Add more vectorisation tests. Add test case.

Add vectorisation test for vector creation, load, and store
statements.

Convert C to C++ since vectorisation requires C++.

Add test case.

Beautify vectorsation templates.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/Vectors/trunk@26 105869f7-3296-0410-a4ea-f4349344b45a

15 files changed, 810 insertions, 107 deletions

diff --git a/param.ccl b/param.ccl
index dc5d37e..57fe198 100644
--- a/param.ccl
+++ b/param.ccl
@@ -1 +1,5 @@
 # Parameter definitions for thorn Vectors
+
+BOOLEAN verbose "Verbose output during vector tests"
+{
+} "no"
diff --git a/src/make.code.defn b/src/make.code.defn
index dea6494..5c61b31 100644
--- a/src/make.code.defn
+++ b/src/make.code.defn
@@ -1,7 +1,7 @@
 # Main make.code.defn file for thorn Vectors
 
 # Source files in this directory
-SRCS = vectors.c test.c
+SRCS = vectors.cc test.cc
 
 # Subdirectories containing source files
 SUBDIRS = 
diff --git a/src/test.c b/src/test.c
deleted file mode 100644
index 680e775..0000000
--- a/src/test.c
+++ /dev/null
@@ -1,83 +0,0 @@
-#include "cctk.h" 
-#include "cctk_Arguments.h" 
-#include "cctk_Parameters.h" 
-#include "vectors.h"
-#include <math.h>
-
-#define VECTEST(testname, vecexpr, scalarexpr)                  \
-{                                                               \
-  CCTK_REAL_VEC rv = vecexpr;                                   \
-  for(int i=0; i<CCTK_REAL_VEC_SIZE; i++) {                     \
-    CCTK_REAL res = scalarexpr;                                 \
-    CCTK_REAL vecres = vec_elt(rv,i);                           \
-    if(vecres == res)                                           \
-      passed++;                                                 \
-    else                                                        \
-      CCTK_VWarn(CCTK_WARN_ALERT, __LINE__, __FILE__,           \
-        CCTK_THORNSTRING, "Failed test %s", testname);          \
-    numtests++;                                                 \
-  }                                                             \
-}
-
-void Vectors_Test(CCTK_ARGUMENTS)
-{
-  DECLARE_CCTK_ARGUMENTS;
-  DECLARE_CCTK_PARAMETERS;
-
-  CCTK_INT passed = 0, numtests=0;
-
-  CCTK_REAL a[CCTK_REAL_VEC_SIZE];
-  CCTK_REAL b[CCTK_REAL_VEC_SIZE];
-  CCTK_REAL c[CCTK_REAL_VEC_SIZE];
-
-  for(int i=0; i<CCTK_REAL_VEC_SIZE; i++) {
-    a[i] =  (i+1)*1.23456789;
-    b[i] = -(i+1)*9.87654321;
-    c[i] =  (i+1)*1.01010101;
-  }
-
-  CCTK_REAL_VEC av = vec_loadu(a[0]);
-  CCTK_REAL_VEC bv = vec_loadu(b[0]);
-  CCTK_REAL_VEC cv = vec_loadu(c[0]);
-  CCTK_REAL_VEC rv = vec_loadu(c[0]);
-
-  /* TODO: Add individual tests for vec_set1, vec_set, vec_elt0, vec_elt
-           vec_load, vec_loadu, vec_loadu_maybe, vec_loadu_maybe3
-           vec_store, vec_store_nta, vec_store_nta_partial_lo,
-           vec_store_nta_partial_hi, vec_store_nta_partial_mid */
-
-  VECTEST("kpos",   kpos(av),           +a[i]               );
-  VECTEST("kneg",   kneg(av),           -a[i]               );
-
-  VECTEST("kadd",   kadd(av, bv),       a[i] + b[i]         );
-  VECTEST("ksub",   ksub(av, bv),       a[i] - b[i]         );
-  VECTEST("kmul",   kmul(av, bv),       a[i] * b[i]         );
-  VECTEST("kdiv",   kdiv(av, bv),       a[i] / b[i]         );
-
-  VECTEST("kmadd",  kmadd(av, bv, cv),   a[i] * b[i] + c[i] );
-  VECTEST("kmsub",  kmsub(av, bv, cv),   a[i] * b[i] - c[i] );
-  VECTEST("knmadd", knmadd(av, bv, cv), -a[i] * b[i] - c[i] );
-  VECTEST("knmsub", knmsub(av, bv, cv), -a[i] * b[i] + c[i] );
-
-  VECTEST("kexp",   kexp(av),           exp(a[i])           );
-  VECTEST("kfabs",  kfabs(av),          fabs(a[i])          );
-  VECTEST("kfmax",  kfmax(av, bv),      fmax(a[i], b[i])    );
-  VECTEST("kfmin",  kfmin(av, bv),      fmin(a[i], b[i])    );
-  VECTEST("kfnabs", kfnabs(av),         -fabs(a[i])         );
-  VECTEST("klog",   klog(av),           log(a[i])           );
-  VECTEST("kpow",   kpow(av, 3.14159),  pow(a[i], 3.14159)  );
-  VECTEST("ksqrt",  ksqrt(av),          sqrt(a[i])          );
-
-  VECTEST("kifpos positive", kifpos(av, bv, cv), signbit(a[i]) ? c[i] : b[i]);
-  VECTEST("kifpos negative", kifpos(bv, bv, cv), signbit(b[i]) ? c[i] : b[i]);
