Teuchos_PrintDouble.cpp

// @HEADER
// *****************************************************************************
//                    Teuchos: Common Tools Package
//
// Copyright 2004 NTESS and the Teuchos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#include "Teuchos_PrintDouble.hpp"
#include "Teuchos_BigUInt.hpp"

#include <cstring>

namespace Teuchos {

namespace {

int ndigits_for(std::uint32_t x) {
  int n = 0;
  while (x) {
    ++n;
    x /= 10;
  }
  return n;
}

}

void print_double(std::ostream& os, double v) {
  char buffer[64];
  constexpr std::uint64_t one = 1;
  constexpr std::uint64_t p = 53;
  std::uint64_t pun;
  std::memcpy(&pun, &v, sizeof(v));
  auto sign = pun >> 63;
  pun -= sign << 63;
  auto be = pun >> (p - 1);
  pun -= be << (p - 1);
  auto m = pun;
  int bp = 0;
  if (be == 2047) {
    if (m == 0) {
      if (sign) buffer[bp++] = '-';
      buffer[bp++] = 'i';
      buffer[bp++] = 'n';
      buffer[bp++] = 'f';
    } else {
      buffer[bp++] = 'n';
      buffer[bp++] = 'a';
      buffer[bp++] = 'n';
    }
  } else {
    if (sign) buffer[bp++] = '-';
    std::uint64_t f;
    if (be == 0) {
      f = m;
    } else {
      f = m + (one << (p - 1));
    }
    auto e = std::int64_t(be) - 1075;
    BigUInt<34> r, s, mp, mm;
    if (e >= 0) {
      if (f != (one << (p - 1))) {
        r = BigUInt<34>(f);
        r <<= (e + 1);
        s = BigUInt<34>(2);
        mp = BigUInt<34>(1);
        mp <<= e;
        mm = BigUInt<34>(1);
        mm <<= e;
      } else {
        r = BigUInt<34>(f);
        r <<= (e + 2);
        s = BigUInt<34>(2 * 2);
        mp = BigUInt<34>(1);
        mp <<= (e + 1);
        mm = BigUInt<34>(1);
        mm <<= e;
      }
    } else {
      if ((be == 0) || (f != (one << (p - 1)))) {
        r = BigUInt<34>(f);
        r <<= 1;
        s = BigUInt<34>(1);
        s <<= (1 - e);
        mp = BigUInt<34>(1);
        mm = BigUInt<34>(1);
      } else {
        r = BigUInt<34>(f);
        r <<= 2;
        s = BigUInt<34>(1);
        s <<= (2 - e);
        mp = BigUInt<34>(2);
        mm = BigUInt<34>(1);
      }
    }
    std::int32_t k = 0;
    BigUInt<34> B_k{1};
    auto r_p_mp = r + mp;
    auto r_p_mp_comp = comp(r_p_mp, s);
    if (r_p_mp_comp == 0) {
    } else if (r_p_mp_comp == 1) {
      while (r_p_mp > (s * B_k)) {
        ++k, B_k *= 10;
      }
    } else {
      while ((r_p_mp * B_k) < s) {
        --k, B_k *= 10;
      }
      ++k;
      B_k = B_k / 10;
    }
    if (k >= 0) {
      s = s * B_k;
    } else {
      r = r * B_k;
      mp = mp * B_k;
      mm = mm * B_k;
    }
    char last_d = '0';
    int n;
    for (n = 0; true; ++n) {
      auto r_x_10 = r;
      r_x_10 *= 10;
      auto d_np1 = r_x_10 / s;
      auto cond1 = r < mm;
      auto cond2 = (r + mp) > s;
      if (cond1 && cond2) {
        r <<= 1;
        if (r < s) {
          buffer[bp++] = last_d;
        } else {
          buffer[bp++] = last_d + 1;
        }
        break;
      } else if (cond1) {
        buffer[bp++] = last_d;
        break;
      } else if (cond2) {
        buffer[bp++] = last_d + 1;
        break;
      } else {
        if (n) buffer[bp++] = last_d;
        r = r_x_10;
        r -= (s * d_np1);
        mp *= 10;
        mm *= 10;
        last_d = char(d_np1[0]) + '0';
      }
    }
    if (v == 0.0) {
      k = 1;
      ++n;
    }
    int dot_pos = -1;
    bool do_scientific = false;
    if (0 <= k && k <= n) {
      // dot is touching significant digits
      dot_pos = k;
    } else if (k < 0) {
      auto nchars_sci = ndigits_for(-k + 1) + 2;
      if (n > 1) nchars_sci += 1; // add a dot to scientific notation if more than one digit
      if (nchars_sci < (-k + 1)) {
        // scientific notation requires fewer chars than trailing zeros
        if (n > 1) dot_pos = 1;
        do_scientific = true;
      } else {
        // trailing zeros are no more chars than scientific
        for (int i = 0; i < n; ++i) {
          buffer[bp + (-k) - i - 1] = buffer[bp - i - 1];
        }
        for (int i = 0; i < -k; ++i) {
          buffer[bp - n + i] = '0';
        }
        dot_pos = bp - n;
        bp += -k;
        n += -k;
      }
    } else if (k > n) {
      auto nchars_sci = ndigits_for(k - 1) + 1;
      if (n > 1) nchars_sci += 1; // add a dot to scientific notation if more than one digit
      if (nchars_sci < ((k-n)+1)) {
        // scientific notation requires fewer chars than trailing zeros
        if (n > 1) dot_pos = 1;
        do_scientific = true;
      } else {
        // trailing zeros are no more chars than scientific
        for (; n < k; ++n) buffer[bp++] = '0';
        dot_pos = n;
      }
    }
    if (dot_pos != -1) {
      for (int i = 0; i < (n - dot_pos) && i < bp; ++i) buffer[bp - i] = buffer[bp - i - 1];
      buffer[bp - n + dot_pos] = '.';
      ++bp;
    }
    if (do_scientific) {
      buffer[bp++] = 'e';
      auto decimal_exponent = (k - 1);
      if (decimal_exponent < 0) {
        buffer[bp++] = '-';
        decimal_exponent = -decimal_exponent;
      }
      int ne;
      for (ne = 0; decimal_exponent; ++ne) {
        buffer[bp++] = char(decimal_exponent % 10) + '0';
        decimal_exponent /= 10;
      }
      for (int i = 0; i < ne / 2; ++i) {
        auto tmp = buffer[bp - ne + i];
        buffer[bp - ne + i] = buffer[bp - i - 1];
        buffer[bp - i - 1] = tmp;
      }
    }
  }
  buffer[bp] = '\0';
  os << buffer;
}

}