Merge pull request #504 from pocketpy/test-math-py34

[no ci] Add math tests from python 3.4

src/common/dmath.c

@@ -126,10 +126,11 @@ double dmath_log10(double x) {
 }
 
 double dmath_pow(double base, double exp) {
-    int exp_int = (int)exp;
+    int64_t exp_int = (int64_t)exp;
     if(exp_int == exp) {
         if(exp_int == 0) return 1;
         if(exp_int < 0) {
+			if(base == 0) return DMATH_NAN;
             base = 1 / base;
             exp_int = -exp_int;
         }
@@ -142,6 +143,7 @@ double dmath_pow(double base, double exp) {
         return res;
     }
     if (base > 0) {
+		if(base == 1.0) return 1.0;
         return dmath_exp(exp * dmath_log(base));
     }
     if (base == 0) {
@@ -462,6 +464,7 @@ static double zig_r64(double z) {
 
 // https://github.com/ziglang/zig/blob/master/lib/std/math/asin.zig
 double dmath_asin(double x) {
+	if(!(x >= -1 && x <= 1)) return DMATH_NAN;
     const double pio2_hi = 1.57079632679489655800e+00;
     const double pio2_lo = 6.12323399573676603587e-17;
 
@@ -526,20 +529,78 @@ double dmath_atan(double x) {
     return dmath_asin(x / dmath_sqrt(1 + x * x));
 }
 
-double dmath_atan2(double y, double x) {
-    if (x > 0) {
-        return dmath_atan(y / x);
-    } else if (x < 0 && y >= 0) {
-        return dmath_atan(y / x) + DMATH_PI;
-    } else if (x < 0 && y < 0) {
-        return dmath_atan(y / x) - DMATH_PI;
-    } else if (x == 0 && y > 0) {
-        return DMATH_PI / 2;
-    } else if (x == 0 && y < 0) {
-        return -DMATH_PI / 2;
-    } else {
-        return DMATH_NAN;
-    }
+double dmath_atan2(double y, double x)
+{
+	const double
+	pi     = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
+	pi_lo  = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+	double z;
+	uint32_t m,lx,ly,ix,iy;
+
+	if (dmath_isnan(x) || dmath_isnan(y))
+		return x+y;
+
+	// EXTRACT_WORDS(ix, lx, x);
+	// EXTRACT_WORDS(iy, ly, y);
+	union Float64Bits ux = { .f = x }, uy = { .f = y };
+	ix = (uint32_t)(ux.i >> 32);
+	iy = (uint32_t)(uy.i >> 32);
+	lx = (uint32_t)(ux.i & 0xFFFFFFFF);
+	ly = (uint32_t)(uy.i & 0xFFFFFFFF);
+
+	if ((ix-0x3ff00000 | lx) == 0)  /* x = 1.0 */
+		return dmath_atan(y);
+	m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
+	ix = ix & 0x7fffffff;
+	iy = iy & 0x7fffffff;
+
+	/* when y = 0 */
+	if ((iy|ly) == 0) {
+		switch(m) {
+		case 0:
+		case 1: return y;   /* atan(+-0,+anything)=+-0 */
+		case 2: return  pi; /* atan(+0,-anything) = pi */
+		case 3: return -pi; /* atan(-0,-anything) =-pi */
+		}
+	}
+	/* when x = 0 */
+	if ((ix|lx) == 0)
+		return m&1 ? -pi/2 : pi/2;
+	/* when x is INF */
+	if (ix == 0x7ff00000) {
+		if (iy == 0x7ff00000) {
+			switch(m) {
+			case 0: return  pi/4;   /* atan(+INF,+INF) */
+			case 1: return -pi/4;   /* atan(-INF,+INF) */
+			case 2: return  3*pi/4; /* atan(+INF,-INF) */
+			case 3: return -3*pi/4; /* atan(-INF,-INF) */
+			}
+		} else {
+			switch(m) {
+			case 0: return  0.0; /* atan(+...,+INF) */
+			case 1: return -0.0; /* atan(-...,+INF) */
+			case 2: return  pi;  /* atan(+...,-INF) */
+			case 3: return -pi;  /* atan(-...,-INF) */
+			}
+		}
+	}
+	/* |y/x| > 0x1p64 */
+	if (ix+(64<<20) < iy || iy == 0x7ff00000)
+		return m&1 ? -pi/2 : pi/2;
+
+	/* z = atan(|y/x|) without spurious underflow */
+	if ((m&2) && iy+(64<<20) < ix)  /* |y/x| < 0x1p-64, x<0 */
+		z = 0;
+	else
+		z = dmath_atan(dmath_fabs(y/x));
+	switch (m) {
+	case 0: return z;              /* atan(+,+) */
+	case 1: return -z;             /* atan(-,+) */
+	case 2: return pi - (z-pi_lo); /* atan(+,-) */
+	default: /* case 3 */
+		return (z-pi_lo) - pi; /* atan(-,-) */
+	}
 }
 
 ////////////////////////////////////////////////////////////////////
@@ -566,6 +627,8 @@ int dmath_isfinite(double x) {
 
 // https://github.com/kraj/musl/blob/kraj/master/src/math/fmod.c
 double dmath_fmod(double x, double y) {
+	if(y == 0) return DMATH_NAN;
+	
 	union Float64Bits ux = { .f = x }, uy = { .f = y };
 	int ex = ux.i>>52 & 0x7ff;
 	int ey = uy.i>>52 & 0x7ff;
@@ -644,7 +707,7 @@ double dmath_fabs(double x) {
 
 double dmath_ceil(double x) {
 	if(!dmath_isfinite(x)) return x;
-    int int_part = (int)x;
+    int64_t int_part = (int64_t)x;
     if (x > 0 && x != (double)int_part) {
         return (double)(int_part + 1);
     }
@@ -653,7 +716,7 @@ double dmath_ceil(double x) {
 
 double dmath_floor(double x) {
 	if(!dmath_isfinite(x)) return x;
-    int int_part = (int)x;
+    int64_t int_part = (int64_t)x;
     if (x < 0 && x != (double)int_part) {
         return (double)(int_part - 1);
     }
@@ -661,7 +724,7 @@ double dmath_floor(double x) {
 }
 
 double dmath_trunc(double x) {
-    return (double)((int)x);
+    return (double)((int64_t)x);
 }
 
 // https://github.com/kraj/musl/blob/kraj/master/src/math/modf.c

src/modules/math.c

@@ -2,7 +2,6 @@
 #include "pocketpy/common/dmath.h"
 #include "pocketpy/interpreter/vm.h"
 
-
 #define ONE_ARG_FUNC(name, func)                                                                   \
     static bool math_##name(int argc, py_Ref argv) {                                               \
         PY_CHECK_ARGC(1);                                                                          \
@@ -12,6 +11,15 @@
         return true;                                                                               \
     }
 
+#define ONE_ARG_INT_FUNC(name, func)                                                               \
+    static bool math_##name(int argc, py_Ref argv) {                                               \
+        PY_CHECK_ARGC(1);                                                                          \
+        double x;                                                                                  \
+        if(!py_castfloat(py_arg(0), &x)) return false;                                             \
+        py_newint(py_retval(), (py_i64)func(x));                                                   \
+        return true;                                                                               \
+    }
+
 #define ONE_ARG_BOOL_FUNC(name, func)                                                              \
     static bool math_##name(int argc, py_Ref argv) {                                               \
         PY_CHECK_ARGC(1);                                                                          \
@@ -31,10 +39,10 @@
         return true;                                                                               \
     }
 
-ONE_ARG_FUNC(ceil, dmath_ceil)
+ONE_ARG_INT_FUNC(ceil, dmath_ceil)
+ONE_ARG_INT_FUNC(floor, dmath_floor)
+ONE_ARG_INT_FUNC(trunc, dmath_trunc)
 ONE_ARG_FUNC(fabs, dmath_fabs)
-ONE_ARG_FUNC(floor, dmath_floor)
-ONE_ARG_FUNC(trunc, dmath_trunc)
 
 static bool math_fsum(int argc, py_Ref argv) {
     PY_CHECK_ARGC(1);
@@ -90,6 +98,10 @@ ONE_ARG_FUNC(exp, dmath_exp)
 static bool math_log(int argc, py_Ref argv) {
     double x;
     if(!py_castfloat(py_arg(0), &x)) return false;
+    if(x <= 0) {
+        py_newfloat(py_retval(), DMATH_NAN);
+        return true;
+    }
     if(argc == 1) {
         py_newfloat(py_retval(), dmath_log(x));
     } else if(argc == 2) {
@@ -104,9 +116,7 @@ static bool math_log(int argc, py_Ref argv) {
 
 ONE_ARG_FUNC(log2, dmath_log2)
 ONE_ARG_FUNC(log10, dmath_log10)
-
 TWO_ARG_FUNC(pow, dmath_pow)
-
 ONE_ARG_FUNC(sqrt, dmath_sqrt)
 
 ONE_ARG_FUNC(acos, dmath_acos)
@@ -135,8 +145,8 @@ static bool math_radians(int argc, py_Ref argv) {
     return true;
 }
 
-TWO_ARG_FUNC(fmod, dmath_fmod)
 TWO_ARG_FUNC(copysign, dmath_copysign)
+TWO_ARG_FUNC(fmod, dmath_fmod)
 
 static bool math_modf(int argc, py_Ref argv) {
     PY_CHECK_ARGC(1);

tests/931_math.py

@@ -0,0 +1,1059 @@
+# https://github.com/python/cpython/blob/v3.4.10/Lib/test/test_math.py
+
+# Python test set -- math module
+# XXXX Should not do tests around zero only
+
+import math
+import os
+import sys
+
+requires_IEEE_754 = lambda f: f
+
+eps = 1e-5
+NAN = float('nan')
+INF = float('inf')
+NINF = float('-inf')
+
+# detect evidence of double-rounding: fsum is not always correctly
+# rounded on machines that suffer from double rounding.
+x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer
+HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)
+print("HAVE_DOUBLE_ROUNDING =", HAVE_DOUBLE_ROUNDING)
+
+# locate file with test values
+# if __name__ == '__main__':
+#     file = sys.argv[0]
+# else:
+#     file = __file__
+
+math_testcases = 'tests/math_testcases.txt'
+test_file = 'tests/cmath_testcases.txt'
+
+def to_ulps(x):
+    """Convert a non-NaN float x to an integer, in such a way that
+    adjacent floats are converted to adjacent integers.  Then
+    abs(ulps(x) - ulps(y)) gives the difference in ulps between two
+    floats.
+
+    The results from this function will only make sense on platforms
+    where C doubles are represented in IEEE 754 binary64 format.
+
+    """
+    n = struct.unpack('<q', struct.pack('<d', x))[0] # type: ignore
+    if n < 0:
+        n = ~(n+2**63)
+    return n
+
+def ulps_check(expected, got, ulps=20):
+    if abs(expected - got) > eps:
+        return "error = {}; permitted error = {}".format(got - expected, eps)
+    return
+
+    """Given non-NaN floats `expected` and `got`,
+    check that they're equal to within the given number of ulps.
+
+    Returns None on success and an error message on failure."""
+
+    ulps_error = to_ulps(got) - to_ulps(expected)
+    if abs(ulps_error) <= ulps:
+        return None
+    return "error = {} ulps; permitted error = {} ulps".format(ulps_error,
+                                                               ulps)
+
+# Here's a pure Python version of the math.factorial algorithm, for
+# documentation and comparison purposes.
+#
+# Formula:
+#
+#   factorial(n) = factorial_odd_part(n) << (n - count_set_bits(n))
+#
+# where
+#
+#   factorial_odd_part(n) = product_{i >= 0} product_{0 < j <= n >> i; j odd} j
+#
+# The outer product above is an infinite product, but once i >= n.bit_length,
+# (n >> i) < 1 and the corresponding term of the product is empty.  So only the
+# finitely many terms for 0 <= i < n.bit_length() contribute anything.
+#
+# We iterate downwards from i == n.bit_length() - 1 to i == 0.  The inner
+# product in the formula above starts at 1 for i == n.bit_length(); for each i
+# < n.bit_length() we get the inner product for i from that for i + 1 by
+# multiplying by all j in {n >> i+1 < j <= n >> i; j odd}.  In Python terms,
+# this set is range((n >> i+1) + 1 | 1, (n >> i) + 1 | 1, 2).
+
+def count_set_bits(n):
+    """Number of '1' bits in binary expansion of a nonnnegative integer."""
+    return 1 + count_set_bits(n & n - 1) if n else 0
+
+def partial_product(start, stop):
+    """Product of integers in range(start, stop, 2), computed recursively.
+    start and stop should both be odd, with start <= stop.
+
+    """
+    numfactors = (stop - start) >> 1
+    if not numfactors:
+        return 1
+    elif numfactors == 1:
+        return start
+    else:
+        mid = (start + numfactors) | 1
+        return partial_product(start, mid) * partial_product(mid, stop)
+
+def py_factorial(n):
+    """Factorial of nonnegative integer n, via "Binary Split Factorial Formula"
+    described at http://www.luschny.de/math/factorial/binarysplitfact.html
+
+    """
+    inner = outer = 1
+    for i in reversed(range(n.bit_length())):
+        inner *= partial_product((n >> i + 1) + 1 | 1, (n >> i) + 1 | 1)
+        outer *= inner
+    return outer << (n - count_set_bits(n))
+
+def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323):
+    """Determine whether non-NaN floats a and b are equal to within a
+    (small) rounding error.  The default values for rel_err and
+    abs_err are chosen to be suitable for platforms where a float is
+    represented by an IEEE 754 double.  They allow an error of between
+    9 and 19 ulps."""
+
+    # need to special case infinities, since inf - inf gives nan
+    if math.isinf(expected) and got == expected:
+        return None
+
+    error = got - expected
+
+    permitted_error = max(abs_err, rel_err * abs(expected))
+    if abs(error) < permitted_error:
+        return None
+    return "error = {}; permitted error = {}".format(error,
+                                                     permitted_error)
+
+def parse_mtestfile(fname):
+    """Parse a file with test values
+
+    -- starts a comment
+    blank lines, or lines containing only a comment, are ignored
+    other lines are expected to have the form
+      id fn arg -> expected [flag]*
+
+    """
+    with open(fname, 'rt') as fp:
+        for line in fp.read().split('\n'):
+            # strip comments, and skip blank lines
+            if '--' in line:
+                line = line[:line.index('--')]
+            if not line.strip():
+                continue
+
+            lhs, rhs = line.split('->')
+            id, fn, arg = lhs.split()
+            rhs_pieces = rhs.split()
+            exp = rhs_pieces[0]
+            flags = rhs_pieces[1:]
+
+            yield (id, fn, float(arg), float(exp), flags)
+
+def parse_testfile(fname):
+    """Parse a file with test values
+
+    Empty lines or lines starting with -- are ignored
+    yields id, fn, arg_real, arg_imag, exp_real, exp_imag
+    """
+    with open(fname, 'rt') as fp:
+        for line in fp.read().split('\n'):
+            # skip comment lines and blank lines
+            if line.startswith('--') or not line.strip():
+                continue
+
+            lhs, rhs = line.split('->')
+            id, fn, arg_real, arg_imag = lhs.split()
+            rhs_pieces = rhs.split()
+            exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
+            flags = rhs_pieces[2:]
+
+            yield (id, fn,
+                   float(arg_real), float(arg_imag),
+                   float(exp_real), float(exp_imag),
+                   flags
+                  )
+
+
+class TestCase:
+    def fail(self, msg):
+        print(msg)
+        # assert False
+        exit(1)
+    
+    def assertEqual(self, a, b):
+        if a != b:
+            self.fail(f'{a!r} != {b!r}')
+
+    def assertAlmostEqual(self, a, b):
+        tol = eps
+        if abs(a-b) > tol:
+            self.fail(f'{a!r} != {b!r} within {tol!r}')
+
+    def assertRaises(self, exc, func, *args, **kwargs):
+        try:
+            func(*args, **kwargs)
+            self.fail(f'Expected {exc} but no exception was raised')
+        except exc:
+            return
+        except Exception as e:
+            self.fail(f'Expected {exc} but got {type(e)}: {e}')            
+
+    def assertNaN(self, x):
+        if not math.isnan(x):
+            self.fail(f'{x!r} is not NaN')
+
+    def assertTrue(self, x):
+        if not x:
+            self.fail(f'{x!r} is not true')
+
+    def assertFalse(self, x):
+        if x:
+            self.fail(f'{x!r} is not false')
+    
+    def assertIs(self, a, b):
+        if a is not b:
+            self.fail(f'{a!r} is not {b!r}')
+
+
+class TestCeil:
+    def __ceil__(self):
+        return 42
+class TestNoCeil:
+    pass
+class TestFloor:
+    def __floor__(self):
+        return 42
+class TestNoFloor:
+    pass
+class TestTrunc(object):
+    def __trunc__(self):
+        return 23
+class TestNoTrunc(object):
+    pass
+
+class MathTests(TestCase):
+
+    def ftest(self, name, value, expected):
+        if abs(value-expected) > eps:
+            # Use %r instead of %f so the error message
+            # displays full precision. Otherwise discrepancies
+            # in the last few bits will lead to very confusing
+            # error messages
+            self.fail('%s returned %r, expected %r' %
+                      (name, value, expected))
+
+    def testConstants(self):
+        self.ftest('pi', math.pi, 3.1415926)
+        self.ftest('e', math.e, 2.7182818)
+
+    def testAcos(self):
+        self.assertRaises(TypeError, math.acos)
+        self.ftest('acos(-1)', math.acos(-1), math.pi)
+        self.ftest('acos(0)', math.acos(0), math.pi/2)
+        self.ftest('acos(1)', math.acos(1), 0)
+        self.assertNaN(math.acos(INF))
+        self.assertNaN(math.acos(NINF))
+        self.assertTrue(math.isnan(math.acos(NAN)))
+
+    def testAcosh(self):
+        return
+        self.assertRaises(TypeError, math.acosh)
+        self.ftest('acosh(1)', math.acosh(1), 0)
+        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
+        self.assertRaises(ValueError, math.acosh, 0)
+        self.assertRaises(ValueError, math.acosh, -1)
+        self.assertEqual(math.acosh(INF), INF)
+        self.assertRaises(ValueError, math.acosh, NINF)
+        self.assertTrue(math.isnan(math.acosh(NAN)))
+
+    def testAsin(self):
+        self.assertRaises(TypeError, math.asin)
+        self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
+        self.ftest('asin(0)', math.asin(0), 0)
+        self.ftest('asin(1)', math.asin(1), math.pi/2)
+        self.assertNaN(math.asin(INF))
+        self.assertNaN(math.asin(NINF))
+        self.assertTrue(math.isnan(math.asin(NAN)))
+
+    def testAsinh(self):
+        return
+        self.assertRaises(TypeError, math.asinh)
+        self.ftest('asinh(0)', math.asinh(0), 0)
+        self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
+        self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
+        self.assertEqual(math.asinh(INF), INF)
+        self.assertEqual(math.asinh(NINF), NINF)
+        self.assertTrue(math.isnan(math.asinh(NAN)))
+
+    def testAtan(self):
+        self.assertRaises(TypeError, math.atan)
+        self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
+        self.ftest('atan(0)', math.atan(0), 0)
+        self.ftest('atan(1)', math.atan(1), math.pi/4)
+        self.ftest('atan(inf)', math.atan(INF), math.pi/2)
+        self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
+        self.assertTrue(math.isnan(math.atan(NAN)))
+
+    def testAtanh(self):
+        return
+        self.assertRaises(TypeError, math.atan)
+        self.ftest('atanh(0)', math.atanh(0), 0)
+        self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
+        self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
+        self.assertRaises(ValueError, math.atanh, 1)
+        self.assertRaises(ValueError, math.atanh, -1)
+        self.assertRaises(ValueError, math.atanh, INF)
+        self.assertRaises(ValueError, math.atanh, NINF)
+        self.assertTrue(math.isnan(math.atanh(NAN)))
+
+    def testAtan2(self):
+        self.assertRaises(TypeError, math.atan2)
+        self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
+        self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
+        self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
+        self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
+        self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
+
+        # math.atan2(0, x)
+        self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
+        self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
+        self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
+        self.assertEqual(math.atan2(0., 0.), 0.)
+        self.assertEqual(math.atan2(0., 2.3), 0.)
+        self.assertEqual(math.atan2(0., INF), 0.)
+        self.assertTrue(math.isnan(math.atan2(0., NAN)))
+        # math.atan2(-0, x)
+        self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
+        self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
+        self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
+        self.assertEqual(math.atan2(-0., 0.), -0.)
+        self.assertEqual(math.atan2(-0., 2.3), -0.)
+        self.assertEqual(math.atan2(-0., INF), -0.)
+        self.assertTrue(math.isnan(math.atan2(-0., NAN)))
+        # math.atan2(INF, x)
+        self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
+        self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
+        self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
+        self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
+        self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
+        self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
+        self.assertTrue(math.isnan(math.atan2(INF, NAN)))
+        # math.atan2(NINF, x)
+        self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
+        self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
+        self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
+        self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
+        self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
+        self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
+        self.assertTrue(math.isnan(math.atan2(NINF, NAN)))
+        # math.atan2(+finite, x)
+        self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
+        self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
+        self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
+        self.assertEqual(math.atan2(2.3, INF), 0.)
+        self.assertTrue(math.isnan(math.atan2(2.3, NAN)))
+        # math.atan2(-finite, x)
+        self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
+        self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
+        self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
+        self.assertEqual(math.atan2(-2.3, INF), -0.)
+        self.assertTrue(math.isnan(math.atan2(-2.3, NAN)))
+        # math.atan2(NAN, x)
+        self.assertTrue(math.isnan(math.atan2(NAN, NINF)))
+        self.assertTrue(math.isnan(math.atan2(NAN, -2.3)))
+        self.assertTrue(math.isnan(math.atan2(NAN, -0.)))
+        self.assertTrue(math.isnan(math.atan2(NAN, 0.)))
+        self.assertTrue(math.isnan(math.atan2(NAN, 2.3)))
+        self.assertTrue(math.isnan(math.atan2(NAN, INF)))
+        self.assertTrue(math.isnan(math.atan2(NAN, NAN)))
+
+    def testCeil(self):
+        self.assertRaises(TypeError, math.ceil)
+        self.assertEqual(int, type(math.ceil(0.5)))
+        self.ftest('ceil(0.5)', math.ceil(0.5), 1)
+        self.ftest('ceil(1.0)', math.ceil(1.0), 1)
+        self.ftest('ceil(1.5)', math.ceil(1.5), 2)
+        self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
+        self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
+        self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
+        #self.assertEqual(math.ceil(INF), INF)
+        #self.assertEqual(math.ceil(NINF), NINF)
+        #self.assertTrue(math.isnan(math.ceil(NAN)))
+
+        if 0:
+            self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
+            self.assertRaises(TypeError, math.ceil, TestNoCeil())
+
+            t = TestNoCeil()
+            t.__ceil__ = lambda *args: args # type: ignore
+            self.assertRaises(TypeError, math.ceil, t)
+            self.assertRaises(TypeError, math.ceil, t, 0)
+
+    @requires_IEEE_754
+    def testCopysign(self):
+        self.assertEqual(math.copysign(1, 42), 1.0)
+        self.assertEqual(math.copysign(0., 42), 0.0)
+        self.assertEqual(math.copysign(1., -42), -1.0)
+        self.assertEqual(math.copysign(3, 0.), 3.0)
+        self.assertEqual(math.copysign(4., -0.), -4.0)
+
+        self.assertRaises(TypeError, math.copysign)
+        # copysign should let us distinguish signs of zeros
+        self.assertEqual(math.copysign(1., 0.), 1.)
+        self.assertEqual(math.copysign(1., -0.), -1.)
+        self.assertEqual(math.copysign(INF, 0.), INF)
+        self.assertEqual(math.copysign(INF, -0.), NINF)
+        self.assertEqual(math.copysign(NINF, 0.), INF)
+        self.assertEqual(math.copysign(NINF, -0.), NINF)
+        # and of infinities
+        self.assertEqual(math.copysign(1., INF), 1.)
+        self.assertEqual(math.copysign(1., NINF), -1.)
+        self.assertEqual(math.copysign(INF, INF), INF)
+        self.assertEqual(math.copysign(INF, NINF), NINF)
+        self.assertEqual(math.copysign(NINF, INF), INF)
+        self.assertEqual(math.copysign(NINF, NINF), NINF)
+        self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
+        self.assertTrue(math.isnan(math.copysign(NAN, INF)))
+        self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
+        self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
+        # copysign(INF, NAN) may be INF or it may be NINF, since
+        # we don't know whether the sign bit of NAN is set on any
+        # given platform.
+        self.assertTrue(math.isinf(math.copysign(INF, NAN)))
+        # similarly, copysign(2., NAN) could be 2. or -2.
+        self.assertEqual(abs(math.copysign(2., NAN)), 2.)
+
+    def testCos(self):
+        self.assertRaises(TypeError, math.cos)
+        self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
+        self.ftest('cos(0)', math.cos(0), 1)
+        self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
+        self.ftest('cos(pi)', math.cos(math.pi), -1)
+        try:
+            self.assertTrue(math.isnan(math.cos(INF)))
+            self.assertTrue(math.isnan(math.cos(NINF)))
+        except ValueError:
+            self.assertRaises(ValueError, math.cos, INF)
+            self.assertRaises(ValueError, math.cos, NINF)
+        self.assertTrue(math.isnan(math.cos(NAN)))
+
+    def testCosh(self):
+        return
+        self.assertRaises(TypeError, math.cosh)
+        self.ftest('cosh(0)', math.cosh(0), 1)
+        self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
+        self.assertEqual(math.cosh(INF), INF)
+        self.assertEqual(math.cosh(NINF), INF)
+        self.assertTrue(math.isnan(math.cosh(NAN)))
+
+    def testDegrees(self):
+        self.assertRaises(TypeError, math.degrees)
+        self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
+        self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
+        self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
+
+    def testExp(self):
+        self.assertRaises(TypeError, math.exp)
+        self.ftest('exp(-1)', math.exp(-1), 1/math.e)
+        self.ftest('exp(0)', math.exp(0), 1)
