) && !(uy & MANTBITS_DP64)))
        /* x or y is infinity. ISO C99 defines that we must
           return +infinity, even if the other argument is NaN.
           Note that the computation of x*x + y*y above will already
           have raised invalid if either x or y is a signalling NaN. */
        return infinity_with_flags(0);
      else
        /* One or both of x or y is NaN, and neither is infinity.
           Raise invalid if it's a signalling NaN */
        return retval;
    }
 
  /* Set x = abs(x) and y = abs(y) */
  PUT_BITS_DP64(ux, x);
  PUT_BITS_DP64(uy, y);
 
  /* The difference in exponents between x and y */
  dexp = (int)(xexp - yexp);
  expadjust = 0;
 
  if (ux == 0)
    /* x is zero */
    return y;
  else if (uy == 0)
    /* y is zero */
    return x;
  else if (dexp > MANTLENGTH_DP64 + 1 || dexp < -MANTLENGTH_DP64 - 1)
    /* One of x and y is insignificant compared to the other */
    return x + y; /* Raise inexact */
  else if (xexp > EXPBIAS_DP64 + 500 || yexp > EXPBIAS_DP64 + 500)
    {
      /* Danger of overflow; scale down by 2**600. */
      expadjust = 600;
      ux -= 0x2580000000000000;
      PUT_BITS_DP64(ux, x);
      uy -= 0x2580000000000000;
      PUT_BITS_DP64(uy, y);
    }
  else if (xexp < EXPBIAS_DP64 - 500 || yexp < EXPBIAS_DP64 - 500)
    {
      /* Danger of underflow; scale up by 2**600. */
      expadjust = -600;
      if (xexp == 0)
        {
          /* x is denormal - handle by adding 601 to the exponent
           and then subtracting a correction for the implicit bit */
          PUT_BITS_DP64(ux + 0x2590000000000000, x);
          x -= 9.23297861778573578076e-128; /* 0x2590000000000000 */
          GET_BITS_DP64(x, ux);
        }
      else
        {
          /* x is normal - just increase the exponent by 600 */
          ux += 0x2580000000000000;
          PUT_BITS_DP64(ux, x);
        }
      if (yexp == 0)
        {
          PUT_BITS_DP64(uy + 0x2590000000000000, y);
          y -= 9.23297861778573578076e-128; /* 0x2590000000000000 */
          GET_BITS_DP64(y, uy);
        }
      else
        {
          uy += 0x2580000000000000;
          PUT_BITS_DP64(uy, y);
        }
    }
 
 
#ifdef FAST_BUT_GREATER_THAN_ONE_ULP
  /* Not awful, but results in accuracy loss larger than 1 ulp */
  r = x*x + y*y;
#else
  /* Slower but more accurate */
 
  /* Sort so that x is greater than y */
  if (x < y)
    {
      u = y;
      y = x;
      x = u;
      ut = ux;
      ux = uy;
      uy = ut;
    }
 
  /* Split x into hx and tx, head and tail */
  PUT_BITS_DP64(ux & 0xfffffffff8000000, hx);
  tx = x - hx;
 
  PUT_BITS_DP64(uy & 0xfffffffff8000000, hy);
  ty = y - hy;
 
  /* Compute r = x*x + y*y with extra precision */
  x2 = x*x;
  y2 = y*y;
  hs = x2 + y2;
 
  if (dexp == 0)
    /* We take most care when x and y have equal exponents,
       i.e. are almost the same size */
    ts = (((x2 - hs) + y2) +
          ((hx * hx - x2) + 2 * hx * tx) + tx * tx) +
      ((hy * hy - y2) + 2 * hy * ty) + ty * ty;
  else
    ts = (((x2 - hs) + y2) +
          ((hx * hx - x2) + 2 * hx * tx) + tx * tx);
 
  r = hs + ts;
#endif
 
  /* The sqrt can introduce another half ulp error. */
  /* VC++ intrinsic call */
  _mm_store_sd(&retval, _mm_sqrt_sd(_mm_setzero_pd(), _mm_load_sd(&r)));
 
  /* If necessary scale the result back. This may lead to
     overflow but if so that's the correct result. */
  retval = scaleDouble_1(retval, expadjust);
 
  if (retval > large)
    /* The result overflowed. Deal with errno. */
    return _handle_error("_hypot", OP_HYPOT, PINFBITPATT_DP64, _OVERFLOW,
                        AMD_F_OVERFLOW | AMD_F_INEXACT, ERANGE, x, y, 2);
 
  return retval;
}