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softfloat.c

/*
 * Floating point emulation support for subnormalised numbers on SH4
 * architecture This file is derived from the SoftFloat IEC/IEEE
 * Floating-point Arithmetic Package, Release 2 the original license of
 * which is reproduced below.
 *
 * ========================================================================
 *
 * This C source file is part of the SoftFloat IEC/IEEE Floating-point
 * Arithmetic Package, Release 2.
 *
 * Written by John R. Hauser.  This work was made possible in part by the
 * International Computer Science Institute, located at Suite 600, 1947 Center
 * Street, Berkeley, California 94704.  Funding was partially provided by the
 * National Science Foundation under grant MIP-9311980.  The original version
 * of this code was written as part of a project to build a fixed-point vector
 * processor in collaboration with the University of California at Berkeley,
 * overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
 * is available through the web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
 * arithmetic/softfloat.html'.
 *
 * THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort
 * has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
 * TIMES RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO
 * PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
 * AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
 *
 * Derivative works are acceptable, even for commercial purposes, so long as
 * (1) they include prominent notice that the work is derivative, and (2) they
 * include prominent notice akin to these three paragraphs for those parts of
 * this code that are retained.
 *
 * ========================================================================
 *
 * SH4 modifications by Ismail Dhaoui <ismail.dhaoui@st.com>
 * and Kamel Khelifi <kamel.khelifi@st.com>
 */
#include <linux/kernel.h>
#include <cpu/fpu.h>

#define LIT64( a ) a##LL

typedef char flag;
typedef unsigned char uint8;
typedef signed char int8;
typedef int uint16;
typedef int int16;
typedef unsigned int uint32;
typedef signed int int32;

typedef unsigned long long int bits64;
typedef signed long long int sbits64;

typedef unsigned char bits8;
typedef signed char sbits8;
typedef unsigned short int bits16;
typedef signed short int sbits16;
typedef unsigned int bits32;
typedef signed int sbits32;

typedef unsigned long long int uint64;
typedef signed long long int int64;

typedef unsigned long int float32;
typedef unsigned long long float64;

extern void float_raise(unsigned int flags);    /* in fpu.c */
extern int float_rounding_mode(void);     /* in fpu.c */

inline bits64 extractFloat64Frac(float64 a);
inline flag extractFloat64Sign(float64 a);
inline int16 extractFloat64Exp(float64 a);
inline int16 extractFloat32Exp(float32 a);
inline flag extractFloat32Sign(float32 a);
inline bits32 extractFloat32Frac(float32 a);
inline float64 packFloat64(flag zSign, int16 zExp, bits64 zSig);
inline void shift64RightJamming(bits64 a, int16 count, bits64 * zPtr);
inline float32 packFloat32(flag zSign, int16 zExp, bits32 zSig);
inline void shift32RightJamming(bits32 a, int16 count, bits32 * zPtr);
float64 float64_sub(float64 a, float64 b);
float32 float32_sub(float32 a, float32 b);
float32 float32_add(float32 a, float32 b);
float64 float64_add(float64 a, float64 b);
float64 float64_div(float64 a, float64 b);
float32 float32_div(float32 a, float32 b);
float32 float32_mul(float32 a, float32 b);
float64 float64_mul(float64 a, float64 b);
inline void add128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
               bits64 * z1Ptr);
inline void sub128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
               bits64 * z1Ptr);
inline void mul64To128(bits64 a, bits64 b, bits64 * z0Ptr, bits64 * z1Ptr);

static int8 countLeadingZeros32(bits32 a);
static int8 countLeadingZeros64(bits64 a);
static float64 normalizeRoundAndPackFloat64(flag zSign, int16 zExp,
                                  bits64 zSig);
static float64 subFloat64Sigs(float64 a, float64 b, flag zSign);
static float64 addFloat64Sigs(float64 a, float64 b, flag zSign);
static float32 roundAndPackFloat32(flag zSign, int16 zExp, bits32 zSig);
static float32 normalizeRoundAndPackFloat32(flag zSign, int16 zExp,
                                  bits32 zSig);
static float64 roundAndPackFloat64(flag zSign, int16 zExp, bits64 zSig);
static float32 subFloat32Sigs(float32 a, float32 b, flag zSign);
static float32 addFloat32Sigs(float32 a, float32 b, flag zSign);
static void normalizeFloat64Subnormal(bits64 aSig, int16 * zExpPtr,
                              bits64 * zSigPtr);
static bits64 estimateDiv128To64(bits64 a0, bits64 a1, bits64 b);
static void normalizeFloat32Subnormal(bits32 aSig, int16 * zExpPtr,
                              bits32 * zSigPtr);

