uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 307 insertions, 0 deletions

diff --git a/libm/ldouble/monotl.c b/libm/ldouble/monotl.c
new file mode 100644
index 000000000..86b85eca1
--- /dev/null
+++ b/libm/ldouble/monotl.c
@@ -0,0 +1,307 @@
+
+/* monot.c
+   Floating point function test vectors.
+
+   Arguments and function values are synthesized for NPTS points in
+   the vicinity of each given tabulated test point.  The points are
+   chosen to be near and on either side of the likely function algorithm
+   domain boundaries.  Since the function programs change their methods
+   at these points, major coding errors or monotonicity failures might be
+   detected.
+
+   August, 1998
+   S. L. Moshier  */
+
+
+#include <stdio.h>
+
+/* Avoid including math.h.  */
+long double frexpl (long double, int *);
+long double ldexpl (long double, int);
+
+/* Number of test points to generate on each side of tabulated point.  */
+#define NPTS 100
+
+/* Functions of one variable.  */
+long double expl (long double);
+long double logl (long double);
+long double sinl (long double);
+long double cosl (long double);
+long double tanl (long double);
+long double atanl (long double);
+long double asinl (long double);
+long double acosl (long double);
+long double sinhl (long double);
+long double coshl (long double);
+long double tanhl (long double);
+long double asinhl (long double);
+long double acoshl (long double);
+long double atanhl (long double);
+long double gammal (long double);
+long double fabsl (long double);
+long double floorl (long double);
+
+struct oneargument
+  {
+    char *name;			/* Name of the function. */
+    long double (*func) (long double);
+    long double arg1;		/* Function argument, assumed exact.  */
+    long double answer1;	/* Exact, close to function value.  */
+    long double answer2;	/* answer1 + answer2 has extended precision. */
+    long double derivative;	/* dy/dx evaluated at x = arg1. */
+    int thresh;			/* Error report threshold. 2 = 1 ULP approx. */
+  };
+
+/* Add this to error threshold test[i].thresh.  */
+#define OKERROR 2
+
+/* Unit of relative error in test[i].thresh.  */
+static long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
+
+/* extern double MACHEP; */
+
+
+struct oneargument test1[] =
+{
+  {"exp", expl, 1.0L, 2.7182769775390625L,
+   4.85091998273536028747e-6L, 2.71828182845904523536L, 1},
+  {"exp", expl, -1.0L, 3.678741455078125e-1L,
+    5.29566362982159552377e-6L, 3.678794411714423215955e-1L, 1},
+  {"exp", expl, 0.5L, 1.648712158203125L,
+    9.1124970031468486507878e-6L, 1.64872127070012814684865L, 1},
+  {"exp", expl, -0.5L, 6.065216064453125e-1L,
+    9.0532673209236037995e-6L, 6.0653065971263342360e-1L, 1},
+  {"exp", expl, 2.0L, 7.3890533447265625L,
+    2.75420408772723042746e-6L, 7.38905609893065022723L, 1},
+  {"exp", expl, -2.0L, 1.353302001953125e-1L,
+    5.08304130019189399949e-6L, 1.3533528323661269189e-1L, 1},
+  {"log", logl, 1.41421356237309492343L, 3.465728759765625e-1L,
+   7.1430341006605745676897e-7L, 7.0710678118654758708668e-1L, 1},
+  {"log", logl, 7.07106781186547461715e-1L, -3.46588134765625e-1L,
