int
main ()
{
int i;
/* The use of 'volatile' guarantees that excess precision bits are dropped
when dealing with denormalized numbers. It is necessary on x86 systems
where double-floats are not IEEE compliant by default, to avoid that the
results become platform and compiler option dependent. 'volatile' is a
portable alternative to gcc's -ffloat-store option. */
volatile double x;
{ /* NaN. */
int exp = -9999;
double mantissa;
x = NaNd ();
mantissa = frexp (x, &exp);
ASSERT (isnand (mantissa));
}
{ /* Positive infinity. */
int exp = -9999;
double mantissa;
x = 1.0 / 0.0;
mantissa = frexp (x, &exp);
ASSERT (mantissa == x);
}
{ /* Negative infinity. */
int exp = -9999;
double mantissa;
x = -1.0 / 0.0;
mantissa = frexp (x, &exp);
ASSERT (mantissa == x);
}
{ /* Positive zero. */
int exp = -9999;
double mantissa;
x = 0.0;
mantissa = frexp (x, &exp);
ASSERT (exp == 0);
ASSERT (mantissa == x);
ASSERT (!signbit (mantissa));
}
{ /* Negative zero. */
int exp = -9999;
double mantissa;
x = -zero;
mantissa = frexp (x, &exp);
ASSERT (exp == 0);
ASSERT (mantissa == x);
ASSERT (signbit (mantissa));
}
for (i = 1, x = 1.0; i <= DBL_MAX_EXP; i++, x *= 2.0)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.5);
}
for (i = 1, x = 1.0; i >= DBL_MIN_EXP; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.5);
}
for (; i >= DBL_MIN_EXP - 100 && x > 0.0; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.5);
}
for (i = 1, x = -1.0; i <= DBL_MAX_EXP; i++, x *= 2.0)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == -0.5);
}
for (i = 1, x = -1.0; i >= DBL_MIN_EXP; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == -0.5);
}
for (; i >= DBL_MIN_EXP - 100 && x < 0.0; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == -0.5);
}
for (i = 1, x = 1.01; i <= DBL_MAX_EXP; i++, x *= 2.0)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.505);
}
for (i = 1, x = 1.01; i >= DBL_MIN_EXP; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.505);
}
for (; i >= DBL_MIN_EXP - 100 && x > 0.0; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa >= 0.5);
ASSERT (mantissa < 1.0);
ASSERT (mantissa == my_ldexp (x, - exp));
}
for (i = 1, x = 1.73205; i <= DBL_MAX_EXP; i++, x *= 2.0)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.866025);
}
for (i = 1, x = 1.73205; i >= DBL_MIN_EXP; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i);
ASSERT (mantissa == 0.866025);
}
for (; i >= DBL_MIN_EXP - 100 && x > 0.0; i--, x *= 0.5)
{
int exp = -9999;
double mantissa = frexp (x, &exp);
ASSERT (exp == i || exp == i + 1);
ASSERT (mantissa >= 0.5);
ASSERT (mantissa < 1.0);
ASSERT (mantissa == my_ldexp (x, - exp));
}
return 0;
}
// isnanf() broken on Intel Solaris use isnand()
inline int g_isnan(float f) { return isnand(f); }
int
main (void)
{
int status = 0;
/* Subject sequence empty or invalid. */
{
const char input[] = "";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " ";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " +";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " .";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " .e0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input); /* IRIX 6.5, OSF/1 5.1 */
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " +.e-0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input); /* IRIX 6.5, OSF/1 5.1 */
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " in";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
}
{
const char input[] = " na";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
}
/* Simple floating point values. */
{
const char input[] = "1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = "1.";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = ".5";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
/* FIXME - gnulib's version is rather inaccurate. It would be
nice to guarantee an exact result, but for now, we settle for a
1-ulp error. */
ASSERT (FABS (result - 0.5) < DBL_EPSILON);
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = " 1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = "+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = "-1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == -1.0);
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = "1e0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 3);
ASSERT (errno == 0);
}
{
const char input[] = "1e+0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 4);
ASSERT (errno == 0);
}
{
const char input[] = "1e-0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 4);
ASSERT (errno == 0);
}
{
const char input[] = "1e1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 10.0);
ASSERT (ptr == input + 3);
ASSERT (errno == 0);
}
{
const char input[] = "5e-1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
/* FIXME - gnulib's version is rather inaccurate. It would be
nice to guarantee an exact result, but for now, we settle for a
1-ulp error. */
ASSERT (FABS (result - 0.5) < DBL_EPSILON);
ASSERT (ptr == input + 4);
ASSERT (errno == 0);
}
/* Zero. */
{
const char input[] = "0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = ".0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = "0e0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 3);
ASSERT (errno == 0);
}
{
const char input[] = "0e+9999999";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 10);
ASSERT (errno == 0);
}
{
const char input[] = "0e-9999999";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 10);
ASSERT (errno == 0);
}
{
const char input[] = "-0";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!!signbit (result) == !!signbit (minus_zerod)); /* IRIX 6.5, OSF/1 4.0 */
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
/* Suffixes. */
{
const char input[] = "1f";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = "1.f";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = "1e";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = "1e+";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = "1e-";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = "1E 2";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* HP-UX 11.11, IRIX 6.5, OSF/1 4.0 */
ASSERT (ptr == input + 1); /* HP-UX 11.11, IRIX 6.5 */
ASSERT (errno == 0);
}
{
const char input[] = "0x";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "00x1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 2);
ASSERT (errno == 0);
}
{
const char input[] = "-0x";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!!signbit (result) == !!signbit (minus_zerod)); /* Mac OS X 10.3, FreeBSD 6.2, IRIX 6.5, OSF/1 4.0 */
ASSERT (ptr == input + 2); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0xg";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0xp";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0XP";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0x.";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0xp+";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0xp+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "0x.p+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input + 1); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, AIX 7.1 */
