scalbn and ldexp rounding edge cases

scalbn-ldexp-test.c

#include <errno.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

const char* round_mode_to_str(int round_mode) {
  switch (round_mode) {
    case FE_TONEAREST:  return "NEAR";
    case FE_UPWARD:     return "UP__";
    case FE_DOWNWARD:   return "DOWN";
    case FE_TOWARDZERO: return "ZERO";
    default:
      fprintf(stderr, "unhandled mode: %d\n", round_mode);
      abort();
  }
}

const char* errhandling_mode() {
#if defined(MATH_ERRNO) && defined(MATH_ERREXCEPT)
  int mode = math_errhandling;
  if (mode == MATH_ERRNO) return "errno";
  if (mode == MATH_ERREXCEPT) return "errexcept";
  if (mode == (MATH_ERRNO | MATH_ERREXCEPT)) return "errno|errexcept";
  static char buf[128];
  snprintf(buf, sizeof(buf), "[unknown:%d]", mode);
  return buf;
#else
  return "<MATH_ERRNO and/or MATH_ERREXCEPT not defined>";
#endif
}

enum {
  kExceptMask = FE_DIVBYZERO | FE_INEXACT | FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW
};

char* except_to_str(int exc, char* buf) {
  char* ptr = buf;
  *ptr = '\0';
  if (exc & FE_DIVBYZERO)   *ptr++ = '/';
  if (exc & FE_INEXACT)     *ptr++ = '~';
  if (exc & FE_INVALID)     *ptr++ = '!';
  if (exc & FE_OVERFLOW)    *ptr++ = 'o';
  if (exc & FE_UNDERFLOW)   *ptr++ = 'u';
  *ptr++ = '\0';

  return buf;
}

const char* err_to_str(int err) {
  switch (err) {
    case 0: return "0";
    case ERANGE: return "ERANGE";
    case EDOM: return "EDOM";
    default: return strerror(err);
  }
}

static void dump_result(double result, int err, int exc) {
  char exc_buf[42];
  printf("[%a errno=%s exc=%s]", result, err_to_str(err), except_to_str(exc, exc_buf));
}

static void test_value(int round_mode, double x, int adj) {
  fesetround(round_mode);
  double result;

  printf("    round_mode=%s, x=%a, adj=%d: ", round_mode_to_str(round_mode), x, adj);

  feclearexcept(kExceptMask);
  errno = 0;
  double ldexp_result = ldexp(x, adj);
  int ldexp_err = errno;
  int ldexp_exc = fetestexcept(kExceptMask);

  feclearexcept(kExceptMask);
  errno = 0;
  double scalbn_result = scalbn(x, adj);
  int scalbn_err = errno;
  int scalbn_exc = fetestexcept(kExceptMask);

  if (scalbn_result == ldexp_result && scalbn_err == ldexp_err && scalbn_exc == ldexp_exc) {
    printf("both:");
    dump_result(scalbn_result, scalbn_err, scalbn_exc);
  } else {
    printf("scalbn:");
    dump_result(scalbn_result, scalbn_err, scalbn_exc);
    printf(" ldexp:");
    dump_result(ldexp_result, ldexp_err, ldexp_exc);
  }

  if (fegetround() != round_mode) {
    printf("error: rounding mode changed to %d\n", fegetround());
  }

  printf("\n");
}

int main() {
  printf("math_errhandling=%s\n", errhandling_mode());

  printf("normal to normal:\n");
  test_value(FE_TONEAREST, 1, 4);

  printf("normal to subnormal (is errno set?):\n");
  test_value(FE_TONEAREST, DBL_MIN, -1);

  printf("overflow:\n");
  test_value(FE_TONEAREST,  DBL_MAX, 1);
  test_value(FE_TONEAREST,  -DBL_MAX, 1);
  test_value(FE_DOWNWARD,   DBL_MAX, 1);
  test_value(FE_TOWARDZERO, DBL_MAX, 1);
  test_value(FE_UPWARD,     -DBL_MAX, 1);
  test_value(FE_TOWARDZERO, -DBL_MAX, 1);

  printf("underflow:\n");
  test_value(FE_TONEAREST,  DBL_MIN, -100);
  test_value(FE_TOWARDZERO, DBL_MIN, -100);
  test_value(FE_DOWNWARD,   DBL_MIN, -100);
  test_value(FE_UPWARD,     DBL_MIN, -100);

  test_value(FE_TONEAREST,  -DBL_MIN, -100);
  test_value(FE_TOWARDZERO, -DBL_MIN, -100);
  test_value(FE_UPWARD,     -DBL_MIN, -100);
  test_value(FE_DOWNWARD,   -DBL_MIN, -100);