-  VECTEST("kifpos 0",     kifpos(ToReal(0.),bv,cv),  signbit(0.)?c[i]:b[i]);
-  VECTEST("kifpos -0",    kifpos(ToReal(-0.),bv,cv), signbit(-0.)?c[i]:b[i]);
-
-  if (passed != numtests)
-    CCTK_VWarn(CCTK_WARN_ABORT, __LINE__, __FILE__, CCTK_THORNSTRING,
-      "Failed %d correctness tests", numtests - passed);
-  else
-    CCTK_VInfo(CCTK_THORNSTRING, "%d/%d tests passed ", passed, numtests);
-
-  return;
-}
diff --git a/src/test.cc b/src/test.cc
new file mode 100644
index 0000000..7e76362
--- /dev/null
+++ b/src/test.cc
@@ -0,0 +1,184 @@
+#include "cctk.h" 
+#include "cctk_Arguments.h" 
+#include "cctk_Parameters.h" 
+#include "vectors.h"
+#include <math.h>
+#include <stdio.h>
+
+#define SCALARTEST(testname, vecexpr, scalarexpr)                       \
+do {                                                                    \
+  if (verbose)                                                          \
+    CCTK_VInfo (CCTK_THORNSTRING, "Test %s...", testname);              \
+  CCTK_REAL res = (scalarexpr);                                         \
+  CCTK_REAL vecres = (vecexpr);                                         \
+  if(vecres == res)                                                     \
+    passed++;                                                           \
+  else                                                                  \
+    CCTK_VParamWarn(CCTK_THORNSTRING, "Failed test %s", (testname));    \
+  numtests++;                                                           \
+} while(0)
+
+#define VECTEST(testname, vecexpr, scalarexpr)                          \
+do {                                                                    \
+  if (verbose)                                                          \
+    CCTK_VInfo (CCTK_THORNSTRING, "Test %s...", testname);              \
+  CCTK_REAL_VEC rv = (vecexpr);                                         \
+  for(int i=0; i<CCTK_REAL_VEC_SIZE; i++) {                             \
+    CCTK_REAL res = (scalarexpr);                                       \
+    CCTK_REAL vecres = vec_elt(rv,i);                                   \
+    if(vecres == res)                                                   \
+      passed++;                                                         \
+    else                                                                \
+      CCTK_VParamWarn(CCTK_THORNSTRING, "Failed test %s", (testname));  \
+    numtests++;                                                         \
+  }                                                                     \
+} while(0)
+
+extern "C"
+void Vectors_Test(CCTK_ARGUMENTS)
+{
+  DECLARE_CCTK_ARGUMENTS;
+  DECLARE_CCTK_PARAMETERS;
+
+  CCTK_INFO ("Testing vectorisation... [errors may result in segfaults]");
+  fflush (stdout);
+
+  char testname[100];
+
+  int passed = 0, numtests = 0;
+
+  CCTK_REAL a[CCTK_REAL_VEC_SIZE];
+  CCTK_REAL b[CCTK_REAL_VEC_SIZE];
+  CCTK_REAL c[CCTK_REAL_VEC_SIZE];
+
+  for(int i=0; i<CCTK_REAL_VEC_SIZE; i++) {
+    a[i] =  (i+1)*1.23456789;
+    b[i] = -(i+1)*9.87654321;
+    c[i] =  (i+1)*1.01010101;
+  }
+
+  CCTK_REAL_VEC av = vec_loadu(a[0]);
+  CCTK_REAL_VEC bv = vec_loadu(b[0]);
+  CCTK_REAL_VEC cv = vec_loadu(c[0]);
+
+  /* l and lv are similar to a and av, except that it is larger, and
+     guaranteed to be aligned */
+  CCTK_REAL_VEC lv[4];
+  lv[0] = vec_loadu(a[0]);
+  lv[1] = vec_loadu(b[0]);
+  lv[2] = vec_loadu(c[0]);
+  lv[3] = vec_loadu(a[0]);
+  CCTK_REAL *const l = (CCTK_REAL*)&lv[0];
+
+  /* s and sv are similar to a and av, but are aligned and not
+     initialised */
+  CCTK_REAL_VEC sv;
+  CCTK_REAL *const s = (CCTK_REAL*)&sv;
+
+  /* TODO: Add individual tests for vec_set1, vec_set, vec_elt0, vec_elt
+           vec_load, vec_loadu, vec_loadu_maybe, vec_loadu_maybe3
+           vec_store, vec_store_nta, vec_store_nta_partial_lo,
+           vec_store_nta_partial_hi, vec_store_nta_partial_mid */
+
+  VECTEST("vec_set1", vec_set1(a[0]),  a[0]);
+#if CCTK_REAL_VEC_SIZE == 1
+  VECTEST("vec_set", vec_set(a[0]), a[i]);
+#elif CCTK_REAL_VEC_SIZE == 2
+  VECTEST("vec_set", vec_set(a[0],a[1]), a[i]);
+#elif CCTK_REAL_VEC_SIZE == 4
+  VECTEST("vec_set", vec_set(a[0],a[1],a[2],a[3]), a[i]);
+#else