ASSERT (errno == 0);
}
{
const char input[] = "1p+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
{
const char input[] = "1P+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + 1);
ASSERT (errno == 0);
}
/* Overflow/underflow. */
{
const char input[] = "1E1000000";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == HUGE_VAL);
ASSERT (ptr == input + 9); /* OSF/1 5.1 */
ASSERT (errno == ERANGE);
}
{
const char input[] = "-1E1000000";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == -HUGE_VAL);
ASSERT (ptr == input + 10);
ASSERT (errno == ERANGE);
}
{
const char input[] = "1E-100000";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (0.0 <= result && result <= DBL_MIN);
ASSERT (!signbit (result));
ASSERT (ptr == input + 9);
ASSERT (errno == ERANGE);
}
{
const char input[] = "-1E-100000";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (-DBL_MIN <= result && result <= 0.0);
#if 0
/* FIXME - this is glibc bug 5995; POSIX allows returning positive
0 on negative underflow, even though quality of implementation
demands preserving the sign. Disable this test until fixed
glibc is more prevalent. */
ASSERT (!!signbit (result) == !!signbit (minus_zerod)); /* glibc-2.3.6, mingw */
#endif
ASSERT (ptr == input + 10);
ASSERT (errno == ERANGE);
}
{
const char input[] = "1E 1000000";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* HP-UX 11.11, IRIX 6.5, OSF/1 4.0 */
ASSERT (ptr == input + 1); /* HP-UX 11.11, IRIX 6.5 */
ASSERT (errno == 0);
}
{
const char input[] = "0x1P 1000000";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
/* Infinity. */
{
const char input[] = "iNf";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == HUGE_VAL); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + 3); /* OpenBSD 4.0, HP-UX 11.00, IRIX 6.5, OSF/1 5.1, Solaris 9, mingw */
ASSERT (errno == 0); /* HP-UX 11.11, OSF/1 4.0 */
}
{
const char input[] = "-InF";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == -HUGE_VAL); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + 4); /* OpenBSD 4.0, HP-UX 11.00, IRIX 6.5, OSF/1 4.0, Solaris 9, mingw */
ASSERT (errno == 0); /* HP-UX 11.11, OSF/1 4.0 */
}
{
const char input[] = "infinite";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == HUGE_VAL); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + 3); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (errno == 0); /* OSF/1 4.0 */
}
{
const char input[] = "infinitY";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == HUGE_VAL); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + 8); /* OpenBSD 4.0, HP-UX 11.00, IRIX 6.5, OSF/1 5.1, Solaris 9, mingw */
ASSERT (errno == 0); /* HP-UX 11.11, OSF/1 4.0 */
}
{
const char input[] = "infinitY.";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == HUGE_VAL); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + 8); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (errno == 0); /* OSF/1 4.0 */
}
/* NaN. Some processors set the sign bit of the default NaN, so all
we check is that using a sign changes the result. */
{
const char input[] = "-nan";
char *ptr1;
char *ptr2;
double result1;
double result2;
errno = 0;
result1 = strtod (input, &ptr1);
result2 = strtod (input + 1, &ptr2);
#if 1 /* All known CPUs support NaNs. */
ASSERT (isnand (result1)); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (isnand (result2)); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
# if 0
/* Sign bits of NaN is a portability sticking point, not worth
worrying about. */
ASSERT (!!signbit (result1) != !!signbit (result2)); /* glibc-2.3.6, IRIX 6.5, OSF/1 5.1, mingw */
# endif
ASSERT (ptr1 == input + 4); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, Solaris 2.5.1, mingw */
ASSERT (ptr2 == input + 4); /* OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, Solaris 2.5.1, mingw */
ASSERT (errno == 0); /* HP-UX 11.11 */
#else
ASSERT (result1 == 0.0);
ASSERT (result2 == 0.0);
ASSERT (!signbit (result1));
ASSERT (!signbit (result2));
ASSERT (ptr1 == input);
ASSERT (ptr2 == input + 1);
ASSERT (errno == 0 || errno == EINVAL);
#endif
}
{
const char input[] = "+nan(";
char *ptr1;
char *ptr2;
double result1;
double result2;
errno = 0;
result1 = strtod (input, &ptr1);
result2 = strtod (input + 1, &ptr2);
#if 1 /* All known CPUs support NaNs. */
ASSERT (isnand (result1)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (isnand (result2)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (!!signbit (result1) == !!signbit (result2));
ASSERT (ptr1 == input + 4); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 2.5.1, mingw */
ASSERT (ptr2 == input + 4); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 2.5.1, mingw */
ASSERT (errno == 0);
#else
ASSERT (result1 == 0.0);
ASSERT (result2 == 0.0);
ASSERT (!signbit (result1));
ASSERT (!signbit (result2));
ASSERT (ptr1 == input);
ASSERT (ptr2 == input + 1);
ASSERT (errno == 0 || errno == EINVAL);
#endif
}
{
const char input[] = "-nan()";
char *ptr1;
char *ptr2;
double result1;
double result2;
errno = 0;
result1 = strtod (input, &ptr1);
result2 = strtod (input + 1, &ptr2);
#if 1 /* All known CPUs support NaNs. */
ASSERT (isnand (result1)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (isnand (result2)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
# if 0
/* Sign bits of NaN is a portability sticking point, not worth
worrying about. */
ASSERT (!!signbit (result1) != !!signbit (result2)); /* glibc-2.3.6, IRIX 6.5, OSF/1 5.1, mingw */
# endif
ASSERT (ptr1 == input + 6); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr2 == input + 6); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (errno == 0);
#else
ASSERT (result1 == 0.0);
ASSERT (result2 == 0.0);
ASSERT (!signbit (result1));
ASSERT (!signbit (result2));
ASSERT (ptr1 == input);
ASSERT (ptr2 == input + 1);
ASSERT (errno == 0 || errno == EINVAL);
#endif
}
{
const char input[] = " nan().";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
#if 1 /* All known CPUs support NaNs. */
ASSERT (isnand (result)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + 6); /* glibc-2.3.6, Mac OS X 10.3, FreeBSD 6.2, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (errno == 0);
#else
ASSERT (result == 0.0);
ASSERT (!signbit (result));
ASSERT (ptr == input);
ASSERT (errno == 0 || errno == EINVAL);
#endif
}
{
/* The behavior of nan(0) is implementation-defined, but all
implementations we know of which handle optional
n-char-sequences handle nan(0) the same as nan(). */
const char input[] = "-nan(0).";
char *ptr1;
char *ptr2;
double result1;
double result2;
errno = 0;
result1 = strtod (input, &ptr1);
result2 = strtod (input + 1, &ptr2);
#if 1 /* All known CPUs support NaNs. */
ASSERT (isnand (result1)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (isnand (result2)); /* OpenBSD 4.0, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