inline bits64 extractFloat64Frac(float64 a)
{
      return a & LIT64(0x000FFFFFFFFFFFFF);
}

inline flag extractFloat64Sign(float64 a)
{
      return a >> 63;
}

inline int16 extractFloat64Exp(float64 a)
{
      return (a >> 52) & 0x7FF;
}

inline int16 extractFloat32Exp(float32 a)
{
      return (a >> 23) & 0xFF;
}

inline flag extractFloat32Sign(float32 a)
{
      return a >> 31;
}

inline bits32 extractFloat32Frac(float32 a)
{
      return a & 0x007FFFFF;
}

inline float64 packFloat64(flag zSign, int16 zExp, bits64 zSig)
{
      return (((bits64) zSign) << 63) + (((bits64) zExp) << 52) + zSig;
}

inline void shift64RightJamming(bits64 a, int16 count, bits64 * zPtr)
{
      bits64 z;

      if (count == 0) {
            z = a;
      } else if (count < 64) {
            z = (a >> count) | ((a << ((-count) & 63)) != 0);
      } else {
            z = (a != 0);
      }
      *zPtr = z;
}

static int8 countLeadingZeros32(bits32 a)
{
      static const int8 countLeadingZerosHigh[] = {
            8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
            3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
            2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
            2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
      };
      int8 shiftCount;

      shiftCount = 0;
      if (a < 0x10000) {
            shiftCount += 16;
            a <<= 16;
      }
      if (a < 0x1000000) {
            shiftCount += 8;
            a <<= 8;
      }
      shiftCount += countLeadingZerosHigh[a >> 24];
      return shiftCount;

}

static int8 countLeadingZeros64(bits64 a)
{
      int8 shiftCount;

      shiftCount = 0;
      if (a < ((bits64) 1) << 32) {
            shiftCount += 32;
      } else {
            a >>= 32;
      }
      shiftCount += countLeadingZeros32(a);
      return shiftCount;

}

static float64 normalizeRoundAndPackFloat64(flag zSign, int16 zExp, bits64 zSig)
{
      int8 shiftCount;

      shiftCount = countLeadingZeros64(zSig) - 1;
      return roundAndPackFloat64(zSign, zExp - shiftCount,
                           zSig << shiftCount);

}

static float64 subFloat64Sigs(float64 a, float64 b, flag zSign)
{
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig;
      int16 expDiff;

      aSig = extractFloat64Frac(a);
      aExp = extractFloat64Exp(a);
      bSig = extractFloat64Frac(b);
      bExp = extractFloat64Exp(b);
      expDiff = aExp - bExp;
      aSig <<= 10;
      bSig <<= 10;
      if (0 < expDiff)
            goto aExpBigger;
      if (expDiff < 0)
            goto bExpBigger;
      if (aExp == 0) {
            aExp = 1;
            bExp = 1;
      }
      if (bSig < aSig)
            goto aBigger;
      if (aSig < bSig)
            goto bBigger;
      return packFloat64(float_rounding_mode() == FPSCR_RM_ZERO, 0, 0);
      bExpBigger:
      if (bExp == 0x7FF) {
            return packFloat64(zSign ^ 1, 0x7FF, 0);
      }
      if (aExp == 0) {
            ++expDiff;
      } else {
            aSig |= LIT64(0x4000000000000000);
      }
      shift64RightJamming(aSig, -expDiff, &aSig);
      bSig |= LIT64(0x4000000000000000);
      bBigger:
      zSig = bSig - aSig;
      zExp = bExp;
      zSign ^= 1;
      goto normalizeRoundAndPack;
      aExpBigger:
      if (aExp == 0x7FF) {
            return a;
      }
      if (bExp == 0) {
            --expDiff;
      } else {
            bSig |= LIT64(0x4000000000000000);
      }
      shift64RightJamming(bSig, expDiff, &bSig);
      aSig |= LIT64(0x4000000000000000);
      aBigger:
      zSig = aSig - bSig;
      zExp = aExp;
      normalizeRoundAndPack:
      --zExp;
      return normalizeRoundAndPackFloat64(zSign, zExp, zSig);