  printf("subnormal -- not underflow, but rounds:\n");
  test_value(FE_TONEAREST, DBL_TRUE_MIN * 7.0, -1);
  test_value(FE_UPWARD,    DBL_TRUE_MIN * 7.0, -1);
  test_value(FE_DOWNWARD,  DBL_TRUE_MIN * 7.0, -1);

  printf("subnormal rounding -- MSVC: scalbn rounds to nearest-even, ldexp rounds towards zero:\n");
  for (int sign = 1; sign >= -1; sign -= 2) {
    for (int mult = 9; mult <= 13; mult += 2) {
      test_value(FE_TONEAREST, DBL_TRUE_MIN * mult * sign, -1);
      test_value(FE_UPWARD,    DBL_TRUE_MIN * mult * sign, -1);
      test_value(FE_DOWNWARD,  DBL_TRUE_MIN * mult * sign, -1);
    }
  }

  return 0;
}

zzz-output-gcc-x64-debian.txt

math_errhandling=errno|errexcept
normal to normal:
    round_mode=NEAR, x=0x1p+0, adj=4: both:[0x1p+4 errno=0 exc=]
normal to subnormal (is errno set?):
    round_mode=NEAR, x=0x1p-1022, adj=-1: both:[0x0.8p-1022 errno=0 exc=]
overflow:
    round_mode=NEAR, x=0x1.fffffffffffffp+1023, adj=1: both:[inf errno=ERANGE exc=~o]
    round_mode=NEAR, x=-0x1.fffffffffffffp+1023, adj=1: both:[-inf errno=ERANGE exc=~o]
    round_mode=DOWN, x=0x1.fffffffffffffp+1023, adj=1: both:[0x1.fffffffffffffp+1023 errno=0 exc=~o]
    round_mode=ZERO, x=0x1.fffffffffffffp+1023, adj=1: both:[0x1.fffffffffffffp+1023 errno=0 exc=~o]
    round_mode=UP__, x=-0x1.fffffffffffffp+1023, adj=1: both:[-0x1.fffffffffffffp+1023 errno=0 exc=~o]
    round_mode=ZERO, x=-0x1.fffffffffffffp+1023, adj=1: both:[-0x1.fffffffffffffp+1023 errno=0 exc=~o]
underflow:
    round_mode=NEAR, x=0x1p-1022, adj=-100: both:[0x0p+0 errno=ERANGE exc=~u]
    round_mode=ZERO, x=0x1p-1022, adj=-100: both:[0x0p+0 errno=ERANGE exc=~u]
    round_mode=DOWN, x=0x1p-1022, adj=-100: both:[0x0p+0 errno=ERANGE exc=~u]
    round_mode=UP__, x=0x1p-1022, adj=-100: both:[0x0.0000000000001p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x1p-1022, adj=-100: both:[-0x0p+0 errno=ERANGE exc=~u]
    round_mode=ZERO, x=-0x1p-1022, adj=-100: both:[-0x0p+0 errno=ERANGE exc=~u]
    round_mode=UP__, x=-0x1p-1022, adj=-100: both:[-0x0p+0 errno=ERANGE exc=~u]
    round_mode=DOWN, x=-0x1p-1022, adj=-100: both:[-0x0.0000000000001p-1022 errno=0 exc=~u]
subnormal -- not underflow, but rounds:
    round_mode=NEAR, x=0x0.0000000000007p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.0000000000007p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.0000000000007p-1022, adj=-1: both:[0x0.0000000000003p-1022 errno=0 exc=~u]
subnormal rounding -- MSVC: scalbn rounds to nearest-even, ldexp rounds towards zero:
    round_mode=NEAR, x=0x0.0000000000009p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.0000000000009p-1022, adj=-1: both:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.0000000000009p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=0x0.000000000000bp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.000000000000bp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.000000000000bp-1022, adj=-1: both:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=0x0.000000000000dp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.000000000000dp-1022, adj=-1: both:[0x0.0000000000007p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.000000000000dp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.0000000000009p-1022, adj=-1: both:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.0000000000009p-1022, adj=-1: both:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.0000000000009p-1022, adj=-1: both:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.000000000000bp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.000000000000bp-1022, adj=-1: both:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.000000000000bp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.000000000000dp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.000000000000dp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.000000000000dp-1022, adj=-1: both:[-0x0.0000000000007p-1022 errno=0 exc=~u]