# if 0
/* Sign bits of NaN is a portability sticking point, not worth
worrying about. */
ASSERT (!!signbit (result1) != !!signbit (result2)); /* glibc-2.3.6, IRIX 6.5, OSF/1 5.1, mingw */
# endif
ASSERT (ptr1 == input + 7); /* glibc-2.3.6, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr2 == input + 7); /* glibc-2.3.6, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (errno == 0);
#else
ASSERT (result1 == 0.0);
ASSERT (result2 == 0.0);
ASSERT (!signbit (result1));
ASSERT (!signbit (result2));
ASSERT (ptr1 == input);
ASSERT (ptr2 == input + 1);
ASSERT (errno == 0 || errno == EINVAL);
#endif
}
/* Hex. */
{
const char input[] = "0xa";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 10.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0XA";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 10.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0x1p";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0x1p+";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0x1P+";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0x1p+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 2.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 6); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0X1P+1";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 2.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 6); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0x1p+1a";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 2.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 6); /* NetBSD 3.0, OpenBSD 4.0, AIX 5.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
{
const char input[] = "0x1p 2";
char *ptr;
double result;
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* NetBSD 3.0, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (ptr == input + 3); /* NetBSD 3.0, OpenBSD 4.0, AIX 7.1, HP-UX 11.11, IRIX 6.5, OSF/1 5.1, Solaris 10, mingw */
ASSERT (errno == 0);
}
/* Large buffers. */
{
size_t m = 1000000;
char *input = malloc (m + 1);
if (input)
{
char *ptr;
double result;
memset (input, '\t', m - 1);
input[m - 1] = '1';
input[m] = '\0';
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + m);
ASSERT (errno == 0);
}
free (input);
}
{
size_t m = 1000000;
char *input = malloc (m + 1);
if (input)
{
char *ptr;
double result;
memset (input, '0', m - 1);
input[m - 1] = '1';
input[m] = '\0';
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0);
ASSERT (ptr == input + m);
ASSERT (errno == 0);
}
free (input);
}
#if 0
/* Newlib has an artificial limit of 20000 for the exponent. TODO -
gnulib should fix this. */
{
size_t m = 1000000;
char *input = malloc (m + 1);
if (input)
{
char *ptr;
double result;
input[0] = '.';
memset (input + 1, '0', m - 10);
input[m - 9] = '1';
input[m - 8] = 'e';
input[m - 7] = '+';
input[m - 6] = '9';
input[m - 5] = '9';
input[m - 4] = '9';
input[m - 3] = '9';
input[m - 2] = '9';
input[m - 1] = '1';
input[m] = '\0';
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* Mac OS X 10.3, FreeBSD 6.2, NetBSD 3.0, OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + m); /* OSF/1 5.1 */
ASSERT (errno == 0); /* Mac OS X 10.3, FreeBSD 6.2, NetBSD 3.0, OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
}
free (input);
}
{
size_t m = 1000000;
char *input = malloc (m + 1);
if (input)
{
char *ptr;
double result;
input[0] = '1';
memset (input + 1, '0', m - 9);
input[m - 8] = 'e';
input[m - 7] = '-';
input[m - 6] = '9';
input[m - 5] = '9';
input[m - 4] = '9';
input[m - 3] = '9';
input[m - 2] = '9';
input[m - 1] = '1';
input[m] = '\0';
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 1.0); /* Mac OS X 10.3, FreeBSD 6.2, NetBSD 3.0, OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
ASSERT (ptr == input + m);
ASSERT (errno == 0); /* Mac OS X 10.3, FreeBSD 6.2, NetBSD 3.0, OpenBSD 4.0, IRIX 6.5, OSF/1 5.1, mingw */
}
free (input);
}
#endif
{
size_t m = 1000000;
char *input = malloc (m + 1);
if (input)
{
char *ptr;
double result;
input[0] = '-';
input[1] = '0';
input[2] = 'e';
input[3] = '1';
memset (input + 4, '0', m - 3);
input[m] = '\0';
errno = 0;
result = strtod (input, &ptr);
ASSERT (result == 0.0);
ASSERT (!!signbit (result) == !!signbit (minus_zerod)); /* IRIX 6.5, OSF/1 4.0 */
ASSERT (ptr == input + m);
ASSERT (errno == 0);
}
free (input);
}
/* Rounding. */
/* TODO - is it worth some tests of rounding for typical IEEE corner
cases, such as .5 ULP rounding up to the smallest denormal and
not causing underflow, or DBL_MIN - .5 ULP not causing an
infinite loop? */
return status;
}
inline int g_isnan(double f) { return isnand(f); }
int gl_isfinited (double x)
{
return !isnand (x) && x - x == zerod;
}
int isnan(double x)
{
return isnand(x);
}
int
main ()
{
/* Finite values. */
ASSERT (!isnand (3.141));
ASSERT (!isnand (3.141e30));
ASSERT (!isnand (3.141e-30));
ASSERT (!isnand (-2.718));
ASSERT (!isnand (-2.718e30));
ASSERT (!isnand (-2.718e-30));
ASSERT (!isnand (0.0));
ASSERT (!isnand (-0.0));
/* Infinite values. */
ASSERT (!isnand (1.0 / 0.0));
ASSERT (!isnand (-1.0 / 0.0));
/* Quiet NaN. */
ASSERT (isnand (NaNd ()));
#if defined DBL_EXPBIT0_WORD && defined DBL_EXPBIT0_BIT
/* Signalling NaN. */
{
#define NWORDS \
((sizeof (double) + sizeof (unsigned int) - 1) / sizeof (unsigned int))
typedef union { double value; unsigned int word[NWORDS]; } memory_double;
memory_double m;
m.value = NaNd ();
# if DBL_EXPBIT0_BIT > 0
m.word[DBL_EXPBIT0_WORD] ^= (unsigned int) 1 << (DBL_EXPBIT0_BIT - 1);
# else
m.word[DBL_EXPBIT0_WORD + (DBL_EXPBIT0_WORD < NWORDS / 2 ? 1 : - 1)]
^= (unsigned int) 1 << (sizeof (unsigned int) * CHAR_BIT - 1);
# endif
m.word[DBL_EXPBIT0_WORD + (DBL_EXPBIT0_WORD < NWORDS / 2 ? 1 : - 1)]
|= (unsigned int) 1 << DBL_EXPBIT0_BIT;
ASSERT (isnand (m.value));
}
#endif
return 0;
}
double
log1p (double x)
{
if (isnand (x))
return x;
if (x <= -1.0)
{
if (x == -1.0)
/* Return -Infinity. */
return - HUGE_VAL;
else
{
/* Return NaN. */
#if defined _MSC_VER || (defined __sgi && !defined __GNUC__)
static double zero;
return zero / zero;
#else
return 0.0 / 0.0;
#endif
}
}
if (x < -0.5 || x > 1.0)
return log (1.0 + x);
/* Here -0.5 <= x <= 1.0. */
if (x == 0.0)
/* Return a zero with the same sign as x. */
return x;
/* Decompose x into
1 + x = (1 + m/256) * (1 + y)
where
m is an integer, -128 <= m <= 256,
y is a number, |y| <= 1/256.
y is computed as
y = (256 * x - m) / (256 + m).
Then
log(1+x) = log(m/256) + log(1+y)
The first summand is a table lookup.
The second summand is computed
- either through the power series
log(1+y) = y
- 1/2 * y^2
+ 1/3 * y^3
- 1/4 * y^4
+ 1/5 * y^5
- 1/6 * y^6
+ 1/7 * y^7
- 1/8 * y^8
+ 1/9 * y^9
- 1/10 * y^10
+ 1/11 * y^11
- 1/12 * y^12
+ 1/13 * y^13
- 1/14 * y^14
+ 1/15 * y^15
- ...
- or as log(1+y) = log((1+z)/(1-z)) = 2 * atanh(z)
where z = y/(2+y)
and atanh(z) is computed through its power series:
atanh(z) = z
+ 1/3 * z^3
+ 1/5 * z^5
+ 1/7 * z^7
+ 1/9 * z^9
+ 1/11 * z^11
+ 1/13 * z^13
+ 1/15 * z^15
+ ...