}
static float64 addFloat64Sigs(float64 a, float64 b, flag zSign)
{
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig;
      int16 expDiff;

      aSig = extractFloat64Frac(a);
      aExp = extractFloat64Exp(a);
      bSig = extractFloat64Frac(b);
      bExp = extractFloat64Exp(b);
      expDiff = aExp - bExp;
      aSig <<= 9;
      bSig <<= 9;
      if (0 < expDiff) {
            if (aExp == 0x7FF) {
                  return a;
            }
            if (bExp == 0) {
                  --expDiff;
            } else {
                  bSig |= LIT64(0x2000000000000000);
            }
            shift64RightJamming(bSig, expDiff, &bSig);
            zExp = aExp;
      } else if (expDiff < 0) {
            if (bExp == 0x7FF) {
                  return packFloat64(zSign, 0x7FF, 0);
            }
            if (aExp == 0) {
                  ++expDiff;
            } else {
                  aSig |= LIT64(0x2000000000000000);
            }
            shift64RightJamming(aSig, -expDiff, &aSig);
            zExp = bExp;
      } else {
            if (aExp == 0x7FF) {
                  return a;
            }
            if (aExp == 0)
                  return packFloat64(zSign, 0, (aSig + bSig) >> 9);
            zSig = LIT64(0x4000000000000000) + aSig + bSig;
            zExp = aExp;
            goto roundAndPack;
      }
      aSig |= LIT64(0x2000000000000000);
      zSig = (aSig + bSig) << 1;
      --zExp;
      if ((sbits64) zSig < 0) {
            zSig = aSig + bSig;
            ++zExp;
      }
      roundAndPack:
      return roundAndPackFloat64(zSign, zExp, zSig);

}

inline float32 packFloat32(flag zSign, int16 zExp, bits32 zSig)
{
      return (((bits32) zSign) << 31) + (((bits32) zExp) << 23) + zSig;
}

inline void shift32RightJamming(bits32 a, int16 count, bits32 * zPtr)
{
      bits32 z;
      if (count == 0) {
            z = a;
      } else if (count < 32) {
            z = (a >> count) | ((a << ((-count) & 31)) != 0);
      } else {
            z = (a != 0);
      }
      *zPtr = z;
}

static float32 roundAndPackFloat32(flag zSign, int16 zExp, bits32 zSig)
{
      flag roundNearestEven;
      int8 roundIncrement, roundBits;
      flag isTiny;

      /* SH4 has only 2 rounding modes - round to nearest and round to zero */
      roundNearestEven = (float_rounding_mode() == FPSCR_RM_NEAREST);
      roundIncrement = 0x40;
      if (!roundNearestEven) {
            roundIncrement = 0;
      }
      roundBits = zSig & 0x7F;
      if (0xFD <= (bits16) zExp) {
            if ((0xFD < zExp)
                || ((zExp == 0xFD)
                  && ((sbits32) (zSig + roundIncrement) < 0))
                ) {
                  float_raise(FPSCR_CAUSE_OVERFLOW | FPSCR_CAUSE_INEXACT);
                  return packFloat32(zSign, 0xFF,
                                 0) - (roundIncrement == 0);
            }
            if (zExp < 0) {
                  isTiny = (zExp < -1)
                      || (zSig + roundIncrement < 0x80000000);
                  shift32RightJamming(zSig, -zExp, &zSig);
                  zExp = 0;
                  roundBits = zSig & 0x7F;
                  if (isTiny && roundBits)
                        float_raise(FPSCR_CAUSE_UNDERFLOW);
            }
      }
      if (roundBits)
            float_raise(FPSCR_CAUSE_INEXACT);
      zSig = (zSig + roundIncrement) >> 7;
      zSig &= ~(((roundBits ^ 0x40) == 0) & roundNearestEven);
      if (zSig == 0)
            zExp = 0;
      return packFloat32(zSign, zExp, zSig);