+        self.ftest('exp(1)', math.exp(1), math.e)
+        self.assertEqual(math.exp(INF), INF)
+        self.assertEqual(math.exp(NINF), 0.)
+        self.assertTrue(math.isnan(math.exp(NAN)))
+
+    def testFabs(self):
+        self.assertRaises(TypeError, math.fabs)
+        self.ftest('fabs(-1)', math.fabs(-1), 1)
+        self.ftest('fabs(0)', math.fabs(0), 0)
+        self.ftest('fabs(1)', math.fabs(1), 1)
+
+    def testFactorial(self):
+        self.assertEqual(math.factorial(0), 1)
+        # self.assertEqual(math.factorial(0.0), 1)
+        total = 1
+        for i in range(1, 20):
+            total *= i
+            self.assertEqual(math.factorial(i), total)
+            # self.assertEqual(math.factorial(float(i)), total)
+            self.assertEqual(math.factorial(i), py_factorial(i))
+        self.assertRaises(ValueError, math.factorial, -1)
+        # self.assertRaises(ValueError, math.factorial, -1.0)
+        # self.assertRaises(ValueError, math.factorial, math.pi)
+        # self.assertRaises(OverflowError, math.factorial, sys.maxsize+1)
+        # self.assertRaises(OverflowError, math.factorial, 10e100)
+
+    def testFloor(self):
+        self.assertRaises(TypeError, math.floor)
+        self.assertEqual(int, type(math.floor(0.5)))
+        self.ftest('floor(0.5)', math.floor(0.5), 0)
+        self.ftest('floor(1.0)', math.floor(1.0), 1)
+        self.ftest('floor(1.5)', math.floor(1.5), 1)
+        self.ftest('floor(-0.5)', math.floor(-0.5), -1)
+        self.ftest('floor(-1.0)', math.floor(-1.0), -1)
+        self.ftest('floor(-1.5)', math.floor(-1.5), -2)
+        # pow() relies on floor() to check for integers
+        # This fails on some platforms - so check it here
+        # self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
+        # self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
+        #self.assertEqual(math.ceil(INF), INF)
+        #self.assertEqual(math.ceil(NINF), NINF)
+        #self.assertTrue(math.isnan(math.floor(NAN)))
+
+        if 0:
+            self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
+            self.assertRaises(TypeError, math.floor, TestNoFloor())
+
+            t = TestNoFloor()
+            t.__floor__ = lambda *args: args # type: ignore
+            self.assertRaises(TypeError, math.floor, t)
+            self.assertRaises(TypeError, math.floor, t, 0)
+
+    def testFmod(self):
+        self.assertRaises(TypeError, math.fmod)
+        self.ftest('fmod(10, 1)', math.fmod(10, 1), 0.0)
+        self.ftest('fmod(10, 0.5)', math.fmod(10, 0.5), 0.0)
+        self.ftest('fmod(10, 1.5)', math.fmod(10, 1.5), 1.0)
+        self.ftest('fmod(-10, 1)', math.fmod(-10, 1), -0.0)
+        self.ftest('fmod(-10, 0.5)', math.fmod(-10, 0.5), -0.0)
+        self.ftest('fmod(-10, 1.5)', math.fmod(-10, 1.5), -1.0)
+        self.assertTrue(math.isnan(math.fmod(NAN, 1.)))
+        self.assertTrue(math.isnan(math.fmod(1., NAN)))
+        self.assertTrue(math.isnan(math.fmod(NAN, NAN)))
+        self.assertNaN(math.fmod(1., 0.))
+        self.assertNaN(math.fmod(INF, 1.))
+        self.assertNaN(math.fmod(NINF, 1.))
+        self.assertNaN(math.fmod(INF, 0.))
+        self.assertEqual(math.fmod(3.0, INF), 3.0)
+        self.assertEqual(math.fmod(-3.0, INF), -3.0)
+        self.assertEqual(math.fmod(3.0, NINF), 3.0)
+        self.assertEqual(math.fmod(-3.0, NINF), -3.0)
+        self.assertEqual(math.fmod(0.0, 3.0), 0.0)
+        self.assertEqual(math.fmod(0.0, NINF), 0.0)
+
+    def testFrexp(self):
+        return
+        self.assertRaises(TypeError, math.frexp)
+
+        def testfrexp(name, result, expected):
+            (mant, exp), (emant, eexp) = result, expected
+            if abs(mant-emant) > eps or exp != eexp:
+                self.fail('%s returned %r, expected %r'%\
+                          (name, result, expected))
+
+        testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
+        testfrexp('frexp(0)', math.frexp(0), (0, 0))
+        testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
+        testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
+
+        self.assertEqual(math.frexp(INF)[0], INF)
+        self.assertEqual(math.frexp(NINF)[0], NINF)
+        self.assertTrue(math.isnan(math.frexp(NAN)[0]))
+
+    @requires_IEEE_754
+    def testFsum(self):
+        return
+
+    def testHypot(self):
+        return
+        self.assertRaises(TypeError, math.hypot)
+        self.ftest('hypot(0,0)', math.hypot(0,0), 0)
+        self.ftest('hypot(3,4)', math.hypot(3,4), 5)
+        self.assertEqual(math.hypot(NAN, INF), INF)
+        self.assertEqual(math.hypot(INF, NAN), INF)
+        self.assertEqual(math.hypot(NAN, NINF), INF)
+        self.assertEqual(math.hypot(NINF, NAN), INF)
+        self.assertTrue(math.isnan(math.hypot(1.0, NAN)))
+        self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))
+
+    def testLdexp(self):
+        return
+        self.assertRaises(TypeError, math.ldexp)
+        self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
+        self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
+        self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
+        self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
+        self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
+        self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
+        self.assertEqual(math.ldexp(1., -1000000), 0.)
+        self.assertEqual(math.ldexp(-1., -1000000), -0.)
+        self.assertEqual(math.ldexp(INF, 30), INF)
+        self.assertEqual(math.ldexp(NINF, -213), NINF)
+        self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
+
+        # large second argument
+        for n in [10**5, 10**10, 10**20, 10**40]:
+            self.assertEqual(math.ldexp(INF, -n), INF)
+            self.assertEqual(math.ldexp(NINF, -n), NINF)
+            self.assertEqual(math.ldexp(1., -n), 0.)
+            self.assertEqual(math.ldexp(-1., -n), -0.)
+            self.assertEqual(math.ldexp(0., -n), 0.)
+            self.assertEqual(math.ldexp(-0., -n), -0.)
+            self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
+
+            self.assertRaises(OverflowError, math.ldexp, 1., n)
+            self.assertRaises(OverflowError, math.ldexp, -1., n)
+            self.assertEqual(math.ldexp(0., n), 0.)
+            self.assertEqual(math.ldexp(-0., n), -0.)
+            self.assertEqual(math.ldexp(INF, n), INF)
+            self.assertEqual(math.ldexp(NINF, n), NINF)
+            self.assertTrue(math.isnan(math.ldexp(NAN, n)))
+
+    def testLog(self):
+        self.assertRaises(TypeError, math.log)
+        self.ftest('log(1/e)', math.log(1/math.e), -1)
+        self.ftest('log(1)', math.log(1), 0)
+        self.ftest('log(e)', math.log(math.e), 1)
+        self.ftest('log(32,2)', math.log(32,2), 5)
+        self.ftest('log(10**4, 10)', math.log(10**4, 10), 4)
+        # self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
+        # self.ftest('log(10**1000)', math.log(10**1000), 2302.5850929940457)
+        self.assertNaN(math.log(-1.5))
+        self.assertNaN(math.log(-10**10))
+        self.assertNaN(math.log(NINF))
+        self.assertEqual(math.log(INF), INF)
+        self.assertTrue(math.isnan(math.log(NAN)))
+
+    def testLog1p(self):
+        return
+        self.assertRaises(TypeError, math.log1p)
+        n= 2**90
+        self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))
+
+    @requires_IEEE_754
+    def testLog2(self):
+        self.assertRaises(TypeError, math.log2)
+
+        # Check some integer values
+        self.assertEqual(math.log2(1), 0.0)
+        self.assertEqual(math.log2(2), 1.0)
+        self.assertEqual(math.log2(4), 2.0)
+
+        # Large integer values
+        self.assertEqual(math.log2(2**23), 23.0)
+        self.assertEqual(math.log2(2**24), 24.0)
+        self.assertEqual(math.log2(2**20), 20.0)
+
+        self.assertNaN(math.log2(-1.5))
+        self.assertNaN(math.log2(NINF))
+        self.assertNaN(math.log2(NAN))
+
+    @requires_IEEE_754
+    # log2() is not accurate enough on Mac OS X Tiger (10.4)
+    # @support.requires_mac_ver(10, 5)
+    def testLog2Exact(self):
+        return
+        # Check that we get exact equality for log2 of powers of 2.
+        actual = [math.log2(math.ldexp(1.0, n)) for n in range(-1074, 1024)]
+        expected = [float(n) for n in range(-1074, 1024)]
+        self.assertEqual(actual, expected)
+
+    def testLog10(self):
+        self.assertRaises(TypeError, math.log10)
+        self.ftest('log10(0.1)', math.log10(0.1), -1)
+        self.ftest('log10(1)', math.log10(1), 0)
+        self.ftest('log10(10)', math.log10(10), 1)
+        self.ftest('log10(10**4)', math.log10(10**4), 4)
+        self.assertNaN(math.log10(-1.5))
+        self.assertNaN(math.log10(-10**4))
+        self.assertNaN(math.log10(NINF))
+        self.assertEqual(math.log(INF), INF)
+        self.assertTrue(math.isnan(math.log10(NAN)))
+
+    def testModf(self):
+        self.assertRaises(TypeError, math.modf)
+
+        def testmodf(name, result, expected):
+            (v1, v2), (e1, e2) = result, expected
+            if abs(v1-e1) > eps or abs(v2-e2):
+                self.fail('%s returned %r, expected %r'%\
+                          (name, result, expected))
+
+        testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
+        testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
+
+        self.assertEqual(math.modf(INF), (0.0, INF))
+        self.assertEqual(math.modf(NINF), (-0.0, NINF))
+
+        modf_nan = math.modf(NAN)
+        self.assertTrue(math.isnan(modf_nan[0]))
+        self.assertTrue(math.isnan(modf_nan[1]))
+
+    def testPow(self):
+        self.assertRaises(TypeError, math.pow)
+        self.ftest('pow(0,1)', math.pow(0,1), 0)
+        self.ftest('pow(1,0)', math.pow(1,0), 1)
+        self.ftest('pow(2,1)', math.pow(2,1), 2)
+        self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
+        self.assertEqual(math.pow(INF, 1), INF)
+        self.assertEqual(math.pow(NINF, 1), NINF)
+        self.assertEqual((math.pow(1, INF)), 1.)
+        self.assertEqual((math.pow(1, NINF)), 1.)
+        self.assertTrue(math.isnan(math.pow(NAN, 1)))
+        self.assertTrue(math.isnan(math.pow(2, NAN)))
+        self.assertTrue(math.isnan(math.pow(0, NAN)))
+        self.assertEqual(math.pow(1, NAN), 1)
+
+        # pow(0., x)
+        self.assertEqual(math.pow(0., INF), 0.)
+        self.assertEqual(math.pow(0., 3.), 0.)
+        self.assertEqual(math.pow(0., 2.3), 0.)
+        self.assertEqual(math.pow(0., 2.), 0.)
+        self.assertEqual(math.pow(0., 0.), 1.)
+        self.assertEqual(math.pow(0., -0.), 1.)
+
+        # self.assertRaises(ValueError, math.pow, 0., -2.)
+        # self.assertRaises(ValueError, math.pow, 0., -2.3)
+        # self.assertRaises(ValueError, math.pow, 0., -3.)
+        # self.assertRaises(ValueError, math.pow, 0., NINF)
+        self.assertTrue(math.isnan(math.pow(0., -2.)))
+        self.assertTrue(math.isnan(math.pow(0., -2.3)))
+        self.assertTrue(math.isnan(math.pow(0., -3.)))
+        self.assertTrue(math.isnan(math.pow(0., NINF)))
+
+        self.assertTrue(math.isnan(math.pow(0., NAN)))
+
+        # pow(INF, x)
+        self.assertEqual(math.pow(INF, INF), INF)
+        self.assertEqual(math.pow(INF, 3.), INF)
+        self.assertEqual(math.pow(INF, 2.3), INF)
+        self.assertEqual(math.pow(INF, 2.), INF)
+        self.assertEqual(math.pow(INF, 0.), 1.)
+        self.assertEqual(math.pow(INF, -0.), 1.)
+        self.assertEqual(math.pow(INF, -2.), 0.)
+        self.assertEqual(math.pow(INF, -2.3), 0.)
+        self.assertEqual(math.pow(INF, -3.), 0.)
+        self.assertEqual(math.pow(INF, NINF), 0.)
+        self.assertTrue(math.isnan(math.pow(INF, NAN)))
+
+        # pow(-0., x)
+        self.assertEqual(math.pow(-0., INF), 0.)
+        self.assertEqual(math.pow(-0., 3.), -0.)
+        self.assertEqual(math.pow(-0., 2.3), 0.)
+        self.assertEqual(math.pow(-0., 2.), 0.)
+        self.assertEqual(math.pow(-0., 0.), 1.)
+        self.assertEqual(math.pow(-0., -0.), 1.)
+        # self.assertRaises(ValueError, math.pow, -0., -2.)
+        # self.assertRaises(ValueError, math.pow, -0., -2.3)
+        # self.assertRaises(ValueError, math.pow, -0., -3.)
+        # self.assertRaises(ValueError, math.pow, -0., NINF)
+        self.assertTrue(math.isnan(math.pow(-0., NAN)))
+
+        # pow(NINF, x)
+        if 0:
+            self.assertEqual(math.pow(NINF, INF), INF)
+            self.assertEqual(math.pow(NINF, 3.), NINF)
+            self.assertEqual(math.pow(NINF, 2.3), INF)
+            self.assertEqual(math.pow(NINF, 2.), INF)
+            self.assertEqual(math.pow(NINF, 0.), 1.)
+            self.assertEqual(math.pow(NINF, -0.), 1.)
+            self.assertEqual(math.pow(NINF, -2.), 0.)
+            self.assertEqual(math.pow(NINF, -2.3), 0.)
+            self.assertEqual(math.pow(NINF, -3.), -0.)
+            self.assertEqual(math.pow(NINF, NINF), 0.)
+            self.assertTrue(math.isnan(math.pow(NINF, NAN)))
+
+        # pow(-1, x)
+        self.assertEqual(math.pow(-1., 3.), -1.)
+        # self.assertRaises(ValueError, math.pow, -1., 2.3)
+        self.assertTrue(math.isnan(math.pow(-1., 2.3)))
+        self.assertEqual(math.pow(-1., 2.), 1.)
+        self.assertEqual(math.pow(-1., 0.), 1.)
+        self.assertEqual(math.pow(-1., -0.), 1.)
+        self.assertEqual(math.pow(-1., -2.), 1.)
+        # self.assertRaises(ValueError, math.pow, -1., -2.3)
+        self.assertTrue(math.isnan(math.pow(-1., -2.3)))
+        self.assertEqual(math.pow(-1., -3.), -1.)
+        self.assertTrue(math.isnan(math.pow(-1., NAN)))
+
+        # pow(1, x)
+        self.assertEqual(math.pow(1., INF), 1.)
+        self.assertEqual(math.pow(1., 3.), 1.)
+        self.assertEqual(math.pow(1., 2.3), 1.)
+        self.assertEqual(math.pow(1., 2.), 1.)
+        self.assertEqual(math.pow(1., 0.), 1.)
+        self.assertEqual(math.pow(1., -0.), 1.)
+        self.assertEqual(math.pow(1., -2.), 1.)
+        self.assertEqual(math.pow(1., -2.3), 1.)
+        self.assertEqual(math.pow(1., -3.), 1.)
+        self.assertEqual(math.pow(1., NINF), 1.)
+        self.assertEqual(math.pow(1., NAN), 1.)
+
+        # pow(x, 0) should be 1 for any x
+        self.assertEqual(math.pow(2.3, 0.), 1.)
+        self.assertEqual(math.pow(-2.3, 0.), 1.)
+        self.assertEqual(math.pow(NAN, 0.), 1.)
+        self.assertEqual(math.pow(2.3, -0.), 1.)
+        self.assertEqual(math.pow(-2.3, -0.), 1.)
+        self.assertEqual(math.pow(NAN, -0.), 1.)
+
+        # pow(x, y) is invalid if x is negative and y is not integral
+        # self.assertRaises(ValueError, math.pow, -1., 2.3)
+        # self.assertRaises(ValueError, math.pow, -15., -3.1)
+        self.assertTrue(math.isnan(math.pow(-1., 2.3)))
+        self.assertTrue(math.isnan(math.pow(-15., -3.1)))
+
+        # pow(x, NINF)
+        self.assertEqual(math.pow(1.9, NINF), 0.)
+        self.assertEqual(math.pow(1.1, NINF), 0.)
+        self.assertEqual(math.pow(0.9, NINF), INF)
+        self.assertEqual(math.pow(0.1, NINF), INF)
+        # self.assertEqual(math.pow(-0.1, NINF), INF)
+        # self.assertEqual(math.pow(-0.9, NINF), INF)
+        # self.assertEqual(math.pow(-1.1, NINF), 0.)
+        # self.assertEqual(math.pow(-1.9, NINF), 0.)
+
+        # pow(x, INF)
+        self.assertEqual(math.pow(1.9, INF), INF)
+        self.assertEqual(math.pow(1.1, INF), INF)
+        self.assertEqual(math.pow(0.9, INF), 0.)
+        self.assertEqual(math.pow(0.1, INF), 0.)
+        # self.assertEqual(math.pow(-0.1, INF), 0.)
+        # self.assertEqual(math.pow(-0.9, INF), 0.)
+        # self.assertEqual(math.pow(-1.1, INF), INF)
+        # self.assertEqual(math.pow(-1.9, INF), INF)
+
+        # pow(x, y) should work for x negative, y an integer
+        self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
+        self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
+        self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
+        self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
+        self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
+        self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
+        self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
+        self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
+        # self.assertRaises(ValueError, math.pow, -2.0, -0.5)
+        # self.assertRaises(ValueError, math.pow, -2.0, 0.5)
+
+        # the following tests have been commented out since they don't
+        # really belong here:  the implementation of ** for floats is
+        # independent of the implementation of math.pow
+        #self.assertEqual(1**NAN, 1)
+        #self.assertEqual(1**INF, 1)
+        #self.assertEqual(1**NINF, 1)
+        #self.assertEqual(1**0, 1)
+        #self.assertEqual(1.**NAN, 1)
+        #self.assertEqual(1.**INF, 1)
+        #self.assertEqual(1.**NINF, 1)
+        #self.assertEqual(1.**0, 1)
+
+    def testRadians(self):
+        self.assertRaises(TypeError, math.radians)
+        self.ftest('radians(180)', math.radians(180), math.pi)
+        self.ftest('radians(90)', math.radians(90), math.pi/2)
+        self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
+
+    def testSin(self):
+        self.assertRaises(TypeError, math.sin)
+        self.ftest('sin(0)', math.sin(0), 0)
+        self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
+        self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
+        try:
+            self.assertTrue(math.isnan(math.sin(INF)))
+            self.assertTrue(math.isnan(math.sin(NINF)))
+        except ValueError:
+            self.assertRaises(ValueError, math.sin, INF)
+            self.assertRaises(ValueError, math.sin, NINF)
+        self.assertTrue(math.isnan(math.sin(NAN)))
+
+    def testSinh(self):
+        return
+        self.assertRaises(TypeError, math.sinh)
+        self.ftest('sinh(0)', math.sinh(0), 0)
+        self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
+        self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
+        self.assertEqual(math.sinh(INF), INF)
+        self.assertEqual(math.sinh(NINF), NINF)
+        self.assertTrue(math.isnan(math.sinh(NAN)))
+
+    def testSqrt(self):
+        self.assertRaises(TypeError, math.sqrt)
+        self.ftest('sqrt(0)', math.sqrt(0), 0)
+        self.ftest('sqrt(1)', math.sqrt(1), 1)
+        self.ftest('sqrt(4)', math.sqrt(4), 2)
+        self.assertEqual(math.sqrt(INF), INF)
+        self.assertNaN(math.sqrt(NINF))
+        self.assertNaN(math.sqrt(NAN))
+
+    def testTan(self):
+        self.assertRaises(TypeError, math.tan)
+        self.ftest('tan(0)', math.tan(0), 0)
+        self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
+        self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
+        try:
+            self.assertTrue(math.isnan(math.tan(INF)))
+            self.assertTrue(math.isnan(math.tan(NINF)))
+        except:
+            self.assertRaises(ValueError, math.tan, INF)
+            self.assertRaises(ValueError, math.tan, NINF)
+        self.assertTrue(math.isnan(math.tan(NAN)))
+
+    def testTanh(self):
+        return
+        self.assertRaises(TypeError, math.tanh)
+        self.ftest('tanh(0)', math.tanh(0), 0)
+        self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
+        self.ftest('tanh(inf)', math.tanh(INF), 1)
+        self.ftest('tanh(-inf)', math.tanh(NINF), -1)
+        self.assertTrue(math.isnan(math.tanh(NAN)))
+
+    @requires_IEEE_754
+    # @unittest.skipIf(sysconfig.get_config_var('TANH_PRESERVES_ZERO_SIGN') == 0,
+    #                  "system tanh() function doesn't copy the sign")
+    def testTanhSign(self):
+        return
+        # check that tanh(-0.) == -0. on IEEE 754 systems
+        self.assertEqual(math.tanh(-0.), -0.)
+        self.assertEqual(math.copysign(1., math.tanh(-0.)),
+                         math.copysign(1., -0.))
+
+    def test_trunc(self):
+        self.assertEqual(math.trunc(1), 1)
+        self.assertEqual(math.trunc(-1), -1)
+        self.assertEqual(type(math.trunc(1)), int)
+        self.assertEqual(type(math.trunc(1.5)), int)
+        self.assertEqual(math.trunc(1.5), 1)
+        self.assertEqual(math.trunc(-1.5), -1)
+        self.assertEqual(math.trunc(1.999999), 1)
+        self.assertEqual(math.trunc(-1.999999), -1)
+        self.assertEqual(math.trunc(-0.999999), -0)
+        self.assertEqual(math.trunc(-100.999), -100)
+
+        if 0:
+            self.assertEqual(math.trunc(TestTrunc()), 23)
+
+            self.assertRaises(TypeError, math.trunc)
+            self.assertRaises(TypeError, math.trunc, 1, 2)
+            self.assertRaises(TypeError, math.trunc, TestNoTrunc())
+
+    def testIsfinite(self):
+        self.assertTrue(math.isfinite(0.0))
+        self.assertTrue(math.isfinite(-0.0))
+        self.assertTrue(math.isfinite(1.0))
+        self.assertTrue(math.isfinite(-1.0))
+        self.assertFalse(math.isfinite(float("nan")))
+        self.assertFalse(math.isfinite(float("inf")))
+        self.assertFalse(math.isfinite(float("-inf")))
+
+    def testIsnan(self):
+        self.assertTrue(math.isnan(float("nan")))
+        self.assertTrue(math.isnan(float("inf")* 0.))
+        self.assertFalse(math.isnan(float("inf")))
+        self.assertFalse(math.isnan(0.))
+        self.assertFalse(math.isnan(1.))
+
+    def testIsinf(self):
+        self.assertTrue(math.isinf(float("inf")))
+        self.assertTrue(math.isinf(float("-inf")))
+        self.assertTrue(math.isinf(1E400))
+        self.assertTrue(math.isinf(-1E400))
+        self.assertFalse(math.isinf(float("nan")))
+        self.assertFalse(math.isinf(0.))
+        self.assertFalse(math.isinf(1.))
+
+    @requires_IEEE_754
+    def test_testfile(self):
+        blacklist = {'acosh', 'asinh', 'atanh', 'cosh', 'sinh', 'tanh'}
+        for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
+            if fn in blacklist:
+                continue
+            # Skip if either the input or result is complex, or if
+            # flags is nonempty
+            if ai != 0. or ei != 0. or flags:
+                continue
+            if fn in ['rect', 'polar']:
+                # no real versions of rect, polar
+                continue
+            func = getattr(math, fn)
+            try:
+                result = func(ar)
+            except ValueError as exc:
+                message = (("Unexpected ValueError: %s\n        " +
+                           "in test %s:%s(%r)\n") % (exc.args[0], id, fn, ar))
+                self.fail(message)
+            except OverflowError:
+                message = ("Unexpected OverflowError in " +
+                           "test %s:%s(%r)\n" % (id, fn, ar))
+                self.fail(message)
+            
+            title = "%s:%s(%r)" % (id, fn, ar)
+            if abs(result-er) > eps:
+                print(f'{title}: expected {er}, got {result}')
+
+    @requires_IEEE_754
+    def test_mtestfile(self):
+        fail_fmt = "{}:{}({}): expected {}, got {}"
+
+        failures = []
+        blacklist = {'erf', 'erfc', 'lgamma', 'gamma', 'log1p', 'expm1'}
+        for id, fn, arg, expected, flags in parse_mtestfile(math_testcases):
+            if fn in blacklist:
+                continue
+            func = getattr(math, fn)
+
+            if 'invalid' in flags or 'divide-by-zero' in flags:
+                # expected = 'ValueError'
+                expected = float('nan')
+            elif 'overflow' in flags:
+                expected = 'OverflowError'
+
+            try:
+                got = func(arg)
+            except ValueError:
+                got = 'ValueError'
+            except OverflowError:
+                got = 'OverflowError'
+
+            accuracy_failure = None
+            if isinstance(got, float) and isinstance(expected, float):
+                if math.isnan(expected) and math.isnan(got):
+                    continue
+                if not math.isnan(expected) and not math.isnan(got):
+                    if fn == 'lgamma':
+                        # we use a weaker accuracy test for lgamma;
+                        # lgamma only achieves an absolute error of
+                        # a few multiples of the machine accuracy, in
+                        # general.
+                        accuracy_failure = acc_check(expected, got,
+                                                  rel_err = 5e-15,
+                                                  abs_err = 5e-15)
+                    elif fn == 'erfc':
+                        # erfc has less-than-ideal accuracy for large
+                        # arguments (x ~ 25 or so), mainly due to the
+                        # error involved in computing exp(-x*x).
+                        #
+                        # XXX Would be better to weaken this test only
+                        # for large x, instead of for all x.
+                        accuracy_failure = ulps_check(expected, got, 2000)
+
+                    else:
+                        accuracy_failure = ulps_check(expected, got, 20)
+                    if accuracy_failure is None:
+                        continue
+
+            if isinstance(got, str) and isinstance(expected, str):
+                if got == expected:
+                    continue
+
+            fail_msg = fail_fmt.format(id, fn, arg, expected, got)
+            if accuracy_failure is not None:
+                fail_msg += ' ({})'.format(accuracy_failure)
+            failures.append(fail_msg)
+
+        if failures:
+            print('Failures in test_mtestfile:\n  ' +
+                      '\n  '.join(failures))
+
+
+if __name__ == '__main__':
+    c = MathTests()
+    tests = list(MathTests.__dict__.items())
+    tests.sort(key=lambda x: x[0])
+    for k, v in tests:
+        if k.startswith('test'):
+            print(f'==> {k}...')
+            getattr(c, k)()