Since |z| <= 1/511 < 0.002, the relative contribution of the z^9
term is < 1/9*0.002^8 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we
can truncate the series after the z^7 term. */
{
double m = round (x * 256.0);
double y = ((x * 256.0) - m) / (m + 256.0);
double z = y / (2.0 + y);
/* Coefficients of the power series for atanh(z). */
#define ATANH_COEFF_1 1.0
#define ATANH_COEFF_3 0.333333333333333333333333333333333333334
#define ATANH_COEFF_5 0.2
#define ATANH_COEFF_7 0.142857142857142857142857142857142857143
#define ATANH_COEFF_9 0.1111111111111111111111111111111111111113
#define ATANH_COEFF_11 0.090909090909090909090909090909090909091
#define ATANH_COEFF_13 0.076923076923076923076923076923076923077
#define ATANH_COEFF_15 0.066666666666666666666666666666666666667
double z2 = z * z;
double atanh_z =
(((ATANH_COEFF_7
* z2 + ATANH_COEFF_5)
* z2 + ATANH_COEFF_3)
* z2 + ATANH_COEFF_1)
* z;
/* log_table[i] = log((i + 128) / 256).
Computed in GNU clisp through
(setf (long-float-digits) 128)
(setq a 0L0)
(setf (long-float-digits) 256)
(dotimes (i 385)
(format t " ~D,~%"
(float (log (* (/ (+ i 128) 256) 1L0)) a))) */
static const double log_table[385] =
{
-0.693147180559945309417232121458176568075,
-0.6853650401178903604697692213970398044,
-0.677642994023980055266378075415729732197,
-0.669980121278410931188432960495886651496,
-0.662375521893191621046203913861404403985,
-0.65482831625780871022347679633437927773,
-0.647337644528651106250552853843513225963,
-0.639902666041133026551361927671647791137,
-0.632522558743510466836625989417756304788,
-0.625196518651437560022666843685547154042,
-0.617923759322357783718626781474514153438,
-0.61070351134887071814907205278986876216,
-0.60353502187025817679728065207969203929,
-0.59641755410139419712166106497071313106,
-0.58935038687830174459117031769420187977,
-0.582332814219655195222425952134964639978,
-0.575364144903561854878438011987654863008,
-0.568443702058988073553825606077313299585,
-0.561570822771226036828515992768693405624,
-0.554744857700826173731906247856527380683,
-0.547965170715447412135297057717612244552,
-0.541231138534103334345428696561292056747,
-0.534542150383306725323860946832334992828,
-0.527897607664638146541620672180936254347,
-0.52129692363328608707713317540302930314,
-0.514739523087127012297831879947234599722,
-0.50822484206593331675332852879892694707,
-0.50175232756031585480793331389686769463,
-0.495321437230025429054660050261215099,
-0.488931639131254417913411735261937295862,
-0.482582411452595671747679308725825054355,
-0.476273242259330949798142595713829069596,
-0.470003629245735553650937031148342064701,
-0.463773079495099479425751396412036696525,
-0.457581109247178400339643902517133157939,
-0.451427243672800141272924605544662667972,
-0.445311016655364052636629355711651820077,
-0.43923197057898186527990882355156990061,
-0.4331896561230192424451526269158655235,
-0.427183632062807368078106194920633178807,
-0.421213465076303550585562626925177406092,
-0.415278729556489003230882088534775334993,
-0.409379007429300711070330899107921801414,
-0.403513887976902632538339065932507598071,
-0.397682967666109433030550215403212372894,
-0.391885849981783528404356583224421075418,
-0.386122145265033447342107580922798666387,
-0.380391470556048421030985561769857535915,
-0.374693449441410693606984907867576972481,
-0.369027711905733333326561361023189215893,
-0.363393894187477327602809309537386757124,
-0.357791638638807479160052541644010369001,
-0.352220593589352099112142921677820359633,
-0.346680413213736728498769933032403617363,
-0.341170757402767124761784665198737642087,
-0.33569129163814153519122263131727209364,
-0.330241686870576856279407775480686721935,
-0.324821619401237656369001967407777741178,
-0.31943077076636122859621528874235306143,
-0.314068827624975851026378775827156709194,
-0.308735481649613269682442058976885699557,
-0.303430429419920096046768517454655701024,
-0.298153372319076331310838085093194799765,
-0.292904016432932602487907019463045397996,
-0.287682072451780927439219005993827431504,
-0.282487255574676923482925918282353780414,
-0.277319285416234343803903228503274262719,
-0.272177885915815673288364959951380595626,
-0.267062785249045246292687241862699949179,
-0.261973715741573968558059642502581569596,
-0.256910413785027239068190798397055267412,
-0.251872619755070079927735679796875342712,
-0.2468600779315257978846419408385075613265,
-0.24187253642048672427253973837916408939,
-0.2369097470783577150364265832942468196375,
-0.2319714654377751430492321958603212094726,
-0.2270574506353460848586128739534071682175,
-0.222167465341154296870334265401817316702,
-0.2173012756899813951520225351537951559,
-0.212458651214193401740613666010165016867,
-0.2076393647782445016154410442673876674964,
-0.202843192514751471266885961812429707545,
-0.1980699137620937948192675366153429027185,
-0.193319311003495979595900706211132426563,
-0.188591169807550022358923589720001638093,
-0.183885278770137362613157202229852743197,
-0.179201429457710992616226033183958974965,
-0.174539416351899677264255125093377869519,
-0.169899036795397472900424896523305726435,
-0.165280090939102924303339903679875604517,
-0.160682381690473465543308397998034325468,
-0.156105714663061654850502877304344269052,
-0.1515498981272009378406898175577424691056,
-0.1470147429618096590348349122269674042104,
-0.142500062607283030157283942253263107981,
-0.1380056730194437167017517619422725179055,
-0.1335313926245226231463436209313499745895,
-0.129077042275142343345847831367985856258,
-0.124642445207276597338493356591214304499,
-0.1202274269981598003244753948319154994493,
-0.115831815525121705099120059938680166568,
-0.1114554409253228268966213677328042273655,
-0.1070981355563671005131126851708522185606,
-0.1027597339577689347753154133345778104976,
-0.098440072813252519902888574928971234883,
-0.094138990913861910035632096996525066015,
-0.0898563291218610470766469347968659624282,
-0.0855919303354035139161469686670511961825,
-0.0813456394539524058873423550293617843895,
-0.077117303344431289769666193261475917783,
-0.072906770808087780565737488890929711303,
-0.0687138925480518083746933774035034481663,
-0.064538521137571171672923915683992928129,
-0.0603805109889074798714456529545968095868,
-0.0562397183228760777967376942769773768851,
-0.0521160011390140183616307870527840213665,
-0.0480092191863606077520036253234446621373,
-0.0439192339348354905263921515528654458042,
-0.0398459085471996706586162402473026835046,
-0.0357891078515852792753420982122404025613,
-0.0317486983145803011569962827485256299276,
-0.0277245480148548604671395114515163869272,