}

static float32 normalizeRoundAndPackFloat32(flag zSign, int16 zExp, bits32 zSig)
{
      int8 shiftCount;

      shiftCount = countLeadingZeros32(zSig) - 1;
      return roundAndPackFloat32(zSign, zExp - shiftCount,
                           zSig << shiftCount);
}

static float64 roundAndPackFloat64(flag zSign, int16 zExp, bits64 zSig)
{
      flag roundNearestEven;
      int16 roundIncrement, roundBits;
      flag isTiny;

      /* SH4 has only 2 rounding modes - round to nearest and round to zero */
      roundNearestEven = (float_rounding_mode() == FPSCR_RM_NEAREST);
      roundIncrement = 0x200;
      if (!roundNearestEven) {
            roundIncrement = 0;
      }
      roundBits = zSig & 0x3FF;
      if (0x7FD <= (bits16) zExp) {
            if ((0x7FD < zExp)
                || ((zExp == 0x7FD)
                  && ((sbits64) (zSig + roundIncrement) < 0))
                ) {
                  float_raise(FPSCR_CAUSE_OVERFLOW | FPSCR_CAUSE_INEXACT);
                  return packFloat64(zSign, 0x7FF,
                                 0) - (roundIncrement == 0);
            }
            if (zExp < 0) {
                  isTiny = (zExp < -1)
                      || (zSig + roundIncrement <
                        LIT64(0x8000000000000000));
                  shift64RightJamming(zSig, -zExp, &zSig);
                  zExp = 0;
                  roundBits = zSig & 0x3FF;
                  if (isTiny && roundBits)
                        float_raise(FPSCR_CAUSE_UNDERFLOW);
            }
      }
      if (roundBits)
            float_raise(FPSCR_CAUSE_INEXACT);
      zSig = (zSig + roundIncrement) >> 10;
      zSig &= ~(((roundBits ^ 0x200) == 0) & roundNearestEven);
      if (zSig == 0)
            zExp = 0;
      return packFloat64(zSign, zExp, zSig);

}

static float32 subFloat32Sigs(float32 a, float32 b, flag zSign)
{
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig, zSig;
      int16 expDiff;

      aSig = extractFloat32Frac(a);
      aExp = extractFloat32Exp(a);
      bSig = extractFloat32Frac(b);
      bExp = extractFloat32Exp(b);
      expDiff = aExp - bExp;
      aSig <<= 7;
      bSig <<= 7;
      if (0 < expDiff)
            goto aExpBigger;
      if (expDiff < 0)
            goto bExpBigger;
      if (aExp == 0) {
            aExp = 1;
            bExp = 1;
      }
      if (bSig < aSig)
            goto aBigger;
      if (aSig < bSig)
            goto bBigger;
      return packFloat32(float_rounding_mode() == FPSCR_RM_ZERO, 0, 0);
      bExpBigger:
      if (bExp == 0xFF) {
            return packFloat32(zSign ^ 1, 0xFF, 0);
      }
      if (aExp == 0) {
            ++expDiff;
      } else {
            aSig |= 0x40000000;
      }
      shift32RightJamming(aSig, -expDiff, &aSig);
      bSig |= 0x40000000;
      bBigger:
      zSig = bSig - aSig;
      zExp = bExp;
      zSign ^= 1;
      goto normalizeRoundAndPack;
      aExpBigger:
      if (aExp == 0xFF) {
            return a;
      }
      if (bExp == 0) {
            --expDiff;
      } else {
            bSig |= 0x40000000;
      }
      shift32RightJamming(bSig, expDiff, &bSig);
      aSig |= 0x40000000;
      aBigger:
      zSig = aSig - bSig;
      zExp = aExp;
      normalizeRoundAndPack:
      --zExp;
      return normalizeRoundAndPackFloat32(zSign, zExp, zSig);