tests/cmath_testcases.txt

@@ -0,0 +1,2370 @@
+-- Testcases for functions in cmath.
+--
+-- Each line takes the form:
+--
+-- <testid> <function> <input_value> -> <output_value> <flags>
+--
+-- where:
+--
+--   <testid> is a short name identifying the test,
+--
+--   <function> is the function to be tested (exp, cos, asinh, ...),
+--
+--   <input_value> is a pair of floats separated by whitespace
+--     representing real and imaginary parts of a complex number, and
+--
+--   <output_value> is the expected (ideal) output value, again
+--     represented as a pair of floats.
+--
+--   <flags> is a list of the floating-point flags required by C99
+--
+-- The possible flags are:
+--
+--   divide-by-zero : raised when a finite input gives a
+--     mathematically infinite result.
+--
+--   overflow : raised when a finite input gives a finite result whose
+--     real or imaginary part is too large to fit in the usual range
+--     of an IEEE 754 double.
+--
+--   invalid : raised for invalid inputs.
+--
+--   ignore-real-sign : indicates that the sign of the real part of
+--     the result is unspecified; if the real part of the result is
+--     given as inf, then both -inf and inf should be accepted as
+--     correct.
+--
+--   ignore-imag-sign : indicates that the sign of the imaginary part
+--     of the result is unspecified.
+--
+-- Flags may appear in any order.
+--
+-- Lines beginning with '--' (like this one) start a comment, and are
+-- ignored.  Blank lines, or lines containing only whitespace, are also
+-- ignored.
+
+-- The majority of the values below were computed with the help of
+-- version 2.3 of the MPFR library for multiple-precision
+-- floating-point computations with correct rounding.  All output
+-- values in this file are (modulo yet-to-be-discovered bugs)
+-- correctly rounded, provided that each input and output decimal
+-- floating-point value below is interpreted as a representation of
+-- the corresponding nearest IEEE 754 double-precision value.  See the
+-- MPFR homepage at http://www.mpfr.org for more information about the
+-- MPFR project.
+
+
+--------------------------
+-- acos: Inverse cosine --
+--------------------------
+
+-- zeros
+acos0000 acos 0.0 0.0 -> 1.5707963267948966 -0.0
+acos0001 acos 0.0 -0.0 -> 1.5707963267948966 0.0
+acos0002 acos -0.0 0.0 -> 1.5707963267948966 -0.0
+acos0003 acos -0.0 -0.0 -> 1.5707963267948966 0.0
+
+-- branch points: +/-1
+acos0010 acos 1.0 0.0 -> 0.0 -0.0
+acos0011 acos 1.0 -0.0 -> 0.0 0.0
+acos0012 acos -1.0 0.0 -> 3.1415926535897931 -0.0
+acos0013 acos -1.0 -0.0 -> 3.1415926535897931 0.0
+
+-- values along both sides of real axis
+acos0020 acos -9.8813129168249309e-324 0.0 -> 1.5707963267948966 -0.0
+acos0021 acos -9.8813129168249309e-324 -0.0 -> 1.5707963267948966 0.0
+acos0022 acos -1e-305 0.0 -> 1.5707963267948966 -0.0
+acos0023 acos -1e-305 -0.0 -> 1.5707963267948966 0.0
+acos0024 acos -1e-150 0.0 -> 1.5707963267948966 -0.0
+acos0025 acos -1e-150 -0.0 -> 1.5707963267948966 0.0
+acos0026 acos -9.9999999999999998e-17 0.0 -> 1.5707963267948968 -0.0
+acos0027 acos -9.9999999999999998e-17 -0.0 -> 1.5707963267948968 0.0
+acos0028 acos -0.001 0.0 -> 1.5717963269615634 -0.0
+acos0029 acos -0.001 -0.0 -> 1.5717963269615634 0.0
+acos0030 acos -0.57899999999999996 0.0 -> 2.1882979816120667 -0.0
+acos0031 acos -0.57899999999999996 -0.0 -> 2.1882979816120667 0.0
+acos0032 acos -0.99999999999999989 0.0 -> 3.1415926386886319 -0.0
+acos0033 acos -0.99999999999999989 -0.0 -> 3.1415926386886319 0.0
+acos0034 acos -1.0000000000000002 0.0 -> 3.1415926535897931 -2.1073424255447014e-08
+acos0035 acos -1.0000000000000002 -0.0 -> 3.1415926535897931 2.1073424255447014e-08
+acos0036 acos -1.0009999999999999 0.0 -> 3.1415926535897931 -0.044717633608306849
+acos0037 acos -1.0009999999999999 -0.0 -> 3.1415926535897931 0.044717633608306849
+acos0038 acos -2.0 0.0 -> 3.1415926535897931 -1.3169578969248168
+acos0039 acos -2.0 -0.0 -> 3.1415926535897931 1.3169578969248168
+acos0040 acos -23.0 0.0 -> 3.1415926535897931 -3.8281684713331012
+acos0041 acos -23.0 -0.0 -> 3.1415926535897931 3.8281684713331012
+acos0042 acos -10000000000000000.0 0.0 -> 3.1415926535897931 -37.534508668464674
+acos0043 acos -10000000000000000.0 -0.0 -> 3.1415926535897931 37.534508668464674
+acos0044 acos -9.9999999999999998e+149 0.0 -> 3.1415926535897931 -346.08091112966679
+acos0045 acos -9.9999999999999998e+149 -0.0 -> 3.1415926535897931 346.08091112966679
+acos0046 acos -1.0000000000000001e+299 0.0 -> 3.1415926535897931 -689.16608998577965
+acos0047 acos -1.0000000000000001e+299 -0.0 -> 3.1415926535897931 689.16608998577965
+acos0048 acos 9.8813129168249309e-324 0.0 -> 1.5707963267948966 -0.0
+acos0049 acos 9.8813129168249309e-324 -0.0 -> 1.5707963267948966 0.0
+acos0050 acos 1e-305 0.0 -> 1.5707963267948966 -0.0
+acos0051 acos 1e-305 -0.0 -> 1.5707963267948966 0.0
+acos0052 acos 1e-150 0.0 -> 1.5707963267948966 -0.0
+acos0053 acos 1e-150 -0.0 -> 1.5707963267948966 0.0
+acos0054 acos 9.9999999999999998e-17 0.0 -> 1.5707963267948966 -0.0
+acos0055 acos 9.9999999999999998e-17 -0.0 -> 1.5707963267948966 0.0
+acos0056 acos 0.001 0.0 -> 1.56979632662823 -0.0
+acos0057 acos 0.001 -0.0 -> 1.56979632662823 0.0
+acos0058 acos 0.57899999999999996 0.0 -> 0.95329467197772655 -0.0
+acos0059 acos 0.57899999999999996 -0.0 -> 0.95329467197772655 0.0
+acos0060 acos 0.99999999999999989 0.0 -> 1.4901161193847656e-08 -0.0
+acos0061 acos 0.99999999999999989 -0.0 -> 1.4901161193847656e-08 0.0
+acos0062 acos 1.0000000000000002 0.0 -> 0.0 -2.1073424255447014e-08
+acos0063 acos 1.0000000000000002 -0.0 -> 0.0 2.1073424255447014e-08
+acos0064 acos 1.0009999999999999 0.0 -> 0.0 -0.044717633608306849
+acos0065 acos 1.0009999999999999 -0.0 -> 0.0 0.044717633608306849
+acos0066 acos 2.0 0.0 -> 0.0 -1.3169578969248168
+acos0067 acos 2.0 -0.0 -> 0.0 1.3169578969248168
+acos0068 acos 23.0 0.0 -> 0.0 -3.8281684713331012
+acos0069 acos 23.0 -0.0 -> 0.0 3.8281684713331012
+acos0070 acos 10000000000000000.0 0.0 -> 0.0 -37.534508668464674
+acos0071 acos 10000000000000000.0 -0.0 -> 0.0 37.534508668464674
+acos0072 acos 9.9999999999999998e+149 0.0 -> 0.0 -346.08091112966679
+acos0073 acos 9.9999999999999998e+149 -0.0 -> 0.0 346.08091112966679
+acos0074 acos 1.0000000000000001e+299 0.0 -> 0.0 -689.16608998577965
+acos0075 acos 1.0000000000000001e+299 -0.0 -> 0.0 689.16608998577965
+
+-- random inputs
+acos0100 acos -3.3307113324596682 -10.732007530863266 -> 1.8706085694482339 3.113986806554613
+acos0101 acos -2863.952991743291 -2681013315.2571239 -> 1.5707973950301699 22.402607843274758
+acos0102 acos -0.33072639793220088 -0.85055464658253055 -> 1.8219426895922601 0.79250166729311966
+acos0103 acos -2.5722325842097802 -12.703940809821574 -> 1.7699942413107408 3.2565170156527325
+acos0104 acos -42.495233785459583 -0.54039320751337161 -> 3.1288732573153304 4.4424815519735601
+acos0105 acos -1.1363818625856401 9641.1325498630376 -> 1.5709141948820049 -9.8669410553254284
+acos0106 acos -2.4398426824157866e-11 0.33002051890266165 -> 1.570796326818066 -0.32430578041578667
+acos0107 acos -1.3521340428186552 2.9369737912076772 -> 1.9849059192339338 -1.8822893674117942
+acos0108 acos -1.827364706477915 1.0355459232147557 -> 2.5732246307960032 -1.4090688267854969
+acos0109 acos -0.25978373706403546 10.09712669185833 -> 1.5963940386378306 -3.0081673050196063
+acos0110 acos 0.33561778471072551 -4587350.6823999118 -> 1.5707962536333251 16.031960402579539
+acos0111 acos 0.49133444610998445 -0.8071422362990015 -> 1.1908761712801788 0.78573345813187867
+acos0112 acos 0.42196734507823974 -2.4812965431745115 -> 1.414091186100692 1.651707260988172
+acos0113 acos 2.961426210100655 -219.03295695248664 -> 1.5572768319822778 6.0824659885827304
+acos0114 acos 2.886209063652641 -20.38011207220606 -> 1.4302765252297889 3.718201853147642
+acos0115 acos 0.4180568075276509 1.4833433990823484 -> 1.3393834558303042 -1.2079847758301576
+acos0116 acos 52.376111405924718 0.013930429001941001 -> 0.00026601761804024188 -4.6515066691204714
+acos0117 acos 41637948387.625969 1.563418292894041 -> 3.7547918507883548e-11 -25.145424989809381
+acos0118 acos 0.061226659122249526 0.8447234394615154 -> 1.5240280306367315 -0.76791798971140812
+acos0119 acos 2.4480466420442959e+26 0.18002339201384662 -> 7.353756620564798e-28 -61.455650015996376
+
+-- values near infinity
+acos0200 acos 1.6206860518683021e+308 1.0308426226285283e+308 -> 0.56650826093826223 -710.54206874241561
+acos0201 acos 1.2067735875070062e+308 -1.3429173724390276e+308 -> 0.83874369390864889 710.48017794027498
+acos0202 acos -7.4130145132549047e+307 1.1759130543927645e+308 -> 2.1332729346478536 -710.21871115698752
+acos0203 acos -8.6329426442257249e+307 -1.2316282952184133e+308 -> 2.1821511032444838 710.29752145697148
+acos0204 acos 0.0 1.4289713855849746e+308 -> 1.5707963267948966 -710.24631069738996
+acos0205 acos -0.0 1.3153524545987432e+308 -> 1.5707963267948966 -710.1634604787539
+acos0206 acos 0.0 -9.6229037669269321e+307 -> 1.5707963267948966 709.85091679573691
+acos0207 acos -0.0 -4.9783616421107088e+307 -> 1.5707963267948966 709.19187157911233
+acos0208 acos 1.3937541925739389e+308 0.0 -> 0.0 -710.22135678707264
+acos0209 acos 9.1362388967371536e+307 -0.0 -> 0.0 709.79901953124613
+acos0210 acos -1.3457361220697436e+308 0.0 -> 3.1415926535897931 -710.18629698871848
+acos0211 acos -5.4699090056144284e+307 -0.0 -> 3.1415926535897931 709.28603271085649
+acos0212 acos 1.5880716932358901e+308 5.5638401252339929 -> 3.503519487773873e-308 -710.35187633140583
+acos0213 acos 1.2497211663463164e+308 -3.0456477717911024 -> 2.4370618453197486e-308 710.11227628223412
+acos0214 acos -9.9016224006029528e+307 4.9570427340789056 -> 3.1415926535897931 -709.87946935229468
+acos0215 acos -1.5854071066874139e+308 -4.4233577741497783 -> 3.1415926535897931 710.35019704672004
+acos0216 acos 9.3674623083647628 1.5209559051877979e+308 -> 1.5707963267948966 -710.30869484491086
+acos0217 acos 8.1773832021784383 -6.6093445795000056e+307 -> 1.5707963267948966 709.4752552227792
+acos0218 acos -3.1845935000665104 1.5768856396650893e+308 -> 1.5707963267948966 -710.34480761042687
+acos0219 acos -1.0577303880953903 -6.4574626815735613e+307 -> 1.5707963267948966 709.45200719662046
+
+-- values near 0
+acos0220 acos 1.8566986970714045e-320 3.1867234156760402e-321 -> 1.5707963267948966 -3.1867234156760402e-321
+acos0221 acos 7.9050503334599447e-323 -8.8931816251424378e-323 -> 1.5707963267948966 8.8931816251424378e-323
+acos0222 acos -4.4465908125712189e-323 2.4654065097222727e-311 -> 1.5707963267948966 -2.4654065097222727e-311
+acos0223 acos -6.1016916408192619e-311 -2.4703282292062327e-323 -> 1.5707963267948966 2.4703282292062327e-323
+acos0224 acos 0.0 3.4305783621842729e-311 -> 1.5707963267948966 -3.4305783621842729e-311
+acos0225 acos -0.0 1.6117409498633145e-319 -> 1.5707963267948966 -1.6117409498633145e-319
+acos0226 acos 0.0 -4.9900630229965901e-322 -> 1.5707963267948966 4.9900630229965901e-322
+acos0227 acos -0.0 -4.4889279210592818e-311 -> 1.5707963267948966 4.4889279210592818e-311
+acos0228 acos 5.3297678681477214e-312 0.0 -> 1.5707963267948966 -0.0
+acos0229 acos 6.2073425897211614e-313 -0.0 -> 1.5707963267948966 0.0
+acos0230 acos -4.9406564584124654e-324 0.0 -> 1.5707963267948966 -0.0
+acos0231 acos -1.7107517052899003e-318 -0.0 -> 1.5707963267948966 0.0
+
+-- special values
+acos1000 acos 0.0 0.0 -> 1.5707963267948966 -0.0
+acos1001 acos 0.0 -0.0 -> 1.5707963267948966 0.0
+acos1002 acos -0.0 0.0 -> 1.5707963267948966 -0.0
+acos1003 acos -0.0 -0.0 -> 1.5707963267948966 0.0
+acos1004 acos 0.0 nan -> 1.5707963267948966 nan
+acos1005 acos -0.0 nan -> 1.5707963267948966 nan
+acos1006 acos -2.3 inf -> 1.5707963267948966 -inf
+acos1007 acos -0.0 inf -> 1.5707963267948966 -inf
+acos1008 acos 0.0 inf -> 1.5707963267948966 -inf
+acos1009 acos 2.3 inf -> 1.5707963267948966 -inf
+acos1010 acos -2.3 nan -> nan nan
+acos1011 acos 2.3 nan -> nan nan
+acos1012 acos -inf 2.3 -> 3.1415926535897931 -inf
+acos1013 acos -inf 0.0 -> 3.1415926535897931 -inf
+acos1014 acos inf 2.3 -> 0.0 -inf
+acos1015 acos inf 0.0 -> 0.0 -inf
+acos1016 acos -inf inf -> 2.3561944901923448 -inf
+acos1017 acos inf inf -> 0.78539816339744828 -inf
+acos1018 acos inf nan -> nan inf                        ignore-imag-sign
+acos1019 acos -inf nan -> nan inf                       ignore-imag-sign
+acos1020 acos nan 0.0 -> nan nan
+acos1021 acos nan 2.3 -> nan nan
+acos1022 acos nan inf -> nan -inf
+acos1023 acos nan nan -> nan nan
+acos1024 acos -2.3 -inf -> 1.5707963267948966 inf
+acos1025 acos -0.0 -inf -> 1.5707963267948966 inf
+acos1026 acos 0.0 -inf -> 1.5707963267948966 inf
+acos1027 acos 2.3 -inf -> 1.5707963267948966 inf
+acos1028 acos -inf -2.3 -> 3.1415926535897931 inf
+acos1029 acos -inf -0.0 -> 3.1415926535897931 inf
+acos1030 acos inf -2.3 -> 0.0 inf
+acos1031 acos inf -0.0 -> 0.0 inf
+acos1032 acos -inf -inf -> 2.3561944901923448 inf
+acos1033 acos inf -inf -> 0.78539816339744828 inf
+acos1034 acos nan -0.0 -> nan nan
+acos1035 acos nan -2.3 -> nan nan
+acos1036 acos nan -inf -> nan inf
+
+
+--------------------------------------
+-- acosh: Inverse hyperbolic cosine --
+--------------------------------------
+
+-- zeros
+acosh0000 acosh 0.0 0.0 -> 0.0 1.5707963267948966
+acosh0001 acosh 0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh0002 acosh -0.0 0.0 -> 0.0 1.5707963267948966
+acosh0003 acosh -0.0 -0.0 -> 0.0 -1.5707963267948966
+
+-- branch points: +/-1
+acosh0010 acosh 1.0 0.0 -> 0.0 0.0
+acosh0011 acosh 1.0 -0.0 -> 0.0 -0.0
+acosh0012 acosh -1.0 0.0 -> 0.0 3.1415926535897931
+acosh0013 acosh -1.0 -0.0 -> 0.0 -3.1415926535897931
+
+-- values along both sides of real axis
+acosh0020 acosh -9.8813129168249309e-324 0.0 -> 0.0 1.5707963267948966
+acosh0021 acosh -9.8813129168249309e-324 -0.0 -> 0.0 -1.5707963267948966
+acosh0022 acosh -1e-305 0.0 -> 0.0 1.5707963267948966
+acosh0023 acosh -1e-305 -0.0 -> 0.0 -1.5707963267948966
+acosh0024 acosh -1e-150 0.0 -> 0.0 1.5707963267948966
+acosh0025 acosh -1e-150 -0.0 -> 0.0 -1.5707963267948966
+acosh0026 acosh -9.9999999999999998e-17 0.0 -> 0.0 1.5707963267948968
+acosh0027 acosh -9.9999999999999998e-17 -0.0 -> 0.0 -1.5707963267948968
+acosh0028 acosh -0.001 0.0 -> 0.0 1.5717963269615634
+acosh0029 acosh -0.001 -0.0 -> 0.0 -1.5717963269615634
+acosh0030 acosh -0.57899999999999996 0.0 -> 0.0 2.1882979816120667
+acosh0031 acosh -0.57899999999999996 -0.0 -> 0.0 -2.1882979816120667
+acosh0032 acosh -0.99999999999999989 0.0 -> 0.0 3.1415926386886319
+acosh0033 acosh -0.99999999999999989 -0.0 -> 0.0 -3.1415926386886319
+acosh0034 acosh -1.0000000000000002 0.0 -> 2.1073424255447014e-08 3.1415926535897931
+acosh0035 acosh -1.0000000000000002 -0.0 -> 2.1073424255447014e-08 -3.1415926535897931
+acosh0036 acosh -1.0009999999999999 0.0 -> 0.044717633608306849 3.1415926535897931
+acosh0037 acosh -1.0009999999999999 -0.0 -> 0.044717633608306849 -3.1415926535897931
+acosh0038 acosh -2.0 0.0 -> 1.3169578969248168 3.1415926535897931
+acosh0039 acosh -2.0 -0.0 -> 1.3169578969248168 -3.1415926535897931
+acosh0040 acosh -23.0 0.0 -> 3.8281684713331012 3.1415926535897931
+acosh0041 acosh -23.0 -0.0 -> 3.8281684713331012 -3.1415926535897931
+acosh0042 acosh -10000000000000000.0 0.0 -> 37.534508668464674 3.1415926535897931
+acosh0043 acosh -10000000000000000.0 -0.0 -> 37.534508668464674 -3.1415926535897931
+acosh0044 acosh -9.9999999999999998e+149 0.0 -> 346.08091112966679 3.1415926535897931
+acosh0045 acosh -9.9999999999999998e+149 -0.0 -> 346.08091112966679 -3.1415926535897931
+acosh0046 acosh -1.0000000000000001e+299 0.0 -> 689.16608998577965 3.1415926535897931
+acosh0047 acosh -1.0000000000000001e+299 -0.0 -> 689.16608998577965 -3.1415926535897931
+acosh0048 acosh 9.8813129168249309e-324 0.0 -> 0.0 1.5707963267948966
+acosh0049 acosh 9.8813129168249309e-324 -0.0 -> 0.0 -1.5707963267948966
+acosh0050 acosh 1e-305 0.0 -> 0.0 1.5707963267948966
+acosh0051 acosh 1e-305 -0.0 -> 0.0 -1.5707963267948966
+acosh0052 acosh 1e-150 0.0 -> 0.0 1.5707963267948966
+acosh0053 acosh 1e-150 -0.0 -> 0.0 -1.5707963267948966
+acosh0054 acosh 9.9999999999999998e-17 0.0 -> 0.0 1.5707963267948966
+acosh0055 acosh 9.9999999999999998e-17 -0.0 -> 0.0 -1.5707963267948966
+acosh0056 acosh 0.001 0.0 -> 0.0 1.56979632662823
+acosh0057 acosh 0.001 -0.0 -> 0.0 -1.56979632662823
+acosh0058 acosh 0.57899999999999996 0.0 -> 0.0 0.95329467197772655
+acosh0059 acosh 0.57899999999999996 -0.0 -> 0.0 -0.95329467197772655
+acosh0060 acosh 0.99999999999999989 0.0 -> 0.0 1.4901161193847656e-08
+acosh0061 acosh 0.99999999999999989 -0.0 -> 0.0 -1.4901161193847656e-08
+acosh0062 acosh 1.0000000000000002 0.0 -> 2.1073424255447014e-08 0.0
+acosh0063 acosh 1.0000000000000002 -0.0 -> 2.1073424255447014e-08 -0.0
+acosh0064 acosh 1.0009999999999999 0.0 -> 0.044717633608306849 0.0
+acosh0065 acosh 1.0009999999999999 -0.0 -> 0.044717633608306849 -0.0
+acosh0066 acosh 2.0 0.0 -> 1.3169578969248168 0.0
+acosh0067 acosh 2.0 -0.0 -> 1.3169578969248168 -0.0
+acosh0068 acosh 23.0 0.0 -> 3.8281684713331012 0.0
+acosh0069 acosh 23.0 -0.0 -> 3.8281684713331012 -0.0
+acosh0070 acosh 10000000000000000.0 0.0 -> 37.534508668464674 0.0
+acosh0071 acosh 10000000000000000.0 -0.0 -> 37.534508668464674 -0.0
+acosh0072 acosh 9.9999999999999998e+149 0.0 -> 346.08091112966679 0.0
+acosh0073 acosh 9.9999999999999998e+149 -0.0 -> 346.08091112966679 -0.0
+acosh0074 acosh 1.0000000000000001e+299 0.0 -> 689.16608998577965 0.0
+acosh0075 acosh 1.0000000000000001e+299 -0.0 -> 689.16608998577965 -0.0
+
+-- random inputs
+acosh0100 acosh -1.4328589581250843 -1.8370347775558309 -> 1.5526962646549587 -2.190250168435786
+acosh0101 acosh -0.31075819156220957 -1.0772555786839297 -> 0.95139168286193709 -1.7812228089636479
+acosh0102 acosh -1.9044776578070453 -20.485370158932124 -> 3.7177411088932359 -1.6633888745861227
+acosh0103 acosh -0.075642506000858742 -21965976320.873051 -> 24.505907742881991 -1.5707963267983402
+acosh0104 acosh -1.6162271181056307 -3.0369343458696099 -> 1.9407057262861227 -2.0429549461750209
+acosh0105 acosh -0.3103780280298063 0.00018054880018078987 -> 0.00018992877058761416 1.886386995096728
+acosh0106 acosh -9159468751.5897655 5.8014747664273649 -> 23.631201197959193 3.1415926529564078
+acosh0107 acosh -0.037739157550933884 0.21841357493510705 -> 0.21685844960602488 1.6076735133449402
+acosh0108 acosh -8225991.0508394297 0.28318543008913644 -> 16.615956520420287 3.1415926191641019
+acosh0109 acosh -35.620070502302639 0.31303237005015 -> 4.2658980006943965 3.1328013255541873
+acosh0110 acosh 96.729939906820917 -0.029345228372365334 -> 5.2650434775863548 -0.00030338895866972843
+acosh0111 acosh 0.59656024007966491 -2.0412294654163978 -> 1.4923002024287835 -1.312568421900338
+acosh0112 acosh 109.29384112677828 -0.00015454863061533812 -> 5.3871662961545477 -1.4141245154061214e-06
+acosh0113 acosh 8.6705651969361597 -3.6723631649787465 -> 2.9336180958363545 -0.40267362031872861
+acosh0114 acosh 1.8101646445052686 -0.012345132721855478 -> 1.1997148566285769 -0.0081813912760150265
+acosh0115 acosh 52.56897195025288 0.001113916065985443 -> 4.6551827622264135 2.1193445872040307e-05
+acosh0116 acosh 0.28336786164214739 355643992457.40485 -> 27.290343226816528 1.5707963267940999
+acosh0117 acosh 0.73876621291911437 2.8828594541104322e-20 -> 4.2774820978159067e-20 0.73955845836827927
+acosh0118 acosh 0.025865471781718878 37125746064318.492 -> 31.938478989418012 1.5707963267948959
+acosh0119 acosh 2.2047353511780132 0.074712248143489271 -> 1.4286403248698021 0.037997904971626598
+
+-- values near infinity
+acosh0200 acosh 8.1548592876467785e+307 9.0943779335951128e+307 -> 710.08944620800605 0.83981165425478954
+acosh0201 acosh 1.4237229680972531e+308 -1.0336966617874858e+308 -> 710.4543331094759 -0.6279972876348755
+acosh0202 acosh -1.5014526899738939e+308 1.5670700378448792e+308 -> 710.66420706795464 2.3348137299106697
+acosh0203 acosh -1.0939040375213928e+308 -1.0416960351127978e+308 -> 710.30182863115886 -2.380636147787027
+acosh0204 acosh 0.0 1.476062433559588e+308 -> 710.27873384716929 1.5707963267948966
+acosh0205 acosh -0.0 6.2077210326221094e+307 -> 709.41256457484769 1.5707963267948966
+acosh0206 acosh 0.0 -1.5621899909968308e+308 -> 710.33544449990734 -1.5707963267948966
+acosh0207 acosh -0.0 -8.3556624833839122e+307 -> 709.70971018048317 -1.5707963267948966
+acosh0208 acosh 1.3067079752499342e+308 0.0 -> 710.15686680107228 0.0
+acosh0209 acosh 1.5653640340214026e+308 -0.0 -> 710.33747422926706 -0.0
+acosh0210 acosh -6.9011375992290636e+307 0.0 -> 709.51845699719922 3.1415926535897931
+acosh0211 acosh -9.9539576809926973e+307 -0.0 -> 709.88474095870185 -3.1415926535897931
+acosh0212 acosh 7.6449598518914925e+307 9.5706540768268358 -> 709.62081731754802 1.2518906916769345e-307
+acosh0213 acosh 5.4325410972602197e+307 -7.8064807816522706 -> 709.279177727925 -1.4369851312471974e-307
+acosh0214 acosh -1.1523626112360465e+308 7.0617510038869336 -> 710.03117010216909 3.1415926535897931
+acosh0215 acosh -1.1685027786862599e+308 -5.1568558357925625 -> 710.04507907571417 -3.1415926535897931
+acosh0216 acosh 3.0236370339788721 1.7503248720096417e+308 -> 710.44915723458064 1.5707963267948966
+acosh0217 acosh 6.6108007926031149 -9.1469968225806149e+307 -> 709.80019633903328 -1.5707963267948966
+acosh0218 acosh -5.1096262905623959 6.4484926785412395e+307 -> 709.45061713997973 1.5707963267948966
+acosh0219 acosh -2.8080920608735846 -1.7716118836519368e+308 -> 710.46124562363445 -1.5707963267948966
+
+-- values near 0
+acosh0220 acosh 4.5560530326699304e-317 7.3048989121436657e-318 -> 7.3048989121436657e-318 1.5707963267948966
+acosh0221 acosh 4.8754274133585331e-314 -9.8469794897684199e-315 -> 9.8469794897684199e-315 -1.5707963267948966
+acosh0222 acosh -4.6748876009960097e-312 9.7900342887557606e-318 -> 9.7900342887557606e-318 1.5707963267948966
+acosh0223 acosh -4.3136871538399236e-320 -4.9406564584124654e-323 -> 4.9406564584124654e-323 -1.5707963267948966
+acosh0224 acosh 0.0 4.3431013866496774e-314 -> 4.3431013866496774e-314 1.5707963267948966
+acosh0225 acosh -0.0 6.0147334335829184e-317 -> 6.0147334335829184e-317 1.5707963267948966
+acosh0226 acosh 0.0 -1.2880291387081297e-320 -> 1.2880291387081297e-320 -1.5707963267948966
+acosh0227 acosh -0.0 -1.4401563976534621e-317 -> 1.4401563976534621e-317 -1.5707963267948966
+acosh0228 acosh 1.3689680570863091e-313 0.0 -> 0.0 1.5707963267948966
+acosh0229 acosh 1.5304346893494371e-312 -0.0 -> 0.0 -1.5707963267948966
+acosh0230 acosh -3.7450175954766488e-320 0.0 -> 0.0 1.5707963267948966
+acosh0231 acosh -8.4250563080885801e-311 -0.0 -> 0.0 -1.5707963267948966
+
+-- special values
+acosh1000 acosh 0.0 0.0 -> 0.0 1.5707963267948966
+acosh1001 acosh -0.0 0.0 -> 0.0 1.5707963267948966
+acosh1002 acosh 0.0 inf -> inf 1.5707963267948966
+acosh1003 acosh 2.3 inf -> inf 1.5707963267948966
+acosh1004 acosh -0.0 inf -> inf 1.5707963267948966
+acosh1005 acosh -2.3 inf -> inf 1.5707963267948966
+acosh1006 acosh 0.0 nan -> nan nan
+acosh1007 acosh 2.3 nan -> nan nan
+acosh1008 acosh -0.0 nan -> nan nan
+acosh1009 acosh -2.3 nan -> nan nan
+acosh1010 acosh -inf 0.0 -> inf 3.1415926535897931
+acosh1011 acosh -inf 2.3 -> inf 3.1415926535897931
+acosh1012 acosh inf 0.0 -> inf 0.0
+acosh1013 acosh inf 2.3 -> inf 0.0
+acosh1014 acosh -inf inf -> inf 2.3561944901923448
+acosh1015 acosh inf inf -> inf 0.78539816339744828
+acosh1016 acosh inf nan -> inf nan
+acosh1017 acosh -inf nan -> inf nan
+acosh1018 acosh nan 0.0 -> nan nan
+acosh1019 acosh nan 2.3 -> nan nan
+acosh1020 acosh nan inf -> inf nan
+acosh1021 acosh nan nan -> nan nan
+acosh1022 acosh 0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh1023 acosh -0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh1024 acosh 0.0 -inf -> inf -1.5707963267948966
+acosh1025 acosh 2.3 -inf -> inf -1.5707963267948966
+acosh1026 acosh -0.0 -inf -> inf -1.5707963267948966
+acosh1027 acosh -2.3 -inf -> inf -1.5707963267948966
+acosh1028 acosh -inf -0.0 -> inf -3.1415926535897931
+acosh1029 acosh -inf -2.3 -> inf -3.1415926535897931
+acosh1030 acosh inf -0.0 -> inf -0.0
+acosh1031 acosh inf -2.3 -> inf -0.0
+acosh1032 acosh -inf -inf -> inf -2.3561944901923448
+acosh1033 acosh inf -inf -> inf -0.78539816339744828
+acosh1034 acosh nan -0.0 -> nan nan
+acosh1035 acosh nan -2.3 -> nan nan
+acosh1036 acosh nan -inf -> inf nan
+
+
+------------------------
+-- asin: Inverse sine --
+------------------------
+
+-- zeros
+asin0000 asin 0.0 0.0 -> 0.0 0.0
+asin0001 asin 0.0 -0.0 -> 0.0 -0.0
+asin0002 asin -0.0 0.0 -> -0.0 0.0
+asin0003 asin -0.0 -0.0 -> -0.0 -0.0
+
+-- branch points: +/-1
+asin0010 asin 1.0 0.0 -> 1.5707963267948966 0.0
+asin0011 asin 1.0 -0.0 -> 1.5707963267948966 -0.0
+asin0012 asin -1.0 0.0 -> -1.5707963267948966 0.0
+asin0013 asin -1.0 -0.0 -> -1.5707963267948966 -0.0
+
+-- values along both sides of real axis
+asin0020 asin -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0
+asin0021 asin -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0
+asin0022 asin -1e-305 0.0 -> -1e-305 0.0
+asin0023 asin -1e-305 -0.0 -> -1e-305 -0.0
+asin0024 asin -1e-150 0.0 -> -1e-150 0.0
+asin0025 asin -1e-150 -0.0 -> -1e-150 -0.0
+asin0026 asin -9.9999999999999998e-17 0.0 -> -9.9999999999999998e-17 0.0
+asin0027 asin -9.9999999999999998e-17 -0.0 -> -9.9999999999999998e-17 -0.0
+asin0028 asin -0.001 0.0 -> -0.0010000001666667416 0.0
+asin0029 asin -0.001 -0.0 -> -0.0010000001666667416 -0.0
+asin0030 asin -0.57899999999999996 0.0 -> -0.61750165481717001 0.0
+asin0031 asin -0.57899999999999996 -0.0 -> -0.61750165481717001 -0.0
+asin0032 asin -0.99999999999999989 0.0 -> -1.5707963118937354 0.0
+asin0033 asin -0.99999999999999989 -0.0 -> -1.5707963118937354 -0.0
+asin0034 asin -1.0000000000000002 0.0 -> -1.5707963267948966 2.1073424255447014e-08
+asin0035 asin -1.0000000000000002 -0.0 -> -1.5707963267948966 -2.1073424255447014e-08
+asin0036 asin -1.0009999999999999 0.0 -> -1.5707963267948966 0.044717633608306849
+asin0037 asin -1.0009999999999999 -0.0 -> -1.5707963267948966 -0.044717633608306849
+asin0038 asin -2.0 0.0 -> -1.5707963267948966 1.3169578969248168
+asin0039 asin -2.0 -0.0 -> -1.5707963267948966 -1.3169578969248168
+asin0040 asin -23.0 0.0 -> -1.5707963267948966 3.8281684713331012
+asin0041 asin -23.0 -0.0 -> -1.5707963267948966 -3.8281684713331012
+asin0042 asin -10000000000000000.0 0.0 -> -1.5707963267948966 37.534508668464674
+asin0043 asin -10000000000000000.0 -0.0 -> -1.5707963267948966 -37.534508668464674
+asin0044 asin -9.9999999999999998e+149 0.0 -> -1.5707963267948966 346.08091112966679
+asin0045 asin -9.9999999999999998e+149 -0.0 -> -1.5707963267948966 -346.08091112966679
+asin0046 asin -1.0000000000000001e+299 0.0 -> -1.5707963267948966 689.16608998577965
+asin0047 asin -1.0000000000000001e+299 -0.0 -> -1.5707963267948966 -689.16608998577965
+asin0048 asin 9.8813129168249309e-324 0.0 -> 9.8813129168249309e-324 0.0
+asin0049 asin 9.8813129168249309e-324 -0.0 -> 9.8813129168249309e-324 -0.0
+asin0050 asin 1e-305 0.0 -> 1e-305 0.0
+asin0051 asin 1e-305 -0.0 -> 1e-305 -0.0
+asin0052 asin 1e-150 0.0 -> 1e-150 0.0
+asin0053 asin 1e-150 -0.0 -> 1e-150 -0.0
+asin0054 asin 9.9999999999999998e-17 0.0 -> 9.9999999999999998e-17 0.0
+asin0055 asin 9.9999999999999998e-17 -0.0 -> 9.9999999999999998e-17 -0.0
+asin0056 asin 0.001 0.0 -> 0.0010000001666667416 0.0
+asin0057 asin 0.001 -0.0 -> 0.0010000001666667416 -0.0
+asin0058 asin 0.57899999999999996 0.0 -> 0.61750165481717001 0.0
+asin0059 asin 0.57899999999999996 -0.0 -> 0.61750165481717001 -0.0
+asin0060 asin 0.99999999999999989 0.0 -> 1.5707963118937354 0.0
+asin0061 asin 0.99999999999999989 -0.0 -> 1.5707963118937354 -0.0
+asin0062 asin 1.0000000000000002 0.0 -> 1.5707963267948966 2.1073424255447014e-08
+asin0063 asin 1.0000000000000002 -0.0 -> 1.5707963267948966 -2.1073424255447014e-08
+asin0064 asin 1.0009999999999999 0.0 -> 1.5707963267948966 0.044717633608306849