-0.0237165266173160421183468505286730579517,
-0.0197245053477785891192717326571593033246,
-0.015748356968139168607549511460828269521,
-0.0117879557520422404691605618900871263399,
-0.0078431774610258928731840424909435816546,
-0.00391389932113632909231778364357266484272,
0.0,
0.00389864041565732301393734309584290701073,
0.00778214044205494894746290006113676367813,
0.01165061721997527413559144280921434893315,
0.0155041865359652541508540460424468358779,
0.01934296284313093463590553454155047018545,
0.0231670592815343782287991609622899165794,
0.0269765876982020757480692925396595457815,
0.0307716586667536883710282075967721640917,
0.0345523815066597334073715005898328652816,
0.038318864302136599193755325123797290346,
0.042071213920687054375203805926962379448,
0.045809536031294203166679267614663342114,
0.049533935122276630882096208829824573267,
0.0532445145188122828658701937865287769396,
0.0569413764001384247590131015404494943015,
0.0606246218164348425806061320404202632862,
0.0642943507053972572162284502656114944857,
0.0679506619085077493945652777726294140346,
0.071593653187008817925605272752092034269,
0.075223421237587525698605339983662414637,
0.078840061707776024531540577859198294559,
0.082443669211074591268160068668307805914,
0.086034337341803153381797826721996075141,
0.0896121586896871326199514693784845287854,
0.093177224854183289768781353027759396216,
0.096729626458551112295571056487463437015,
0.1002694531636751493081301751297276601964,
0.1037967936816435648260618037639746883066,
0.1073117357890880506671750303711543368066,
0.1108143663402901141948061693232119280986,
0.1143047712800586336342591448151747734094,
0.1177830356563834545387941094705217050686,
0.1212492436328696851612122640808405265723,
0.1247034785009572358634065153808632684918,
0.128145822691930038174109886961074873852,
0.1315763577887192725887161286894831624516,
0.134995164537504830601983291147085645626,
0.138402322859119135685325873601649187393,
0.1417979118602573498789527352804727189846,
0.1451820098444978972819350637405643235226,
0.1485546943231371429098223170672938691604,
0.151916042025841975071803424896884511328,
0.1552661289111239515223833017101021786436,
0.1586050301766385840933711746258415752456,
0.161932820269313253240338285123614220592,
0.165249572895307162875611449277240313729,
0.1685553610298066669415865321701023169345,
0.171850256926659222340098946055147264935,
0.1751343321278491480142914649863898412374,
0.1784076574728182971194002415109419683545,
0.181670303107634678260605595617079739242,
0.184922338494011992663903592659249621006,
0.1881638324181829868259905803105539806714,
0.191394852999629454609298807561308873447,
0.194615467699671658858138593767269731516,
0.1978257433299198803625720711969614690756,
0.201025746060590741340908337591797808969,
0.204215541428690891503820386196239272214,
0.2073951943460705871587455788490062338536,
0.210564769107349637669552812732351513721,
0.2137243293977181388619051976331987647734,
0.216873938300614359619089525744347498479,
0.220013658305282095907358638661628360712,
0.2231435513142097557662950903098345033745,
0.226263678650453389361787082280390161607,
0.229374101064845829991480725046139871551,
0.232474878743094064920705078095567528222,
0.235566071312766909077588218941043410137,
0.2386477378501750099171491363522813392526,
0.241719936887145168144307515913513900104,
0.244782726417690916434704717466314811104,
0.247836163904581256780602765746524747999,
0.25088030628580941658844644154994089393,
0.253915209980963444137323297906606667466,
0.256940930897500425446759867911224262093,
0.259957524436926066972079494542311044577,
0.26296504550088135182072917321108602859,
0.265963548497137941339125926537543389269,
0.268953087345503958932974357924497845489,
0.271933715483641758831669494532999161983,
0.274905485872799249167009582983018668293,
0.277868451003456306186350032923401233082,
0.280822662900887784639519758873134832073,
0.28376817313064459834690122235025476666,
0.286705032803954314653250930842073965668,
0.289633292583042676878893055525668970004,
0.292553002686377439978201258664126644308,
0.295464212893835876386681906054964195182,
0.298366972551797281464900430293496918012,
0.301261330578161781012875538233755492657,
0.304147335467296717015819874720446989991,
0.30702503529491186207512454053537790169,
0.309894477722864687861624550833227164546,
0.31275571000389688838624655968831903216,
0.315608778986303334901366180667483174144,
0.318453731118534615810247213590599595595,
0.321290612453734292057863145522557457887,
0.324119468654211976090670760434987352183,
0.326940344995853320592356894073809191681,
0.329753286372467981814422811920789810952,
0.332558337300076601412275626573419425269,
0.335355541921137830257179579814166199074,
0.338144944008716397710235913939267433111,
0.340926586970593210305089199780356208443,
0.34370051385331844468019789211029452987,
0.346466767346208580918462188425772950712,
0.349225389785288304181275421187371759687,
0.35197642315717818465544745625943892599,
0.354719909102929028355011218999317665826,
0.357455888921803774226009490140904474434,
0.360184403575007796281574967493016620926,
0.362905493689368453137824345977489846141,
0.365619199560964711319396875217046453067,
0.368325561158707653048230154050398826898,
0.371024618127872663911964910806824955394,
0.373716409793584080821016832715823506644,
0.376400975164253065997877633436251593315,
0.379078352934969458390853345631019858882,
0.38174858149084833985966626493567607862,
0.384411698910332039734790062481290868519,
0.387067742968448287898902502261817665695,
0.38971675114002521337046360400352086705,
0.392358760602863872479379611988215363485,
0.39499380824086897810639403636498176831,
0.397621930647138489104829072973405554918,
0.40024316412701270692932510199513117008,
0.402857544701083514655197565487057707577,
0.405465108108164381978013115464349136572,
0.408065889808221748430198682969084124381,
0.410659924985268385934306203175822787661,
0.41324724855021933092547601552548590025,
0.415827895143710965613328892954902305356,
0.418401899138883817510763261966760106515,
0.42096929464412963612886716150679597245,
0.423530115505803295718430478017910109426,
0.426084395310900063124544879595476618897,
0.428632167389698760206812276426639053152,
0.43117346481837134085917247895559499848,
0.433708320421559393435847903042186017095,
0.436236766774918070349041323061121300663,
0.438758836207627937745575058511446738878,
0.441274560804875229489496441661301225362,
0.443783972410300981171768440588146426918,
0.446287102628419511532590180619669006749,
0.448783982827006710512822115683937186274,