}

static float32 addFloat32Sigs(float32 a, float32 b, flag zSign)
{
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig, zSig;
      int16 expDiff;

      aSig = extractFloat32Frac(a);
      aExp = extractFloat32Exp(a);
      bSig = extractFloat32Frac(b);
      bExp = extractFloat32Exp(b);
      expDiff = aExp - bExp;
      aSig <<= 6;
      bSig <<= 6;
      if (0 < expDiff) {
            if (aExp == 0xFF) {
                  return a;
            }
            if (bExp == 0) {
                  --expDiff;
            } else {
                  bSig |= 0x20000000;
            }
            shift32RightJamming(bSig, expDiff, &bSig);
            zExp = aExp;
      } else if (expDiff < 0) {
            if (bExp == 0xFF) {
                  return packFloat32(zSign, 0xFF, 0);
            }
            if (aExp == 0) {
                  ++expDiff;
            } else {
                  aSig |= 0x20000000;
            }
            shift32RightJamming(aSig, -expDiff, &aSig);
            zExp = bExp;
      } else {
            if (aExp == 0xFF) {
                  return a;
            }
            if (aExp == 0)
                  return packFloat32(zSign, 0, (aSig + bSig) >> 6);
            zSig = 0x40000000 + aSig + bSig;
            zExp = aExp;
            goto roundAndPack;
      }
      aSig |= 0x20000000;
      zSig = (aSig + bSig) << 1;
      --zExp;
      if ((sbits32) zSig < 0) {
            zSig = aSig + bSig;
            ++zExp;
      }
      roundAndPack:
      return roundAndPackFloat32(zSign, zExp, zSig);

}

float64 float64_sub(float64 a, float64 b)
{
      flag aSign, bSign;

      aSign = extractFloat64Sign(a);
      bSign = extractFloat64Sign(b);
      if (aSign == bSign) {
            return subFloat64Sigs(a, b, aSign);
      } else {
            return addFloat64Sigs(a, b, aSign);
      }

}

float32 float32_sub(float32 a, float32 b)
{
      flag aSign, bSign;

      aSign = extractFloat32Sign(a);
      bSign = extractFloat32Sign(b);
      if (aSign == bSign) {
            return subFloat32Sigs(a, b, aSign);
      } else {
            return addFloat32Sigs(a, b, aSign);
      }

}

float32 float32_add(float32 a, float32 b)
{
      flag aSign, bSign;

      aSign = extractFloat32Sign(a);
      bSign = extractFloat32Sign(b);
      if (aSign == bSign) {
            return addFloat32Sigs(a, b, aSign);
      } else {
            return subFloat32Sigs(a, b, aSign);
      }

}

float64 float64_add(float64 a, float64 b)
{
      flag aSign, bSign;

      aSign = extractFloat64Sign(a);
      bSign = extractFloat64Sign(b);
      if (aSign == bSign) {
            return addFloat64Sigs(a, b, aSign);
      } else {
            return subFloat64Sigs(a, b, aSign);
      }
}

static void
normalizeFloat64Subnormal(bits64 aSig, int16 * zExpPtr, bits64 * zSigPtr)
{
      int8 shiftCount;

      shiftCount = countLeadingZeros64(aSig) - 11;
      *zSigPtr = aSig << shiftCount;
      *zExpPtr = 1 - shiftCount;
}

inline void add128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
               bits64 * z1Ptr)
{
      bits64 z1;

      z1 = a1 + b1;
      *z1Ptr = z1;
      *z0Ptr = a0 + b0 + (z1 < a1);
}

inline void
sub128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
       bits64 * z1Ptr)
{
      *z1Ptr = a1 - b1;
      *z0Ptr = a0 - b0 - (a1 < b1);
}

static bits64 estimateDiv128To64(bits64 a0, bits64 a1, bits64 b)
{
      bits64 b0, b1;
      bits64 rem0, rem1, term0, term1;
      bits64 z;
      if (b <= a0)
            return LIT64(0xFFFFFFFFFFFFFFFF);
      b0 = b >> 32;
      z = (b0 << 32 <= a0) ? LIT64(0xFFFFFFFF00000000) : (a0 / b0) << 32;
      mul64To128(b, z, &term0, &term1);
      sub128(a0, a1, term0, term1, &rem0, &rem1);
      while (((sbits64) rem0) < 0) {
            z -= LIT64(0x100000000);
            b1 = b << 32;
            add128(rem0, rem1, b0, b1, &rem0, &rem1);
      }
      rem0 = (rem0 << 32) | (rem1 >> 32);
      z |= (b0 << 32 <= rem0) ? 0xFFFFFFFF : rem0 / b0;
      return z;
}

