text: //===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is dual licensed under the MIT and the University of Illinois Open
  // Source Licenses. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file is a configuration header for soft-float routines in compiler-rt.
  // This file does not provide any part of the compiler-rt interface, but defines
  // many useful constants and utility routines that are used in the
  // implementation of the soft-float routines in compiler-rt.
  //
  // Assumes that float and double correspond to the IEEE-754 binary32 and
  // binary64 types, respectively, and that integer endianness matches floating
  // point endianness on the target platform.
  //
  //===----------------------------------------------------------------------===//
  
  #ifndef FP_LIB_HEADER
  #define FP_LIB_HEADER
  
  #include <stdint.h>
  #include <limits.h>
  
  typedef unsigned long long uint64_t;
  
  #define UINT32_C(x)     (x##U)
  
  #if defined SINGLE_PRECISION
  
  typedef uint32_t rep_t;
  typedef int32_t srep_t;
  typedef float fp_t;
  #define REP_C UINT32_C
  #define significandBits 23
  
  static inline int rep_clz(rep_t a)
  {
      return __builtin_clz(a);
  }
  
  // 32x32 --> 64 bit multiply
  static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo)
  {
      const uint64_t product = (uint64_t)a*b;
      *hi = product >> 32;
      *lo = product;
  }
  
  #elif defined DOUBLE_PRECISION
  
  typedef uint64_t rep_t;
  typedef int64_t srep_t;
  typedef double fp_t;
  #define REP_C UINT64_C
  #define significandBits 52
  
  static inline int rep_clz(rep_t a)
  {
  #if defined __LP64__
      return __builtin_clzl(a);
  #else
      if (a & REP_C(0xffffffff00000000))
          return __builtin_clz(a >> 32);
      else
          return 32 + __builtin_clz(a & REP_C(0xffffffff));
  #endif
  }
  
  #define loWord(a) (a & 0xffffffffU)
  #define hiWord(a) (a >> 32)
  
  // 64x64 -> 128 wide multiply for platforms that don't have such an operation;
  // many 64-bit platforms have this operation, but they tend to have hardware
  // floating-point, so we don't bother with a special case for them here.
  static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo)
  {
      // Each of the component 32x32 -> 64 products
      const uint64_t plolo = loWord(a) * loWord(b);
      const uint64_t plohi = loWord(a) * hiWord(b);
      const uint64_t philo = hiWord(a) * loWord(b);
      const uint64_t phihi = hiWord(a) * hiWord(b);
      // Sum terms that contribute to lo in a way that allows us to get the carry
      const uint64_t r0 = loWord(plolo);
      const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
      *lo = r0 + (r1 << 32);
      // Sum terms contributing to hi with the carry from lo
      *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
  }
  
  #else
  #error Either SINGLE_PRECISION or DOUBLE_PRECISION must be defined.
  #endif
  
  #define typeWidth       (sizeof(rep_t)*CHAR_BIT)
  #define exponentBits    (typeWidth - significandBits - 1)
  #define maxExponent     ((1 << exponentBits) - 1)
  #define exponentBias    (maxExponent >> 1)
  
  #define implicitBit     (REP_C(1) << significandBits)
  #define significandMask (implicitBit - 1U)
  #define signBit         (REP_C(1) << (significandBits + exponentBits))
  #define absMask         (signBit - 1U)
  #define exponentMask    (absMask ^ significandMask)
  #define oneRep          ((rep_t)exponentBias << significandBits)
  #define infRep          exponentMask
  #define quietBit        (implicitBit >> 1)
  #define qnanRep         (exponentMask | quietBit)
  
  static inline rep_t toRep(fp_t x)
  {
      const union { fp_t f; rep_t i; } rep = {.f = x};
      return rep.i;
  }
  
  static inline fp_t fromRep(rep_t x)
  {
      const union { fp_t f; rep_t i; } rep = {.i = x};
      return rep.f;
  }
  
  static inline int normalize(rep_t *significand)
  {
      const int shift = rep_clz(*significand) - rep_clz(implicitBit);
      *significand <<= shift;
      return 1 - shift;
  }
  
  static inline void wideLeftShift(rep_t *hi, rep_t *lo, int count)
  {
      *hi = *hi << count | *lo >> (typeWidth - count);
      *lo = *lo << count;
  }
  
  static inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, unsigned int count)
  {
      if (count < typeWidth) {
          int sticky = (*lo << (typeWidth - count)) != 0;
          *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
          *hi = *hi >> count;
      }
      else if (count < 2*typeWidth) {
          int sticky = (*hi << (2*typeWidth - count) | *lo) != 0;
          *lo = *hi >> (count - typeWidth) | sticky;
          *hi = 0;
      } else {
          int sticky = (*hi | *lo) != 0;
          *lo = sticky;
          *hi = 0;
      }
  }
  
  #endif // FP_LIB_HEADER
  