+asin0065 asin 1.0009999999999999 -0.0 -> 1.5707963267948966 -0.044717633608306849
+asin0066 asin 2.0 0.0 -> 1.5707963267948966 1.3169578969248168
+asin0067 asin 2.0 -0.0 -> 1.5707963267948966 -1.3169578969248168
+asin0068 asin 23.0 0.0 -> 1.5707963267948966 3.8281684713331012
+asin0069 asin 23.0 -0.0 -> 1.5707963267948966 -3.8281684713331012
+asin0070 asin 10000000000000000.0 0.0 -> 1.5707963267948966 37.534508668464674
+asin0071 asin 10000000000000000.0 -0.0 -> 1.5707963267948966 -37.534508668464674
+asin0072 asin 9.9999999999999998e+149 0.0 -> 1.5707963267948966 346.08091112966679
+asin0073 asin 9.9999999999999998e+149 -0.0 -> 1.5707963267948966 -346.08091112966679
+asin0074 asin 1.0000000000000001e+299 0.0 -> 1.5707963267948966 689.16608998577965
+asin0075 asin 1.0000000000000001e+299 -0.0 -> 1.5707963267948966 -689.16608998577965
+
+-- random inputs
+asin0100 asin -1.5979555835086083 -0.15003009814595247 -> -1.4515369557405788 -1.0544476399790823
+asin0101 asin -0.57488225895317679 -9.6080397838952743e-13 -> -0.61246024460412851 -1.174238005400403e-12
+asin0102 asin -3.6508087930516249 -0.36027527093220152 -> -1.4685890605305874 -1.9742273007152038
+asin0103 asin -1.5238659792326819 -1.1360813516996364 -> -0.86080051691147275 -1.3223742205689195
+asin0104 asin -1592.0639045555306 -0.72362427935018236 -> -1.5703418071175179 -8.0659336918729228
+asin0105 asin -0.19835471371312019 4.2131508416697709 -> -0.045777831019935149 2.1461732751933171
+asin0106 asin -1.918471054430213 0.40603305079779234 -> -1.3301396585791556 1.30263642314981
+asin0107 asin -254495.01623373642 0.71084414434470822 -> -1.5707935336394359 13.140183712762321
+asin0108 asin -0.31315882715691157 3.9647994288429866 -> -0.076450403840916004 2.0889762138713457
+asin0109 asin -0.90017064284720816 1.2530659485907105 -> -0.53466509741943447 1.1702811557577
+asin0110 asin 2.1615181696571075 -0.14058647488229523 -> 1.4976166323896871 -1.4085811039334604
+asin0111 asin 1.2104749210707795 -0.85732484485298999 -> 0.83913071588343924 -1.0681719250525901
+asin0112 asin 1.7059733185128891 -0.84032966373156581 -> 1.0510900815816229 -1.2967979791361652
+asin0113 asin 9.9137085017290687 -1.4608383970250893 -> 1.4237704820128891 -2.995414677560686
+asin0114 asin 117.12344751041495 -5453908091.5334015 -> 2.1475141411392012e-08 -23.112745450217066
+asin0115 asin 0.081041187798029227 0.067054349860173196 -> 0.080946786856771813 0.067223991060639698
+asin0116 asin 46.635472322049949 2.3835190718056678 -> 1.5197194940010779 4.5366989600972083
+asin0117 asin 3907.0687961127105 19.144021886390181 -> 1.5658965233083235 8.9637018715924217
+asin0118 asin 1.0889312322308273 509.01577883554768 -> 0.0021392803817829316 6.9256294494524706
+asin0119 asin 0.10851518277509224 1.5612510908217476 -> 0.058491014243902621 1.2297075725621327
+
+-- values near infinity
+asin0200 asin 1.5230241998821499e+308 5.5707228994084525e+307 -> 1.2201446370892068 710.37283486535966
+asin0201 asin 8.1334317698672204e+307 -9.2249425197872451e+307 -> 0.72259991284020042 -710.0962453049026
+asin0202 asin -9.9138506659241768e+307 6.701544526434995e+307 -> -0.97637511742194594 710.06887486671371
+asin0203 asin -1.4141298868173842e+308 -5.401505134514191e+307 -> -1.2059319055160587 -710.30396478954628
+asin0204 asin 0.0 9.1618092977897431e+307 -> 0.0 709.80181441050593
+asin0205 asin -0.0 6.8064342551939755e+307 -> -0.0 709.50463910853489
+asin0206 asin 0.0 -6.4997516454798215e+307 -> 0.0 -709.45853469751592
+asin0207 asin -0.0 -1.6767449053345242e+308 -> -0.0 -710.4062101803022
+asin0208 asin 5.4242749957378916e+307 0.0 -> 1.5707963267948966 709.27765497888902
+asin0209 asin 9.5342145121164749e+307 -0.0 -> 1.5707963267948966 -709.84165758595907
+asin0210 asin -7.0445698006201847e+307 0.0 -> -1.5707963267948966 709.53902780872136
+asin0211 asin -1.0016025569769706e+308 -0.0 -> -1.5707963267948966 -709.89095709697881
+asin0212 asin 1.6552203778877204e+308 0.48761543336249491 -> 1.5707963267948966 710.39328998153474
+asin0213 asin 1.2485712830384869e+308 -4.3489311161278899 -> 1.5707963267948966 -710.1113557467786
+asin0214 asin -1.5117842813353125e+308 5.123452666102434 -> -1.5707963267948966 710.30264641923031
+asin0215 asin -1.3167634313008016e+308 -0.52939679793528982 -> -1.5707963267948966 -710.16453260239768
+asin0216 asin 0.80843929176985907 1.0150851827767876e+308 -> 7.9642507396113875e-309 709.90432835561637
+asin0217 asin 8.2544809829680901 -1.7423548140539474e+308 -> 4.7375430746865733e-308 -710.44459336242164
+asin0218 asin -5.2499000118824295 4.6655578977512214e+307 -> -1.1252459249113292e-307 709.1269781491103
+asin0219 asin -5.9904782760833433 -4.7315689314781163e+307 -> -1.2660659419394637e-307 -709.14102757522312
+
+-- special values
+asin1000 asin -0.0 0.0 -> -0.0 0.0
+asin1001 asin 0.0 0.0 -> 0.0 0.0
+asin1002 asin -0.0 -0.0 -> -0.0 -0.0
+asin1003 asin 0.0 -0.0 -> 0.0 -0.0
+asin1004 asin -inf 0.0 -> -1.5707963267948966 inf
+asin1005 asin -inf 2.2999999999999998 -> -1.5707963267948966 inf
+asin1006 asin nan 0.0 -> nan nan
+asin1007 asin nan 2.2999999999999998 -> nan nan
+asin1008 asin -0.0 inf -> -0.0 inf
+asin1009 asin -2.2999999999999998 inf -> -0.0 inf
+asin1010 asin -inf inf -> -0.78539816339744828 inf
+asin1011 asin nan inf -> nan inf
+asin1012 asin -0.0 nan -> -0.0 nan
+asin1013 asin -2.2999999999999998 nan -> nan nan
+asin1014 asin -inf nan -> nan inf ignore-imag-sign
+asin1015 asin nan nan -> nan nan
+asin1016 asin inf 0.0 -> 1.5707963267948966 inf
+asin1017 asin inf 2.2999999999999998 -> 1.5707963267948966 inf
+asin1018 asin 0.0 inf -> 0.0 inf
+asin1019 asin 2.2999999999999998 inf -> 0.0 inf
+asin1020 asin inf inf -> 0.78539816339744828 inf
+asin1021 asin 0.0 nan -> 0.0 nan
+asin1022 asin 2.2999999999999998 nan -> nan nan
+asin1023 asin inf nan -> nan inf ignore-imag-sign
+asin1024 asin inf -0.0 -> 1.5707963267948966 -inf
+asin1025 asin inf -2.2999999999999998 -> 1.5707963267948966 -inf
+asin1026 asin nan -0.0 -> nan nan
+asin1027 asin nan -2.2999999999999998 -> nan nan
+asin1028 asin 0.0 -inf -> 0.0 -inf
+asin1029 asin 2.2999999999999998 -inf -> 0.0 -inf
+asin1030 asin inf -inf -> 0.78539816339744828 -inf
+asin1031 asin nan -inf -> nan -inf
+asin1032 asin -inf -0.0 -> -1.5707963267948966 -inf
+asin1033 asin -inf -2.2999999999999998 -> -1.5707963267948966 -inf
+asin1034 asin -0.0 -inf -> -0.0 -inf
+asin1035 asin -2.2999999999999998 -inf -> -0.0 -inf
+asin1036 asin -inf -inf -> -0.78539816339744828 -inf
+
+
+------------------------------------
+-- asinh: Inverse hyperbolic sine --
+------------------------------------
+
+-- zeros
+asinh0000 asinh 0.0 0.0 -> 0.0 0.0
+asinh0001 asinh 0.0 -0.0 -> 0.0 -0.0
+asinh0002 asinh -0.0 0.0 -> -0.0 0.0
+asinh0003 asinh -0.0 -0.0 -> -0.0 -0.0
+
+-- branch points: +/-i
+asinh0010 asinh 0.0 1.0 -> 0.0 1.5707963267948966
+asinh0011 asinh 0.0 -1.0 -> 0.0 -1.5707963267948966
+asinh0012 asinh -0.0 1.0 -> -0.0 1.5707963267948966
+asinh0013 asinh -0.0 -1.0 -> -0.0 -1.5707963267948966
+
+-- values along both sides of imaginary axis
+asinh0020 asinh 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324
+asinh0021 asinh -0.0 -9.8813129168249309e-324 -> -0.0 -9.8813129168249309e-324
+asinh0022 asinh 0.0 -1e-305 -> 0.0 -1e-305
+asinh0023 asinh -0.0 -1e-305 -> -0.0 -1e-305
+asinh0024 asinh 0.0 -1e-150 -> 0.0 -1e-150
+asinh0025 asinh -0.0 -1e-150 -> -0.0 -1e-150
+asinh0026 asinh 0.0 -9.9999999999999998e-17 -> 0.0 -9.9999999999999998e-17
+asinh0027 asinh -0.0 -9.9999999999999998e-17 -> -0.0 -9.9999999999999998e-17
+asinh0028 asinh 0.0 -0.001 -> 0.0 -0.0010000001666667416
+asinh0029 asinh -0.0 -0.001 -> -0.0 -0.0010000001666667416
+asinh0030 asinh 0.0 -0.57899999999999996 -> 0.0 -0.61750165481717001
+asinh0031 asinh -0.0 -0.57899999999999996 -> -0.0 -0.61750165481717001
+asinh0032 asinh 0.0 -0.99999999999999989 -> 0.0 -1.5707963118937354
+asinh0033 asinh -0.0 -0.99999999999999989 -> -0.0 -1.5707963118937354
+asinh0034 asinh 0.0 -1.0000000000000002 -> 2.1073424255447014e-08 -1.5707963267948966
+asinh0035 asinh -0.0 -1.0000000000000002 -> -2.1073424255447014e-08 -1.5707963267948966
+asinh0036 asinh 0.0 -1.0009999999999999 -> 0.044717633608306849 -1.5707963267948966
+asinh0037 asinh -0.0 -1.0009999999999999 -> -0.044717633608306849 -1.5707963267948966
+asinh0038 asinh 0.0 -2.0 -> 1.3169578969248168 -1.5707963267948966
+asinh0039 asinh -0.0 -2.0 -> -1.3169578969248168 -1.5707963267948966
+asinh0040 asinh 0.0 -20.0 -> 3.6882538673612966 -1.5707963267948966
+asinh0041 asinh -0.0 -20.0 -> -3.6882538673612966 -1.5707963267948966
+asinh0042 asinh 0.0 -10000000000000000.0 -> 37.534508668464674 -1.5707963267948966
+asinh0043 asinh -0.0 -10000000000000000.0 -> -37.534508668464674 -1.5707963267948966
+asinh0044 asinh 0.0 -9.9999999999999998e+149 -> 346.08091112966679 -1.5707963267948966
+asinh0045 asinh -0.0 -9.9999999999999998e+149 -> -346.08091112966679 -1.5707963267948966
+asinh0046 asinh 0.0 -1.0000000000000001e+299 -> 689.16608998577965 -1.5707963267948966
+asinh0047 asinh -0.0 -1.0000000000000001e+299 -> -689.16608998577965 -1.5707963267948966
+asinh0048 asinh 0.0 9.8813129168249309e-324 -> 0.0 9.8813129168249309e-324
+asinh0049 asinh -0.0 9.8813129168249309e-324 -> -0.0 9.8813129168249309e-324
+asinh0050 asinh 0.0 1e-305 -> 0.0 1e-305
+asinh0051 asinh -0.0 1e-305 -> -0.0 1e-305
+asinh0052 asinh 0.0 1e-150 -> 0.0 1e-150
+asinh0053 asinh -0.0 1e-150 -> -0.0 1e-150
+asinh0054 asinh 0.0 9.9999999999999998e-17 -> 0.0 9.9999999999999998e-17
+asinh0055 asinh -0.0 9.9999999999999998e-17 -> -0.0 9.9999999999999998e-17
+asinh0056 asinh 0.0 0.001 -> 0.0 0.0010000001666667416
+asinh0057 asinh -0.0 0.001 -> -0.0 0.0010000001666667416
+asinh0058 asinh 0.0 0.57899999999999996 -> 0.0 0.61750165481717001
+asinh0059 asinh -0.0 0.57899999999999996 -> -0.0 0.61750165481717001
+asinh0060 asinh 0.0 0.99999999999999989 -> 0.0 1.5707963118937354
+asinh0061 asinh -0.0 0.99999999999999989 -> -0.0 1.5707963118937354
+asinh0062 asinh 0.0 1.0000000000000002 -> 2.1073424255447014e-08 1.5707963267948966
+asinh0063 asinh -0.0 1.0000000000000002 -> -2.1073424255447014e-08 1.5707963267948966
+asinh0064 asinh 0.0 1.0009999999999999 -> 0.044717633608306849 1.5707963267948966
+asinh0065 asinh -0.0 1.0009999999999999 -> -0.044717633608306849 1.5707963267948966
+asinh0066 asinh 0.0 2.0 -> 1.3169578969248168 1.5707963267948966
+asinh0067 asinh -0.0 2.0 -> -1.3169578969248168 1.5707963267948966
+asinh0068 asinh 0.0 20.0 -> 3.6882538673612966 1.5707963267948966
+asinh0069 asinh -0.0 20.0 -> -3.6882538673612966 1.5707963267948966
+asinh0070 asinh 0.0 10000000000000000.0 -> 37.534508668464674 1.5707963267948966
+asinh0071 asinh -0.0 10000000000000000.0 -> -37.534508668464674 1.5707963267948966
+asinh0072 asinh 0.0 9.9999999999999998e+149 -> 346.08091112966679 1.5707963267948966
+asinh0073 asinh -0.0 9.9999999999999998e+149 -> -346.08091112966679 1.5707963267948966
+asinh0074 asinh 0.0 1.0000000000000001e+299 -> 689.16608998577965 1.5707963267948966
+asinh0075 asinh -0.0 1.0000000000000001e+299 -> -689.16608998577965 1.5707963267948966
+
+-- random inputs
+asinh0100 asinh -0.5946402853710423 -0.044506548910000145 -> -0.56459775392653022 -0.038256221441536356
+asinh0101 asinh -0.19353958046180916 -0.017489624793193454 -> -0.19237926804196651 -0.017171741895336792
+asinh0102 asinh -0.033117585138955893 -8.5256414015933757 -> -2.8327758348650969 -1.5668848791092411
+asinh0103 asinh -1.5184043184035716 -0.73491245339073275 -> -1.2715891419764005 -0.39204624408542355
+asinh0104 asinh -0.60716120271208818 -0.28900743958436542 -> -0.59119299421187232 -0.24745931678118135
+asinh0105 asinh -0.0237177865112429 2.8832601052166313 -> -1.7205820772413236 1.5620261702963094
+asinh0106 asinh -2.3906812342743979 2.6349216848574013 -> -1.9609636249445124 0.8142142660574706
+asinh0107 asinh -0.0027605019787620517 183.85588476550555 -> -5.9072920005445066 1.5707813120847871
+asinh0108 asinh -0.99083661164404713 0.028006797051617648 -> -0.8750185251283995 0.019894099615994653
+asinh0109 asinh -3.0362951937986393 0.86377266758504867 -> -1.8636030714685221 0.26475058859950168
+asinh0110 asinh 0.34438464536152769 -0.71603790174885029 -> 0.43985415690734164 -0.71015037409294324
+asinh0111 asinh 4.4925124413876256 -60604595352.871613 -> 25.520783738612078 -1.5707963267207683
+asinh0112 asinh 2.3213991428170337 -7.5459667007307258 -> 2.7560464993451643 -1.270073210856117
+asinh0113 asinh 0.21291939741682028 -1.2720428814784408 -> 0.77275088137338266 -1.3182099250896895
+asinh0114 asinh 6.6447359379455957 -0.97196191666946996 -> 2.602830695139672 -0.14368247412319965
+asinh0115 asinh 7.1326256655083746 2.1516360452706857 -> 2.7051146374367212 0.29051701669727581
+asinh0116 asinh 0.18846550905063442 3.4705348585339832 -> 1.917697875799296 1.514155593347924
+asinh0117 asinh 0.19065075303281598 0.26216814548222012 -> 0.19603050785932474 0.26013422809614117
+asinh0118 asinh 2.0242004665739719 0.70510281647495787 -> 1.4970366212896002 0.30526007200481453
+asinh0119 asinh 37.336596461576057 717.29157391678234 -> 7.269981997945294 1.5187910219576033
+
+-- values near infinity
+asinh0200 asinh 1.0760517500874541e+308 1.1497786241240167e+308 -> 710.34346055651815 0.81850936961793475
+asinh0201 asinh 1.1784839328845529e+308 -1.6478429586716638e+308 -> 710.59536255783678 -0.94996311735607697
+asinh0202 asinh -4.8777682248909193e+307 1.4103736217538474e+308 -> -710.28970147376992 1.2378239519096443
+asinh0203 asinh -1.2832478903233108e+308 -1.5732392613155698e+308 -> -710.59750164290745 -0.88657181439322452
+asinh0204 asinh 0.0 6.8431383856345372e+307 -> 709.51001718444604 1.5707963267948966
+asinh0205 asinh -0.0 8.601822432238051e+307 -> -709.73874482126689 1.5707963267948966
+asinh0206 asinh 0.0 -5.5698396067303782e+307 -> 709.30413698733742 -1.5707963267948966
+asinh0207 asinh -0.0 -7.1507777734621804e+307 -> -709.55399186002705 -1.5707963267948966
+asinh0208 asinh 1.6025136110019349e+308 0.0 -> 710.3609292261076 0.0
+asinh0209 asinh 1.3927819858239114e+308 -0.0 -> 710.22065899832899 -0.0
+asinh0210 asinh -6.0442994056210995e+307 0.0 -> -709.38588631057621 0.0
+asinh0211 asinh -1.2775271979042634e+308 -0.0 -> -710.13428215553972 -0.0
+asinh0212 asinh 1.0687496260268489e+308 1.0255615699476961 -> 709.95584521407841 9.5959010882679093e-309
+asinh0213 asinh 1.0050967333370962e+308 -0.87668970117333433 -> 709.89443961168183 -8.7224410556242882e-309
+asinh0214 asinh -5.7161452814862392e+307 8.2377808413450122 -> -709.33006540611166 1.4411426644501116e-307
+asinh0215 asinh -8.2009040727653315e+307 -6.407409526654976 -> -709.69101513070109 -7.8130526461510088e-308
+asinh0216 asinh 6.4239368496483982 1.6365990821551427e+308 -> 710.38197618101287 1.5707963267948966
+asinh0217 asinh 5.4729111423315882 -1.1227237438144211e+308 -> 710.00511346983546 -1.5707963267948966
+asinh0218 asinh -8.3455818297412723 1.443172020182019e+308 -> -710.25619930551818 1.5707963267948966
+asinh0219 asinh -2.6049726230372441 -1.7952291144022702e+308 -> -710.47448847685644 -1.5707963267948966
+
+-- values near 0
+asinh0220 asinh 1.2940113339664088e-314 6.9169190417774516e-323 -> 1.2940113339664088e-314 6.9169190417774516e-323
+asinh0221 asinh 2.3848478863874649e-315 -3.1907655025717717e-310 -> 2.3848478863874649e-315 -3.1907655025717717e-310
+asinh0222 asinh -3.0097643679641622e-316 4.6936236354918422e-322 -> -3.0097643679641622e-316 4.6936236354918422e-322
+asinh0223 asinh -1.787997087755751e-308 -8.5619622834902341e-310 -> -1.787997087755751e-308 -8.5619622834902341e-310
+asinh0224 asinh 0.0 1.2491433448427325e-314 -> 0.0 1.2491433448427325e-314
+asinh0225 asinh -0.0 2.5024072154538062e-308 -> -0.0 2.5024072154538062e-308
+asinh0226 asinh 0.0 -2.9643938750474793e-323 -> 0.0 -2.9643938750474793e-323
+asinh0227 asinh -0.0 -2.9396905927554169e-320 -> -0.0 -2.9396905927554169e-320
+asinh0228 asinh 5.64042930029359e-317 0.0 -> 5.64042930029359e-317 0.0
+asinh0229 asinh 3.3833911866596068e-318 -0.0 -> 3.3833911866596068e-318 -0.0
+asinh0230 asinh -4.9406564584124654e-324 0.0 -> -4.9406564584124654e-324 0.0
+asinh0231 asinh -2.2211379227994845e-308 -0.0 -> -2.2211379227994845e-308 -0.0
+
+-- special values
+asinh1000 asinh 0.0 0.0 -> 0.0 0.0
+asinh1001 asinh 0.0 -0.0 -> 0.0 -0.0
+asinh1002 asinh -0.0 0.0 -> -0.0 0.0
+asinh1003 asinh -0.0 -0.0 -> -0.0 -0.0
+asinh1004 asinh 0.0 inf -> inf 1.5707963267948966
+asinh1005 asinh 2.3 inf -> inf 1.5707963267948966
+asinh1006 asinh 0.0 nan -> nan nan
+asinh1007 asinh 2.3 nan -> nan nan
+asinh1008 asinh inf 0.0 -> inf 0.0
+asinh1009 asinh inf 2.3 -> inf 0.0
+asinh1010 asinh inf inf -> inf 0.78539816339744828
+asinh1011 asinh inf nan -> inf nan
+asinh1012 asinh nan 0.0 -> nan 0.0
+asinh1013 asinh nan 2.3 -> nan nan
+asinh1014 asinh nan inf -> inf nan                      ignore-real-sign
+asinh1015 asinh nan nan -> nan nan
+asinh1016 asinh 0.0 -inf -> inf -1.5707963267948966
+asinh1017 asinh 2.3 -inf -> inf -1.5707963267948966
+asinh1018 asinh inf -0.0 -> inf -0.0
+asinh1019 asinh inf -2.3 -> inf -0.0
+asinh1020 asinh inf -inf -> inf -0.78539816339744828
+asinh1021 asinh nan -0.0 -> nan -0.0
+asinh1022 asinh nan -2.3 -> nan nan
+asinh1023 asinh nan -inf -> inf nan                     ignore-real-sign
+asinh1024 asinh -0.0 -inf -> -inf -1.5707963267948966
+asinh1025 asinh -2.3 -inf -> -inf -1.5707963267948966
+asinh1026 asinh -0.0 nan -> nan nan
+asinh1027 asinh -2.3 nan -> nan nan
+asinh1028 asinh -inf -0.0 -> -inf -0.0
+asinh1029 asinh -inf -2.3 -> -inf -0.0
+asinh1030 asinh -inf -inf -> -inf -0.78539816339744828
+asinh1031 asinh -inf nan -> -inf nan
+asinh1032 asinh -0.0 inf -> -inf 1.5707963267948966
+asinh1033 asinh -2.3 inf -> -inf 1.5707963267948966
+asinh1034 asinh -inf 0.0 -> -inf 0.0
+asinh1035 asinh -inf 2.3 -> -inf 0.0
+asinh1036 asinh -inf inf -> -inf 0.78539816339744828
+
+
+---------------------------
+-- atan: Inverse tangent --
+---------------------------
+
+-- zeros
+-- These are tested in testAtanSign in test_cmath.py
+-- atan0000 atan 0.0 0.0 -> 0.0 0.0
+-- atan0001 atan 0.0 -0.0 -> 0.0 -0.0
+-- atan0002 atan -0.0 0.0 -> -0.0 0.0
+-- atan0003 atan -0.0 -0.0 -> -0.0 -0.0
+
+-- values along both sides of imaginary axis
+atan0010 atan 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324
+atan0011 atan -0.0 -9.8813129168249309e-324 -> -0.0 -9.8813129168249309e-324
+atan0012 atan 0.0 -1e-305 -> 0.0 -1e-305
+atan0013 atan -0.0 -1e-305 -> -0.0 -1e-305
+atan0014 atan 0.0 -1e-150 -> 0.0 -1e-150
+atan0015 atan -0.0 -1e-150 -> -0.0 -1e-150
+atan0016 atan 0.0 -9.9999999999999998e-17 -> 0.0 -9.9999999999999998e-17
+atan0017 atan -0.0 -9.9999999999999998e-17 -> -0.0 -9.9999999999999998e-17
+atan0018 atan 0.0 -0.001 -> 0.0 -0.0010000003333335333
+atan0019 atan -0.0 -0.001 -> -0.0 -0.0010000003333335333
+atan0020 atan 0.0 -0.57899999999999996 -> 0.0 -0.6609570902866303
+atan0021 atan -0.0 -0.57899999999999996 -> -0.0 -0.6609570902866303
+atan0022 atan 0.0 -0.99999999999999989 -> 0.0 -18.714973875118524
+atan0023 atan -0.0 -0.99999999999999989 -> -0.0 -18.714973875118524
+atan0024 atan 0.0 -1.0000000000000002 -> 1.5707963267948966 -18.36840028483855
+atan0025 atan -0.0 -1.0000000000000002 -> -1.5707963267948966 -18.36840028483855
+atan0026 atan 0.0 -1.0009999999999999 -> 1.5707963267948966 -3.8007011672919218
+atan0027 atan -0.0 -1.0009999999999999 -> -1.5707963267948966 -3.8007011672919218
+atan0028 atan 0.0 -2.0 -> 1.5707963267948966 -0.54930614433405489
+atan0029 atan -0.0 -2.0 -> -1.5707963267948966 -0.54930614433405489
+atan0030 atan 0.0 -20.0 -> 1.5707963267948966 -0.050041729278491265
+atan0031 atan -0.0 -20.0 -> -1.5707963267948966 -0.050041729278491265
+atan0032 atan 0.0 -10000000000000000.0 -> 1.5707963267948966 -9.9999999999999998e-17
+atan0033 atan -0.0 -10000000000000000.0 -> -1.5707963267948966 -9.9999999999999998e-17
+atan0034 atan 0.0 -9.9999999999999998e+149 -> 1.5707963267948966 -1e-150
+atan0035 atan -0.0 -9.9999999999999998e+149 -> -1.5707963267948966 -1e-150
+atan0036 atan 0.0 -1.0000000000000001e+299 -> 1.5707963267948966 -9.9999999999999999e-300
+atan0037 atan -0.0 -1.0000000000000001e+299 -> -1.5707963267948966 -9.9999999999999999e-300
+atan0038 atan 0.0 9.8813129168249309e-324 -> 0.0 9.8813129168249309e-324
+atan0039 atan -0.0 9.8813129168249309e-324 -> -0.0 9.8813129168249309e-324
+atan0040 atan 0.0 1e-305 -> 0.0 1e-305
+atan0041 atan -0.0 1e-305 -> -0.0 1e-305
+atan0042 atan 0.0 1e-150 -> 0.0 1e-150
+atan0043 atan -0.0 1e-150 -> -0.0 1e-150
+atan0044 atan 0.0 9.9999999999999998e-17 -> 0.0 9.9999999999999998e-17
+atan0045 atan -0.0 9.9999999999999998e-17 -> -0.0 9.9999999999999998e-17
+atan0046 atan 0.0 0.001 -> 0.0 0.0010000003333335333
+atan0047 atan -0.0 0.001 -> -0.0 0.0010000003333335333
+atan0048 atan 0.0 0.57899999999999996 -> 0.0 0.6609570902866303
+atan0049 atan -0.0 0.57899999999999996 -> -0.0 0.6609570902866303
+atan0050 atan 0.0 0.99999999999999989 -> 0.0 18.714973875118524
+atan0051 atan -0.0 0.99999999999999989 -> -0.0 18.714973875118524
+atan0052 atan 0.0 1.0000000000000002 -> 1.5707963267948966 18.36840028483855
+atan0053 atan -0.0 1.0000000000000002 -> -1.5707963267948966 18.36840028483855
+atan0054 atan 0.0 1.0009999999999999 -> 1.5707963267948966 3.8007011672919218
+atan0055 atan -0.0 1.0009999999999999 -> -1.5707963267948966 3.8007011672919218
+atan0056 atan 0.0 2.0 -> 1.5707963267948966 0.54930614433405489
+atan0057 atan -0.0 2.0 -> -1.5707963267948966 0.54930614433405489
+atan0058 atan 0.0 20.0 -> 1.5707963267948966 0.050041729278491265
+atan0059 atan -0.0 20.0 -> -1.5707963267948966 0.050041729278491265
+atan0060 atan 0.0 10000000000000000.0 -> 1.5707963267948966 9.9999999999999998e-17
+atan0061 atan -0.0 10000000000000000.0 -> -1.5707963267948966 9.9999999999999998e-17
+atan0062 atan 0.0 9.9999999999999998e+149 -> 1.5707963267948966 1e-150
+atan0063 atan -0.0 9.9999999999999998e+149 -> -1.5707963267948966 1e-150
+atan0064 atan 0.0 1.0000000000000001e+299 -> 1.5707963267948966 9.9999999999999999e-300
+atan0065 atan -0.0 1.0000000000000001e+299 -> -1.5707963267948966 9.9999999999999999e-300
+
+-- random inputs
+atan0100 atan -0.32538873661060214 -1.5530461550412578 -> -1.3682728427554227 -0.69451401598762041
+atan0101 atan -0.45863393495197929 -4799.1747094903594 -> -1.5707963068820623 -0.00020836916050636145
+atan0102 atan -8.3006999685976162 -2.6788890251790938 -> -1.4619862771810199 -0.034811669653327826
+atan0103 atan -1.8836307682985314 -1.1441976638861771 -> -1.1839984370871612 -0.20630956157312796
+atan0104 atan -0.00063230482407491669 -4.9312520961829485 -> -1.5707692093223147 -0.20563867743008304
+atan0105 atan -0.84278137150065946 179012.37493146997 -> -1.5707963267685969 5.5862059836425272e-06
+atan0106 atan -0.95487853984049287 14.311334539886177 -> -1.5661322859434561 0.069676024526232005
+atan0107 atan -1.3513252539663239 6.0500727021632198e-08 -> -0.93371676315220975 2.140800269742656e-08
+atan0108 atan -0.20566254458595795 0.11933771944159823 -> -0.20556463711174916 0.11493405387141732
+atan0109 atan -0.58563718795408559 0.64438965423212868 -> -0.68361089300233124 0.46759762751800249
+atan0110 atan 48.479267751948292 -78.386382460112543 -> 1.5650888770910523 -0.0092276811373297584
+atan0111 atan 1.0575373914056061 -0.75988012377296987 -> 0.94430886722043594 -0.31915698126703118
+atan0112 atan 4444810.4314677203 -0.56553404593942558 -> 1.5707961018134231 -2.8625446437701909e-14
+atan0113 atan 0.010101405082520009 -0.032932668550282478 -> 0.01011202676646334 -0.032941214776834996
+atan0114 atan 1.5353585300154911 -2.1947099346796519 -> 1.3400310739206394 -0.29996003607449045
+atan0115 atan 0.21869457055670882 9.9915684254007093 -> 1.5685846078876444 0.1003716881759439
+atan0116 atan 0.17783290150246836 0.064334689863650957 -> 0.17668728064286277 0.062435808728873846
+atan0117 atan 15.757474087615918 383.57262142534 -> 1.5706894060369621 0.0026026817278826603
+atan0118 atan 10.587017408533317 0.21720238081843438 -> 1.4766594681336236 0.0019199097383010061
+atan0119 atan 0.86026078678781204 0.1230148609359502 -> 0.7147259322534929 0.070551221954286605
+
+-- values near infinity
+atan0200 atan 7.8764397011195798e+307 8.1647921137746308e+307 -> 1.5707963267948966 6.3439446939604493e-309
+atan0201 atan 1.5873698696131487e+308 -1.0780367422960641e+308 -> 1.5707963267948966 -2.9279309368530781e-309
+atan0202 atan -1.5844551864825834e+308 1.0290657809098675e+308 -> -1.5707963267948966 2.8829614736961417e-309
+atan0203 atan -1.3168792562524032e+308 -9.088432341614825e+307 -> -1.5707963267948966 -3.5499373057390056e-309
+atan0204 atan 0.0 1.0360465742258337e+308 -> 1.5707963267948966 9.6520757355646018e-309
+atan0205 atan -0.0 1.0045063210373196e+308 -> -1.5707963267948966 9.955138947929503e-309
+atan0206 atan 0.0 -9.5155296715763696e+307 -> 1.5707963267948966 -1.050913648020118e-308
+atan0207 atan -0.0 -1.5565700490496501e+308 -> -1.5707963267948966 -6.4243816114189071e-309
+atan0208 atan 1.2956339389525244e+308 0.0 -> 1.5707963267948966 0.0
+atan0209 atan 1.4408126243772151e+308 -0.0 -> 1.5707963267948966 -0.0
+atan0210 atan -1.0631786461936417e+308 0.0 -> -1.5707963267948966 0.0
+atan0211 atan -1.0516056964171069e+308 -0.0 -> -1.5707963267948966 -0.0
+atan0212 atan 1.236162319603838e+308 4.6827953496242936 -> 1.5707963267948966 0.0
+atan0213 atan 7.000516472897218e+307 -5.8631608017844163 -> 1.5707963267948966 -0.0
+atan0214 atan -1.5053444003338508e+308 5.1199197268420313 -> -1.5707963267948966 0.0
+atan0215 atan -1.399172518147259e+308 -3.5687766472913673 -> -1.5707963267948966 -0.0
+atan0216 atan 8.1252833070803021 6.2782953917343822e+307 -> 1.5707963267948966 1.5927890256908564e-308
+atan0217 atan 2.8034285947515167 -1.3378049775753878e+308 -> 1.5707963267948966 -7.4749310756219562e-309
+atan0218 atan -1.4073509988974953 1.6776381785968355e+308 -> -1.5707963267948966 5.9607608646364569e-309
+atan0219 atan -2.7135551527592119 -1.281567445525738e+308 -> -1.5707963267948966 -7.8029447727565326e-309
+
+-- imaginary part = +/-1, real part tiny
+atan0300 atan -1e-150 -1.0 -> -0.78539816339744828 -173.04045556483339
+atan0301 atan 1e-155 1.0 -> 0.78539816339744828 178.79691829731851
+atan0302 atan 9.9999999999999999e-161 -1.0 -> 0.78539816339744828 -184.55338102980363
+atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875
+atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692
+
+-- special values
+atan1000 atan -0.0 0.0 -> -0.0 0.0
+atan1001 atan nan 0.0 -> nan 0.0
+atan1002 atan -0.0 1.0 -> -0.0 inf divide-by-zero
+atan1003 atan -inf 0.0 -> -1.5707963267948966 0.0
+atan1004 atan -inf 2.2999999999999998 -> -1.5707963267948966 0.0
+atan1005 atan nan 2.2999999999999998 -> nan nan
+atan1006 atan -0.0 inf -> -1.5707963267948966 0.0
+atan1007 atan -2.2999999999999998 inf -> -1.5707963267948966 0.0
+atan1008 atan -inf inf -> -1.5707963267948966 0.0
+atan1009 atan nan inf -> nan 0.0
+atan1010 atan -0.0 nan -> nan nan
+atan1011 atan -2.2999999999999998 nan -> nan nan
+atan1012 atan -inf nan -> -1.5707963267948966 0.0 ignore-imag-sign
+atan1013 atan nan nan -> nan nan
+atan1014 atan 0.0 0.0 -> 0.0 0.0
+atan1015 atan 0.0 1.0 -> 0.0 inf divide-by-zero
+atan1016 atan inf 0.0 -> 1.5707963267948966 0.0
+atan1017 atan inf 2.2999999999999998 -> 1.5707963267948966 0.0
+atan1018 atan 0.0 inf -> 1.5707963267948966 0.0
+atan1019 atan 2.2999999999999998 inf -> 1.5707963267948966 0.0
+atan1020 atan inf inf -> 1.5707963267948966 0.0
+atan1021 atan 0.0 nan -> nan nan
+atan1022 atan 2.2999999999999998 nan -> nan nan
+atan1023 atan inf nan -> 1.5707963267948966 0.0 ignore-imag-sign
+atan1024 atan 0.0 -0.0 -> 0.0 -0.0
+atan1025 atan nan -0.0 -> nan -0.0
+atan1026 atan 0.0 -1.0 -> 0.0 -inf divide-by-zero
+atan1027 atan inf -0.0 -> 1.5707963267948966 -0.0
+atan1028 atan inf -2.2999999999999998 -> 1.5707963267948966 -0.0
+atan1029 atan nan -2.2999999999999998 -> nan nan
+atan1030 atan 0.0 -inf -> 1.5707963267948966 -0.0