zzz-output-llvm-mingw-20201020-ucrt-x86_64.txt

math_errhandling=<MATH_ERRNO and/or MATH_ERREXCEPT not defined>
normal to normal:
    round_mode=NEAR, x=0x1.0000000000000p+0, adj=4: both:[0x1.0000000000000p+4 errno=0 exc=]
normal to subnormal (is errno set?):
    round_mode=NEAR, x=0x1.0000000000000p-1022, adj=-1: both:[0x0.8000000000000p-1022 errno=0 exc=]
overflow:
    round_mode=NEAR, x=0x1.fffffffffffffp+1023, adj=1: scalbn:[inf errno=0 exc=~o] ldexp:[inf errno=ERANGE exc=~o]
    round_mode=NEAR, x=-0x1.fffffffffffffp+1023, adj=1: scalbn:[-inf errno=0 exc=~o] ldexp:[-inf errno=ERANGE exc=~o]
    round_mode=DOWN, x=0x1.fffffffffffffp+1023, adj=1: both:[0x1.fffffffffffffp+1023 errno=0 exc=~o]
    round_mode=ZERO, x=0x1.fffffffffffffp+1023, adj=1: both:[0x1.fffffffffffffp+1023 errno=0 exc=~o]
    round_mode=UP__, x=-0x1.fffffffffffffp+1023, adj=1: both:[-0x1.fffffffffffffp+1023 errno=0 exc=~o]
    round_mode=ZERO, x=-0x1.fffffffffffffp+1023, adj=1: both:[-0x1.fffffffffffffp+1023 errno=0 exc=~o]
underflow:
    round_mode=NEAR, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=0 exc=~u] ldexp:[0x0.0000000000000p+0 errno=ERANGE exc=~u]
    round_mode=ZERO, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=0 exc=~u] ldexp:[0x0.0000000000000p+0 errno=ERANGE exc=~u]
    round_mode=DOWN, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=0 exc=~u] ldexp:[0x0.0000000000000p+0 errno=ERANGE exc=~u]
    round_mode=UP__, x=0x1.0000000000000p-1022, adj=-100: both:[0x0.0000000000001p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=0 exc=~u] ldexp:[-0x0.0000000000000p+0 errno=ERANGE exc=~u]
    round_mode=ZERO, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=0 exc=~u] ldexp:[-0x0.0000000000000p+0 errno=ERANGE exc=~u]
    round_mode=UP__, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=0 exc=~u] ldexp:[-0x0.0000000000000p+0 errno=ERANGE exc=~u]
    round_mode=DOWN, x=-0x1.0000000000000p-1022, adj=-100: both:[-0x0.0000000000001p-1022 errno=0 exc=~u]
subnormal -- not underflow, but rounds:
    round_mode=NEAR, x=0x0.0000000000007p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.0000000000007p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.0000000000007p-1022, adj=-1: both:[0x0.0000000000003p-1022 errno=0 exc=~u]
subnormal rounding -- MSVC: scalbn rounds to nearest-even, ldexp rounds towards zero:
    round_mode=NEAR, x=0x0.0000000000009p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.0000000000009p-1022, adj=-1: both:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.0000000000009p-1022, adj=-1: both:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=0x0.000000000000bp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.000000000000bp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.000000000000bp-1022, adj=-1: both:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=0x0.000000000000dp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.000000000000dp-1022, adj=-1: both:[0x0.0000000000007p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.000000000000dp-1022, adj=-1: both:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.0000000000009p-1022, adj=-1: both:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.0000000000009p-1022, adj=-1: both:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.0000000000009p-1022, adj=-1: both:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.000000000000bp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.000000000000bp-1022, adj=-1: both:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.000000000000bp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.000000000000dp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.000000000000dp-1022, adj=-1: both:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.000000000000dp-1022, adj=-1: both:[-0x0.0000000000007p-1022 errno=0 exc=~u]

