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, 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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, 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