+#  error "Unsupported vector size"
+#endif
+  SCALARTEST("vec_elt0", vec_elt0(av),    a[0]);
+  for (int d=0; d<CCTK_REAL_VEC_SIZE; ++d) {
+    snprintf (testname, sizeof testname, "vec_elt[%d]", d);
+    SCALARTEST(testname, vec_elt(av,d), a[d]);
+  }
+
+  /* These tests will probably fail with a segfault, if they fail */
+  VECTEST("vec_load", vec_load(*l), l[i]);
+  for (int d=0; d<CCTK_REAL_VEC_SIZE; ++d) {
+    snprintf (testname, sizeof testname, "vec_loadu[%d]", d);
+    VECTEST(testname, vec_loadu(l[d]), l[i+d]);
+  }
+  for (int d=0; d<CCTK_REAL_VEC_SIZE; ++d) {
+    snprintf (testname, sizeof testname, "vec_loadu_maybe[%d]", d);
+    VECTEST(testname, vec_loadu_maybe(d,l[d]), l[i+d]);
+  }
+  for (int d1=0; d1<CCTK_REAL_VEC_SIZE; ++d1) {
+    for (int d2=0; d2<CCTK_REAL_VEC_SIZE; ++d2) {
+      for (int d3=0; d3<CCTK_REAL_VEC_SIZE; ++d3) {
+        if (! VECTORISE_ALIGNED_ARRAYS || (d2==0 && d3==0)) {
+          snprintf (testname, sizeof testname,
+                    "vec_loadu_maybe3[%d,%d,%d]", d1,d2,d3);
+          VECTEST(testname,
+                  vec_loadu_maybe3(d1,d2,d3,l[d1+d2+d3]), l[i+d1+d2+d3]);
+        }
+      }
+    }
+  }
+
+  /* These tests may fail with a segfault, if they fail */
+  sv = av; vec_store(*s, bv);
+  VECTEST("vec_store", sv, b[i]);
+  sv = av; vec_store_nta(*s, bv);
+  VECTEST("vec_store_nta", sv, b[i]);
+  /* The partial stores are not implemented for d==0 and
+     d==CCTK_REAL_VEC_SIZE-1 (because these are trivial) */
+  for (int d=1; d<CCTK_REAL_VEC_SIZE-1; ++d) {
+    sv = av; vec_store_nta_partial_lo(*s, bv, d);
+    snprintf (testname, sizeof testname, "vec_store_nta_partial_lo[%d]", d);
+    VECTEST(testname, sv, i<d ? b[i] : a[i]);
+  }
+  for (int d=1; d<CCTK_REAL_VEC_SIZE-1; ++d) {
+    sv = av; vec_store_nta_partial_hi(*s, bv, d);
+    snprintf (testname, sizeof testname, "vec_store_nta_partial_hi[%d]", d);
+    VECTEST(testname, sv, i>=CCTK_REAL_VEC_SIZE-d ? b[i] : a[i]);
+  }
+  for (int dlo=1; dlo<CCTK_REAL_VEC_SIZE-1; ++dlo) {
+    for (int dhi=1; dhi<CCTK_REAL_VEC_SIZE-1; ++dhi) {
+      sv = av; vec_store_nta_partial_mid(*s, bv, dlo, dhi);
+      snprintf (testname, sizeof testname,
+                "vec_store_nta_partial_mid[%d,%d]", dlo, dhi);
+      VECTEST(testname, sv, i<dlo && i>=CCTK_REAL_VEC_SIZE-dhi ? b[i] : a[i]);
+    }
+  }
+
+  VECTEST("kpos",   kpos(av),           +a[i]               );
+  VECTEST("kneg",   kneg(av),           -a[i]               );
+
+  VECTEST("kadd",   kadd(av, bv),       a[i] + b[i]         );
+  VECTEST("ksub",   ksub(av, bv),       a[i] - b[i]         );
+  VECTEST("kmul",   kmul(av, bv),       a[i] * b[i]         );
+  VECTEST("kdiv",   kdiv(av, bv),       a[i] / b[i]         );
+
+  VECTEST("kmadd",  kmadd(av, bv, cv),   a[i] * b[i] + c[i] );
+  VECTEST("kmsub",  kmsub(av, bv, cv),   a[i] * b[i] - c[i] );
+  VECTEST("knmadd", knmadd(av, bv, cv), -a[i] * b[i] - c[i] );
+  VECTEST("knmsub", knmsub(av, bv, cv), -a[i] * b[i] + c[i] );
+
+  VECTEST("kexp",   kexp(av),           exp(a[i])           );
+  VECTEST("kfabs",  kfabs(av),          fabs(a[i])          );
+  VECTEST("kfmax",  kfmax(av, bv),      fmax(a[i], b[i])    );
+  VECTEST("kfmin",  kfmin(av, bv),      fmin(a[i], b[i])    );
+  VECTEST("kfnabs", kfnabs(av),         -fabs(a[i])         );
+  VECTEST("klog",   klog(av),           log(a[i])           );
+  VECTEST("kpow",   kpow(av, 3.14159),  pow(a[i], 3.14159)  );
+  VECTEST("ksqrt",  ksqrt(av),          sqrt(a[i])          );
+
+  VECTEST("kifpos positive",
+          kifpos(av, bv, cv), std::signbit(a[i]) ? c[i] : b[i]);
+  VECTEST("kifpos negative",
+          kifpos(bv, bv, cv), std::signbit(b[i]) ? c[i] : b[i]);
+  VECTEST("kifpos 0",  kifpos(vec_set1(0.),bv,cv),  b[i]);
+  VECTEST("kifpos -0", kifpos(vec_set1(-0.),bv,cv), c[i]);
+
+  if (passed != numtests)
+    CCTK_VWarn(CCTK_WARN_ALERT, __LINE__, __FILE__, CCTK_THORNSTRING,
+      "Failed %d correctness tests", numtests - passed);
+  else
+    CCTK_VInfo(CCTK_THORNSTRING, "%d/%d tests passed ", passed, numtests);
+
+  return;
+}
diff --git a/src/vectors-4-SSE.h b/src/vectors-4-SSE.h
index d04d0b7..49925c1 100644
--- a/src/vectors-4-SSE.h
+++ b/src/vectors-4-SSE.h
@@ -5,6 +5,9 @@
 