+atan1031 atan 2.2999999999999998 -inf -> 1.5707963267948966 -0.0
+atan1032 atan inf -inf -> 1.5707963267948966 -0.0
+atan1033 atan nan -inf -> nan -0.0
+atan1034 atan -0.0 -0.0 -> -0.0 -0.0
+atan1035 atan -0.0 -1.0 -> -0.0 -inf divide-by-zero
+atan1036 atan -inf -0.0 -> -1.5707963267948966 -0.0
+atan1037 atan -inf -2.2999999999999998 -> -1.5707963267948966 -0.0
+atan1038 atan -0.0 -inf -> -1.5707963267948966 -0.0
+atan1039 atan -2.2999999999999998 -inf -> -1.5707963267948966 -0.0
+atan1040 atan -inf -inf -> -1.5707963267948966 -0.0
+
+
+---------------------------------------
+-- atanh: Inverse hyperbolic tangent --
+---------------------------------------
+
+-- zeros
+-- These are tested in testAtanhSign in test_cmath.py
+-- atanh0000 atanh 0.0 0.0 -> 0.0 0.0
+-- atanh0001 atanh 0.0 -0.0 -> 0.0 -0.0
+-- atanh0002 atanh -0.0 0.0 -> -0.0 0.0
+-- atanh0003 atanh -0.0 -0.0 -> -0.0 -0.0
+
+-- values along both sides of real axis
+atanh0010 atanh -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0
+atanh0011 atanh -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0
+atanh0012 atanh -1e-305 0.0 -> -1e-305 0.0
+atanh0013 atanh -1e-305 -0.0 -> -1e-305 -0.0
+atanh0014 atanh -1e-150 0.0 -> -1e-150 0.0
+atanh0015 atanh -1e-150 -0.0 -> -1e-150 -0.0
+atanh0016 atanh -9.9999999999999998e-17 0.0 -> -9.9999999999999998e-17 0.0
+atanh0017 atanh -9.9999999999999998e-17 -0.0 -> -9.9999999999999998e-17 -0.0
+atanh0018 atanh -0.001 0.0 -> -0.0010000003333335333 0.0
+atanh0019 atanh -0.001 -0.0 -> -0.0010000003333335333 -0.0
+atanh0020 atanh -0.57899999999999996 0.0 -> -0.6609570902866303 0.0
+atanh0021 atanh -0.57899999999999996 -0.0 -> -0.6609570902866303 -0.0
+atanh0022 atanh -0.99999999999999989 0.0 -> -18.714973875118524 0.0
+atanh0023 atanh -0.99999999999999989 -0.0 -> -18.714973875118524 -0.0
+atanh0024 atanh -1.0000000000000002 0.0 -> -18.36840028483855 1.5707963267948966
+atanh0025 atanh -1.0000000000000002 -0.0 -> -18.36840028483855 -1.5707963267948966
+atanh0026 atanh -1.0009999999999999 0.0 -> -3.8007011672919218 1.5707963267948966
+atanh0027 atanh -1.0009999999999999 -0.0 -> -3.8007011672919218 -1.5707963267948966
+atanh0028 atanh -2.0 0.0 -> -0.54930614433405489 1.5707963267948966
+atanh0029 atanh -2.0 -0.0 -> -0.54930614433405489 -1.5707963267948966
+atanh0030 atanh -23.0 0.0 -> -0.043505688494814884 1.5707963267948966
+atanh0031 atanh -23.0 -0.0 -> -0.043505688494814884 -1.5707963267948966
+atanh0032 atanh -10000000000000000.0 0.0 -> -9.9999999999999998e-17 1.5707963267948966
+atanh0033 atanh -10000000000000000.0 -0.0 -> -9.9999999999999998e-17 -1.5707963267948966
+atanh0034 atanh -9.9999999999999998e+149 0.0 -> -1e-150 1.5707963267948966
+atanh0035 atanh -9.9999999999999998e+149 -0.0 -> -1e-150 -1.5707963267948966
+atanh0036 atanh -1.0000000000000001e+299 0.0 -> -9.9999999999999999e-300 1.5707963267948966
+atanh0037 atanh -1.0000000000000001e+299 -0.0 -> -9.9999999999999999e-300 -1.5707963267948966
+atanh0038 atanh 9.8813129168249309e-324 0.0 -> 9.8813129168249309e-324 0.0
+atanh0039 atanh 9.8813129168249309e-324 -0.0 -> 9.8813129168249309e-324 -0.0
+atanh0040 atanh 1e-305 0.0 -> 1e-305 0.0
+atanh0041 atanh 1e-305 -0.0 -> 1e-305 -0.0
+atanh0042 atanh 1e-150 0.0 -> 1e-150 0.0
+atanh0043 atanh 1e-150 -0.0 -> 1e-150 -0.0
+atanh0044 atanh 9.9999999999999998e-17 0.0 -> 9.9999999999999998e-17 0.0
+atanh0045 atanh 9.9999999999999998e-17 -0.0 -> 9.9999999999999998e-17 -0.0
+atanh0046 atanh 0.001 0.0 -> 0.0010000003333335333 0.0
+atanh0047 atanh 0.001 -0.0 -> 0.0010000003333335333 -0.0
+atanh0048 atanh 0.57899999999999996 0.0 -> 0.6609570902866303 0.0
+atanh0049 atanh 0.57899999999999996 -0.0 -> 0.6609570902866303 -0.0
+atanh0050 atanh 0.99999999999999989 0.0 -> 18.714973875118524 0.0
+atanh0051 atanh 0.99999999999999989 -0.0 -> 18.714973875118524 -0.0
+atanh0052 atanh 1.0000000000000002 0.0 -> 18.36840028483855 1.5707963267948966
+atanh0053 atanh 1.0000000000000002 -0.0 -> 18.36840028483855 -1.5707963267948966
+atanh0054 atanh 1.0009999999999999 0.0 -> 3.8007011672919218 1.5707963267948966
+atanh0055 atanh 1.0009999999999999 -0.0 -> 3.8007011672919218 -1.5707963267948966
+atanh0056 atanh 2.0 0.0 -> 0.54930614433405489 1.5707963267948966
+atanh0057 atanh 2.0 -0.0 -> 0.54930614433405489 -1.5707963267948966
+atanh0058 atanh 23.0 0.0 -> 0.043505688494814884 1.5707963267948966
+atanh0059 atanh 23.0 -0.0 -> 0.043505688494814884 -1.5707963267948966
+atanh0060 atanh 10000000000000000.0 0.0 -> 9.9999999999999998e-17 1.5707963267948966
+atanh0061 atanh 10000000000000000.0 -0.0 -> 9.9999999999999998e-17 -1.5707963267948966
+atanh0062 atanh 9.9999999999999998e+149 0.0 -> 1e-150 1.5707963267948966
+atanh0063 atanh 9.9999999999999998e+149 -0.0 -> 1e-150 -1.5707963267948966
+atanh0064 atanh 1.0000000000000001e+299 0.0 -> 9.9999999999999999e-300 1.5707963267948966
+atanh0065 atanh 1.0000000000000001e+299 -0.0 -> 9.9999999999999999e-300 -1.5707963267948966
+
+-- random inputs
+atanh0100 atanh -0.54460925980633501 -0.54038050126721027 -> -0.41984265808446974 -0.60354153938352828
+atanh0101 atanh -1.6934614269829051 -0.48807386108113621 -> -0.58592769102243281 -1.3537837470975898
+atanh0102 atanh -1.3467293985501207 -0.47868354895395876 -> -0.69961624370709985 -1.1994450156570076
+atanh0103 atanh -5.6142232418984888 -544551613.39307702 -> -1.8932657550925744e-17 -1.5707963249585235
+atanh0104 atanh -0.011841460381263651 -3.259978899823385 -> -0.0010183936547405188 -1.2731614020743838
+atanh0105 atanh -0.0073345736950029532 0.35821949670922248 -> -0.0065004869024682466 0.34399359971920895
+atanh0106 atanh -13.866782244320014 0.9541129545860273 -> -0.071896852055058899 1.5658322704631409
+atanh0107 atanh -708.59964982780775 21.984802159266675 -> -0.0014098779074189741 1.5707525842838959
+atanh0108 atanh -30.916832076030602 1.3691897138829843 -> -0.032292682045743676 1.5693652094847115
+atanh0109 atanh -0.57461806339861754 0.29534797443913063 -> -0.56467464472482765 0.39615612824172625
+atanh0110 atanh 0.40089246737415685 -1.632285984300659 -> 0.1063832707890608 -1.0402821335326482
+atanh0111 atanh 2119.6167688262176 -1.5383653437377242e+17 -> 8.9565008518382049e-32 -1.5707963267948966
+atanh0112 atanh 756.86017850941641 -6.6064087133223817 -> 0.0013211481136820046 -1.5707847948702234
+atanh0113 atanh 4.0490617718041602 -2.5784456791040652e-12 -> 0.25218425538553618 -1.5707963267947291
+atanh0114 atanh 10.589254957173523 -0.13956391149624509 -> 0.094700890282197664 -1.5695407140217623
+atanh0115 atanh 1.0171187553160499 0.70766113465354019 -> 0.55260251975367791 0.96619711116641682
+atanh0116 atanh 0.031645502527750849 0.067319983726544394 -> 0.031513018344086742 0.067285437670549036
+atanh0117 atanh 0.13670177624994517 0.43240089361857947 -> 0.11538933151017253 0.41392008145336212
+atanh0118 atanh 0.64173899243596688 2.9008577686695256 -> 0.065680142424134405 1.2518535724053921
+atanh0119 atanh 0.19313813528025942 38.799619150741869 -> 0.00012820765917366644 1.5450292202823612
+
+-- values near infinity
+atanh0200 atanh 5.3242646831347954e+307 1.3740396080084153e+308 -> 2.4519253616695576e-309 1.5707963267948966
+atanh0201 atanh 1.158701641241358e+308 -6.5579268873375853e+307 -> 6.5365375267795098e-309 -1.5707963267948966
+atanh0202 atanh -1.3435325735762247e+308 9.8947369259601547e+307 -> -4.8256680906589956e-309 1.5707963267948966
+atanh0203 atanh -1.4359857522598942e+308 -9.4701204702391004e+307 -> -4.8531282262872645e-309 -1.5707963267948966
+atanh0204 atanh 0.0 5.6614181068098497e+307 -> 0.0 1.5707963267948966
+atanh0205 atanh -0.0 6.9813212721450139e+307 -> -0.0 1.5707963267948966
+atanh0206 atanh 0.0 -7.4970613060311453e+307 -> 0.0 -1.5707963267948966
+atanh0207 atanh -0.0 -1.5280601880314068e+308 -> -0.0 -1.5707963267948966
+atanh0208 atanh 8.2219472336000745e+307 0.0 -> 1.2162568933954813e-308 1.5707963267948966
+atanh0209 atanh 1.4811519617280899e+308 -0.0 -> 6.7515017083951325e-309 -1.5707963267948966
+atanh0210 atanh -1.2282016263598785e+308 0.0 -> -8.1419856360537615e-309 1.5707963267948966
+atanh0211 atanh -1.0616427760154426e+308 -0.0 -> -9.4193642399489563e-309 -1.5707963267948966
+atanh0212 atanh 1.2971536510180682e+308 5.2847948452333293 -> 7.7091869510998328e-309 1.5707963267948966
+atanh0213 atanh 1.1849860977411851e+308 -7.9781906447459949 -> 8.4389175696339014e-309 -1.5707963267948966
+atanh0214 atanh -1.4029969422586635e+308 0.93891986543663375 -> -7.127599283218073e-309 1.5707963267948966
+atanh0215 atanh -4.7508098912248211e+307 -8.2702421247039908 -> -2.1049042645278043e-308 -1.5707963267948966
+atanh0216 atanh 8.2680742115769998 8.1153898410918065e+307 -> 0.0 1.5707963267948966
+atanh0217 atanh 1.2575325146218885 -1.4746679147661649e+308 -> 0.0 -1.5707963267948966
+atanh0218 atanh -2.4618803682310899 1.3781522717005568e+308 -> -0.0 1.5707963267948966
+atanh0219 atanh -4.0952386694788112 -1.231083376353703e+308 -> -0.0 -1.5707963267948966
+
+-- values near 0
+atanh0220 atanh 3.8017563659811628e-314 2.6635484239074319e-312 -> 3.8017563659811628e-314 2.6635484239074319e-312
+atanh0221 atanh 1.7391110733611878e-321 -4.3547800672541419e-313 -> 1.7391110733611878e-321 -4.3547800672541419e-313
+atanh0222 atanh -5.9656816081325078e-317 9.9692253555416263e-313 -> -5.9656816081325078e-317 9.9692253555416263e-313
+atanh0223 atanh -6.5606671178400239e-313 -2.1680936406357335e-309 -> -6.5606671178400239e-313 -2.1680936406357335e-309
+atanh0224 atanh 0.0 2.5230944401820779e-319 -> 0.0 2.5230944401820779e-319
+atanh0225 atanh -0.0 5.6066569490064658e-320 -> -0.0 5.6066569490064658e-320
+atanh0226 atanh 0.0 -2.4222487249468377e-317 -> 0.0 -2.4222487249468377e-317
+atanh0227 atanh -0.0 -3.0861101089206037e-316 -> -0.0 -3.0861101089206037e-316
+atanh0228 atanh 3.1219222884393986e-310 0.0 -> 3.1219222884393986e-310 0.0
+atanh0229 atanh 9.8926337564976196e-309 -0.0 -> 9.8926337564976196e-309 -0.0
+atanh0230 atanh -1.5462535092918154e-312 0.0 -> -1.5462535092918154e-312 0.0
+atanh0231 atanh -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0
+
+-- real part = +/-1, imaginary part tiny
+atanh0300 atanh 1.0 1e-153 -> 176.49433320432448 0.78539816339744828
+atanh0301 atanh 1.0 9.9999999999999997e-155 -> 177.64562575082149 0.78539816339744828
+atanh0302 atanh -1.0 1e-161 -> -185.70467357630065 0.78539816339744828
+atanh0303 atanh 1.0 -1e-165 -> 190.30984376228875 -0.78539816339744828
+atanh0304 atanh -1.0 -9.8813129168249309e-324 -> -372.22003596069061 -0.78539816339744828
+
+-- special values
+atanh1000 atanh 0.0 0.0 -> 0.0 0.0
+atanh1001 atanh 0.0 nan -> 0.0 nan
+atanh1002 atanh 1.0 0.0 -> inf 0.0                      divide-by-zero
+atanh1003 atanh 0.0 inf -> 0.0 1.5707963267948966
+atanh1004 atanh 2.3 inf -> 0.0 1.5707963267948966
+atanh1005 atanh 2.3 nan -> nan nan
+atanh1006 atanh inf 0.0 -> 0.0 1.5707963267948966
+atanh1007 atanh inf 2.3 -> 0.0 1.5707963267948966
+atanh1008 atanh inf inf -> 0.0 1.5707963267948966
+atanh1009 atanh inf nan -> 0.0 nan
+atanh1010 atanh nan 0.0 -> nan nan
+atanh1011 atanh nan 2.3 -> nan nan
+atanh1012 atanh nan inf -> 0.0 1.5707963267948966       ignore-real-sign
+atanh1013 atanh nan nan -> nan nan
+atanh1014 atanh 0.0 -0.0 -> 0.0 -0.0
+atanh1015 atanh 1.0 -0.0 -> inf -0.0                    divide-by-zero
+atanh1016 atanh 0.0 -inf -> 0.0 -1.5707963267948966
+atanh1017 atanh 2.3 -inf -> 0.0 -1.5707963267948966
+atanh1018 atanh inf -0.0 -> 0.0 -1.5707963267948966
+atanh1019 atanh inf -2.3 -> 0.0 -1.5707963267948966
+atanh1020 atanh inf -inf -> 0.0 -1.5707963267948966
+atanh1021 atanh nan -0.0 -> nan nan
+atanh1022 atanh nan -2.3 -> nan nan
+atanh1023 atanh nan -inf -> 0.0 -1.5707963267948966     ignore-real-sign
+atanh1024 atanh -0.0 -0.0 -> -0.0 -0.0
+atanh1025 atanh -0.0 nan -> -0.0 nan
+atanh1026 atanh -1.0 -0.0 -> -inf -0.0                  divide-by-zero
+atanh1027 atanh -0.0 -inf -> -0.0 -1.5707963267948966
+atanh1028 atanh -2.3 -inf -> -0.0 -1.5707963267948966
+atanh1029 atanh -2.3 nan -> nan nan
+atanh1030 atanh -inf -0.0 -> -0.0 -1.5707963267948966
+atanh1031 atanh -inf -2.3 -> -0.0 -1.5707963267948966
+atanh1032 atanh -inf -inf -> -0.0 -1.5707963267948966
+atanh1033 atanh -inf nan -> -0.0 nan
+atanh1034 atanh -0.0 0.0 -> -0.0 0.0
+atanh1035 atanh -1.0 0.0 -> -inf 0.0                    divide-by-zero
+atanh1036 atanh -0.0 inf -> -0.0 1.5707963267948966
+atanh1037 atanh -2.3 inf -> -0.0 1.5707963267948966
+atanh1038 atanh -inf 0.0 -> -0.0 1.5707963267948966
+atanh1039 atanh -inf 2.3 -> -0.0 1.5707963267948966
+atanh1040 atanh -inf inf -> -0.0 1.5707963267948966
+
+
+----------------------------
+-- log: Natural logarithm --
+----------------------------
+
+log0000 log 1.0 0.0 -> 0.0 0.0
+log0001 log 1.0 -0.0 -> 0.0 -0.0
+log0002 log -1.0 0.0 -> 0.0 3.1415926535897931
+log0003 log -1.0 -0.0 -> 0.0 -3.1415926535897931
+-- values along both sides of real axis
+log0010 log -9.8813129168249309e-324 0.0 -> -743.74692474082133 3.1415926535897931
+log0011 log -9.8813129168249309e-324 -0.0 -> -743.74692474082133 -3.1415926535897931
+log0012 log -1e-305 0.0 -> -702.28845336318398 3.1415926535897931
+log0013 log -1e-305 -0.0 -> -702.28845336318398 -3.1415926535897931
+log0014 log -1e-150 0.0 -> -345.38776394910684 3.1415926535897931
+log0015 log -1e-150 -0.0 -> -345.38776394910684 -3.1415926535897931
+log0016 log -9.9999999999999998e-17 0.0 -> -36.841361487904734 3.1415926535897931
+log0017 log -9.9999999999999998e-17 -0.0 -> -36.841361487904734 -3.1415926535897931
+log0018 log -0.001 0.0 -> -6.9077552789821368 3.1415926535897931
+log0019 log -0.001 -0.0 -> -6.9077552789821368 -3.1415926535897931
+log0020 log -0.57899999999999996 0.0 -> -0.54645280140914188 3.1415926535897931
+log0021 log -0.57899999999999996 -0.0 -> -0.54645280140914188 -3.1415926535897931
+log0022 log -0.99999999999999989 0.0 -> -1.1102230246251565e-16 3.1415926535897931
+log0023 log -0.99999999999999989 -0.0 -> -1.1102230246251565e-16 -3.1415926535897931
+log0024 log -1.0000000000000002 0.0 -> 2.2204460492503128e-16 3.1415926535897931
+log0025 log -1.0000000000000002 -0.0 -> 2.2204460492503128e-16 -3.1415926535897931
+log0026 log -1.0009999999999999 0.0 -> 0.00099950033308342321 3.1415926535897931
+log0027 log -1.0009999999999999 -0.0 -> 0.00099950033308342321 -3.1415926535897931
+log0028 log -2.0 0.0 -> 0.69314718055994529 3.1415926535897931
+log0029 log -2.0 -0.0 -> 0.69314718055994529 -3.1415926535897931
+log0030 log -23.0 0.0 -> 3.1354942159291497 3.1415926535897931
+log0031 log -23.0 -0.0 -> 3.1354942159291497 -3.1415926535897931
+log0032 log -10000000000000000.0 0.0 -> 36.841361487904734 3.1415926535897931
+log0033 log -10000000000000000.0 -0.0 -> 36.841361487904734 -3.1415926535897931
+log0034 log -9.9999999999999998e+149 0.0 -> 345.38776394910684 3.1415926535897931
+log0035 log -9.9999999999999998e+149 -0.0 -> 345.38776394910684 -3.1415926535897931
+log0036 log -1.0000000000000001e+299 0.0 -> 688.47294280521965 3.1415926535897931
+log0037 log -1.0000000000000001e+299 -0.0 -> 688.47294280521965 -3.1415926535897931
+log0038 log 9.8813129168249309e-324 0.0 -> -743.74692474082133 0.0
+log0039 log 9.8813129168249309e-324 -0.0 -> -743.74692474082133 -0.0
+log0040 log 1e-305 0.0 -> -702.28845336318398 0.0
+log0041 log 1e-305 -0.0 -> -702.28845336318398 -0.0
+log0042 log 1e-150 0.0 -> -345.38776394910684 0.0
+log0043 log 1e-150 -0.0 -> -345.38776394910684 -0.0
+log0044 log 9.9999999999999998e-17 0.0 -> -36.841361487904734 0.0
+log0045 log 9.9999999999999998e-17 -0.0 -> -36.841361487904734 -0.0
+log0046 log 0.001 0.0 -> -6.9077552789821368 0.0
+log0047 log 0.001 -0.0 -> -6.9077552789821368 -0.0
+log0048 log 0.57899999999999996 0.0 -> -0.54645280140914188 0.0
+log0049 log 0.57899999999999996 -0.0 -> -0.54645280140914188 -0.0
+log0050 log 0.99999999999999989 0.0 -> -1.1102230246251565e-16 0.0
+log0051 log 0.99999999999999989 -0.0 -> -1.1102230246251565e-16 -0.0
+log0052 log 1.0000000000000002 0.0 -> 2.2204460492503128e-16 0.0
+log0053 log 1.0000000000000002 -0.0 -> 2.2204460492503128e-16 -0.0
+log0054 log 1.0009999999999999 0.0 -> 0.00099950033308342321 0.0
+log0055 log 1.0009999999999999 -0.0 -> 0.00099950033308342321 -0.0
+log0056 log 2.0 0.0 -> 0.69314718055994529 0.0
+log0057 log 2.0 -0.0 -> 0.69314718055994529 -0.0
+log0058 log 23.0 0.0 -> 3.1354942159291497 0.0
+log0059 log 23.0 -0.0 -> 3.1354942159291497 -0.0
+log0060 log 10000000000000000.0 0.0 -> 36.841361487904734 0.0
+log0061 log 10000000000000000.0 -0.0 -> 36.841361487904734 -0.0
+log0062 log 9.9999999999999998e+149 0.0 -> 345.38776394910684 0.0
+log0063 log 9.9999999999999998e+149 -0.0 -> 345.38776394910684 -0.0
+log0064 log 1.0000000000000001e+299 0.0 -> 688.47294280521965 0.0
+log0065 log 1.0000000000000001e+299 -0.0 -> 688.47294280521965 -0.0
+
+-- random inputs
+log0066 log -1.9830454945186191e-16 -2.0334448025673346 -> 0.70973130194329803 -1.5707963267948968
+log0067 log -0.96745853024741857 -0.84995816228299692 -> 0.25292811398722387 -2.4207570438536905
+log0068 log -0.1603644313948418 -0.2929942111041835 -> -1.0965857872427374 -2.0715870859971419
+log0069 log -0.15917913168438699 -0.25238799251132177 -> -1.2093477313249901 -2.1334784232033863
+log0070 log -0.68907818535078802 -3.0693105853476346 -> 1.1460398629184565 -1.7916403813913211
+log0071 log -17.268133447565589 6.8165120014604756 -> 2.9212694465974836 2.7656245081603164
+log0072 log -1.7153894479690328 26.434055372802636 -> 3.2767542953718003 1.6355986276341734
+log0073 log -8.0456794648936578e-06 0.19722758057570208 -> -1.6233969848296075 1.5708371206810101
+log0074 log -2.4306442691323173 0.6846919750700996 -> 0.92633592001969589 2.8670160576718331
+log0075 log -3.5488049250888194 0.45324040643185254 -> 1.2747008374256426 3.0145640007885111
+log0076 log 0.18418516851510189 -0.26062518836212617 -> -1.1421287121940344 -0.95558440841183434
+log0077 log 2.7124837795638399 -13.148769067133387 -> 2.5971659975706802 -1.3673583045209439
+log0078 log 3.6521275476169149e-13 -3.7820543023170673e-05 -> -10.182658136741569 -1.5707963171384316
+log0079 log 5.0877545813862239 -1.2834978326786852 -> 1.6576856213076328 -0.24711583497738485
+log0080 log 0.26477986808461512 -0.67659001194187429 -> -0.31944085207999973 -1.197773671987121
+log0081 log 0.0014754261398071962 5.3514691608205442 -> 1.6773711707153829 1.5705206219261802
+log0082 log 0.29667334462157885 0.00020056045042584795 -> -1.2151233667079588 0.00067603114168689204
+log0083 log 0.82104233671099425 3.9005387130133102 -> 1.3827918965299593 1.3633304701848363
+log0084 log 0.27268135358180667 124.42088110945804 -> 4.8236724223559229 1.5686047258789015
+log0085 log 0.0026286959168267485 0.47795808180573013 -> -0.73821712137809126 1.5652965360960087
+
+-- values near infinity
+log0100 log 1.0512025744003172e+308 7.2621669750664611e+307 -> 709.44123967814494 0.60455434048332968
+log0101 log 5.5344249034372126e+307 -1.2155859158431275e+308 -> 709.48562300345679 -1.143553056717973
+log0102 log -1.3155575403469408e+308 1.1610793541663864e+308 -> 709.75847809546428 2.41848796504974
+log0103 log -1.632366720973235e+308 -1.54299446211448e+308 -> 710.00545236515586 -2.3843326028455087
+log0104 log 0.0 5.9449276692327712e+307 -> 708.67616191258526 1.5707963267948966
+log0105 log -0.0 1.1201850459025692e+308 -> 709.30970253338171 1.5707963267948966
+log0106 log 0.0 -1.6214225933466528e+308 -> 709.6795125501086 -1.5707963267948966
+log0107 log -0.0 -1.7453269791591058e+308 -> 709.75315056087379 -1.5707963267948966
+log0108 log 1.440860577601428e+308 0.0 -> 709.56144920058262 0.0
+log0109 log 1.391515176148282e+308 -0.0 -> 709.52660185041327 -0.0
+log0110 log -1.201354401295296e+308 0.0 -> 709.37965823023956 3.1415926535897931
+log0111 log -1.6704337825976804e+308 -0.0 -> 709.70929198492399 -3.1415926535897931
+log0112 log 7.2276974655190223e+307 7.94879711369164 -> 708.87154406512104 1.0997689307850458e-307
+log0113 log 1.1207859593716076e+308 -6.1956200868221147 -> 709.31023883080104 -5.5279244310803286e-308
+log0114 log -4.6678933874471045e+307 9.947107893220382 -> 708.43433142431388 3.1415926535897931
+log0115 log -1.5108012453950142e+308 -5.3117197179375619 -> 709.60884877835008 -3.1415926535897931
+log0116 log 7.4903750871504435 1.5320703776626352e+308 -> 709.62282865085137 1.5707963267948966
+log0117 log 5.9760325525654778 -8.0149473997349123e+307 -> 708.97493177248396 -1.5707963267948966
+log0118 log -7.880194206386629 1.7861845814767441e+308 -> 709.77629046837137 1.5707963267948966
+log0119 log -9.886438993852865 -6.19235781080747e+307 -> 708.71693946977302 -1.5707963267948966
+
+-- values near 0
+log0120 log 2.2996867579227779e-308 6.7861840770939125e-312 -> -708.36343567717392 0.00029509166223339815
+log0121 log 6.9169190417774516e-323 -9.0414013188948118e-322 -> -739.22766796468386 -1.4944423210001669
+log0122 log -1.5378064962914011e-316 1.8243628389354635e-310 -> -713.20014803142965 1.5707971697228842
+log0123 log -2.3319898483706837e-321 -2.2358763941866371e-313 -> -719.9045008332522 -1.570796337224766
+log0124 log 0.0 3.872770101081121e-315 -> -723.96033425374401 1.5707963267948966
+log0125 log -0.0 9.6342800939043076e-322 -> -739.16707236281752 1.5707963267948966
+log0126 log 0.0 -2.266099393427834e-308 -> -708.37814861757965 -1.5707963267948966
+log0127 log -0.0 -2.1184695673766626e-315 -> -724.56361036731812 -1.5707963267948966
+log0128 log 1.1363509854348671e-322 0.0 -> -741.30457770545206 0.0
+log0129 log 3.5572726500569751e-322 -0.0 -> -740.16340580236522 -0.0
+log0130 log -2.3696071074040593e-310 0.0 -> -712.93865466421641 3.1415926535897931
+log0131 log -2.813283897266934e-317 -0.0 -> -728.88512203138862 -3.1415926535897931
+
+-- values near the unit circle
+log0200 log -0.59999999999999998 0.80000000000000004 -> 2.2204460492503132e-17 2.2142974355881808
+log0201 log 0.79999999999999993 0.60000000000000009 -> 6.1629758220391547e-33 0.64350110879328448
+
+-- special values
+log1000 log -0.0 0.0 -> -inf 3.1415926535897931         divide-by-zero
+log1001 log 0.0 0.0 -> -inf 0.0                         divide-by-zero
+log1002 log 0.0 inf -> inf 1.5707963267948966
+log1003 log 2.3 inf -> inf 1.5707963267948966
+log1004 log -0.0 inf -> inf 1.5707963267948966
+log1005 log -2.3 inf -> inf 1.5707963267948966
+log1006 log 0.0 nan -> nan nan
+log1007 log 2.3 nan -> nan nan
+log1008 log -0.0 nan -> nan nan
+log1009 log -2.3 nan -> nan nan
+log1010 log -inf 0.0 -> inf 3.1415926535897931
+log1011 log -inf 2.3 -> inf 3.1415926535897931
+log1012 log inf 0.0 -> inf 0.0
+log1013 log inf 2.3 -> inf 0.0
+log1014 log -inf inf -> inf 2.3561944901923448
+log1015 log inf inf -> inf 0.78539816339744828
+log1016 log inf nan -> inf nan
+log1017 log -inf nan -> inf nan
+log1018 log nan 0.0 -> nan nan
+log1019 log nan 2.3 -> nan nan
+log1020 log nan inf -> inf nan
+log1021 log nan nan -> nan nan
+log1022 log -0.0 -0.0 -> -inf -3.1415926535897931       divide-by-zero
+log1023 log 0.0 -0.0 -> -inf -0.0                       divide-by-zero
+log1024 log 0.0 -inf -> inf -1.5707963267948966
+log1025 log 2.3 -inf -> inf -1.5707963267948966
+log1026 log -0.0 -inf -> inf -1.5707963267948966
+log1027 log -2.3 -inf -> inf -1.5707963267948966
+log1028 log -inf -0.0 -> inf -3.1415926535897931
+log1029 log -inf -2.3 -> inf -3.1415926535897931
+log1030 log inf -0.0 -> inf -0.0
+log1031 log inf -2.3 -> inf -0.0
+log1032 log -inf -inf -> inf -2.3561944901923448
+log1033 log inf -inf -> inf -0.78539816339744828
+log1034 log nan -0.0 -> nan nan
+log1035 log nan -2.3 -> nan nan
+log1036 log nan -inf -> inf nan
+
+
+------------------------------
+-- log10: Logarithm base 10 --
+------------------------------
+
+logt0000 log10 1.0 0.0 -> 0.0 0.0
+logt0001 log10 1.0 -0.0 -> 0.0 -0.0
+logt0002 log10 -1.0 0.0 -> 0.0 1.3643763538418414
+logt0003 log10 -1.0 -0.0 -> 0.0 -1.3643763538418414
+-- values along both sides of real axis
+logt0010 log10 -9.8813129168249309e-324 0.0 -> -323.0051853474518 1.3643763538418414
+logt0011 log10 -9.8813129168249309e-324 -0.0 -> -323.0051853474518 -1.3643763538418414
+logt0012 log10 -1e-305 0.0 -> -305.0 1.3643763538418414
+logt0013 log10 -1e-305 -0.0 -> -305.0 -1.3643763538418414
+logt0014 log10 -1e-150 0.0 -> -150.0 1.3643763538418414
+logt0015 log10 -1e-150 -0.0 -> -150.0 -1.3643763538418414
+logt0016 log10 -9.9999999999999998e-17 0.0 -> -16.0 1.3643763538418414
+logt0017 log10 -9.9999999999999998e-17 -0.0 -> -16.0 -1.3643763538418414
+logt0018 log10 -0.001 0.0 -> -3.0 1.3643763538418414
+logt0019 log10 -0.001 -0.0 -> -3.0 -1.3643763538418414
+logt0020 log10 -0.57899999999999996 0.0 -> -0.23732143627256383 1.3643763538418414
+logt0021 log10 -0.57899999999999996 -0.0 -> -0.23732143627256383 -1.3643763538418414
+logt0022 log10 -0.99999999999999989 0.0 -> -4.821637332766436e-17 1.3643763538418414
+logt0023 log10 -0.99999999999999989 -0.0 -> -4.821637332766436e-17 -1.3643763538418414
+logt0024 log10 -1.0000000000000002 0.0 -> 9.6432746655328696e-17 1.3643763538418414
+logt0025 log10 -1.0000000000000002 -0.0 -> 9.6432746655328696e-17 -1.3643763538418414
+logt0026 log10 -1.0009999999999999 0.0 -> 0.0004340774793185929 1.3643763538418414
+logt0027 log10 -1.0009999999999999 -0.0 -> 0.0004340774793185929 -1.3643763538418414
+logt0028 log10 -2.0 0.0 -> 0.3010299956639812 1.3643763538418414
+logt0029 log10 -2.0 -0.0 -> 0.3010299956639812 -1.3643763538418414
+logt0030 log10 -23.0 0.0 -> 1.3617278360175928 1.3643763538418414
+logt0031 log10 -23.0 -0.0 -> 1.3617278360175928 -1.3643763538418414
+logt0032 log10 -10000000000000000.0 0.0 -> 16.0 1.3643763538418414
+logt0033 log10 -10000000000000000.0 -0.0 -> 16.0 -1.3643763538418414
+logt0034 log10 -9.9999999999999998e+149 0.0 -> 150.0 1.3643763538418414
+logt0035 log10 -9.9999999999999998e+149 -0.0 -> 150.0 -1.3643763538418414
+logt0036 log10 -1.0000000000000001e+299 0.0 -> 299.0 1.3643763538418414
+logt0037 log10 -1.0000000000000001e+299 -0.0 -> 299.0 -1.3643763538418414
+logt0038 log10 9.8813129168249309e-324 0.0 -> -323.0051853474518 0.0
+logt0039 log10 9.8813129168249309e-324 -0.0 -> -323.0051853474518 -0.0
+logt0040 log10 1e-305 0.0 -> -305.0 0.0
+logt0041 log10 1e-305 -0.0 -> -305.0 -0.0
+logt0042 log10 1e-150 0.0 -> -150.0 0.0
+logt0043 log10 1e-150 -0.0 -> -150.0 -0.0
+logt0044 log10 9.9999999999999998e-17 0.0 -> -16.0 0.0
+logt0045 log10 9.9999999999999998e-17 -0.0 -> -16.0 -0.0
+logt0046 log10 0.001 0.0 -> -3.0 0.0
+logt0047 log10 0.001 -0.0 -> -3.0 -0.0
+logt0048 log10 0.57899999999999996 0.0 -> -0.23732143627256383 0.0
+logt0049 log10 0.57899999999999996 -0.0 -> -0.23732143627256383 -0.0
+logt0050 log10 0.99999999999999989 0.0 -> -4.821637332766436e-17 0.0
+logt0051 log10 0.99999999999999989 -0.0 -> -4.821637332766436e-17 -0.0
+logt0052 log10 1.0000000000000002 0.0 -> 9.6432746655328696e-17 0.0
+logt0053 log10 1.0000000000000002 -0.0 -> 9.6432746655328696e-17 -0.0
+logt0054 log10 1.0009999999999999 0.0 -> 0.0004340774793185929 0.0
+logt0055 log10 1.0009999999999999 -0.0 -> 0.0004340774793185929 -0.0
+logt0056 log10 2.0 0.0 -> 0.3010299956639812 0.0
+logt0057 log10 2.0 -0.0 -> 0.3010299956639812 -0.0
+logt0058 log10 23.0 0.0 -> 1.3617278360175928 0.0
+logt0059 log10 23.0 -0.0 -> 1.3617278360175928 -0.0
+logt0060 log10 10000000000000000.0 0.0 -> 16.0 0.0
+logt0061 log10 10000000000000000.0 -0.0 -> 16.0 -0.0
+logt0062 log10 9.9999999999999998e+149 0.0 -> 150.0 0.0
+logt0063 log10 9.9999999999999998e+149 -0.0 -> 150.0 -0.0
+logt0064 log10 1.0000000000000001e+299 0.0 -> 299.0 0.0
+logt0065 log10 1.0000000000000001e+299 -0.0 -> 299.0 -0.0
+
+-- random inputs
+logt0066 log10 -1.9830454945186191e-16 -2.0334448025673346 -> 0.30823238806798503 -0.68218817692092071
+logt0067 log10 -0.96745853024741857 -0.84995816228299692 -> 0.10984528422284802 -1.051321426174086
+logt0068 log10 -0.1603644313948418 -0.2929942111041835 -> -0.47624115633305419 -0.89967884023059597
+logt0069 log10 -0.15917913168438699 -0.25238799251132177 -> -0.52521304641665956 -0.92655790645688119