0.451274644139458585144692383079012478686,
0.453759117467120506644794794442263270651,
0.456237433481587594380805538163929748437,
0.458709622626976664843883309250877913511,
0.461175715122170166367999925597855358603,
0.463635740963032513092182277331163919118,
0.466089729924599224558619247504769399859,
0.468537711563239270375665237462973542708,
0.470979715218791012546897856056359251373,
0.473415770016672131372578393236978550606,
0.475845904869963914265209586304381412175,
0.478270148481470280383546145497464809096,
0.480688529345751907676618455448011551209,
0.48310107575113582273837458485214554795,
0.485507815781700807801791077190788900579,
0.487908777319238973246173184132656942487,
0.490303988045193838150346159645746860531,
0.492693475442575255695076950020077845328,
0.495077266797851514597964584842833665358,
0.497455389202818942250859256731684928918,
0.499827869556449329821331415247044141512,
0.502194734566715494273584171951812573586,
0.504556010752395287058308531738174929982,
0.506911724444854354113196312660089270034,
0.509261901789807946804074919228323824878,
0.51160656874906207851888487520338193135,
0.51394575110223431680100608827421759311,
0.51627947444845449617281928478756106467,
0.518607764208045632152976996364798698556,
0.520930645624185312409809834659637709188,
0.52324814376454783651680722493487084164,
0.525560283522927371382427602307131424923,
0.527867089620842385113892217778300963557,
0.530168586609121617841419630845212405063,
0.532464798869471843873923723460142242606,
0.534755750616027675477923292032637111077,
0.537041465896883654566729244153832299024,
0.539321968595608874655355158077341155752,
0.54159728243274437157654230390043409897,
0.543867430967283517663338989065998323965,
0.546132437598135650382397209231209163864,
0.548392325565573162748150286179863158565,
0.550647117952662279259948179204913460093,
0.552896837686677737580717902230624314327,
0.55514150754050159271548035951590405017,
0.557381150134006357049816540361233647898,
0.559615787935422686270888500526826593487,
0.561845443262691817915664819160697456814,
0.564070138284802966071384290090190711817,
0.566289895023115872590849979337124343595,
0.568504735352668712078738764866962263577,
0.5707146810034715448536245647415894503,
0.572919753561785509092756726626261068625,
0.575119974471387940421742546569273429365,
0.577315365034823604318112061519496401506,
0.579505946414642223855274409488070989814,
0.58169173963462248252061075372537234071,
0.583872765580982679097413356975291104927,
0.586049045003578208904119436287324349516,
0.588220598517086043034868221609113995052,
0.590387446602176374641916708123598757576,
0.59254960960667159874199020959329739696,
0.594707107746692789514343546529205333192,
0.59685996110779383658731192302565801002,
0.59900818964608339938160002446165150206,
0.601151813189334836191674317068856441547,
0.603290851438084262340585186661310605647,
0.6054253239667168894375677681414899356,
0.607555250224541795501085152791125371894,
0.609680649536855273481833501660588408785,
0.611801541105992903529889766428814783686,
0.613917944012370492196929119645563790777,
0.616029877215514019647565928196700650293,
0.618137359555078733872689126674816271683,
0.620240409751857528851494632567246856773,
0.62233904640877874159710264120869663505,
0.62443328801189350104253874405467311991,
0.626523152931352759778820859734204069282,
0.628608659422374137744308205774183639946,
0.6306898256261987050837261409313532241,
0.63276666957103782954578646850357975849,
0.634839209173010211969493840510489008123,
0.63690746223706923162049442718119919119,
0.63897144645792072137962398326473680873,
0.64103117942093129105560133440539254671,
0.643086678603027315392053859585132960477,
0.645137961373584701665228496134731905937,
0.647185044995309550122320631377863036675,
0.64922794662510981889083996990531112227,
0.651266683314958103396333353349672108398,
0.653301272012745638758615881210873884572,
0.65533172956312763209494967856962559648,
0.657358072708360030141890023245936165513,
0.659380318089127826115336413370955804038,
0.661398482245365008260235838709650938148,
0.66341258161706625109695030429080128179,
0.665422632545090448950092610006660181147,
0.667428651271956189947234166318980478403,
0.669430653942629267298885270929503510123,
0.67142865660530232331713904200189252584,
0.67342267521216672029796038880101726475,
0.67541272562017673108090414397019748722,
0.677398823591806140809682609997348298556,
0.67938098479579735014710062847376425181,
0.681359224807903068948071559568089441735,
0.683333559111620688164363148387750369654,
0.68530400309891941654404807896723298642,
0.687270572070960267497006884394346103924,
0.689233281238808980324914337814603903233,
0.691192145724141958859604629216309755938,
0.693147180559945309417232121458176568075
};
return log_table[128 + (int)m] + 2.0 * atanh_z;
}
}
double
expm1 (double x)
{
if (isnand (x))
return x;
if (x >= (double) DBL_MAX_EXP * LOG2_PLUS_EPSILON)
/* x > DBL_MAX_EXP * log(2)
hence exp(x) > 2^DBL_MAX_EXP, overflows to Infinity. */
return HUGE_VAL;
if (x <= (double) (- DBL_MANT_DIG) * LOG2_PLUS_EPSILON)
/* x < (- DBL_MANT_DIG) * log(2)
hence 0 < exp(x) < 2^-DBL_MANT_DIG,
hence -1 < exp(x)-1 < -1 + 2^-DBL_MANT_DIG
rounds to -1. */
return -1.0;
if (x <= - LOG2_PLUS_EPSILON)
/* 0 < exp(x) < 1/2.
Just compute exp(x), then subtract 1. */
return exp (x) - 1.0;
if (x == 0.0)
/* Return a zero with the same sign as x. */
return x;
/* Decompose x into
x = n * log(2) + m * log(2)/256 + y
where
n is an integer, n >= -1,
m is an integer, -128 <= m <= 128,
y is a number, |y| <= log(2)/512 + epsilon = 0.00135...
Then
exp(x) = 2^n * exp(m * log(2)/256) * exp(y)
Compute each factor minus one, then combine them through the
formula (1+a)*(1+b) = 1 + (a+b*(1+a)),
that is (1+a)*(1+b) - 1 = a + b*(1+a).
The first factor is an ldexpl() call.
The second factor is a table lookup.
The third factor minus one is computed
- either as sinh(y) + sinh(y)^2 / (cosh(y) + 1)
where sinh(y) is computed through the power series:
sinh(y) = y + y^3/3! + y^5/5! + ...
and cosh(y) is computed as hypot(1, sinh(y)),
- or as exp(2*z) - 1 = 2 * tanh(z) / (1 - tanh(z))
where z = y/2
and tanh(z) is computed through its power series:
tanh(z) = z
- 1/3 * z^3
+ 2/15 * z^5
- 17/315 * z^7
+ 62/2835 * z^9
- 1382/155925 * z^11
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
z^7 term is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can
truncate the series after the z^5 term.
Given the usual bounds DBL_MAX_EXP <= 16384, DBL_MANT_DIG <= 120, we
can estimate x: -84 <= x <= 11357.