 
 
+#include <assert.h>
+#include <math.h>
+
 #include <xmmintrin.h>
 #ifdef __SSE4_1__
 // Intel's SSE 4.1
@@ -309,12 +312,11 @@ static const union {
 #ifdef __SSE4_1__
 #  define k4ifpos(x,y,z) (_mm_blendv_ps(y,z,x))
 #else
-#include <math.h>
-#ifdef __cplusplus
-#define SGN(x) std::signbit(x)
-#else
-#define SGN(x) signbit(x)
-#endif
+#  ifdef __cplusplus
+#    define SGN(x) std::signbit(x)
+#  else
+#    define SGN(x) signbit(x)
+#  endif
 #  define k4ifpos(x,y,z)                                        \
   ({                                                            \
     CCTK_REAL4_VEC const xx=(x_);                               \
diff --git a/src/vectors-4-default.h b/src/vectors-4-default.h
index ac1f1a4..76e96b9 100644
--- a/src/vectors-4-default.h
+++ b/src/vectors-4-default.h
@@ -1,13 +1,16 @@
 // Fallback vectorisation implementation: Do not vectorise
 
-
-
 // We use macros here, so that we are not surprised by compilers which
 // don't like to inline functions. This should also make debug builds
 // (which may not inline) more efficient.
 