+logt0070 log10 -0.68907818535078802 -3.0693105853476346 -> 0.4977187885066448 -0.77809953119328823
+logt0071 log10 -17.268133447565589 6.8165120014604756 -> 1.2686912008098534 1.2010954629104202
+logt0072 log10 -1.7153894479690328 26.434055372802636 -> 1.423076309032751 0.71033145859005309
+logt0073 log10 -8.0456794648936578e-06 0.19722758057570208 -> -0.70503235244987561 0.68220589348055516
+logt0074 log10 -2.4306442691323173 0.6846919750700996 -> 0.40230257845332595 1.2451292533748923
+logt0075 log10 -3.5488049250888194 0.45324040643185254 -> 0.55359553977141063 1.3092085108866405
+logt0076 log10 0.18418516851510189 -0.26062518836212617 -> -0.49602019732913638 -0.41500503556604301
+logt0077 log10 2.7124837795638399 -13.148769067133387 -> 1.1279348613317008 -0.59383616643803216
+logt0078 log10 3.6521275476169149e-13 -3.7820543023170673e-05 -> -4.4222722398941112 -0.68218817272717114
+logt0079 log10 5.0877545813862239 -1.2834978326786852 -> 0.71992371806426847 -0.10732104352159283
+logt0080 log10 0.26477986808461512 -0.67659001194187429 -> -0.13873139935281681 -0.52018649631300229
+logt0081 log10 0.0014754261398071962 5.3514691608205442 -> 0.72847304354528819 0.6820684398178033
+logt0082 log10 0.29667334462157885 0.00020056045042584795 -> -0.52772137299296806 0.00029359659442937261
+logt0083 log10 0.82104233671099425 3.9005387130133102 -> 0.60053889028349361 0.59208690021184018
+logt0084 log10 0.27268135358180667 124.42088110945804 -> 2.094894315538069 0.68123637673656989
+logt0085 log10 0.0026286959168267485 0.47795808180573013 -> -0.32060362226100814 0.67979964816877081
+
+-- values near infinity
+logt0100 log10 1.0512025744003172e+308 7.2621669750664611e+307 -> 308.10641562682065 0.26255461408256975
+logt0101 log10 5.5344249034372126e+307 -1.2155859158431275e+308 -> 308.12569106009209 -0.496638782296212
+logt0102 log10 -1.3155575403469408e+308 1.1610793541663864e+308 -> 308.24419052091019 1.0503359777705266
+logt0103 log10 -1.632366720973235e+308 -1.54299446211448e+308 -> 308.3514500834093 -1.0355024924378222
+logt0104 log10 0.0 5.9449276692327712e+307 -> 307.77414657501117 0.68218817692092071
+logt0105 log10 -0.0 1.1201850459025692e+308 -> 308.04928977068465 0.68218817692092071
+logt0106 log10 0.0 -1.6214225933466528e+308 -> 308.20989622030174 -0.68218817692092071
+logt0107 log10 -0.0 -1.7453269791591058e+308 -> 308.24187680203539 -0.68218817692092071
+logt0108 log10 1.440860577601428e+308 0.0 -> 308.15862195908755 0.0
+logt0109 log10 1.391515176148282e+308 -0.0 -> 308.14348794720007 -0.0
+logt0110 log10 -1.201354401295296e+308 0.0 -> 308.07967114380773 1.3643763538418414
+logt0111 log10 -1.6704337825976804e+308 -0.0 -> 308.22282926451624 -1.3643763538418414
+logt0112 log10 7.2276974655190223e+307 7.94879711369164 -> 307.85899996571993 4.7762357800858463e-308
+logt0113 log10 1.1207859593716076e+308 -6.1956200868221147 -> 308.04952268169455 -2.4007470767963597e-308
+logt0114 log10 -4.6678933874471045e+307 9.947107893220382 -> 307.66912092839902 1.3643763538418414
+logt0115 log10 -1.5108012453950142e+308 -5.3117197179375619 -> 308.1792073341565 -1.3643763538418414
+logt0116 log10 7.4903750871504435 1.5320703776626352e+308 -> 308.18527871564157 0.68218817692092071
+logt0117 log10 5.9760325525654778 -8.0149473997349123e+307 -> 307.90390067652424 -0.68218817692092071
+logt0118 log10 -7.880194206386629 1.7861845814767441e+308 -> 308.25192633617331 0.68218817692092071
+logt0119 log10 -9.886438993852865 -6.19235781080747e+307 -> 307.79185604308338 -0.68218817692092071
+
+-- values near 0
+logt0120 log10 2.2996867579227779e-308 6.7861840770939125e-312 -> -307.63833129662572 0.00012815668056362305
+logt0121 log10 6.9169190417774516e-323 -9.0414013188948118e-322 -> -321.04249706727148 -0.64902805353306059
+logt0122 log10 -1.5378064962914011e-316 1.8243628389354635e-310 -> -309.73888878263222 0.68218854299989429
+logt0123 log10 -2.3319898483706837e-321 -2.2358763941866371e-313 -> -312.65055220919641 -0.68218818145055538
+logt0124 log10 0.0 3.872770101081121e-315 -> -314.41197828323476 0.68218817692092071
+logt0125 log10 -0.0 9.6342800939043076e-322 -> -321.01618073175331 0.68218817692092071
+logt0126 log10 0.0 -2.266099393427834e-308 -> -307.64472104545649 -0.68218817692092071
+logt0127 log10 -0.0 -2.1184695673766626e-315 -> -314.67397777042407 -0.68218817692092071
+logt0128 log10 1.1363509854348671e-322 0.0 -> -321.94448750709819 0.0
+logt0129 log10 3.5572726500569751e-322 -0.0 -> -321.44888284668451 -0.0
+logt0130 log10 -2.3696071074040593e-310 0.0 -> -309.62532365619722 1.3643763538418414
+logt0131 log10 -2.813283897266934e-317 -0.0 -> -316.55078643961042 -1.3643763538418414
+
+-- values near the unit circle
+logt0200 log10 -0.59999999999999998 0.80000000000000004 -> 9.6432746655328709e-18 0.96165715756846815
+logt0201 log10 0.79999999999999993 0.60000000000000009 -> 2.6765463916147622e-33 0.2794689806475476
+
+-- special values
+logt1000 log10 -0.0 0.0 -> -inf 1.3643763538418414         divide-by-zero
+logt1001 log10 0.0 0.0 -> -inf 0.0                         divide-by-zero
+logt1002 log10 0.0 inf -> inf 0.68218817692092071
+logt1003 log10 2.3 inf -> inf 0.68218817692092071
+logt1004 log10 -0.0 inf -> inf 0.68218817692092071
+logt1005 log10 -2.3 inf -> inf 0.68218817692092071
+logt1006 log10 0.0 nan -> nan nan
+logt1007 log10 2.3 nan -> nan nan
+logt1008 log10 -0.0 nan -> nan nan
+logt1009 log10 -2.3 nan -> nan nan
+logt1010 log10 -inf 0.0 -> inf 1.3643763538418414
+logt1011 log10 -inf 2.3 -> inf 1.3643763538418414
+logt1012 log10 inf 0.0 -> inf 0.0
+logt1013 log10 inf 2.3 -> inf 0.0
+logt1014 log10 -inf inf -> inf 1.0232822653813811
+logt1015 log10 inf inf -> inf 0.34109408846046035
+logt1016 log10 inf nan -> inf nan
+logt1017 log10 -inf nan -> inf nan
+logt1018 log10 nan 0.0 -> nan nan
+logt1019 log10 nan 2.3 -> nan nan
+logt1020 log10 nan inf -> inf nan
+logt1021 log10 nan nan -> nan nan
+logt1022 log10 -0.0 -0.0 -> -inf -1.3643763538418414       divide-by-zero
+logt1023 log10 0.0 -0.0 -> -inf -0.0                       divide-by-zero
+logt1024 log10 0.0 -inf -> inf -0.68218817692092071
+logt1025 log10 2.3 -inf -> inf -0.68218817692092071
+logt1026 log10 -0.0 -inf -> inf -0.68218817692092071
+logt1027 log10 -2.3 -inf -> inf -0.68218817692092071
+logt1028 log10 -inf -0.0 -> inf -1.3643763538418414
+logt1029 log10 -inf -2.3 -> inf -1.3643763538418414
+logt1030 log10 inf -0.0 -> inf -0.0
+logt1031 log10 inf -2.3 -> inf -0.0
+logt1032 log10 -inf -inf -> inf -1.0232822653813811
+logt1033 log10 inf -inf -> inf -0.34109408846046035
+logt1034 log10 nan -0.0 -> nan nan
+logt1035 log10 nan -2.3 -> nan nan
+logt1036 log10 nan -inf -> inf nan
+
+
+-----------------------
+-- sqrt: Square root --
+-----------------------
+
+-- zeros
+sqrt0000 sqrt 0.0 0.0 -> 0.0 0.0
+sqrt0001 sqrt 0.0 -0.0 -> 0.0 -0.0
+sqrt0002 sqrt -0.0 0.0 -> 0.0 0.0
+sqrt0003 sqrt -0.0 -0.0 -> 0.0 -0.0
+
+-- values along both sides of real axis
+sqrt0010 sqrt -9.8813129168249309e-324 0.0 -> 0.0 3.1434555694052576e-162
+sqrt0011 sqrt -9.8813129168249309e-324 -0.0 -> 0.0 -3.1434555694052576e-162
+sqrt0012 sqrt -1e-305 0.0 -> 0.0 3.1622776601683791e-153
+sqrt0013 sqrt -1e-305 -0.0 -> 0.0 -3.1622776601683791e-153
+sqrt0014 sqrt -1e-150 0.0 -> 0.0 9.9999999999999996e-76
+sqrt0015 sqrt -1e-150 -0.0 -> 0.0 -9.9999999999999996e-76
+sqrt0016 sqrt -9.9999999999999998e-17 0.0 -> 0.0 1e-08
+sqrt0017 sqrt -9.9999999999999998e-17 -0.0 -> 0.0 -1e-08
+sqrt0018 sqrt -0.001 0.0 -> 0.0 0.031622776601683791
+sqrt0019 sqrt -0.001 -0.0 -> 0.0 -0.031622776601683791
+sqrt0020 sqrt -0.57899999999999996 0.0 -> 0.0 0.76092049518987193
+sqrt0021 sqrt -0.57899999999999996 -0.0 -> 0.0 -0.76092049518987193
+sqrt0022 sqrt -0.99999999999999989 0.0 -> 0.0 0.99999999999999989
+sqrt0023 sqrt -0.99999999999999989 -0.0 -> 0.0 -0.99999999999999989
+sqrt0024 sqrt -1.0000000000000002 0.0 -> 0.0 1.0
+sqrt0025 sqrt -1.0000000000000002 -0.0 -> 0.0 -1.0
+sqrt0026 sqrt -1.0009999999999999 0.0 -> 0.0 1.000499875062461
+sqrt0027 sqrt -1.0009999999999999 -0.0 -> 0.0 -1.000499875062461
+sqrt0028 sqrt -2.0 0.0 -> 0.0 1.4142135623730951
+sqrt0029 sqrt -2.0 -0.0 -> 0.0 -1.4142135623730951
+sqrt0030 sqrt -23.0 0.0 -> 0.0 4.7958315233127191
+sqrt0031 sqrt -23.0 -0.0 -> 0.0 -4.7958315233127191
+sqrt0032 sqrt -10000000000000000.0 0.0 -> 0.0 100000000.0
+sqrt0033 sqrt -10000000000000000.0 -0.0 -> 0.0 -100000000.0
+sqrt0034 sqrt -9.9999999999999998e+149 0.0 -> 0.0 9.9999999999999993e+74
+sqrt0035 sqrt -9.9999999999999998e+149 -0.0 -> 0.0 -9.9999999999999993e+74
+sqrt0036 sqrt -1.0000000000000001e+299 0.0 -> 0.0 3.1622776601683796e+149
+sqrt0037 sqrt -1.0000000000000001e+299 -0.0 -> 0.0 -3.1622776601683796e+149
+sqrt0038 sqrt 9.8813129168249309e-324 0.0 -> 3.1434555694052576e-162 0.0
+sqrt0039 sqrt 9.8813129168249309e-324 -0.0 -> 3.1434555694052576e-162 -0.0
+sqrt0040 sqrt 1e-305 0.0 -> 3.1622776601683791e-153 0.0
+sqrt0041 sqrt 1e-305 -0.0 -> 3.1622776601683791e-153 -0.0
+sqrt0042 sqrt 1e-150 0.0 -> 9.9999999999999996e-76 0.0
+sqrt0043 sqrt 1e-150 -0.0 -> 9.9999999999999996e-76 -0.0
+sqrt0044 sqrt 9.9999999999999998e-17 0.0 -> 1e-08 0.0
+sqrt0045 sqrt 9.9999999999999998e-17 -0.0 -> 1e-08 -0.0
+sqrt0046 sqrt 0.001 0.0 -> 0.031622776601683791 0.0
+sqrt0047 sqrt 0.001 -0.0 -> 0.031622776601683791 -0.0
+sqrt0048 sqrt 0.57899999999999996 0.0 -> 0.76092049518987193 0.0
+sqrt0049 sqrt 0.57899999999999996 -0.0 -> 0.76092049518987193 -0.0
+sqrt0050 sqrt 0.99999999999999989 0.0 -> 0.99999999999999989 0.0
+sqrt0051 sqrt 0.99999999999999989 -0.0 -> 0.99999999999999989 -0.0
+sqrt0052 sqrt 1.0000000000000002 0.0 -> 1.0 0.0
+sqrt0053 sqrt 1.0000000000000002 -0.0 -> 1.0 -0.0
+sqrt0054 sqrt 1.0009999999999999 0.0 -> 1.000499875062461 0.0
+sqrt0055 sqrt 1.0009999999999999 -0.0 -> 1.000499875062461 -0.0
+sqrt0056 sqrt 2.0 0.0 -> 1.4142135623730951 0.0
+sqrt0057 sqrt 2.0 -0.0 -> 1.4142135623730951 -0.0
+sqrt0058 sqrt 23.0 0.0 -> 4.7958315233127191 0.0
+sqrt0059 sqrt 23.0 -0.0 -> 4.7958315233127191 -0.0
+sqrt0060 sqrt 10000000000000000.0 0.0 -> 100000000.0 0.0
+sqrt0061 sqrt 10000000000000000.0 -0.0 -> 100000000.0 -0.0
+sqrt0062 sqrt 9.9999999999999998e+149 0.0 -> 9.9999999999999993e+74 0.0
+sqrt0063 sqrt 9.9999999999999998e+149 -0.0 -> 9.9999999999999993e+74 -0.0
+sqrt0064 sqrt 1.0000000000000001e+299 0.0 -> 3.1622776601683796e+149 0.0
+sqrt0065 sqrt 1.0000000000000001e+299 -0.0 -> 3.1622776601683796e+149 -0.0
+
+-- random inputs
+sqrt0100 sqrt -0.34252542541549913 -223039880.15076211 -> 10560.300180587592 -10560.300196805192
+sqrt0101 sqrt -0.88790791393018909 -5.3307751730827402 -> 1.5027154613689004 -1.7737140896343291
+sqrt0102 sqrt -113916.89291310767 -0.018143374626153858 -> 2.6877817875351178e-05 -337.51576691038952
+sqrt0103 sqrt -0.63187172386197121 -0.26293913366617694 -> 0.16205707495266153 -0.81125471918761971
+sqrt0104 sqrt -0.058185169308906215 -2.3548312990430991 -> 1.0717660342420072 -1.0985752598086966
+sqrt0105 sqrt -1.0580584765935896 0.14400319259151736 -> 0.069837489270111242 1.030987755262468
+sqrt0106 sqrt -1.1667595947504932 0.11159711473953678 -> 0.051598531319315251 1.0813981705111229
+sqrt0107 sqrt -0.5123728411449906 0.026175433648339085 -> 0.018278026262418718 0.71603556293597614
+sqrt0108 sqrt -3.7453400060067228 1.0946500314809635 -> 0.27990088541692498 1.9554243814742367
+sqrt0109 sqrt -0.0027736121575097673 1.0367943000839817 -> 0.71903560338719175 0.72096172651250545
+sqrt0110 sqrt 1501.2559699453188 -1.1997325207283589 -> 38.746047664730959 -0.015481998720355024
+sqrt0111 sqrt 1.4830075326850578 -0.64100878436755349 -> 1.244712815741096 -0.25749264258434584
+sqrt0112 sqrt 0.095395618499734602 -0.48226565701639595 -> 0.54175904053472879 -0.44509239434231551
+sqrt0113 sqrt 0.50109185681863277 -0.54054037379892561 -> 0.7868179858332387 -0.34349772344520979
+sqrt0114 sqrt 0.98779807595367897 -0.00019848758437225191 -> 0.99388031770665153 -9.9854872279921968e-05
+sqrt0115 sqrt 11.845472380792259 0.0010051104581506761 -> 3.4417252072345397 0.00014601840612346451
+sqrt0116 sqrt 2.3558249686735975 0.25605157371744403 -> 1.5371278477386647 0.083288964575761404
+sqrt0117 sqrt 0.77584894123159098 1.0496420627016076 -> 1.0200744386390885 0.51449287568756552
+sqrt0118 sqrt 1.8961715669604893 0.34940793467158854 -> 1.3827991781411615 0.12634080935066902
+sqrt0119 sqrt 0.96025378316565801 0.69573224860140515 -> 1.0358710342209998 0.33581991658093457
+
+-- values near 0
+sqrt0120 sqrt 7.3577938365086866e-313 8.1181408465112743e-319 -> 8.5777583531543516e-157 4.732087634251168e-163
+sqrt0121 sqrt 1.2406883874892108e-310 -5.1210133324269776e-312 -> 1.1140990057468052e-155 -2.2982756945349973e-157
+sqrt0122 sqrt -7.1145453001139502e-322 2.9561379244703735e-314 -> 1.2157585807480286e-157 1.2157586100077242e-157
+sqrt0123 sqrt -4.9963244206801218e-314 -8.4718424423690227e-319 -> 1.8950582312540437e-162 -2.2352459419578971e-157
+sqrt0124 sqrt 0.0 7.699553609385195e-318 -> 1.9620848107797476e-159 1.9620848107797476e-159
+sqrt0125 sqrt -0.0 3.3900826606499415e-309 -> 4.1170879639922327e-155 4.1170879639922327e-155
+sqrt0126 sqrt 0.0 -9.8907989772250828e-319 -> 7.032353438652342e-160 -7.032353438652342e-160
+sqrt0127 sqrt -0.0 -1.3722939367590908e-315 -> 2.6194407196566702e-158 -2.6194407196566702e-158
+sqrt0128 sqrt 7.9050503334599447e-323 0.0 -> 8.8910349979403099e-162 0.0
+sqrt0129 sqrt 1.8623241768349486e-309 -0.0 -> 4.3154654173506579e-155 -0.0
+sqrt0130 sqrt -2.665971134499887e-308 0.0 -> 0.0 1.6327801856036491e-154
+sqrt0131 sqrt -1.5477066694467245e-310 -0.0 -> 0.0 -1.2440685951533077e-155
+
+-- inputs whose absolute value overflows
+sqrt0140 sqrt 1.6999999999999999e+308 -1.6999999999999999e+308 -> 1.4325088230154573e+154 -5.9336458271212207e+153
+sqrt0141 sqrt -1.797e+308 -9.9999999999999999e+306 -> 3.7284476432057307e+152 -1.3410406899802901e+154
+
+-- special values
+sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0
+sqrt1001 sqrt -0.0 0.0 -> 0.0 0.0
+sqrt1002 sqrt 0.0 inf -> inf inf
+sqrt1003 sqrt 2.3 inf -> inf inf
+sqrt1004 sqrt inf inf -> inf inf
+sqrt1005 sqrt -0.0 inf -> inf inf
+sqrt1006 sqrt -2.3 inf -> inf inf
+sqrt1007 sqrt -inf inf -> inf inf
+sqrt1008 sqrt nan inf -> inf inf
+sqrt1009 sqrt 0.0 nan -> nan nan
+sqrt1010 sqrt 2.3 nan -> nan nan
+sqrt1011 sqrt -0.0 nan -> nan nan
+sqrt1012 sqrt -2.3 nan -> nan nan
+sqrt1013 sqrt -inf 0.0 -> 0.0 inf
+sqrt1014 sqrt -inf 2.3 -> 0.0 inf
+sqrt1015 sqrt inf 0.0 -> inf 0.0
+sqrt1016 sqrt inf 2.3 -> inf 0.0
+sqrt1017 sqrt -inf nan -> nan inf       ignore-imag-sign
+sqrt1018 sqrt inf nan -> inf nan
+sqrt1019 sqrt nan 0.0 -> nan nan
+sqrt1020 sqrt nan 2.3 -> nan nan
+sqrt1021 sqrt nan nan -> nan nan
+sqrt1022 sqrt 0.0 -0.0 -> 0.0 -0.0
+sqrt1023 sqrt -0.0 -0.0 -> 0.0 -0.0
+sqrt1024 sqrt 0.0 -inf -> inf -inf
+sqrt1025 sqrt 2.3 -inf -> inf -inf
+sqrt1026 sqrt inf -inf -> inf -inf
+sqrt1027 sqrt -0.0 -inf -> inf -inf
+sqrt1028 sqrt -2.3 -inf -> inf -inf
+sqrt1029 sqrt -inf -inf -> inf -inf
+sqrt1030 sqrt nan -inf -> inf -inf
+sqrt1031 sqrt -inf -0.0 -> 0.0 -inf
+sqrt1032 sqrt -inf -2.3 -> 0.0 -inf
+sqrt1033 sqrt inf -0.0 -> inf -0.0
+sqrt1034 sqrt inf -2.3 -> inf -0.0
+sqrt1035 sqrt nan -0.0 -> nan nan
+sqrt1036 sqrt nan -2.3 -> nan nan
+
+
+-- For exp, cosh, sinh, tanh we limit tests to arguments whose
+-- imaginary part is less than 10 in absolute value:  most math
+-- libraries have poor accuracy for (real) sine and cosine for
+-- large arguments, and the accuracy of these complex functions
+-- suffer correspondingly.
+--
+-- Similarly, for cos, sin and tan we limit tests to arguments
+-- with relatively small real part.
+
+
+-------------------------------
+-- exp: Exponential function --
+-------------------------------
+
+-- zeros
+exp0000 exp 0.0 0.0 -> 1.0 0.0
+exp0001 exp 0.0 -0.0 -> 1.0 -0.0
+exp0002 exp -0.0 0.0 -> 1.0 0.0
+exp0003 exp -0.0 -0.0 -> 1.0 -0.0
+
+-- random inputs
+exp0004 exp -17.957359009564684 -1.108613895795274 -> 7.0869292576226611e-09 -1.4225929202377833e-08
+exp0005 exp -1.4456149663368642e-15 -0.75359817331772239 -> 0.72923148323917997 -0.68426708517419033
+exp0006 exp -0.76008654883512661 -0.46657235480105019 -> 0.41764393109928666 -0.21035108396792854
+exp0007 exp -5.7071614697735731 -2.3744161818115816e-11 -> 0.0033220890242068356 -7.8880219364953578e-14
+exp0008 exp -0.4653981327927097 -5.2236706667445587e-21 -> 0.62788507378216663 -3.2798648420026468e-21
+exp0009 exp -3.2444565242295518 1.1535625304243959 -> 0.015799936931457641 0.035644950380024749
+exp0010 exp -3.0651456337977727 0.87765086532391878 -> 0.029805595629855953 0.035882775180855669
+exp0011 exp -0.11080823753233926 0.96486386300873106 -> 0.50979112534376314 0.73575512419561562
+exp0012 exp -2.5629722598928648 0.019636235754708079 -> 0.077060452853917397 0.0015133717341137684
+exp0013 exp -3.3201709957983357e-10 1.2684017344487268 -> 0.29780699855434889 0.95462610007689186
+exp0014 exp 0.88767276057993272 -0.18953422986895557 -> 2.3859624049858095 -0.45771559132044426
+exp0015 exp 1.5738333486794742 -2.2576803075544328e-11 -> 4.8251091132458654 -1.0893553826776623e-10
+exp0016 exp 1.6408702341813795 -1.438879484380837 -> 0.6786733590689048 -5.1148284173168825
+exp0017 exp 1.820279424202033 -0.020812040370785722 -> 6.1722462896420902 -0.1284755888435051
+exp0018 exp 1.7273965735945873 -0.61140621328954947 -> 4.6067931898799976 -3.2294267694441308
+exp0019 exp 2.5606034306862995 0.098153136008435504 -> 12.881325889966629 1.2684184812864494
+exp0020 exp 10.280368619483029 3.4564622559748535 -> -27721.283321551502 -9028.9663215568835
+exp0021 exp 1.104007405129741e-155 0.21258803067317278 -> 0.97748813933531764 0.21099037290544478
+exp0022 exp 0.027364777809295172 0.00059226603500623363 -> 1.0277424518451876 0.0006086970181346579
+exp0023 exp 0.94356313429255245 3.418530463518592 -> -2.4712285695346194 -0.70242654900218349
+
+-- cases where exp(z) representable, exp(z.real) not
+exp0030 exp 710.0 0.78500000000000003 -> 1.5803016909637158e+308 1.5790437551806911e+308
+exp0031 exp 710.0 -0.78500000000000003 -> 1.5803016909637158e+308 -1.5790437551806911e+308
+
+-- values for which exp(x) is subnormal, or underflows to 0
+exp0040 exp -735.0 0.78500000000000003 -> 4.3976783136329355e-320 4.3942198541120468e-320
+exp0041 exp -735.0 -2.3559999999999999 -> -4.3952079854037293e-320 -4.396690182341253e-320
+exp0042 exp -745.0 0.0 -> 4.9406564584124654e-324 0.0
+exp0043 exp -745.0 0.7 -> 0.0 0.0
+exp0044 exp -745.0 2.1 -> -0.0 0.0
+exp0045 exp -745.0 3.7 -> -0.0 -0.0
+exp0046 exp -745.0 5.3 -> 0.0 -0.0
+
+-- values for which exp(z) overflows
+exp0050 exp 710.0 0.0 -> inf 0.0                        overflow
+exp0051 exp 711.0 0.7 -> inf inf                        overflow
+exp0052 exp 710.0 1.5 -> 1.5802653829857376e+307 inf    overflow
+exp0053 exp 710.0 1.6 -> -6.5231579995501372e+306 inf   overflow
+exp0054 exp 710.0 2.8 -> -inf 7.4836177417448528e+307   overflow
+
+-- special values
+exp1000 exp 0.0 0.0 -> 1.0 0.0
+exp1001 exp -0.0 0.0 -> 1.0 0.0
+exp1002 exp 0.0 inf -> nan nan          invalid
+exp1003 exp 2.3 inf -> nan nan          invalid
+exp1004 exp -0.0 inf -> nan nan         invalid
+exp1005 exp -2.3 inf -> nan nan         invalid
+exp1006 exp 0.0 nan -> nan nan
+exp1007 exp 2.3 nan -> nan nan
+exp1008 exp -0.0 nan -> nan nan
+exp1009 exp -2.3 nan -> nan nan
+exp1010 exp -inf 0.0 -> 0.0 0.0
+exp1011 exp -inf 1.4 -> 0.0 0.0
+exp1012 exp -inf 2.8 -> -0.0 0.0
+exp1013 exp -inf 4.2 -> -0.0 -0.0
+exp1014 exp -inf 5.6 -> 0.0 -0.0
+exp1015 exp -inf 7.0 -> 0.0 0.0
+exp1016 exp inf 0.0 -> inf 0.0
+exp1017 exp inf 1.4 -> inf inf
+exp1018 exp inf 2.8 -> -inf inf
+exp1019 exp inf 4.2 -> -inf -inf
+exp1020 exp inf 5.6 -> inf -inf
+exp1021 exp inf 7.0 -> inf inf
+exp1022 exp -inf inf -> 0.0 0.0         ignore-real-sign ignore-imag-sign
+exp1023 exp inf inf -> inf nan          invalid ignore-real-sign
+exp1024 exp -inf nan -> 0.0 0.0         ignore-real-sign ignore-imag-sign
+exp1025 exp inf nan -> inf nan          ignore-real-sign
+exp1026 exp nan 0.0 -> nan 0.0
+exp1027 exp nan 2.3 -> nan nan
+exp1028 exp nan inf -> nan nan
+exp1029 exp nan nan -> nan nan
+exp1030 exp 0.0 -0.0 -> 1.0 -0.0
+exp1031 exp -0.0 -0.0 -> 1.0 -0.0
+exp1032 exp 0.0 -inf -> nan nan         invalid
+exp1033 exp 2.3 -inf -> nan nan         invalid
+exp1034 exp -0.0 -inf -> nan nan        invalid
+exp1035 exp -2.3 -inf -> nan nan        invalid
+exp1036 exp -inf -0.0 -> 0.0 -0.0
+exp1037 exp -inf -1.4 -> 0.0 -0.0
+exp1038 exp -inf -2.8 -> -0.0 -0.0
+exp1039 exp -inf -4.2 -> -0.0 0.0
+exp1040 exp -inf -5.6 -> 0.0 0.0
+exp1041 exp -inf -7.0 -> 0.0 -0.0
+exp1042 exp inf -0.0 -> inf -0.0
+exp1043 exp inf -1.4 -> inf -inf
+exp1044 exp inf -2.8 -> -inf -inf
+exp1045 exp inf -4.2 -> -inf inf
+exp1046 exp inf -5.6 -> inf inf
+exp1047 exp inf -7.0 -> inf -inf
+exp1048 exp -inf -inf -> 0.0 0.0        ignore-real-sign ignore-imag-sign
+exp1049 exp inf -inf -> inf nan         invalid ignore-real-sign
+exp1050 exp nan -0.0 -> nan -0.0
+exp1051 exp nan -2.3 -> nan nan
+exp1052 exp nan -inf -> nan nan
+
+
+-----------------------------
+-- cosh: Hyperbolic Cosine --
+-----------------------------
+
+-- zeros
+cosh0000 cosh 0.0 0.0 -> 1.0 0.0
+cosh0001 cosh 0.0 -0.0 -> 1.0 -0.0
+cosh0002 cosh -0.0 0.0 -> 1.0 -0.0
+cosh0003 cosh -0.0 -0.0 -> 1.0 0.0
+
+-- random inputs
+cosh0004 cosh -0.85395264297414253 -8.8553756148671958 -> -1.1684340348021185 0.51842195359787435
+cosh0005 cosh -19.584904237211223 -0.066582627994906177 -> 159816812.23336992 10656776.050406246
+cosh0006 cosh -0.11072618401130772 -1.484820215073247 -> 0.086397164744949503 0.11054275637717284
+cosh0007 cosh -3.4764840250681752 -0.48440348288275276 -> 14.325931955190844 7.5242053548737955
+cosh0008 cosh -0.52047063604524602 -0.3603805382775585 -> 1.0653940354683802 0.19193293606252473
+cosh0009 cosh -1.39518962975995 0.0074738604700702906 -> 2.1417031027235969 -0.01415518712296308
+cosh0010 cosh -0.37107064757653541 0.14728085307856609 -> 1.0580601496776991 -0.055712531964568587
+cosh0011 cosh -5.8470200958739653 4.0021722388336292 -> -112.86220667618285 131.24734033545013
+cosh0012 cosh -0.1700261444851883 0.97167540135354513 -> 0.57208748253577946 -0.1410904820240203
+cosh0013 cosh -0.44042397902648783 1.0904791964139742 -> 0.50760322393058133 -0.40333966652010816
+cosh0014 cosh 0.052267552491867299 -3.8889011430644174 -> -0.73452303414639297 0.035540704833537134
+cosh0015 cosh 0.98000764177127453 -1.2548829247784097 -> 0.47220747341416142 -1.0879421432180316
+cosh0016 cosh 0.083594701222644008 -0.88847899930181284 -> 0.63279782419312613 -0.064954566816002285
+cosh0017 cosh 1.38173531783776 -0.43185040816732229 -> 1.9221663374671647 -0.78073830858849347
+cosh0018 cosh 0.57315681120148465 -0.22255760951027942 -> 1.1399733125173004 -0.1335512343605956
+cosh0019 cosh 1.8882512333062347 4.5024932182383797 -> -0.7041602065362691 -3.1573822131964615
+cosh0020 cosh 0.5618219206858317 0.92620452129575348 -> 0.69822380405378381 0.47309067471054522
+cosh0021 cosh 0.54361442847062591 0.64176483583018462 -> 0.92234462074193491 0.34167906495845501
+cosh0022 cosh 0.0014777403107920331 1.3682028122677661 -> 0.2012106963899549 0.001447518137863219
+cosh0023 cosh 2.218885944363501 2.0015727395883687 -> -1.94294321081968 4.1290269176083196
+
+-- large real part
+cosh0030 cosh 710.5 2.3519999999999999 -> -1.2967465239355998e+308 1.3076707908857333e+308
+cosh0031 cosh -710.5 0.69999999999999996 -> 1.4085466381392499e+308 -1.1864024666450239e+308
+
+-- special values
+cosh1000 cosh 0.0 0.0 -> 1.0 0.0
+cosh1001 cosh 0.0 inf -> nan 0.0        invalid ignore-imag-sign
+cosh1002 cosh 0.0 nan -> nan 0.0        ignore-imag-sign
+cosh1003 cosh 2.3 inf -> nan nan        invalid
+cosh1004 cosh 2.3 nan -> nan nan
+cosh1005 cosh inf 0.0 -> inf 0.0
+cosh1006 cosh inf 1.4 -> inf inf
+cosh1007 cosh inf 2.8 -> -inf inf
+cosh1008 cosh inf 4.2 -> -inf -inf
+cosh1009 cosh inf 5.6 -> inf -inf
+cosh1010 cosh inf 7.0 -> inf inf
+cosh1011 cosh inf inf -> inf nan        invalid ignore-real-sign
+cosh1012 cosh inf nan -> inf nan
+cosh1013 cosh nan 0.0 -> nan 0.0        ignore-imag-sign
+cosh1014 cosh nan 2.3 -> nan nan
+cosh1015 cosh nan inf -> nan nan
+cosh1016 cosh nan nan -> nan nan
+cosh1017 cosh 0.0 -0.0 -> 1.0 -0.0
+cosh1018 cosh 0.0 -inf -> nan 0.0       invalid ignore-imag-sign
+cosh1019 cosh 2.3 -inf -> nan nan       invalid
+cosh1020 cosh inf -0.0 -> inf -0.0
+cosh1021 cosh inf -1.4 -> inf -inf
+cosh1022 cosh inf -2.8 -> -inf -inf
+cosh1023 cosh inf -4.2 -> -inf inf
+cosh1024 cosh inf -5.6 -> inf inf
+cosh1025 cosh inf -7.0 -> inf -inf
+cosh1026 cosh inf -inf -> inf nan       invalid ignore-real-sign
+cosh1027 cosh nan -0.0 -> nan 0.0       ignore-imag-sign
+cosh1028 cosh nan -2.3 -> nan nan
+cosh1029 cosh nan -inf -> nan nan
+cosh1030 cosh -0.0 -0.0 -> 1.0 0.0
+cosh1031 cosh -0.0 -inf -> nan 0.0      invalid ignore-imag-sign
+cosh1032 cosh -0.0 nan -> nan 0.0       ignore-imag-sign
+cosh1033 cosh -2.3 -inf -> nan nan      invalid
+cosh1034 cosh -2.3 nan -> nan nan
+cosh1035 cosh -inf -0.0 -> inf 0.0
+cosh1036 cosh -inf -1.4 -> inf inf
+cosh1037 cosh -inf -2.8 -> -inf inf
+cosh1038 cosh -inf -4.2 -> -inf -inf
+cosh1039 cosh -inf -5.6 -> inf -inf
+cosh1040 cosh -inf -7.0 -> inf inf
+cosh1041 cosh -inf -inf -> inf nan      invalid ignore-real-sign
+cosh1042 cosh -inf nan -> inf nan
+cosh1043 cosh -0.0 0.0 -> 1.0 -0.0
+cosh1044 cosh -0.0 inf -> nan 0.0       invalid ignore-imag-sign
+cosh1045 cosh -2.3 inf -> nan nan       invalid
+cosh1046 cosh -inf 0.0 -> inf -0.0
+cosh1047 cosh -inf 1.4 -> inf -inf
+cosh1048 cosh -inf 2.8 -> -inf -inf
+cosh1049 cosh -inf 4.2 -> -inf inf
+cosh1050 cosh -inf 5.6 -> inf inf
+cosh1051 cosh -inf 7.0 -> inf -inf
+cosh1052 cosh -inf inf -> inf nan       invalid ignore-real-sign
+
+
+---------------------------
+-- sinh: Hyperbolic Sine --
+---------------------------
+
+-- zeros
+sinh0000 sinh 0.0 0.0 -> 0.0 0.0
+sinh0001 sinh 0.0 -0.0 -> 0.0 -0.0
+sinh0002 sinh -0.0 0.0 -> -0.0 0.0
+sinh0003 sinh -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+sinh0004 sinh -17.282588091462742 -0.38187948694103546 -> -14867386.857248396 -5970648.6553516639
+sinh0005 sinh -343.91971203143208 -5.0172868877771525e-22 -> -1.1518691776521735e+149 -5.7792581214689021e+127
+sinh0006 sinh -14.178122253300922 -1.9387157579351293 -> 258440.37909034826 -670452.58500946441
+sinh0007 sinh -1.0343810581686239 -1.0970235266369905 -> -0.56070858278092739 -1.4098883258046697
+sinh0008 sinh -0.066126561416368204 -0.070461584169961872 -> -0.066010558700938124 -0.070557276738637542
+sinh0009 sinh -0.37630149150308484 3.3621734692162173 -> 0.37591118119332617 -0.23447115926369383
+sinh0010 sinh -0.049941960978670055 0.40323767020414625 -> -0.045955482136329009 0.3928878494430646
+sinh0011 sinh -16.647852603903715 0.0026852219129082098 -> -8492566.5739382561 22804.480671133562
+sinh0012 sinh -1.476625314303694 0.89473773116683386 -> -1.2982943334382224 1.7966593367791204
+sinh0013 sinh -422.36429577556913 0.10366634502307912 -> -1.3400321008920044e+183 1.3941600948045599e+182
+sinh0014 sinh 0.09108340745641981 -0.40408227416070353 -> 0.083863724802237902 -0.39480716553935602
+sinh0015 sinh 2.036064132067386 -2.6831729961386239 -> -3.37621124363175 -1.723868330002817
+sinh0016 sinh 2.5616717223063317 -0.0078978498622717767 -> 6.4399415853815869 -0.051472264400722133
+sinh0017 sinh 0.336804011985188 -6.5654622971649337 -> 0.32962499307574578 -0.29449170159995197
+sinh0018 sinh 0.23774603755649693 -0.92467195799232049 -> 0.14449839490603389 -0.82109449053556793
+sinh0019 sinh 0.0011388273541465494 1.9676196882949855 -> -0.00044014605389634999 0.92229398407098806
+sinh0020 sinh 3.2443870105663759 0.8054287559616895 -> 8.8702890778527426 9.2610748597042196
+sinh0021 sinh 0.040628908857054738 0.098206391190944958 -> 0.04044426841671233 0.098129544739707392
+sinh0022 sinh 4.7252283918217696e-30 9.1198155642656697 -> -4.5071980561644404e-30 0.30025730701661713