zzz-output-msvc-19.16-x64.txt

math_errhandling=errno|errexcept
normal to normal:
    round_mode=NEAR, x=0x1.0000000000000p+0, adj=4: both:[0x1.0000000000000p+4 errno=0 exc=]
normal to subnormal (is errno set?):
    round_mode=NEAR, x=0x1.0000000000000p-1022, adj=-1: scalbn:[0x0.8000000000000p-1022 errno=0 exc=] ldexp:[0x0.8000000000000p-1022 errno=0 exc=~u]
overflow:
    round_mode=NEAR, x=0x1.fffffffffffffp+1023, adj=1: both:[inf errno=ERANGE exc=~o]
    round_mode=NEAR, x=-0x1.fffffffffffffp+1023, adj=1: both:[-inf errno=ERANGE exc=~o]
    round_mode=DOWN, x=0x1.fffffffffffffp+1023, adj=1: scalbn:[inf errno=ERANGE exc=~o] ldexp:[0x1.fffffffffffffp+1023 errno=ERANGE exc=~o]
    round_mode=ZERO, x=0x1.fffffffffffffp+1023, adj=1: scalbn:[inf errno=ERANGE exc=~o] ldexp:[0x1.fffffffffffffp+1023 errno=ERANGE exc=~o]
    round_mode=UP__, x=-0x1.fffffffffffffp+1023, adj=1: scalbn:[-inf errno=ERANGE exc=~o] ldexp:[-0x1.fffffffffffffp+1023 errno=ERANGE exc=~o]
    round_mode=ZERO, x=-0x1.fffffffffffffp+1023, adj=1: scalbn:[-inf errno=ERANGE exc=~o] ldexp:[-0x1.fffffffffffffp+1023 errno=ERANGE exc=~o]
underflow:
    round_mode=NEAR, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=ZERO, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=DOWN, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=UP__, x=0x1.0000000000000p-1022, adj=-100: scalbn:[0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=NEAR, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[-0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=ZERO, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[-0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=UP__, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[-0x0.0000000000000p+0 errno=0 exc=~u]
    round_mode=DOWN, x=-0x1.0000000000000p-1022, adj=-100: scalbn:[-0x0.0000000000000p+0 errno=ERANGE exc=~u] ldexp:[-0x0.0000000000000p+0 errno=0 exc=~u]
subnormal -- not underflow, but rounds:
    round_mode=NEAR, x=0x0.0000000000007p-1022, adj=-1: scalbn:[0x0.0000000000004p-1022 errno=0 exc=] ldexp:[0x0.0000000000003p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.0000000000007p-1022, adj=-1: scalbn:[0x0.0000000000004p-1022 errno=0 exc=] ldexp:[0x0.0000000000003p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.0000000000007p-1022, adj=-1: scalbn:[0x0.0000000000004p-1022 errno=0 exc=] ldexp:[0x0.0000000000003p-1022 errno=0 exc=~u]
subnormal rounding -- MSVC: scalbn rounds to nearest-even, ldexp rounds towards zero:
    round_mode=NEAR, x=0x0.0000000000009p-1022, adj=-1: scalbn:[0x0.0000000000004p-1022 errno=0 exc=] ldexp:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.0000000000009p-1022, adj=-1: scalbn:[0x0.0000000000004p-1022 errno=0 exc=] ldexp:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.0000000000009p-1022, adj=-1: scalbn:[0x0.0000000000004p-1022 errno=0 exc=] ldexp:[0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=0x0.000000000000bp-1022, adj=-1: scalbn:[0x0.0000000000006p-1022 errno=0 exc=] ldexp:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.000000000000bp-1022, adj=-1: scalbn:[0x0.0000000000006p-1022 errno=0 exc=] ldexp:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.000000000000bp-1022, adj=-1: scalbn:[0x0.0000000000006p-1022 errno=0 exc=] ldexp:[0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=0x0.000000000000dp-1022, adj=-1: scalbn:[0x0.0000000000006p-1022 errno=0 exc=] ldexp:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=0x0.000000000000dp-1022, adj=-1: scalbn:[0x0.0000000000006p-1022 errno=0 exc=] ldexp:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=0x0.000000000000dp-1022, adj=-1: scalbn:[0x0.0000000000006p-1022 errno=0 exc=] ldexp:[0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.0000000000009p-1022, adj=-1: scalbn:[-0x0.0000000000004p-1022 errno=0 exc=] ldexp:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.0000000000009p-1022, adj=-1: scalbn:[-0x0.0000000000004p-1022 errno=0 exc=] ldexp:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.0000000000009p-1022, adj=-1: scalbn:[-0x0.0000000000004p-1022 errno=0 exc=] ldexp:[-0x0.0000000000004p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.000000000000bp-1022, adj=-1: scalbn:[-0x0.0000000000006p-1022 errno=0 exc=] ldexp:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.000000000000bp-1022, adj=-1: scalbn:[-0x0.0000000000006p-1022 errno=0 exc=] ldexp:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.000000000000bp-1022, adj=-1: scalbn:[-0x0.0000000000006p-1022 errno=0 exc=] ldexp:[-0x0.0000000000005p-1022 errno=0 exc=~u]
    round_mode=NEAR, x=-0x0.000000000000dp-1022, adj=-1: scalbn:[-0x0.0000000000006p-1022 errno=0 exc=] ldexp:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=UP__, x=-0x0.000000000000dp-1022, adj=-1: scalbn:[-0x0.0000000000006p-1022 errno=0 exc=] ldexp:[-0x0.0000000000006p-1022 errno=0 exc=~u]
    round_mode=DOWN, x=-0x0.000000000000dp-1022, adj=-1: scalbn:[-0x0.0000000000006p-1022 errno=0 exc=] ldexp:[-0x0.0000000000006p-1022 errno=0 exc=~u]