This means, when dividing x by log(2), where we want x mod log(2)
to be precise to DBL_MANT_DIG bits, we have to use an approximation
to log(2) that has 14+DBL_MANT_DIG bits. */
{
double nm = round (x * LOG2_BY_256_INVERSE); /* = 256 * n + m */
/* n has at most 15 bits, nm therefore has at most 23 bits, therefore
n * LOG2_HI_PART is computed exactly, and n * LOG2_LO_PART is computed
with an absolute error < 2^15 * 2e-10 * 2^-DBL_MANT_DIG. */
double y_tmp = x - nm * LOG2_BY_256_HI_PART;
double y = y_tmp - nm * LOG2_BY_256_LO_PART;
double z = 0.5L * y;
/* Coefficients of the power series for tanh(z). */
#define TANH_COEFF_1 1.0
#define TANH_COEFF_3 -0.333333333333333333333333333333333333334
#define TANH_COEFF_5 0.133333333333333333333333333333333333334
#define TANH_COEFF_7 -0.053968253968253968253968253968253968254
#define TANH_COEFF_9 0.0218694885361552028218694885361552028218
#define TANH_COEFF_11 -0.00886323552990219656886323552990219656886
#define TANH_COEFF_13 0.00359212803657248101692546136990581435026
#define TANH_COEFF_15 -0.00145583438705131826824948518070211191904
double z2 = z * z;
double tanh_z =
((TANH_COEFF_5
* z2 + TANH_COEFF_3)
* z2 + TANH_COEFF_1)
* z;
double exp_y_minus_1 = 2.0 * tanh_z / (1.0 - tanh_z);
int n = (int) round (nm * (1.0 / 256.0));
int m = (int) nm - 256 * n;
/* expm1_table[i] = exp((i - 128) * log(2)/256) - 1.
Computed in GNU clisp through
(setf (long-float-digits) 128)
(setq a 0L0)
(setf (long-float-digits) 256)
(dotimes (i 257)
(format t " ~D,~%"
(float (- (exp (* (/ (- i 128) 256) (log 2L0))) 1) a))) */
static const double expm1_table[257] =
{
-0.292893218813452475599155637895150960716,
-0.290976057839792401079436677742323809165,
-0.289053698915417220095325702647879950038,
-0.287126127947252846596498423285616993819,
-0.285193330804014994382467110862430046956,
-0.283255293316105578740250215722626632811,
-0.281312001275508837198386957752147486471,
-0.279363440435687168635744042695052413926,
-0.277409596511476689981496879264164547161,
-0.275450455178982509740597294512888729286,
-0.273486002075473717576963754157712706214,
-0.271516222799278089184548475181393238264,
-0.269541102909676505674348554844689233423,
-0.267560627926797086703335317887720824384,
-0.265574783331509036569177486867109287348,
-0.263583554565316202492529493866889713058,
-0.261586927030250344306546259812975038038,
-0.259584886088764114771170054844048746036,
-0.257577417063623749727613604135596844722,
-0.255564505237801467306336402685726757248,
-0.253546135854367575399678234256663229163,
-0.251522294116382286608175138287279137577,
-0.2494929651867872398674385184702356751864,
-0.247458134188296727960327722100283867508,
-0.24541778620328863011699022448340323429,
-0.243371906273695048903181511842366886387,
-0.24132047940089265059510885341281062657,
-0.239263490545592708236869372901757573532,
-0.237200924627730846574373155241529522695,
-0.23513276652635648805745654063657412692,
-0.233059001079521999099699248246140670544,
-0.230979613084171535783261520405692115669,
-0.228894587296029588193854068954632579346,
-0.226803908429489222568744221853864674729,
-0.224707561157500020438486294646580877171,
-0.222605530111455713940842831198332609562,
-0.2204977998810815164831359552625710592544,
-0.218384355014321147927034632426122058645,
-0.2162651800172235534675441445217774245016,
-0.214140259353829315375718509234297186439,
-0.212009577446056756772364919909047495547,
-0.209873118673587736597751517992039478005,
-0.2077308673737531349400659265343210916196,
-0.205582807841418027883101951185666435317,
-0.2034289243288665510313756784404656320656,
-0.201269201045686450868589852895683430425,
-0.199103622158653323103076879204523186316,
-0.196932171791614537151556053482436428417,
-0.19475483402537284591023966632129970827,
-0.192571592897569679960015418424270885733,
-0.190382432402568125350119133273631796029,
-0.188187336491335584102392022226559177731,
-0.185986289071326116575890738992992661386,
-0.183779274006362464829286135533230759947,
-0.181566275116517756116147982921992768975,
-0.17934727617799688564586793151548689933,
-0.1771222609230175777406216376370887771665,
-0.1748912130396911245164132617275148983224,
-0.1726541161719028012138814282020908791644,
-0.170410953919191957302175212789218768074,
-0.168161709836631782476831771511804777363,
-0.165906367434708746670203829291463807099,
-0.1636449101792017131905953879307692887046,
-0.161377321491060724103867675441291294819,
-0.15910358474628545696887452376678510496,
-0.15682368327580335203567701228614769857,
-0.154537600365347409013071332406381692911,
-0.152245319255333652509541396360635796882,
-0.149946823140738265249318713251248832456,
-0.147642095170974388162796469615281683674,
-0.145331118449768586448102562484668501975,
-0.143013876035036980698187522160833990549,
-0.140690350938761042185327811771843747742,
-0.138360526126863051392482883127641270248,
-0.136024384519081218878475585385633792948,
-0.133681908988844467561490046485836530346,
-0.131333082363146875502898959063916619876,
-0.128977887422421778270943284404535317759,
-0.126616306900415529961291721709773157771,
-0.1242483234840609219490048572320697039866,
-0.121873919813350258443919690312343389353,
-0.1194930784812080879189542126763637438278,
-0.11710578203336358947830887503073906297,
-0.1147120129682226132300120925687579825894,
-0.1123117537367393737247203999003383961205,
-0.1099049867422877955201404475637647649574,
-0.1074916943405325099278897180135900838485,
-0.1050718588392995019970556101123417014993,
-0.102645462498446406786148378936109092823,
-0.1002124875297324539725723033374854302454,
-0.097772916096688059846161368344495155786,
-0.0953267303144840657307406742107731280055,
-0.092873912249800621875082699818829828767,
-0.0904144439206957158520284361718212536293,
-0.0879483072964733445019372468353990225585,
-0.0854754842975513284540160873038416459095,
-0.0829959567953287682564584052058555719614,
-0.080509706612053141143695628825336081184,
-0.078016715520687037466429613329061550362,
-0.075516965244774535807472733052603963221,
-0.073010437458307215803773464831151680239,
-0.070497113785589807692349282254427317595,
-0.067976975801105477595185454402763710658,
-0.0654500050293807475554878955602008567352,
-0.06291618294485004933500052502277673278,
-0.0603754909717199109794126487955155117284,
-0.0578279104838327751561896480162548451191,
-0.055273422804530448266460732621318468453,
-0.0527120092065171793298906732865376926237,
-0.0501436509117223676387482401930039000769,
-0.0475683290911628981746625337821392744829,
-0.044986024864805103778829470427200864833,