+   1.45444856522566402246e-5L, 1.41421356237309517417L, 1},
+  {"sin", sinl, 7.85398163397448278999e-1L, 7.0709228515625e-1L,
+   1.4496030297502751942956e-5L, 7.071067811865475460497e-1L, 1},
+  {"sin", sinl, -7.85398163397448501044e-1L, -7.071075439453125e-1L,
+   7.62758764840238811175e-7L, 7.07106781186547389040e-1L, 1},
+  {"sin", sinl, 1.570796326794896558L, 9.999847412109375e-1L,
+   1.52587890625e-5L, 6.12323399573676588613e-17L, 1},
+  {"sin", sinl, -1.57079632679489678004L, -1.0L,
+   1.29302922820150306903e-32L, -1.60812264967663649223e-16L, 1},
+  {"sin", sinl, 4.712388980384689674L, -1.0L,
+   1.68722975549458979398e-32L, -1.83697019872102976584e-16L, 1},
+  {"sin", sinl, -4.71238898038468989604L, 9.999847412109375e-1L,
+   1.52587890625e-5L, 3.83475850529283315008e-17L, 1},
+  {"cos", cosl, 3.92699081698724139500E-1L, 9.23873901367187500000E-1L,
+   5.63114409926198633370E-6L, -3.82683432365089757586E-1L, 1},
+  {"cos", cosl, 7.85398163397448278999E-1L, 7.07092285156250000000E-1L,
+   1.44960302975460497458E-5L, -7.07106781186547502752E-1L, 1},
+  {"cos", cosl, 1.17809724509617241850E0L, 3.82675170898437500000E-1L,
+   8.26146665231415693919E-6L, -9.23879532511286738554E-1L, 1},
+  {"cos", cosl, 1.96349540849362069750E0L, -3.82690429687500000000E-1L,
+   6.99732241029898567203E-6L, -9.23879532511286785419E-1L, 1},
+  {"cos", cosl, 2.35619449019234483700E0L, -7.07107543945312500000E-1L,
+   7.62758765040545859856E-7L, -7.07106781186547589348E-1L, 1},
+  {"cos", cosl, 2.74889357189106897650E0L, -9.23889160156250000000E-1L,
+   9.62764496328487887036E-6L, -3.82683432365089870728E-1L, 1},
+  {"cos", cosl, 3.14159265358979311600E0L, -1.00000000000000000000E0L,
+   7.49879891330928797323E-33L, -1.22464679914735317723E-16L, 1},
+  {"tan", tanl, 7.85398163397448278999E-1L, 9.999847412109375e-1L,
+   1.52587890624387676600E-5L, 1.99999999999999987754E0L, 1},
+  {"tan", tanl, 1.17809724509617241850E0L, 2.41419982910156250000E0L,
+   1.37332715322352112604E-5L, 6.82842712474618858345E0L, 1},
+  {"tan", tanl, 1.96349540849362069750E0L, -2.41421508789062500000E0L,
+   1.52551752942854759743E-6L, 6.82842712474619262118E0L, 1},
+  {"tan", tanl, 2.35619449019234483700E0L, -1.00001525878906250000E0L,
+   1.52587890623163029801E-5L, 2.00000000000000036739E0L, 1},
+  {"tan", tanl, 2.74889357189106897650E0L, -4.14215087890625000000E-1L,
+   1.52551752982565655126E-6L, 1.17157287525381000640E0L, 1},
+  {"atan", atanl, 4.14213562373094923430E-1L, 3.92684936523437500000E-1L,
+   1.41451752865477964149E-5L, 8.53553390593273837869E-1L, 1},
+  {"atan", atanl, 1.0L, 7.85385131835937500000E-1L,
+   1.30315615108096156608E-5L, 0.5L, 1},
+  {"atan", atanl, 2.41421356237309492343E0L, 1.17808532714843750000E0L,
+   1.19179477349460632350E-5L, 1.46446609406726250782E-1L, 1},
+  {"atan", atanl, -2.41421356237309514547E0L, -1.17810058593750000000E0L,
+   3.34084132752141908545E-6L, 1.46446609406726227789E-1L, 1},
+  {"atan", atanl, -1.0L, -7.85400390625000000000E-1L,
+   2.22722755169038433915E-6L, 0.5L, 1},
+  {"atan", atanl, -4.14213562373095145475E-1L, -3.92700195312500000000E-1L,