+sinh0023 sinh 0.043713693678420068 0.22512549887532657 -> 0.042624198673416713 0.22344201231217961
+
+-- large real part
+sinh0030 sinh 710.5 -2.3999999999999999 -> -1.3579970564885919e+308 -1.24394470907798e+308
+sinh0031 sinh -710.5 0.80000000000000004 -> -1.2830671601735164e+308 1.3210954193997678e+308
+
+-- special values
+sinh1000 sinh 0.0 0.0 -> 0.0 0.0
+sinh1001 sinh 0.0 inf -> 0.0 nan        invalid ignore-real-sign
+sinh1002 sinh 0.0 nan -> 0.0 nan        ignore-real-sign
+sinh1003 sinh 2.3 inf -> nan nan        invalid
+sinh1004 sinh 2.3 nan -> nan nan
+sinh1005 sinh inf 0.0 -> inf 0.0
+sinh1006 sinh inf 1.4 -> inf inf
+sinh1007 sinh inf 2.8 -> -inf inf
+sinh1008 sinh inf 4.2 -> -inf -inf
+sinh1009 sinh inf 5.6 -> inf -inf
+sinh1010 sinh inf 7.0 -> inf inf
+sinh1011 sinh inf inf -> inf nan        invalid ignore-real-sign
+sinh1012 sinh inf nan -> inf nan        ignore-real-sign
+sinh1013 sinh nan 0.0 -> nan 0.0
+sinh1014 sinh nan 2.3 -> nan nan
+sinh1015 sinh nan inf -> nan nan
+sinh1016 sinh nan nan -> nan nan
+sinh1017 sinh 0.0 -0.0 -> 0.0 -0.0
+sinh1018 sinh 0.0 -inf -> 0.0 nan       invalid ignore-real-sign
+sinh1019 sinh 2.3 -inf -> nan nan       invalid
+sinh1020 sinh inf -0.0 -> inf -0.0
+sinh1021 sinh inf -1.4 -> inf -inf
+sinh1022 sinh inf -2.8 -> -inf -inf
+sinh1023 sinh inf -4.2 -> -inf inf
+sinh1024 sinh inf -5.6 -> inf inf
+sinh1025 sinh inf -7.0 -> inf -inf
+sinh1026 sinh inf -inf -> inf nan       invalid ignore-real-sign
+sinh1027 sinh nan -0.0 -> nan -0.0
+sinh1028 sinh nan -2.3 -> nan nan
+sinh1029 sinh nan -inf -> nan nan
+sinh1030 sinh -0.0 -0.0 -> -0.0 -0.0
+sinh1031 sinh -0.0 -inf -> 0.0 nan      invalid ignore-real-sign
+sinh1032 sinh -0.0 nan -> 0.0 nan       ignore-real-sign
+sinh1033 sinh -2.3 -inf -> nan nan      invalid
+sinh1034 sinh -2.3 nan -> nan nan
+sinh1035 sinh -inf -0.0 -> -inf -0.0
+sinh1036 sinh -inf -1.4 -> -inf -inf
+sinh1037 sinh -inf -2.8 -> inf -inf
+sinh1038 sinh -inf -4.2 -> inf inf
+sinh1039 sinh -inf -5.6 -> -inf inf
+sinh1040 sinh -inf -7.0 -> -inf -inf
+sinh1041 sinh -inf -inf -> inf nan      invalid ignore-real-sign
+sinh1042 sinh -inf nan -> inf nan       ignore-real-sign
+sinh1043 sinh -0.0 0.0 -> -0.0 0.0
+sinh1044 sinh -0.0 inf -> 0.0 nan       invalid ignore-real-sign
+sinh1045 sinh -2.3 inf -> nan nan       invalid
+sinh1046 sinh -inf 0.0 -> -inf 0.0
+sinh1047 sinh -inf 1.4 -> -inf inf
+sinh1048 sinh -inf 2.8 -> inf inf
+sinh1049 sinh -inf 4.2 -> inf -inf
+sinh1050 sinh -inf 5.6 -> -inf -inf
+sinh1051 sinh -inf 7.0 -> -inf inf
+sinh1052 sinh -inf inf -> inf nan       invalid ignore-real-sign
+
+
+------------------------------
+-- tanh: Hyperbolic Tangent --
+------------------------------
+
+-- Disabled test: replaced by test_math.testTanhSign()
+-- and test_cmath.testTanhSign()
+
+-- -- zeros
+-- tanh0000 tanh 0.0 0.0 -> 0.0 0.0
+-- tanh0001 tanh 0.0 -0.0 -> 0.0 -0.0
+-- tanh0002 tanh -0.0 0.0 -> -0.0 0.0
+-- tanh0003 tanh -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+tanh0004 tanh -21.200500450664993 -1.6970729480342996 -> -1.0 1.9241352344849399e-19
+tanh0005 tanh -0.34158771504251928 -8.0848504951747131 -> -2.123711225855613 1.2827526782026006
+tanh0006 tanh -15.454144725193689 -0.23619582288265617 -> -0.99999999999993283 -3.4336684248260036e-14
+tanh0007 tanh -7.6103163119661952 -0.7802748320307008 -> -0.99999999497219438 -4.9064845343755437e-07
+tanh0008 tanh -0.15374717235792129 -0.6351086327306138 -> -0.23246081703561869 -0.71083467433910219
+tanh0009 tanh -0.49101115474392465 0.09723001264886301 -> -0.45844445715492133 0.077191158541805888
+tanh0010 tanh -0.10690612157664491 2.861612800856395 -> -0.11519761626257358 -0.28400488355647507
+tanh0011 tanh -0.91505774192066702 1.5431174597727007 -> -1.381109893068114 0.025160819663709356
+tanh0012 tanh -0.057433367093792223 0.35491159541246459 -> -0.065220499046696953 0.36921788332369498
+tanh0013 tanh -1.3540418621233514 0.18969415642242535 -> -0.88235642861151387 0.043764069984411721
+tanh0014 tanh 0.94864783961003529 -0.11333689578867717 -> 0.74348401861861368 -0.051271042543855221
+tanh0015 tanh 1.9591698133845488 -0.0029654444904578339 -> 0.9610270776968135 -0.00022664240049212933
+tanh0016 tanh 1.0949715796669197 -0.24706642853984456 -> 0.81636574501369386 -0.087767436914149954
+tanh0017 tanh 5770428.2113731047 -3.7160580339833165 -> 1.0 -0.0
+tanh0018 tanh 1.5576782321399629 -1.0357943787966468 -> 1.0403002384895388 -0.081126347894671463
+tanh0019 tanh 0.62378536230552961 2.3471393579560216 -> 0.85582499238960363 -0.53569473646842869
+tanh0020 tanh 17.400628602508025 9.3987059533841979 -> 0.99999999999999845 -8.0175867720530832e-17
+tanh0021 tanh 0.15026177509871896 0.50630349159505472 -> 0.19367536571827768 0.53849847858853661
+tanh0022 tanh 0.57433977530711167 1.0071604546265627 -> 1.0857848159262844 0.69139213955872214
+tanh0023 tanh 0.16291181500449456 0.006972810241567544 -> 0.16149335907551157 0.0067910772903467817
+
+-- large real part
+tanh0030 tanh 710 0.13 -> 1.0 0.0
+tanh0031 tanh -711 7.4000000000000004 -> -1.0 0.0
+tanh0032 tanh 1000 -2.3199999999999998 -> 1.0 0.0
+tanh0033 tanh -1.0000000000000001e+300 -9.6699999999999999 -> -1.0 -0.0
+
+--special values
+tanh1000 tanh 0.0 0.0 -> 0.0 0.0
+tanh1001 tanh 0.0 inf -> nan nan        invalid
+tanh1002 tanh 2.3 inf -> nan nan        invalid
+tanh1003 tanh 0.0 nan -> nan nan
+tanh1004 tanh 2.3 nan -> nan nan
+tanh1005 tanh inf 0.0 -> 1.0 0.0
+tanh1006 tanh inf 0.7 -> 1.0 0.0
+tanh1007 tanh inf 1.4 -> 1.0 0.0
+tanh1008 tanh inf 2.1 -> 1.0 -0.0
+tanh1009 tanh inf 2.8 -> 1.0 -0.0
+tanh1010 tanh inf 3.5 -> 1.0 0.0
+tanh1011 tanh inf inf -> 1.0 0.0        ignore-imag-sign
+tanh1012 tanh inf nan -> 1.0 0.0        ignore-imag-sign
+tanh1013 tanh nan 0.0 -> nan 0.0
+tanh1014 tanh nan 2.3 -> nan nan
+tanh1015 tanh nan inf -> nan nan
+tanh1016 tanh nan nan -> nan nan
+tanh1017 tanh 0.0 -0.0 -> 0.0 -0.0
+tanh1018 tanh 0.0 -inf -> nan nan       invalid
+tanh1019 tanh 2.3 -inf -> nan nan       invalid
+tanh1020 tanh inf -0.0 -> 1.0 -0.0
+tanh1021 tanh inf -0.7 -> 1.0 -0.0
+tanh1022 tanh inf -1.4 -> 1.0 -0.0
+tanh1023 tanh inf -2.1 -> 1.0 0.0
+tanh1024 tanh inf -2.8 -> 1.0 0.0
+tanh1025 tanh inf -3.5 -> 1.0 -0.0
+tanh1026 tanh inf -inf -> 1.0 0.0       ignore-imag-sign
+tanh1027 tanh nan -0.0 -> nan -0.0
+tanh1028 tanh nan -2.3 -> nan nan
+tanh1029 tanh nan -inf -> nan nan
+tanh1030 tanh -0.0 -0.0 -> -0.0 -0.0
+tanh1031 tanh -0.0 -inf -> nan nan      invalid
+tanh1032 tanh -2.3 -inf -> nan nan      invalid
+tanh1033 tanh -0.0 nan -> nan nan
+tanh1034 tanh -2.3 nan -> nan nan
+tanh1035 tanh -inf -0.0 -> -1.0 -0.0
+tanh1036 tanh -inf -0.7 -> -1.0 -0.0
+tanh1037 tanh -inf -1.4 -> -1.0 -0.0
+tanh1038 tanh -inf -2.1 -> -1.0 0.0
+tanh1039 tanh -inf -2.8 -> -1.0 0.0
+tanh1040 tanh -inf -3.5 -> -1.0 -0.0
+tanh1041 tanh -inf -inf -> -1.0 0.0     ignore-imag-sign
+tanh1042 tanh -inf nan -> -1.0 0.0      ignore-imag-sign
+tanh1043 tanh -0.0 0.0 -> -0.0 0.0
+tanh1044 tanh -0.0 inf -> nan nan       invalid
+tanh1045 tanh -2.3 inf -> nan nan       invalid
+tanh1046 tanh -inf 0.0 -> -1.0 0.0
+tanh1047 tanh -inf 0.7 -> -1.0 0.0
+tanh1048 tanh -inf 1.4 -> -1.0 0.0
+tanh1049 tanh -inf 2.1 -> -1.0 -0.0
+tanh1050 tanh -inf 2.8 -> -1.0 -0.0
+tanh1051 tanh -inf 3.5 -> -1.0 0.0
+tanh1052 tanh -inf inf -> -1.0 0.0      ignore-imag-sign
+
+
+-----------------
+-- cos: Cosine --
+-----------------
+
+-- zeros
+cos0000 cos 0.0 0.0 -> 1.0 -0.0
+cos0001 cos 0.0 -0.0 -> 1.0 0.0
+cos0002 cos -0.0 0.0 -> 1.0 0.0
+cos0003 cos -0.0 -0.0 -> 1.0 -0.0
+
+-- random inputs
+cos0004 cos -2.0689194692073034 -0.0016802181751734313 -> -0.47777827208561469 -0.0014760401501695971
+cos0005 cos -0.4209627318177977 -1.8238516774258027 -> 2.9010402201444108 -1.2329207042329617
+cos0006 cos -1.9402181630694557 -2.9751857392891217 -> -3.5465459297970985 -9.1119163586282248
+cos0007 cos -3.3118320290191616 -0.87871302909286142 -> -1.3911528636565498 0.16878141517391701
+cos0008 cos -4.9540404623376872 -0.57949232239026827 -> 0.28062445586552065 0.59467861308508008
+cos0009 cos -0.45374584316245026 1.3950283448373935 -> 1.9247665574290578 0.83004572204761107
+cos0010 cos -0.42578172040176843 1.2715881615413049 -> 1.7517161459489148 0.67863902697363332
+cos0011 cos -0.13862985354300136 0.43587635877670328 -> 1.0859880290361912 0.062157548146672272
+cos0012 cos -0.11073221308966584 9.9384082307326475e-15 -> 0.99387545040722947 1.0982543264065479e-15
+cos0013 cos -1.5027633662054623e-07 0.0069668060249955498 -> 1.0000242682912412 1.0469545565660995e-09
+cos0014 cos 4.9728645490503052 -0.00027479808860952822 -> 0.25754011731975501 -0.00026552849549083186
+cos0015 cos 7.81969303486719 -0.79621523445878783 -> 0.045734882501585063 0.88253139933082991
+cos0016 cos 0.13272421880766716 -0.74668445308718201 -> 1.2806012244432847 0.10825373267437005
+cos0017 cos 4.2396521985973274 -2.2178848380884881 -> -2.1165117057056855 -4.0416492444641401
+cos0018 cos 1.1622206624927296 -0.50400115461197081 -> 0.44884072613370379 0.4823469915034318
+cos0019 cos 1.628772864620884e-08 0.58205705428979282 -> 1.1742319995791435 -1.0024839481956604e-08
+cos0020 cos 2.6385212606111241 2.9886107100937296 -> -8.7209475927161417 -4.7748352107199796
+cos0021 cos 4.8048375263775256 0.0062248852898515658 -> 0.092318702015846243 0.0061983430422306142
+cos0022 cos 7.9914515433858515 0.71659966615501436 -> -0.17375439906936566 -0.77217043527294582
+cos0023 cos 0.45124351152540226 1.6992693993812158 -> 2.543477948972237 -1.1528193694875477
+
+-- special values
+cos1000 cos -0.0 0.0 -> 1.0 0.0
+cos1001 cos -inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1002 cos nan 0.0 -> nan 0.0 ignore-imag-sign
+cos1003 cos -inf 2.2999999999999998 -> nan nan invalid
+cos1004 cos nan 2.2999999999999998 -> nan nan
+cos1005 cos -0.0 inf -> inf 0.0
+cos1006 cos -1.3999999999999999 inf -> inf inf
+cos1007 cos -2.7999999999999998 inf -> -inf inf
+cos1008 cos -4.2000000000000002 inf -> -inf -inf
+cos1009 cos -5.5999999999999996 inf -> inf -inf
+cos1010 cos -7.0 inf -> inf inf
+cos1011 cos -inf inf -> inf nan invalid ignore-real-sign
+cos1012 cos nan inf -> inf nan
+cos1013 cos -0.0 nan -> nan 0.0 ignore-imag-sign
+cos1014 cos -2.2999999999999998 nan -> nan nan
+cos1015 cos -inf nan -> nan nan
+cos1016 cos nan nan -> nan nan
+cos1017 cos 0.0 0.0 -> 1.0 -0.0
+cos1018 cos inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1019 cos inf 2.2999999999999998 -> nan nan invalid
+cos1020 cos 0.0 inf -> inf -0.0
+cos1021 cos 1.3999999999999999 inf -> inf -inf
+cos1022 cos 2.7999999999999998 inf -> -inf -inf
+cos1023 cos 4.2000000000000002 inf -> -inf inf
+cos1024 cos 5.5999999999999996 inf -> inf inf
+cos1025 cos 7.0 inf -> inf -inf
+cos1026 cos inf inf -> inf nan invalid ignore-real-sign
+cos1027 cos 0.0 nan -> nan 0.0 ignore-imag-sign
+cos1028 cos 2.2999999999999998 nan -> nan nan
+cos1029 cos inf nan -> nan nan
+cos1030 cos 0.0 -0.0 -> 1.0 0.0
+cos1031 cos inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1032 cos nan -0.0 -> nan 0.0 ignore-imag-sign
+cos1033 cos inf -2.2999999999999998 -> nan nan invalid
+cos1034 cos nan -2.2999999999999998 -> nan nan
+cos1035 cos 0.0 -inf -> inf 0.0
+cos1036 cos 1.3999999999999999 -inf -> inf inf
+cos1037 cos 2.7999999999999998 -inf -> -inf inf
+cos1038 cos 4.2000000000000002 -inf -> -inf -inf
+cos1039 cos 5.5999999999999996 -inf -> inf -inf
+cos1040 cos 7.0 -inf -> inf inf
+cos1041 cos inf -inf -> inf nan invalid ignore-real-sign
+cos1042 cos nan -inf -> inf nan
+cos1043 cos -0.0 -0.0 -> 1.0 -0.0
+cos1044 cos -inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1045 cos -inf -2.2999999999999998 -> nan nan invalid
+cos1046 cos -0.0 -inf -> inf -0.0
+cos1047 cos -1.3999999999999999 -inf -> inf -inf
+cos1048 cos -2.7999999999999998 -inf -> -inf -inf
+cos1049 cos -4.2000000000000002 -inf -> -inf inf
+cos1050 cos -5.5999999999999996 -inf -> inf inf
+cos1051 cos -7.0 -inf -> inf -inf
+cos1052 cos -inf -inf -> inf nan invalid ignore-real-sign
+
+
+---------------
+-- sin: Sine --
+---------------
+
+-- zeros
+sin0000 sin 0.0 0.0 -> 0.0 0.0
+sin0001 sin 0.0 -0.0 -> 0.0 -0.0
+sin0002 sin -0.0 0.0 -> -0.0 0.0
+sin0003 sin -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+sin0004 sin -0.18691829163163759 -0.74388741985507034 -> -0.2396636733773444 -0.80023231101856751
+sin0005 sin -0.45127453702459158 -461.81339920716164 -> -7.9722299331077877e+199 -1.6450205811004628e+200
+sin0006 sin -0.47669228345768921 -2.7369936564987514 -> -3.557238022267124 -6.8308030771226615
+sin0007 sin -0.31024285525950857 -1.4869219939188296 -> -0.70972676047175209 -1.9985029635426839
+sin0008 sin -4.4194573407025608 -1.405999210989288 -> 2.0702480800802685 0.55362250792180601
+sin0009 sin -1.7810832046434898e-05 0.0016439555384379083 -> -1.7810856113185261e-05 0.0016439562786668375
+sin0010 sin -0.8200017874897666 0.61724876887771929 -> -0.8749078195948865 0.44835295550987758
+sin0011 sin -1.4536502806107114 0.63998575534150415 -> -1.2035709929437679 0.080012187489163708
+sin0012 sin -2.2653412155506079 0.13172760685583729 -> -0.77502093809190431 -0.084554426868229532
+sin0013 sin -0.02613983069491858 0.18404766597776073 -> -0.026580778863127943 0.18502525396735642
+sin0014 sin 1.5743065001054617 -0.53125574272642029 -> 1.1444596332092725 0.0019537598099352077
+sin0015 sin 7.3833101791283289e-20 -0.16453221324236217 -> 7.4834720674379429e-20 -0.16527555646466915
+sin0016 sin 0.34763834641254038 -2.8377416421089565 -> 2.918883541504663 -8.0002718053250224
+sin0017 sin 0.077105785180421563 -0.090056027316200674 -> 0.077341973814471304 -0.089909869380524587
+sin0018 sin 3.9063227798142329e-17 -0.05954098654295524 -> 3.9132490348956512e-17 -0.059576172859837351
+sin0019 sin 0.57333917932544598 8.7785221430594696e-06 -> 0.54244029338302935 7.3747869125301368e-06
+sin0020 sin 0.024861722816513169 0.33044620756118515 -> 0.026228801369651 0.3363889671570689
+sin0021 sin 1.4342727387492671 0.81361889790284347 -> 1.3370960060947923 0.12336137961387163
+sin0022 sin 1.1518087354403725 4.8597235966150558 -> 58.919141989603041 26.237003403758852
+sin0023 sin 0.00087773078406649192 34.792379211312095 -> 565548145569.38245 644329685822700.62
+
+-- special values
+sin1000 sin -0.0 0.0 -> -0.0 0.0
+sin1001 sin -inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1002 sin nan 0.0 -> nan 0.0 ignore-imag-sign
+sin1003 sin -inf 2.2999999999999998 -> nan nan invalid
+sin1004 sin nan 2.2999999999999998 -> nan nan
+sin1005 sin -0.0 inf -> -0.0 inf
+sin1006 sin -1.3999999999999999 inf -> -inf inf
+sin1007 sin -2.7999999999999998 inf -> -inf -inf
+sin1008 sin -4.2000000000000002 inf -> inf -inf
+sin1009 sin -5.5999999999999996 inf -> inf inf
+sin1010 sin -7.0 inf -> -inf inf
+sin1011 sin -inf inf -> nan inf invalid ignore-imag-sign
+sin1012 sin nan inf -> nan inf ignore-imag-sign
+sin1013 sin -0.0 nan -> -0.0 nan
+sin1014 sin -2.2999999999999998 nan -> nan nan
+sin1015 sin -inf nan -> nan nan
+sin1016 sin nan nan -> nan nan
+sin1017 sin 0.0 0.0 -> 0.0 0.0
+sin1018 sin inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1019 sin inf 2.2999999999999998 -> nan nan invalid
+sin1020 sin 0.0 inf -> 0.0 inf
+sin1021 sin 1.3999999999999999 inf -> inf inf
+sin1022 sin 2.7999999999999998 inf -> inf -inf
+sin1023 sin 4.2000000000000002 inf -> -inf -inf
+sin1024 sin 5.5999999999999996 inf -> -inf inf
+sin1025 sin 7.0 inf -> inf inf
+sin1026 sin inf inf -> nan inf invalid ignore-imag-sign
+sin1027 sin 0.0 nan -> 0.0 nan
+sin1028 sin 2.2999999999999998 nan -> nan nan
+sin1029 sin inf nan -> nan nan
+sin1030 sin 0.0 -0.0 -> 0.0 -0.0
+sin1031 sin inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1032 sin nan -0.0 -> nan 0.0 ignore-imag-sign
+sin1033 sin inf -2.2999999999999998 -> nan nan invalid
+sin1034 sin nan -2.2999999999999998 -> nan nan
+sin1035 sin 0.0 -inf -> 0.0 -inf
+sin1036 sin 1.3999999999999999 -inf -> inf -inf
+sin1037 sin 2.7999999999999998 -inf -> inf inf
+sin1038 sin 4.2000000000000002 -inf -> -inf inf
+sin1039 sin 5.5999999999999996 -inf -> -inf -inf
+sin1040 sin 7.0 -inf -> inf -inf
+sin1041 sin inf -inf -> nan inf invalid ignore-imag-sign
+sin1042 sin nan -inf -> nan inf ignore-imag-sign
+sin1043 sin -0.0 -0.0 -> -0.0 -0.0
+sin1044 sin -inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1045 sin -inf -2.2999999999999998 -> nan nan invalid
+sin1046 sin -0.0 -inf -> -0.0 -inf
+sin1047 sin -1.3999999999999999 -inf -> -inf -inf
+sin1048 sin -2.7999999999999998 -inf -> -inf inf
+sin1049 sin -4.2000000000000002 -inf -> inf inf
+sin1050 sin -5.5999999999999996 -inf -> inf -inf
+sin1051 sin -7.0 -inf -> -inf -inf
+sin1052 sin -inf -inf -> nan inf invalid ignore-imag-sign
+
+
+------------------
+-- tan: Tangent --
+------------------
+
+-- zeros
+tan0000 tan 0.0 0.0 -> 0.0 0.0
+tan0001 tan 0.0 -0.0 -> 0.0 -0.0
+tan0002 tan -0.0 0.0 -> -0.0 0.0
+tan0003 tan -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+tan0004 tan -0.56378561833861074 -1.7110276237187664e+73 -> -0.0 -1.0
+tan0005 tan -3.5451633993471915e-12 -2.855471863564059 -> -4.6622441304889575e-14 -0.99340273843093951
+tan0006 tan -2.502442719638696 -0.26742234390504221 -> 0.66735215252994995 -0.39078997935420956
+tan0007 tan -0.87639597720371365 -55.586225523280206 -> -1.0285264565948176e-48 -1.0
+tan0008 tan -0.015783869596427243 -520.05944436039272 -> -0.0 -1.0
+tan0009 tan -0.84643549990725164 2.0749097935396343 -> -0.031412661676959573 1.0033548479526764
+tan0010 tan -0.43613792248559646 8.1082741629458059 -> -1.3879848444644593e-07 0.99999988344224011
+tan0011 tan -1.0820906367833114 0.28571868992480248 -> -1.3622485737936536 0.99089269377971245
+tan0012 tan -1.1477859580220084 1.9021637002708041 -> -0.034348450042071196 1.0293954097901687
+tan0013 tan -0.12465543176953409 3.0606851016344815e-05 -> -0.12530514290387343 3.1087420769945479e-05
+tan0014 tan 3.7582848717525343 -692787020.44038939 -> 0.0 -1.0
+tan0015 tan 2.2321967655142176e-06 -10.090069423008169 -> 1.5369846120622643e-14 -0.99999999655723759
+tan0016 tan 0.88371172390245012 -1.1635053630132823 -> 0.19705017118625889 -1.0196452280843129
+tan0017 tan 2.1347414231849267 -1.9311339960416831 -> -0.038663576915982524 -1.0174399993980778
+tan0018 tan 5.9027945255899974 -2.1574195684607135e-183 -> -0.39986591539281496 -2.5023753167976915e-183
+tan0019 tan 0.44811489490805362 683216075670.07556 -> 0.0 1.0
+tan0020 tan 4.1459766396068325 12.523017205605756 -> 2.4022514758988068e-11 1.0000000000112499
+tan0021 tan 1.7809617968443272 1.5052381702853379 -> -0.044066222118946903 1.0932684517702778
+tan0022 tan 1.1615313900880577 1.7956298728647107 -> 0.041793186826390362 1.0375339546034792
+tan0023 tan 0.067014779477908945 5.8517361577457097 -> 2.2088639754800034e-06 0.9999836182420061
+
+-- special values
+tan1000 tan -0.0 0.0 -> -0.0 0.0
+tan1001 tan -inf 0.0 -> nan nan invalid
+tan1002 tan -inf 2.2999999999999998 -> nan nan invalid
+tan1003 tan nan 0.0 -> nan nan
+tan1004 tan nan 2.2999999999999998 -> nan nan
+tan1005 tan -0.0 inf -> -0.0 1.0
+tan1006 tan -0.69999999999999996 inf -> -0.0 1.0
+tan1007 tan -1.3999999999999999 inf -> -0.0 1.0
+tan1008 tan -2.1000000000000001 inf -> 0.0 1.0
+tan1009 tan -2.7999999999999998 inf -> 0.0 1.0
+tan1010 tan -3.5 inf -> -0.0 1.0
+tan1011 tan -inf inf -> -0.0 1.0 ignore-real-sign
+tan1012 tan nan inf -> -0.0 1.0 ignore-real-sign
+tan1013 tan -0.0 nan -> -0.0 nan
+tan1014 tan -2.2999999999999998 nan -> nan nan
+tan1015 tan -inf nan -> nan nan
+tan1016 tan nan nan -> nan nan
+tan1017 tan 0.0 0.0 -> 0.0 0.0
+tan1018 tan inf 0.0 -> nan nan invalid
+tan1019 tan inf 2.2999999999999998 -> nan nan invalid
+tan1020 tan 0.0 inf -> 0.0 1.0
+tan1021 tan 0.69999999999999996 inf -> 0.0 1.0
+tan1022 tan 1.3999999999999999 inf -> 0.0 1.0
+tan1023 tan 2.1000000000000001 inf -> -0.0 1.0
+tan1024 tan 2.7999999999999998 inf -> -0.0 1.0
+tan1025 tan 3.5 inf -> 0.0 1.0
+tan1026 tan inf inf -> -0.0 1.0 ignore-real-sign
+tan1027 tan 0.0 nan -> 0.0 nan
+tan1028 tan 2.2999999999999998 nan -> nan nan
+tan1029 tan inf nan -> nan nan
+tan1030 tan 0.0 -0.0 -> 0.0 -0.0
+tan1031 tan inf -0.0 -> nan nan invalid
+tan1032 tan inf -2.2999999999999998 -> nan nan invalid
+tan1033 tan nan -0.0 -> nan nan
+tan1034 tan nan -2.2999999999999998 -> nan nan
+tan1035 tan 0.0 -inf -> 0.0 -1.0
+tan1036 tan 0.69999999999999996 -inf -> 0.0 -1.0
+tan1037 tan 1.3999999999999999 -inf -> 0.0 -1.0
+tan1038 tan 2.1000000000000001 -inf -> -0.0 -1.0
+tan1039 tan 2.7999999999999998 -inf -> -0.0 -1.0
+tan1040 tan 3.5 -inf -> 0.0 -1.0
+tan1041 tan inf -inf -> -0.0 -1.0 ignore-real-sign
+tan1042 tan nan -inf -> -0.0 -1.0 ignore-real-sign
+tan1043 tan -0.0 -0.0 -> -0.0 -0.0
+tan1044 tan -inf -0.0 -> nan nan invalid
+tan1045 tan -inf -2.2999999999999998 -> nan nan invalid
+tan1046 tan -0.0 -inf -> -0.0 -1.0
+tan1047 tan -0.69999999999999996 -inf -> -0.0 -1.0
+tan1048 tan -1.3999999999999999 -inf -> -0.0 -1.0
+tan1049 tan -2.1000000000000001 -inf -> 0.0 -1.0
+tan1050 tan -2.7999999999999998 -inf -> 0.0 -1.0
+tan1051 tan -3.5 -inf -> -0.0 -1.0
+tan1052 tan -inf -inf -> -0.0 -1.0 ignore-real-sign
+
+
+------------------------------------------------------------------------
+-- rect: Conversion from polar coordinates to rectangular coordinates --
+------------------------------------------------------------------------
+--
+-- For cmath.rect, we can use the same testcase syntax as for the
+-- complex -> complex functions above, but here the input arguments
+-- should be interpreted as a pair of floating-point numbers rather
+-- than the real and imaginary parts of a complex number.
+--
+-- Here are the 'spirit of C99' rules for rect.  First, the short
+-- version:
+--
+--    rect(x, t) = exp(log(x)+it) for positive-signed x
+--    rect(x, t) = -exp(log(-x)+it) for negative-signed x
+--    rect(nan, t) = exp(nan + it), except that in rect(nan, +-0) the
+--      sign of the imaginary part is unspecified.
+--
+-- and now the long version:
+--
+--   rect(x, -t) = conj(rect(x, t)) for all x and t
+--   rect(-x, t) = -rect(x, t) for all x and t
+--   rect(+0, +0) returns +0 + i0
+--   rect(+0, inf) returns +- 0 +- i0, where the signs of the real and
+--     imaginary parts are unspecified.
+--   rect(x, inf) returns NaN + i NaN and raises the "invalid"
+--     floating-point exception, for finite nonzero x.
+--   rect(inf, inf) returns +-inf + i NaN and raises the "invalid"
+--     floating-point exception (where the sign of the real part of the
+--     result is unspecified).
+--   rect(inf, +0) returns inf+i0
+--   rect(inf, x) returns inf*cis(x), for finite nonzero x
+--   rect(inf, NaN) returns +-inf+i NaN, where the sign of the real part
+--     of the result is unspecified.
+--   rect(NaN, x) returns NaN + i NaN for all nonzero numbers (including
+--     infinities) x
+--   rect(NaN, 0) returns NaN +- i0, where the sign of the imaginary
+--     part is unspecified
+--   rect(NaN, NaN) returns NaN + i NaN
+--   rect(x, NaN) returns NaN + i NaN for finite nonzero x
+--   rect(+0, NaN) return +-0 +- i0, where the signs of the real and
+--     imaginary parts are unspecified.
+
+-- special values
+rect1000 rect 0.0 0.0 -> 0.0 0.0
+rect1001 rect 0.0 inf -> 0.0 0.0        ignore-real-sign ignore-imag-sign
+rect1002 rect 2.3 inf -> nan nan        invalid
+rect1003 rect inf inf -> inf nan        invalid ignore-real-sign
+rect1004 rect inf 0.0 -> inf 0.0
+rect1005 rect inf 1.4 -> inf inf
+rect1006 rect inf 2.8 -> -inf inf
+rect1007 rect inf 4.2 -> -inf -inf
+rect1008 rect inf 5.6 -> inf -inf
+rect1009 rect inf 7.0 -> inf inf
+rect1010 rect nan 0.0 -> nan 0.0        ignore-imag-sign
+rect1011 rect nan 2.3 -> nan nan
+rect1012 rect nan inf -> nan nan
+rect1013 rect nan nan -> nan nan
+rect1014 rect inf nan -> inf nan        ignore-real-sign
+rect1015 rect 2.3 nan -> nan nan
+rect1016 rect 0.0 nan -> 0.0 0.0        ignore-real-sign ignore-imag-sign
+rect1017 rect 0.0 -0.0 -> 0.0 -0.0
+rect1018 rect 0.0 -inf -> 0.0 0.0       ignore-real-sign ignore-imag-sign
+rect1019 rect 2.3 -inf -> nan nan       invalid
+rect1020 rect inf -inf -> inf nan       invalid ignore-real-sign
+rect1021 rect inf -0.0 -> inf -0.0
+rect1022 rect inf -1.4 -> inf -inf
+rect1023 rect inf -2.8 -> -inf -inf
+rect1024 rect inf -4.2 -> -inf inf
+rect1025 rect inf -5.6 -> inf inf
+rect1026 rect inf -7.0 -> inf -inf
+rect1027 rect nan -0.0 -> nan 0.0       ignore-imag-sign
+rect1028 rect nan -2.3 -> nan nan
+rect1029 rect nan -inf -> nan nan
+rect1030 rect -0.0 0.0 -> -0.0 -0.0
+rect1031 rect -0.0 inf -> 0.0 0.0       ignore-real-sign ignore-imag-sign
+rect1032 rect -2.3 inf -> nan nan       invalid
+rect1033 rect -inf inf -> -inf nan      invalid ignore-real-sign
+rect1034 rect -inf 0.0 -> -inf -0.0
+rect1035 rect -inf 1.4 -> -inf -inf
+rect1036 rect -inf 2.8 -> inf -inf
+rect1037 rect -inf 4.2 -> inf inf
+rect1038 rect -inf 5.6 -> -inf inf
+rect1039 rect -inf 7.0 -> -inf -inf
+rect1040 rect -inf nan -> inf nan       ignore-real-sign
+rect1041 rect -2.3 nan -> nan nan
+rect1042 rect -0.0 nan -> 0.0 0.0       ignore-real-sign ignore-imag-sign
+rect1043 rect -0.0 -0.0 -> -0.0 0.0
+rect1044 rect -0.0 -inf -> 0.0 0.0      ignore-real-sign ignore-imag-sign
+rect1045 rect -2.3 -inf -> nan nan      invalid
+rect1046 rect -inf -inf -> -inf nan     invalid ignore-real-sign
+rect1047 rect -inf -0.0 -> -inf 0.0
+rect1048 rect -inf -1.4 -> -inf inf
+rect1049 rect -inf -2.8 -> inf inf
+rect1050 rect -inf -4.2 -> inf -inf
+rect1051 rect -inf -5.6 -> -inf -inf
+rect1052 rect -inf -7.0 -> -inf inf
+
+-------------------------------------------------------------------------
+-- polar: Conversion from rectangular coordinates to polar coordinates --
+-------------------------------------------------------------------------
+--
+-- For cmath.polar, we can use the same testcase syntax as for the
+-- complex -> complex functions above, but here the output arguments
+-- should be interpreted as a pair of floating-point numbers rather
+-- than the real and imaginary parts of a complex number.
+--
+-- Annex G of the C99 standard describes fully both the real and
+-- imaginary parts of polar (as cabs and carg, respectively, which in turn
+-- are defined in terms of the functions hypot and atan2).
+
+-- overflow
+polar0100 polar 1.4e308 1.4e308 -> inf 0.78539816339744828      overflow
+
+-- special values
+polar1000 polar 0.0 0.0 -> 0.0 0.0
+polar1001 polar 0.0 -0.0 -> 0.0 -0.0
+polar1002 polar -0.0 0.0 -> 0.0 3.1415926535897931
+polar1003 polar -0.0 -0.0 -> 0.0 -3.1415926535897931
+polar1004 polar inf 0.0 -> inf 0.0
+polar1005 polar inf 2.3 -> inf 0.0
+polar1006 polar inf inf -> inf 0.78539816339744828
+polar1007 polar 2.3 inf -> inf 1.5707963267948966
+polar1008 polar 0.0 inf -> inf 1.5707963267948966
+polar1009 polar -0.0 inf -> inf 1.5707963267948966
+polar1010 polar -2.3 inf -> inf 1.5707963267948966
+polar1011 polar -inf inf -> inf 2.3561944901923448
+polar1012 polar -inf 2.3 -> inf 3.1415926535897931
+polar1013 polar -inf 0.0 -> inf 3.1415926535897931
+polar1014 polar -inf -0.0 -> inf -3.1415926535897931
+polar1015 polar -inf -2.3 -> inf -3.1415926535897931
+polar1016 polar -inf -inf -> inf -2.3561944901923448
+polar1017 polar -2.3 -inf -> inf -1.5707963267948966
+polar1018 polar -0.0 -inf -> inf -1.5707963267948966
+polar1019 polar 0.0 -inf -> inf -1.5707963267948966
+polar1020 polar 2.3 -inf -> inf -1.5707963267948966
+polar1021 polar inf -inf -> inf -0.78539816339744828
+polar1022 polar inf -2.3 -> inf -0.0
+polar1023 polar inf -0.0 -> inf -0.0
+polar1024 polar nan -inf -> inf nan
+polar1025 polar nan -2.3 -> nan nan
+polar1026 polar nan -0.0 -> nan nan
+polar1027 polar nan 0.0 -> nan nan
+polar1028 polar nan 2.3 -> nan nan
+polar1029 polar nan inf -> inf nan
+polar1030 polar nan nan -> nan nan
+polar1031 polar inf nan -> inf nan
+polar1032 polar 2.3 nan -> nan nan
+polar1033 polar 0.0 nan -> nan nan
+polar1034 polar -0.0 nan -> nan nan
+polar1035 polar -2.3 nan -> nan nan
+polar1036 polar -inf nan -> inf nan