inline void mul64To128(bits64 a, bits64 b, bits64 * z0Ptr, bits64 * z1Ptr)
{
      bits32 aHigh, aLow, bHigh, bLow;
      bits64 z0, zMiddleA, zMiddleB, z1;

      aLow = a;
      aHigh = a >> 32;
      bLow = b;
      bHigh = b >> 32;
      z1 = ((bits64) aLow) * bLow;
      zMiddleA = ((bits64) aLow) * bHigh;
      zMiddleB = ((bits64) aHigh) * bLow;
      z0 = ((bits64) aHigh) * bHigh;
      zMiddleA += zMiddleB;
      z0 += (((bits64) (zMiddleA < zMiddleB)) << 32) + (zMiddleA >> 32);
      zMiddleA <<= 32;
      z1 += zMiddleA;
      z0 += (z1 < zMiddleA);
      *z1Ptr = z1;
      *z0Ptr = z0;

}

static void normalizeFloat32Subnormal(bits32 aSig, int16 * zExpPtr,
                              bits32 * zSigPtr)
{
      int8 shiftCount;

      shiftCount = countLeadingZeros32(aSig) - 8;
      *zSigPtr = aSig << shiftCount;
      *zExpPtr = 1 - shiftCount;

}

float64 float64_div(float64 a, float64 b)
{
      flag aSign, bSign, zSign;
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig;
      bits64 rem0, rem1;
      bits64 term0, term1;

      aSig = extractFloat64Frac(a);
      aExp = extractFloat64Exp(a);
      aSign = extractFloat64Sign(a);
      bSig = extractFloat64Frac(b);
      bExp = extractFloat64Exp(b);
      bSign = extractFloat64Sign(b);
      zSign = aSign ^ bSign;
      if (aExp == 0x7FF) {
            if (bExp == 0x7FF) {
            }
            return packFloat64(zSign, 0x7FF, 0);
      }
      if (bExp == 0x7FF) {
            return packFloat64(zSign, 0, 0);
      }
      if (bExp == 0) {
            if (bSig == 0) {
                  if ((aExp | aSig) == 0) {
                        float_raise(FPSCR_CAUSE_INVALID);
                  }
                  return packFloat64(zSign, 0x7FF, 0);
            }
            normalizeFloat64Subnormal(bSig, &bExp, &bSig);
      }
      if (aExp == 0) {
            if (aSig == 0)
                  return packFloat64(zSign, 0, 0);
            normalizeFloat64Subnormal(aSig, &aExp, &aSig);
      }
      zExp = aExp - bExp + 0x3FD;
      aSig = (aSig | LIT64(0x0010000000000000)) << 10;
      bSig = (bSig | LIT64(0x0010000000000000)) << 11;
      if (bSig <= (aSig + aSig)) {
            aSig >>= 1;
            ++zExp;
      }
      zSig = estimateDiv128To64(aSig, 0, bSig);
      if ((zSig & 0x1FF) <= 2) {
            mul64To128(bSig, zSig, &term0, &term1);
            sub128(aSig, 0, term0, term1, &rem0, &rem1);
            while ((sbits64) rem0 < 0) {
                  --zSig;
                  add128(rem0, rem1, 0, bSig, &rem0, &rem1);
            }
            zSig |= (rem1 != 0);
      }
      return roundAndPackFloat64(zSign, zExp, zSig);