+   1.11361377576267665972E-6L, 8.53553390593273703853E-1L, 1},
+  {"asin", asinl, 3.82683432365089615246E-1L, 3.92684936523437500000E-1L,
+   1.41451752864854321970E-5L, 1.08239220029239389286E0L, 1},
+  {"asin", asinl, 0.5L, 5.23590087890625000000E-1L,
+   8.68770767387307710723E-6L, 1.15470053837925152902E0L, 1},
+  {"asin", asinl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
+   1.30315615107209645016E-5L, 1.41421356237309492343E0L, 1},
+  {"asin", asinl, 9.23879532511286738483E-1L, 1.17808532714843750000E0L,
+   1.19179477349183147612E-5L, 2.61312592975275276483E0L, 1},
+  {"asin", asinl, -0.5L, -5.23605346679687500000E-1L,
+   6.57108138862692289277E-6L, 1.15470053837925152902E0L, 1},
+  {"acos", acosl, 1.95090322016128192573E-1L, 1.37443542480468750000E0L,
+   1.13611408471185777914E-5L, -1.01959115820831832232E0L, 1},
+  {"acos", acosl, 3.82683432365089615246E-1L, 1.17808532714843750000E0L,
+   1.19179477351337991247E-5L, -1.08239220029239389286E0L, 1},
+  {"acos", acosl, 0.5L, 1.04719543457031250000E0L,
+   2.11662628524615421446E-6L, -1.15470053837925152902E0L, 1},
+  {"acos", acosl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
+   1.30315615108982668201E-5L, -1.41421356237309492343E0L, 1},
+  {"acos", acosl, 9.23879532511286738483E-1L, 3.92684936523437500000E-1L,
+   1.41451752867009165605E-5L, -2.61312592975275276483E0L, 1},
+  {"acos", acosl, 9.80785280403230430579E-1L, 1.96334838867187500000E-1L,
+   1.47019821746724723933E-5L, -5.12583089548300990774E0L, 1},
+  {"acos", acosl, -0.5L, 2.09439086914062500000E0L,
+   4.23325257049230842892E-6L, -1.15470053837925152902E0L, 1},
+  {"sinh", sinhl, 1.0L, 1.17518615722656250000E0L,
+   1.50364172389568823819E-5L, 1.54308063481524377848E0L, 1},
+  {"sinh", sinhl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
+   4.25947714184369757620E208L, 4.49423283712885057274E307L, 1},
+  {"sinh", sinhl, 2.22044604925031308085E-16L, 0.00000000000000000000E0L,
+   2.22044604925031308085E-16L, 1.00000000000000000000E0L, 1},
+  {"cosh", coshl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
+   4.25947714184369757620E208L, 4.49423283712885057274E307L, 1},
+  {"cosh", coshl, 1.0L, 1.54307556152343750000E0L,
+   5.07329180627847790562E-6L, 1.17520119364380145688E0L, 1},
+  {"cosh", coshl, 0.5L, 1.12762451171875000000E0L,
+   1.45348763078522622516E-6L, 5.21095305493747361622E-1L, 1},
+  {"tanh", tanhl, 0.5L, 4.62112426757812500000E-1L,
+   4.73050219725850231848E-6L, 7.86447732965927410150E-1L, 1},
+  {"tanh", tanhl, 5.49306144334054780032E-1L, 4.99984741210937500000E-1L,
+   1.52587890624507506378E-5L, 7.50000000000000049249E-1L, 1},
+  {"tanh", tanhl, 0.625L, 5.54595947265625000000E-1L,
+   3.77508375729399903910E-6L, 6.92419147969988069631E-1L, 1},
+  {"asinh", asinhl, 0.5L, 4.81201171875000000000E-1L,
+   1.06531846034474977589E-5L, 8.94427190999915878564E-1L, 1},
+  {"asinh", asinhl, 1.0L, 8.81362915039062500000E-1L,
+   1.06719804805252326093E-5L, 7.07106781186547524401E-1L, 1},
+  {"asinh", asinhl, 2.0L, 1.44363403320312500000E0L,
+   1.44197568534249327674E-6L, 4.47213595499957939282E-1L, 1},
+  {"acosh", acoshl, 2.0L, 1.31695556640625000000E0L,