tests/math_testcases.txt

@@ -0,0 +1,633 @@
+-- Testcases for functions in math.
+--
+-- Each line takes the form:
+--
+-- <testid> <function> <input_value> -> <output_value> <flags>
+--
+-- where:
+--
+--   <testid> is a short name identifying the test,
+--
+--   <function> is the function to be tested (exp, cos, asinh, ...),
+--
+--   <input_value> is a string representing a floating-point value
+--
+--   <output_value> is the expected (ideal) output value, again
+--     represented as a string.
+--
+--   <flags> is a list of the floating-point flags required by C99
+--
+-- The possible flags are:
+--
+--   divide-by-zero : raised when a finite input gives a
+--     mathematically infinite result.
+--
+--   overflow : raised when a finite input gives a finite result that
+--     is too large to fit in the usual range of an IEEE 754 double.
+--
+--   invalid : raised for invalid inputs (e.g., sqrt(-1))
+--
+--   ignore-sign : indicates that the sign of the result is
+--     unspecified; e.g., if the result is given as inf,
+--     then both -inf and inf should be accepted as correct.
+--
+-- Flags may appear in any order.
+--
+-- Lines beginning with '--' (like this one) start a comment, and are
+-- ignored.  Blank lines, or lines containing only whitespace, are also
+-- ignored.
+
+-- Many of the values below were computed with the help of
+-- version 2.4 of the MPFR library for multiple-precision
+-- floating-point computations with correct rounding.  All output
+-- values in this file are (modulo yet-to-be-discovered bugs)
+-- correctly rounded, provided that each input and output decimal
+-- floating-point value below is interpreted as a representation of
+-- the corresponding nearest IEEE 754 double-precision value.  See the
+-- MPFR homepage at http://www.mpfr.org for more information about the
+-- MPFR project.
+
+
+-------------------------
+-- erf: error function --
+-------------------------
+
+erf0000 erf 0.0 -> 0.0
+erf0001 erf -0.0 -> -0.0
+erf0002 erf inf -> 1.0
+erf0003 erf -inf -> -1.0
+erf0004 erf nan -> nan
+
+-- tiny values
+erf0010 erf 1e-308 -> 1.1283791670955125e-308
+erf0011 erf 5e-324 -> 4.9406564584124654e-324
+erf0012 erf 1e-10 -> 1.1283791670955126e-10
+
+-- small integers
+erf0020 erf 1 -> 0.84270079294971489
+erf0021 erf 2 -> 0.99532226501895271
+erf0022 erf 3 -> 0.99997790950300136
+erf0023 erf 4 -> 0.99999998458274209
+erf0024 erf 5 -> 0.99999999999846256
+erf0025 erf 6 -> 1.0
+
+erf0030 erf -1 -> -0.84270079294971489
+erf0031 erf -2 -> -0.99532226501895271
+erf0032 erf -3 -> -0.99997790950300136
+erf0033 erf -4 -> -0.99999998458274209
+erf0034 erf -5 -> -0.99999999999846256
+erf0035 erf -6 -> -1.0
+
+-- huge values should all go to +/-1, depending on sign
+erf0040 erf -40 -> -1.0
+erf0041 erf 1e16 -> 1.0
+erf0042 erf -1e150 -> -1.0
+erf0043 erf 1.7e308 -> 1.0
+
+-- Issue 8986: inputs x with exp(-x*x) near the underflow threshold
+-- incorrectly signalled overflow on some platforms.
+erf0100 erf 26.2 -> 1.0
+erf0101 erf 26.4 -> 1.0
+erf0102 erf 26.6 -> 1.0
+erf0103 erf 26.8 -> 1.0
+erf0104 erf 27.0 -> 1.0
+erf0105 erf 27.2 -> 1.0
+erf0106 erf 27.4 -> 1.0
+erf0107 erf 27.6 -> 1.0
+
+erf0110 erf -26.2 -> -1.0
+erf0111 erf -26.4 -> -1.0
+erf0112 erf -26.6 -> -1.0
+erf0113 erf -26.8 -> -1.0
+erf0114 erf -27.0 -> -1.0
+erf0115 erf -27.2 -> -1.0
+erf0116 erf -27.4 -> -1.0
+erf0117 erf -27.6 -> -1.0
+
+----------------------------------------
+-- erfc: complementary error function --
+----------------------------------------
+
+erfc0000 erfc 0.0 -> 1.0
+erfc0001 erfc -0.0 -> 1.0
+erfc0002 erfc inf -> 0.0
+erfc0003 erfc -inf -> 2.0
+erfc0004 erfc nan -> nan
+
+-- tiny values
+erfc0010 erfc 1e-308 -> 1.0
+erfc0011 erfc 5e-324 -> 1.0
+erfc0012 erfc 1e-10 -> 0.99999999988716204
+
+-- small integers
+erfc0020 erfc 1 -> 0.15729920705028513
+erfc0021 erfc 2 -> 0.0046777349810472662
+erfc0022 erfc 3 -> 2.2090496998585441e-05
+erfc0023 erfc 4 -> 1.541725790028002e-08
+erfc0024 erfc 5 -> 1.5374597944280349e-12
+erfc0025 erfc 6 -> 2.1519736712498913e-17
+
+erfc0030 erfc -1 -> 1.8427007929497148
+erfc0031 erfc -2 -> 1.9953222650189528
+erfc0032 erfc -3 -> 1.9999779095030015
+erfc0033 erfc -4 -> 1.9999999845827421
+erfc0034 erfc -5 -> 1.9999999999984626
+erfc0035 erfc -6 -> 2.0
+
+-- as x -> infinity, erfc(x) behaves like exp(-x*x)/x/sqrt(pi)
+erfc0040 erfc 20 -> 5.3958656116079012e-176
+erfc0041 erfc 25 -> 8.3001725711965228e-274
+erfc0042 erfc 27 -> 5.2370464393526292e-319
+erfc0043 erfc 28 -> 0.0
+
+-- huge values
+erfc0050 erfc -40 -> 2.0
+erfc0051 erfc 1e16 -> 0.0
+erfc0052 erfc -1e150 -> 2.0
+erfc0053 erfc 1.7e308 -> 0.0
+
+-- Issue 8986: inputs x with exp(-x*x) near the underflow threshold
+-- incorrectly signalled overflow on some platforms.
+erfc0100 erfc 26.2 -> 1.6432507924389461e-300
+erfc0101 erfc 26.4 -> 4.4017768588035426e-305
+erfc0102 erfc 26.6 -> 1.0885125885442269e-309
+erfc0103 erfc 26.8 -> 2.4849621571966629e-314
+erfc0104 erfc 27.0 -> 5.2370464393526292e-319
+erfc0105 erfc 27.2 -> 9.8813129168249309e-324
+erfc0106 erfc 27.4 -> 0.0
+erfc0107 erfc 27.6 -> 0.0
+
+erfc0110 erfc -26.2 -> 2.0
+erfc0111 erfc -26.4 -> 2.0
+erfc0112 erfc -26.6 -> 2.0
+erfc0113 erfc -26.8 -> 2.0
+erfc0114 erfc -27.0 -> 2.0
+erfc0115 erfc -27.2 -> 2.0
+erfc0116 erfc -27.4 -> 2.0
+erfc0117 erfc -27.6 -> 2.0
+
+---------------------------------------------------------
+-- lgamma: log of absolute value of the gamma function --
+---------------------------------------------------------
+
+-- special values
+lgam0000 lgamma 0.0 -> inf      divide-by-zero
+lgam0001 lgamma -0.0 -> inf     divide-by-zero
+lgam0002 lgamma inf -> inf
+lgam0003 lgamma -inf -> inf
+lgam0004 lgamma nan -> nan
+
+-- negative integers
+lgam0010 lgamma -1 -> inf       divide-by-zero
+lgam0011 lgamma -2 -> inf       divide-by-zero
+lgam0012 lgamma -1e16 -> inf    divide-by-zero
+lgam0013 lgamma -1e300 -> inf   divide-by-zero
+lgam0014 lgamma -1.79e308 -> inf divide-by-zero
+
+-- small positive integers give factorials
+lgam0020 lgamma 1 -> 0.0
+lgam0021 lgamma 2 -> 0.0
+lgam0022 lgamma 3 -> 0.69314718055994529
+lgam0023 lgamma 4 -> 1.791759469228055
+lgam0024 lgamma 5 -> 3.1780538303479458
+lgam0025 lgamma 6 -> 4.7874917427820458
+
+-- half integers
+lgam0030 lgamma 0.5 -> 0.57236494292470008
+lgam0031 lgamma 1.5 -> -0.12078223763524522
+lgam0032 lgamma 2.5 -> 0.28468287047291918
+lgam0033 lgamma 3.5 -> 1.2009736023470743
+lgam0034 lgamma -0.5 -> 1.2655121234846454
+lgam0035 lgamma -1.5 -> 0.86004701537648098
+lgam0036 lgamma -2.5 -> -0.056243716497674054
+lgam0037 lgamma -3.5 -> -1.309006684993042
+
+-- values near 0
+lgam0040 lgamma 0.1 -> 2.252712651734206
+lgam0041 lgamma 0.01 -> 4.5994798780420219
+lgam0042 lgamma 1e-8 -> 18.420680738180209
+lgam0043 lgamma 1e-16 -> 36.841361487904734
+lgam0044 lgamma 1e-30 -> 69.077552789821368
+lgam0045 lgamma 1e-160 -> 368.41361487904732
+lgam0046 lgamma 1e-308 -> 709.19620864216608
+lgam0047 lgamma 5.6e-309 -> 709.77602713741896
+lgam0048 lgamma 5.5e-309 -> 709.79404564292167
+lgam0049 lgamma 1e-309 -> 711.49879373516012
+lgam0050 lgamma 1e-323 -> 743.74692474082133
+lgam0051 lgamma 5e-324 -> 744.44007192138122
+lgam0060 lgamma -0.1 -> 2.3689613327287886
+lgam0061 lgamma -0.01 -> 4.6110249927528013
+lgam0062 lgamma -1e-8 -> 18.420680749724522
+lgam0063 lgamma -1e-16 -> 36.841361487904734
+lgam0064 lgamma -1e-30 -> 69.077552789821368
+lgam0065 lgamma -1e-160 -> 368.41361487904732
+lgam0066 lgamma -1e-308 -> 709.19620864216608
+lgam0067 lgamma -5.6e-309 -> 709.77602713741896
+lgam0068 lgamma -5.5e-309 -> 709.79404564292167
+lgam0069 lgamma -1e-309 -> 711.49879373516012
+lgam0070 lgamma -1e-323 -> 743.74692474082133
+lgam0071 lgamma -5e-324 -> 744.44007192138122
+
+-- values near negative integers
+lgam0080 lgamma -0.99999999999999989 -> 36.736800569677101
+lgam0081 lgamma -1.0000000000000002 -> 36.043653389117154
+lgam0082 lgamma -1.9999999999999998 -> 35.350506208557213
+lgam0083 lgamma -2.0000000000000004 -> 34.657359027997266
+lgam0084 lgamma -100.00000000000001 -> -331.85460524980607
+lgam0085 lgamma -99.999999999999986 -> -331.85460524980596
+
+-- large inputs
+lgam0100 lgamma 170 -> 701.43726380873704
+lgam0101 lgamma 171 -> 706.57306224578736
+lgam0102 lgamma 171.624 -> 709.78077443669895
+lgam0103 lgamma 171.625 -> 709.78591682948365
+lgam0104 lgamma 172 -> 711.71472580228999
+lgam0105 lgamma 2000 -> 13198.923448054265
+lgam0106 lgamma 2.55998332785163e305 -> 1.7976931348623099e+308
+lgam0107 lgamma 2.55998332785164e305 -> inf overflow
+lgam0108 lgamma 1.7e308 -> inf overflow
+
+-- inputs for which gamma(x) is tiny
+lgam0120 lgamma -100.5 -> -364.90096830942736
+lgam0121 lgamma -160.5 -> -656.88005261126432
+lgam0122 lgamma -170.5 -> -707.99843314507882
+lgam0123 lgamma -171.5 -> -713.14301641168481
+lgam0124 lgamma -176.5 -> -738.95247590846486
+lgam0125 lgamma -177.5 -> -744.13144651738037
+lgam0126 lgamma -178.5 -> -749.3160351186001
+
+lgam0130 lgamma -1000.5 -> -5914.4377011168517
+lgam0131 lgamma -30000.5 -> -279278.6629959144
+lgam0132 lgamma -4503599627370495.5 -> -1.5782258434492883e+17
+
+-- results close to 0:  positive argument ...
+lgam0150 lgamma 0.99999999999999989 -> 6.4083812134800075e-17
+lgam0151 lgamma 1.0000000000000002 -> -1.2816762426960008e-16
+lgam0152 lgamma 1.9999999999999998 -> -9.3876980655431170e-17
+lgam0153 lgamma 2.0000000000000004 -> 1.8775396131086244e-16
+
+-- ... and negative argument
+lgam0160 lgamma -2.7476826467 -> -5.2477408147689136e-11
+lgam0161 lgamma -2.457024738 -> 3.3464637541912932e-10
+
+
+---------------------------
+-- gamma: Gamma function --
+---------------------------
+
+-- special values
+gam0000 gamma 0.0 -> inf        divide-by-zero
+gam0001 gamma -0.0 -> -inf      divide-by-zero
+gam0002 gamma inf -> inf
+gam0003 gamma -inf -> nan       invalid
+gam0004 gamma nan -> nan
+
+-- negative integers inputs are invalid
+gam0010 gamma -1 -> nan         invalid
+gam0011 gamma -2 -> nan         invalid
+gam0012 gamma -1e16 -> nan      invalid
+gam0013 gamma -1e300 -> nan     invalid
+
+-- small positive integers give factorials
+gam0020 gamma 1 -> 1
+gam0021 gamma 2 -> 1
+gam0022 gamma 3 -> 2
+gam0023 gamma 4 -> 6
+gam0024 gamma 5 -> 24
+gam0025 gamma 6 -> 120
+
+-- half integers
+gam0030 gamma 0.5 -> 1.7724538509055161
+gam0031 gamma 1.5 -> 0.88622692545275805
+gam0032 gamma 2.5 -> 1.3293403881791370
+gam0033 gamma 3.5 -> 3.3233509704478426
+gam0034 gamma -0.5 -> -3.5449077018110322
+gam0035 gamma -1.5 -> 2.3632718012073548
+gam0036 gamma -2.5 -> -0.94530872048294190
+gam0037 gamma -3.5 -> 0.27008820585226911
+
+-- values near 0
+gam0040 gamma 0.1 -> 9.5135076986687306
+gam0041 gamma 0.01 -> 99.432585119150602
+gam0042 gamma 1e-8 -> 99999999.422784343
+gam0043 gamma 1e-16 -> 10000000000000000
+gam0044 gamma 1e-30 -> 9.9999999999999988e+29
+gam0045 gamma 1e-160 -> 1.0000000000000000e+160
+gam0046 gamma 1e-308 -> 1.0000000000000000e+308
+gam0047 gamma 5.6e-309 -> 1.7857142857142848e+308
+gam0048 gamma 5.5e-309 -> inf   overflow
+gam0049 gamma 1e-309 -> inf     overflow
+gam0050 gamma 1e-323 -> inf     overflow
+gam0051 gamma 5e-324 -> inf     overflow
+gam0060 gamma -0.1 -> -10.686287021193193
+gam0061 gamma -0.01 -> -100.58719796441078
+gam0062 gamma -1e-8 -> -100000000.57721567
+gam0063 gamma -1e-16 -> -10000000000000000
+gam0064 gamma -1e-30 -> -9.9999999999999988e+29
+gam0065 gamma -1e-160 -> -1.0000000000000000e+160
+gam0066 gamma -1e-308 -> -1.0000000000000000e+308
+gam0067 gamma -5.6e-309 -> -1.7857142857142848e+308
+gam0068 gamma -5.5e-309 -> -inf overflow
+gam0069 gamma -1e-309 -> -inf   overflow
+gam0070 gamma -1e-323 -> -inf   overflow
+gam0071 gamma -5e-324 -> -inf   overflow
+
+-- values near negative integers
+gam0080 gamma -0.99999999999999989 -> -9007199254740992.0
+gam0081 gamma -1.0000000000000002 -> 4503599627370495.5
+gam0082 gamma -1.9999999999999998 -> 2251799813685248.5
+gam0083 gamma -2.0000000000000004 -> -1125899906842623.5
+gam0084 gamma -100.00000000000001 -> -7.5400833348831090e-145
+gam0085 gamma -99.999999999999986 -> 7.5400833348840962e-145
+
+-- large inputs
+gam0100 gamma 170 -> 4.2690680090047051e+304
+gam0101 gamma 171 -> 7.2574156153079990e+306
+gam0102 gamma 171.624 -> 1.7942117599248104e+308
+gam0103 gamma 171.625 -> inf    overflow
+gam0104 gamma 172 -> inf        overflow
+gam0105 gamma 2000 -> inf       overflow
+gam0106 gamma 1.7e308 -> inf    overflow
+
+-- inputs for which gamma(x) is tiny
+gam0120 gamma -100.5 -> -3.3536908198076787e-159
+gam0121 gamma -160.5 -> -5.2555464470078293e-286
+gam0122 gamma -170.5 -> -3.3127395215386074e-308
+gam0123 gamma -171.5 -> 1.9316265431711902e-310
+gam0124 gamma -176.5 -> -1.1956388629358166e-321
+gam0125 gamma -177.5 -> 4.9406564584124654e-324
+gam0126 gamma -178.5 -> -0.0
+gam0127 gamma -179.5 -> 0.0
+gam0128 gamma -201.0001 -> 0.0
+gam0129 gamma -202.9999 -> -0.0
+gam0130 gamma -1000.5 -> -0.0
+gam0131 gamma -1000000000.3 -> -0.0
+gam0132 gamma -4503599627370495.5 -> 0.0
+
+-- inputs that cause problems for the standard reflection formula,
+-- thanks to loss of accuracy in 1-x
+gam0140 gamma -63.349078729022985 -> 4.1777971677761880e-88
+gam0141 gamma -127.45117632943295 -> 1.1831110896236810e-214
+
+
+-----------------------------------------------------------
+-- log1p: log(1 + x), without precision loss for small x --
+-----------------------------------------------------------
+
+-- special values
+log1p0000 log1p 0.0 -> 0.0
+log1p0001 log1p -0.0 -> -0.0
+log1p0002 log1p inf -> inf
+log1p0003 log1p -inf -> nan             invalid
+log1p0004 log1p nan -> nan
+
+-- singularity at -1.0
+log1p0010 log1p -1.0 -> -inf            divide-by-zero
+log1p0011 log1p -0.9999999999999999 -> -36.736800569677101
+
+-- finite values < 1.0 are invalid
+log1p0020 log1p -1.0000000000000002 -> nan invalid
+log1p0021 log1p -1.1 -> nan invalid
+log1p0022 log1p -2.0 -> nan invalid
+log1p0023 log1p -1e300 -> nan invalid
+
+-- tiny x: log1p(x) ~ x
+log1p0110 log1p 5e-324 -> 5e-324
+log1p0111 log1p 1e-320 -> 1e-320
+log1p0112 log1p 1e-300 -> 1e-300
+log1p0113 log1p 1e-150 -> 1e-150
+log1p0114 log1p 1e-20 -> 1e-20
+
+log1p0120 log1p -5e-324 -> -5e-324
+log1p0121 log1p -1e-320 -> -1e-320
+log1p0122 log1p -1e-300 -> -1e-300
+log1p0123 log1p -1e-150 -> -1e-150
+log1p0124 log1p -1e-20 -> -1e-20
+
+-- some (mostly) random small and moderate-sized values
+log1p0200 log1p -0.89156889782277482 -> -2.2216403106762863
+log1p0201 log1p -0.23858496047770464 -> -0.27257668276980057
+log1p0202 log1p -0.011641726191307515 -> -0.011710021654495657
+log1p0203 log1p -0.0090126398571693817 -> -0.0090534993825007650
+log1p0204 log1p -0.00023442805985712781 -> -0.00023445554240995693
+log1p0205 log1p -1.5672870980936349e-5 -> -1.5672993801662046e-5
+log1p0206 log1p -7.9650013274825295e-6 -> -7.9650330482740401e-6
+log1p0207 log1p -2.5202948343227410e-7 -> -2.5202951519170971e-7
+log1p0208 log1p -8.2446372820745855e-11 -> -8.2446372824144559e-11
+log1p0209 log1p -8.1663670046490789e-12 -> -8.1663670046824230e-12
+log1p0210 log1p 7.0351735084656292e-18 -> 7.0351735084656292e-18
+log1p0211 log1p 5.2732161907375226e-12 -> 5.2732161907236188e-12
+log1p0212 log1p 1.0000000000000000e-10 -> 9.9999999995000007e-11
+log1p0213 log1p 2.1401273266000197e-9 -> 2.1401273243099470e-9
+log1p0214 log1p 1.2668914653979560e-8 -> 1.2668914573728861e-8
+log1p0215 log1p 1.6250007816299069e-6 -> 1.6249994613175672e-6
+log1p0216 log1p 8.3740495645839399e-6 -> 8.3740145024266269e-6
+log1p0217 log1p 3.0000000000000001e-5 -> 2.9999550008999799e-5
+log1p0218 log1p 0.0070000000000000001 -> 0.0069756137364252423
+log1p0219 log1p 0.013026235315053002 -> 0.012942123564008787
+log1p0220 log1p 0.013497160797236184 -> 0.013406885521915038
+log1p0221 log1p 0.027625599078135284 -> 0.027250897463483054
+log1p0222 log1p 0.14179687245544870 -> 0.13260322540908789
+
+-- large values
+log1p0300 log1p 1.7976931348623157e+308 -> 709.78271289338397
+log1p0301 log1p 1.0000000000000001e+300 -> 690.77552789821368
+log1p0302 log1p 1.0000000000000001e+70 -> 161.18095650958321
+log1p0303 log1p 10000000000.000000 -> 23.025850930040455
+
+-- other values transferred from testLog1p in test_math
+log1p0400 log1p -0.63212055882855767 -> -1.0000000000000000
+log1p0401 log1p 1.7182818284590451 -> 1.0000000000000000
+log1p0402 log1p 1.0000000000000000 -> 0.69314718055994529
+log1p0403 log1p 1.2379400392853803e+27 -> 62.383246250395075
+
+
+-----------------------------------------------------------
+-- expm1: exp(x) - 1, without precision loss for small x --
+-----------------------------------------------------------
+
+-- special values
+expm10000 expm1 0.0 -> 0.0
+expm10001 expm1 -0.0 -> -0.0
+expm10002 expm1 inf -> inf
+expm10003 expm1 -inf -> -1.0
+expm10004 expm1 nan -> nan
+
+-- expm1(x) ~ x for tiny x
+expm10010 expm1 5e-324 -> 5e-324
+expm10011 expm1 1e-320 -> 1e-320
+expm10012 expm1 1e-300 -> 1e-300
+expm10013 expm1 1e-150 -> 1e-150
+expm10014 expm1 1e-20 -> 1e-20
+
+expm10020 expm1 -5e-324 -> -5e-324
+expm10021 expm1 -1e-320 -> -1e-320
+expm10022 expm1 -1e-300 -> -1e-300
+expm10023 expm1 -1e-150 -> -1e-150
+expm10024 expm1 -1e-20 -> -1e-20
+
+-- moderate sized values, where direct evaluation runs into trouble
+expm10100 expm1 1e-10 -> 1.0000000000500000e-10
+expm10101 expm1 -9.9999999999999995e-08 -> -9.9999995000000163e-8
+expm10102 expm1 3.0000000000000001e-05 -> 3.0000450004500034e-5
+expm10103 expm1 -0.0070000000000000001 -> -0.0069755570667648951
+expm10104 expm1 -0.071499208740094633 -> -0.069002985744820250
+expm10105 expm1 -0.063296004180116799 -> -0.061334416373633009
+expm10106 expm1 0.02390954035597756 -> 0.024197665143819942
+expm10107 expm1 0.085637352649044901 -> 0.089411184580357767
+expm10108 expm1 0.5966174947411006 -> 0.81596588596501485
+expm10109 expm1 0.30247206212075139 -> 0.35319987035848677
+expm10110 expm1 0.74574727375889516 -> 1.1080161116737459
+expm10111 expm1 0.97767512926555711 -> 1.6582689207372185
+expm10112 expm1 0.8450154566787712 -> 1.3280137976535897
+expm10113 expm1 -0.13979260323125264 -> -0.13046144381396060
+expm10114 expm1 -0.52899322039643271 -> -0.41080213643695923
+expm10115 expm1 -0.74083261478900631 -> -0.52328317124797097
+expm10116 expm1 -0.93847766984546055 -> -0.60877704724085946
+expm10117 expm1 10.0 -> 22025.465794806718
+expm10118 expm1 27.0 -> 532048240600.79865
+expm10119 expm1 123 -> 2.6195173187490626e+53
+expm10120 expm1 -12.0 -> -0.99999385578764666
+expm10121 expm1 -35.100000000000001 -> -0.99999999999999944
+
+-- extreme negative values
+expm10201 expm1 -37.0 -> -0.99999999999999989
+expm10200 expm1 -38.0 -> -1.0
+expm10210 expm1 -710.0 -> -1.0
+-- the formula expm1(x) = 2 * sinh(x/2) * exp(x/2) doesn't work so
+-- well when exp(x/2) is subnormal or underflows to zero; check we're
+-- not using it!
+expm10211 expm1 -1420.0 -> -1.0
+expm10212 expm1 -1450.0 -> -1.0
+expm10213 expm1 -1500.0 -> -1.0
+expm10214 expm1 -1e50 -> -1.0
+expm10215 expm1 -1.79e308 -> -1.0
+
+-- extreme positive values
+expm10300 expm1 300 -> 1.9424263952412558e+130
+expm10301 expm1 700 -> 1.0142320547350045e+304
+-- the next test (expm10302) is disabled because it causes failure on
+-- OS X 10.4/Intel: apparently all values over 709.78 produce an
+-- overflow on that platform.  See issue #7575.
+-- expm10302 expm1 709.78271289328393 -> 1.7976931346824240e+308
+expm10303 expm1 709.78271289348402 -> inf overflow
+expm10304 expm1 1000 -> inf overflow
+expm10305 expm1 1e50 -> inf overflow
+expm10306 expm1 1.79e308 -> inf overflow
+
+-- weaker version of expm10302
+expm10307 expm1 709.5 -> 1.3549863193146328e+308
+
+-------------------------
+-- log2: log to base 2 --
+-------------------------
+
+-- special values
+log20000 log2 0.0 -> -inf               -inf
+log20001 log2 -0.0 -> -inf              -inf
+log20002 log2 inf -> inf
+log20003 log2 -inf -> nan               invalid
+log20004 log2 nan -> nan
+
+-- exact value at 1.0
+log20010 log2 1.0 -> 0.0
+
+-- negatives
+log20020 log2 -5e-324 -> nan            invalid
+log20021 log2 -1.0 -> nan               invalid
+log20022 log2 -1.7e-308 -> nan          invalid
+
+-- exact values at powers of 2
+log20100 log2 2.0 -> 1.0
+log20101 log2 4.0 -> 2.0
+log20102 log2 8.0 -> 3.0
+log20103 log2 16.0 -> 4.0
+log20104 log2 32.0 -> 5.0
+log20105 log2 64.0 -> 6.0
+log20106 log2 128.0 -> 7.0
+log20107 log2 256.0 -> 8.0
+log20108 log2 512.0 -> 9.0
+log20109 log2 1024.0 -> 10.0
+log20110 log2 2048.0 -> 11.0
+
+log20200 log2 0.5 -> -1.0
+log20201 log2 0.25 -> -2.0
+log20202 log2 0.125 -> -3.0
+log20203 log2 0.0625 -> -4.0
+
+-- values close to 1.0
+log20300 log2 1.0000000000000002 -> 3.2034265038149171e-16
+log20301 log2 1.0000000001 -> 1.4426951601859516e-10
+log20302 log2 1.00001 -> 1.4426878274712997e-5
+
+log20310 log2 0.9999999999999999 -> -1.6017132519074588e-16
+log20311 log2 0.9999999999 -> -1.4426951603302210e-10
+log20312 log2 0.99999 -> -1.4427022544056922e-5
+
+-- tiny values
+log20400 log2 5e-324 -> -1074.0
+log20401 log2 1e-323 -> -1073.0
+log20402 log2 1.5e-323 -> -1072.4150374992789
+log20403 log2 2e-323 -> -1072.0
+
+log20410 log2 1e-308 -> -1023.1538532253076
+log20411 log2 2.2250738585072014e-308 -> -1022.0
+log20412 log2 4.4501477170144028e-308 -> -1021.0
+log20413 log2 1e-307 -> -1019.8319251304202
+
+-- huge values
+log20500 log2 1.7976931348623157e+308 -> 1024.0
+log20501 log2 1.7e+308 -> 1023.9193879716706
+log20502 log2 8.9884656743115795e+307 -> 1023.0
+
+-- selection of random values
+log20600 log2 -7.2174324841039838e+289 -> nan   invalid
+log20601 log2 -2.861319734089617e+265 -> nan    invalid
+log20602 log2 -4.3507646894008962e+257 -> nan   invalid
+log20603 log2 -6.6717265307520224e+234 -> nan   invalid
+log20604 log2 -3.9118023786619294e+229 -> nan   invalid
+log20605 log2 -1.5478221302505161e+206 -> nan   invalid
+log20606 log2 -1.4380485131364602e+200 -> nan   invalid
+log20607 log2 -3.7235198730382645e+185 -> nan   invalid
+log20608 log2 -1.0472242235095724e+184 -> nan   invalid
+log20609 log2 -5.0141781956163884e+160 -> nan   invalid
+log20610 log2 -2.1157958031160324e+124 -> nan   invalid
+log20611 log2 -7.9677558612567718e+90 -> nan    invalid
+log20612 log2 -5.5553906194063732e+45 -> nan    invalid
+log20613 log2 -16573900952607.953 -> nan        invalid
+log20614 log2 -37198371019.888618 -> nan        invalid
+log20615 log2 -6.0727115121422674e-32 -> nan    invalid
+log20616 log2 -2.5406841656526057e-38 -> nan    invalid
+log20617 log2 -4.9056766703267657e-43 -> nan    invalid
+log20618 log2 -2.1646786075228305e-71 -> nan    invalid
+log20619 log2 -2.470826790488573e-78 -> nan     invalid
+log20620 log2 -3.8661709303489064e-165 -> nan   invalid
+log20621 log2 -1.0516496976649986e-182 -> nan   invalid
+log20622 log2 -1.5935458614317996e-255 -> nan   invalid
+log20623 log2 -2.8750977267336654e-293 -> nan   invalid
+log20624 log2 -7.6079466794732585e-296 -> nan   invalid
+log20625 log2 3.2073253539988545e-307 -> -1018.1505544209213
+log20626 log2 1.674937885472249e-244 -> -809.80634755783126
+log20627 log2 1.0911259044931283e-214 -> -710.76679472274213
+log20628 log2 2.0275372624809709e-154 -> -510.55719818383272
+log20629 log2 7.3926087369631841e-115 -> -379.13564735312292
+log20630 log2 1.3480198206342423e-86 -> -285.25497445094436
+log20631 log2 8.9927384655719947e-83 -> -272.55127136401637
+log20632 log2 3.1452398713597487e-60 -> -197.66251564496875
+log20633 log2 7.0706573215457351e-55 -> -179.88420087782217
+log20634 log2 3.1258285390731669e-49 -> -161.13023800505653
+log20635 log2 8.2253046627829942e-41 -> -133.15898277355879
+log20636 log2 7.8691367397519897e+49 -> 165.75068202732419
+log20637 log2 2.9920561983925013e+64 -> 214.18453534573757
+log20638 log2 4.7827254553946841e+77 -> 258.04629628445673
+log20639 log2 3.1903566496481868e+105 -> 350.47616767491166
+log20640 log2 5.6195082449502419e+113 -> 377.86831861008250
+log20641 log2 9.9625658250651047e+125 -> 418.55752921228753
+log20642 log2 2.7358945220961532e+145 -> 483.13158636923413
+log20643 log2 2.785842387926931e+174 -> 579.49360214860280
+log20644 log2 2.4169172507252751e+193 -> 642.40529039289652
+log20645 log2 3.1689091206395632e+205 -> 682.65924573798395
+log20646 log2 2.535995592365391e+208 -> 692.30359597460460
+log20647 log2 6.2011236566089916e+233 -> 776.64177576730913
+log20648 log2 2.1843274820677632e+253 -> 841.57499717289647
+log20649 log2 8.7493931063474791e+297 -> 989.74182713073981