}

float32 float32_div(float32 a, float32 b)
{
      flag aSign, bSign, zSign;
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig, zSig;

      aSig = extractFloat32Frac(a);
      aExp = extractFloat32Exp(a);
      aSign = extractFloat32Sign(a);
      bSig = extractFloat32Frac(b);
      bExp = extractFloat32Exp(b);
      bSign = extractFloat32Sign(b);
      zSign = aSign ^ bSign;
      if (aExp == 0xFF) {
            if (bExp == 0xFF) {
            }
            return packFloat32(zSign, 0xFF, 0);
      }
      if (bExp == 0xFF) {
            return packFloat32(zSign, 0, 0);
      }
      if (bExp == 0) {
            if (bSig == 0) {
                  return packFloat32(zSign, 0xFF, 0);
            }
            normalizeFloat32Subnormal(bSig, &bExp, &bSig);
      }
      if (aExp == 0) {
            if (aSig == 0)
                  return packFloat32(zSign, 0, 0);
            normalizeFloat32Subnormal(aSig, &aExp, &aSig);
      }
      zExp = aExp - bExp + 0x7D;
      aSig = (aSig | 0x00800000) << 7;
      bSig = (bSig | 0x00800000) << 8;
      if (bSig <= (aSig + aSig)) {
            aSig >>= 1;
            ++zExp;
      }
      zSig = (((bits64) aSig) << 32) / bSig;
      if ((zSig & 0x3F) == 0) {
            zSig |= (((bits64) bSig) * zSig != ((bits64) aSig) << 32);
      }
      return roundAndPackFloat32(zSign, zExp, zSig);

}

float32 float32_mul(float32 a, float32 b)
{
      char aSign, bSign, zSign;
      int aExp, bExp, zExp;
      unsigned int aSig, bSig;
      unsigned long long zSig64;
      unsigned int zSig;

      aSig = extractFloat32Frac(a);
      aExp = extractFloat32Exp(a);
      aSign = extractFloat32Sign(a);
      bSig = extractFloat32Frac(b);
      bExp = extractFloat32Exp(b);
      bSign = extractFloat32Sign(b);
      zSign = aSign ^ bSign;
      if (aExp == 0) {
            if (aSig == 0)
                  return packFloat32(zSign, 0, 0);
            normalizeFloat32Subnormal(aSig, &aExp, &aSig);
      }
      if (bExp == 0) {
            if (bSig == 0)
                  return packFloat32(zSign, 0, 0);
            normalizeFloat32Subnormal(bSig, &bExp, &bSig);
      }
      if ((bExp == 0xff && bSig == 0) || (aExp == 0xff && aSig == 0))
            return roundAndPackFloat32(zSign, 0xff, 0);

      zExp = aExp + bExp - 0x7F;
      aSig = (aSig | 0x00800000) << 7;
      bSig = (bSig | 0x00800000) << 8;
      shift64RightJamming(((unsigned long long)aSig) * bSig, 32, &zSig64);
      zSig = zSig64;
      if (0 <= (signed int)(zSig << 1)) {
            zSig <<= 1;
            --zExp;
      }
      return roundAndPackFloat32(zSign, zExp, zSig);

}

float64 float64_mul(float64 a, float64 b)
{
      char aSign, bSign, zSign;
      int aExp, bExp, zExp;
      unsigned long long int aSig, bSig, zSig0, zSig1;

      aSig = extractFloat64Frac(a);
      aExp = extractFloat64Exp(a);
      aSign = extractFloat64Sign(a);
      bSig = extractFloat64Frac(b);
      bExp = extractFloat64Exp(b);
      bSign = extractFloat64Sign(b);
      zSign = aSign ^ bSign;

      if (aExp == 0) {
            if (aSig == 0)
                  return packFloat64(zSign, 0, 0);
            normalizeFloat64Subnormal(aSig, &aExp, &aSig);
      }
      if (bExp == 0) {
            if (bSig == 0)
                  return packFloat64(zSign, 0, 0);
            normalizeFloat64Subnormal(bSig, &bExp, &bSig);
      }
      if ((aExp == 0x7ff && aSig == 0) || (bExp == 0x7ff && bSig == 0))
            return roundAndPackFloat64(zSign, 0x7ff, 0);

      zExp = aExp + bExp - 0x3FF;
      aSig = (aSig | 0x0010000000000000LL) << 10;
      bSig = (bSig | 0x0010000000000000LL) << 11;
      mul64To128(aSig, bSig, &zSig0, &zSig1);
      zSig0 |= (zSig1 != 0);
      if (0 <= (signed long long int)(zSig0 << 1)) {
            zSig0 <<= 1;
            --zExp;
      }
      return roundAndPackFloat64(zSign, zExp, zSig0);
}

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