+   2.33051856670862504635E-6L, 5.77350269189625764509E-1L, 1},
+  {"acosh", acoshl, 1.5L, 9.62417602539062500000E-1L,
+   6.04758014439499551783E-6L, 8.94427190999915878564E-1L, 1},
+  {"acosh", acoshl, 1.03125L, 2.49343872070312500000E-1L,
+   9.62177257298785143908E-6L, 3.96911150685467059809E0L, 1},
+  {"atanh", atanhl, 0.5L, 5.49301147460937500000E-1L,
+   4.99687311734569762262E-6L, 1.33333333333333333333E0L, 1},
+#if 0
+  {"gamma", gammal, 1.0L, 1.0L,
+   0.0L, -5.772156649015328606e-1L, 1},
+  {"gamma", gammal, 2.0L, 1.0L,
+   0.0L, 4.2278433509846713939e-1L, 1},
+  {"gamma", gammal, 3.0L, 2.0L,
+   0.0L, 1.845568670196934279L, 1},
+  {"gamma", gammal, 4.0L, 6.0L,
+   0.0L, 7.536706010590802836L, 1},
+#endif
+  {"null", NULL, 0.0L, 0.0L, 0.0L, 1},
+};
+
+/* These take care of extra-precise floating point register problems.  */
+volatile long double volat1;
+volatile long double volat2;
+
+
+/* Return the next nearest floating point value to X
+   in the direction of UPDOWN (+1 or -1).
+   (Fails if X is denormalized.)  */
+
+long double
+nextval (x, updown)
+     long double x;
+     int updown;
+{
+  long double m;
+  int i;
+
+  volat1 = x;
+  m = 0.25L * MACHEPL * volat1 * updown;
+  volat2 = volat1 + m;
+  if (volat2 != volat1)
+    printf ("successor failed\n");
+
+  for (i = 2; i < 10; i++)
+    {
+      volat2 = volat1 + i * m;
+      if (volat1 != volat2)
+	return volat2;
+    }
+
+  printf ("nextval failed\n");
+  return volat1;
+}
+
+
+
+
+int
+main ()
+{
+  long double (*fun1) (long double);
+  int i, j, errs, tests;
+  long double x, x0, y, dy, err;
+
+  errs = 0;
+  tests = 0;
+  i = 0;
+
+  for (;;)
+    {
+      fun1 = test1[i].func;
+      if (fun1 == NULL)
+	break;
+      volat1 = test1[i].arg1;
+      x0 = volat1;
+      x = volat1;
+      for (j = 0; j <= NPTS; j++)
+	{
+	  volat1 = x - x0;
+	  dy = volat1 * test1[i].derivative;
+	  dy = test1[i].answer2 + dy;
+	  volat1 = test1[i].answer1 + dy;
+	  volat2 = (*(fun1)) (x);
+	  if (volat2 != volat1)
+	    {
+	      /* Report difference between program result
+		 and extended precision function value.  */
+	      err = volat2 - test1[i].answer1;
+	      err = err - dy;
+	      err = err / volat1;
+	      if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL))
+		{
+		  printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
+			  j, test1[i].name, x, volat2, err);
+		  errs += 1;
+		}
+	    }
+	  x = nextval (x, 1);
+	  tests += 1;
+	}
+
+      x = x0;
+      x = nextval (x, -1);
+      for (j = 1; j < NPTS; j++)
+	{
+	  volat1 = x - x0;
+	  dy = volat1 * test1[i].derivative;
+	  dy = test1[i].answer2 + dy;
+	  volat1 = test1[i].answer1 + dy;
+	  volat2 = (*(fun1)) (x);
+	  if (volat2 != volat1)
+	    {
+	      err = volat2 - test1[i].answer1;
+	      err = err - dy;
+	      err = err / volat1;
+	      if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL))
+		{
+		  printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
+			  j, test1[i].name, x, volat2, err);
+		  errs += 1;
+		}
+	    }
+	  x = nextval (x, -1);
+	  tests += 1;
+	}
+      i += 1;
+    }
+  printf ("%d errors in %d tests\n", errs, tests);
+}