-0.0423967193014263530636943648520845560749,
-0.0398003934184762630513928111129293882558,
-0.0371970281819375355214808849088086316225,
-0.0345866045061864160477270517354652168038,
-0.0319691032538527747009720477166542375817,
-0.0293445052356798073922893825624102948152,
-0.0267127912103833568278979766786970786276,
-0.0240739418845108520444897665995250062307,
-0.0214279379122998654908388741865642544049,
-0.018774759895536286618755114942929674984,
-0.016114388383412110943633198761985316073,
-0.01344680387238284353202993186779328685225,
-0.0107719868060245158708750409344163322253,
-0.00808991757489031507008688867384418356197,
-0.00540057651636682434752231377783368554176,
-0.00270394391452987374234008615207739887604,
0.0,
0.00271127505020248543074558845036204047301,
0.0054299011128028213513839559347998147001,
0.00815589811841751578309489081720103927357,
0.0108892860517004600204097905618605243881,
0.01363008495148943884025892906393992959584,
0.0163783149109530379404931137862940627635,
0.0191339960777379496848780958207928793998,
0.0218971486541166782344801347832994397821,
0.0246677928971356451482890762708149276281,
0.0274459491187636965388611939222137814994,
0.0302316376860410128717079024539045670944,
0.0330248790212284225001082839704609180866,
0.0358256936019571200299832090180813718441,
0.0386341019613787906124366979546397325796,
0.0414501246883161412645460790118931264803,
0.0442737824274138403219664787399290087847,
0.0471050958792898661299072502271122405627,
0.049944085800687266082038126515907909062,
0.0527907730046263271198912029807463031904,
0.05564517836055715880834132515293865216,
0.0585073227945126901057721096837166450754,
0.0613772272892620809505676780038837262945,
0.0642549128844645497886112570015802206798,
0.0671404006768236181695211209928091626068,
0.070033711820241773542411936757623568504,
0.0729348675259755513850354508738275853402,
0.0758438890627910378032286484760570740623,
0.0787607977571197937406800374384829584908,
0.081685614993215201942115594422531125645,
0.0846183622133092378161051719066143416095,
0.0875590609177696653467978309440397078697,
0.090507732665257659207010655760707978993,
0.0934643990728858542282201462504471620805,
0.096429081816376823386138295859248481766,
0.099401802630221985463696968238829904039,
0.1023825833078409435564142094256468575113,
0.1053714457017412555882746962569503110404,
0.1083684117236786380094236494266198501387,
0.111373503344817603850149254228916637444,
0.1143867425958925363088129569196030678004,
0.1174081515673691990545799630857802666544,
0.120437752409606684429003879866313012766,
0.1234755673330198007337297397753214319548,
0.1265216186082418997947986437870347776336,
0.12957592856628814599726498884024982591,
0.1326385195987192279870737236776230843835,
0.135709414157805514240390330676117013429,
0.1387886347566916537038302838415112547204,
0.14187620396956162271229760828788093894,
0.144972144431804219394413888222915895793,
0.148076478840179006778799662697342680031,
0.15118922995298270581775963520198253612,
0.154310420590216039548221528724806960684,
0.157440073633751029613085766293796821108,
0.160578212027498746369459472576090986253,
0.163724858777577513813573599092185312343,
0.166880036952481570555516298414089287832,
0.1700437696832501880802590357927385730016,
0.1732160801636372475348043545132453888896,
0.176396991650281276284645728483848641053,
0.1795865274628759454861005667694405189764,
0.182784710984341029924457204693850757963,
0.185991565660993831371265649534215563735,
0.189207115002721066717499970560475915293,
0.192431382583151222142727558145431011481,
0.1956643920398273745838370498654519757025,
0.1989061670743804817703025579763002069494,
0.202156731452703142096396957497765876,
0.205416109005123825604211432558411335666,
0.208684323626581577354792255889216998483,
0.211961399276801194468168917732493045449,
0.2152473599804688781165202513387984576236,
0.218542229827408361758207148117394510722,
0.221846032972757516903891841911570785834,
0.225158793637145437709464594384845353705,
0.2284805361068700056940089577927818403626,
0.231811284734075935884556653212794816605,
0.235151063936933305692912507415415760296,
0.238499898199816567833368865859612431546,
0.241857812073484048593677468726595605511,
0.245224830175257932775204967486152674173,
0.248600977189204736621766097302495545187,
0.251986277866316270060206031789203597321,
0.255380757024691089579390657442301194598,
0.258784439549716443077860441815162618762,
0.262197350394250708014010258518416459672,
0.265619514578806324196273999873453036297,
0.269050957191733222554419081032338004715,
0.272491703389402751236692044184602176772,
0.27594177839639210038120243475928938891,
0.279401207505669226913587970027852545961,
0.282870016078778280726669781021514051111,
0.286348229546025533601482208069738348358,
0.289835873406665812232747295491552189677,
0.293332973229089436725559789048704304684,
0.296839554651009665933754117792451159835,
0.300355643379650651014140567070917791291,
0.303881265191935898574523648951997368331,
0.30741644593467724479715157747196172848,
0.310961211524764341922991786330755849366,
0.314515587949354658485983613383997794966,
0.318079601266063994690185647066116617661,
0.321653277603157514326511812330609226158,
0.325236643159741294629537095498721674113,
0.32882972420595439547865089632866510792,
0.33243254708316144935164337949073577407,
0.336045138204145773442627904371869759286,
0.339667524053303005360030669724352576023,
0.343299731186835263824217146181630875424,
0.346941786232945835788173713229537282073,
0.350593715892034391408522196060133960038,
0.354255546936892728298014740140702804344,
0.357927306212901046494536695671766697444,
0.361609020638224755585535938831941474643,
0.365300717204011815430698360337542855432,
0.369002422974590611929601132982192832168,
0.372714165087668369284997857144717215791,
0.376435970754530100216322805518686960261,
0.380167867260238095581945274358283464698,
0.383909881963831954872659527265192818003,
0.387662042298529159042861017950775988895,
0.391424375771926187149835529566243446678,
0.395196909966200178275574599249220994717,
0.398979672538311140209528136715194969206,
0.402772691220204706374713524333378817108,
0.40657599381901544248361973255451684411,
0.410389608217270704414375128268675481146,
0.414213562373095048801688724209698078569
};
double t = expm1_table[128 + m];
/* (1+t) * (1+exp_y_minus_1) - 1 = t + (1+t)*exp_y_minus_1 */
double p_minus_1 = t + (1.0 + t) * exp_y_minus_1;
double s = ldexp (1.0, n) - 1.0;
/* (1+s) * (1+p_minus_1) - 1 = s + (1+s)*p_minus_1 */
return s + (1.0 + s) * p_minus_1;
}
}