 
 
+#include <assert.h>
+#include <math.h>
+
+
+
 #define vec4_architecture "scalar (no vectorisation, 32-bit precision)"
 
 // Use CCTK_REAL4
@@ -81,11 +84,10 @@
 #define k4pow(x,a)  (powf(x,a))
 #define k4sqrt(x)   (sqrtf(x))
 
-#include <math.h>
 #ifdef __cplusplus
-#define SGN(x) std::signbit(x)
+#  define SGN(x) std::signbit(x)
 #else
-#define SGN(x) signbit(x)
+#  define SGN(x) signbit(x)
 #endif
 
 #define k4ifpos(x,y,z) (SGN(x)?(z):(y))
diff --git a/src/vectors-8-DoubleHummer.h b/src/vectors-8-DoubleHummer.h
index d5423bb..952f7fb 100644
--- a/src/vectors-8-DoubleHummer.h
+++ b/src/vectors-8-DoubleHummer.h
@@ -5,7 +5,11 @@
 
 
 
-#include <builtins.h>
+#include <assert.h>
+
+#ifdef __cplusplus
+#  include <builtins.h>
+#endif
 
 
 
diff --git a/src/vectors-8-SSE2.h b/src/vectors-8-SSE2.h
index ed84f8b..426a8a5 100644
--- a/src/vectors-8-SSE2.h
+++ b/src/vectors-8-SSE2.h
@@ -5,6 +5,9 @@
 
 
 
+#include <assert.h>
+#include <math.h>
+
 #include <emmintrin.h>
 #ifdef __SSE4_1__
 // Intel's SSE 4.1
@@ -231,12 +234,11 @@ static const union {
     r;                                          \
   })
 #else
-#include <math.h>
-#ifdef __cplusplus
-#define SGN(x) std::signbit(x)
-#else
-#define SGN(x) signbit(x)
-#endif
+#  ifdef __cplusplus
+#    define SGN(x) std::signbit(x)
+#  else
+#    define SGN(x) signbit(x)
+#  endif
 #  define k8ifpos(x_,y_,z_)                                     \
   ({                                                            \
     CCTK_REAL8_VEC const xx=(x_);                               \
diff --git a/src/vectors-8-default.h b/src/vectors-8-default.h
index 279cdb2..aaed7d9 100644
--- a/src/vectors-8-default.h
+++ b/src/vectors-8-default.h
@@ -1,13 +1,16 @@
 // Fallback vectorisation implementation: Do not vectorise
 
-
-
 // We use macros here, so that we are not surprised by compilers which
 // don't like to inline functions. This should also make debug builds
 // (which may not inline) more efficient.
 
 
 
+#include <assert.h>
+#include <math.h>
+
+
+
 #define vec8_architecture "scalar (no vectorisation, 64-bit precision)"
 
 // Use CCTK_REAL8
@@ -81,11 +84,10 @@
 #define k8pow(x,a)  (pow(x,a))
 #define k8sqrt(x)   (sqrt(x))
 
-#include <math.h>
 #ifdef __cplusplus
-#define SGN(x) std::signbit(x)
+#  define SGN(x) std::signbit(x)
 #else
-#define SGN(x) signbit(x)
+#  define SGN(x) signbit(x)
 #endif
 
 #define k8ifpos(x,y,z) (SGN(x)?(z):(y))
diff --git a/src/vectors.c b/src/vectors.cc
index 7588295..ffff4be 100644
--- a/src/vectors.c
+++ b/src/vectors.cc
@@ -4,6 +4,7 @@
 #include "cctk_Parameters.h" 
 #include "vectors.h"
 
+extern "C"
 int Vectors_Startup(void)
 {
   CCTK_VInfo(CCTK_THORNSTRING, "Using vector size %d for architecture %s",
diff --git a/test/vectors.par b/test/vectors.par
new file mode 100644
index 0000000..235a2ae
--- /dev/null
+++ b/test/vectors.par
@@ -0,0 +1,13 @@
+# Activate thorn Vectors to run its self-tests
+ActiveThorns = "Vectors"
+
+Vectors::verbose = yes
+
+# Activate some other thorns to generate one (meaningless) output file
+ActiveThorns = "CartGrid3D CoordBase IOASCII IOUtil PUGH PUGHSlab"
+
+IO::out_dir       = $parfile
+IO::out_fileinfo = "none"
+
+IOASCII::out1D_every = 1
+IOASCII::out1D_vars = "grid::r"
diff --git a/test/vectors/r_3D_diagonal.xg b/test/vectors/r_3D_diagonal.xg
new file mode 100644
index 0000000..60c5ed9
--- /dev/null
+++ b/test/vectors/r_3D_diagonal.xg
@@ -0,0 +1,143 @@
+
+
+"Time = 0.0000000000000
+-0.8660254037844		0.8660254037844
+-0.6735753140546		0.6735753140546
+-0.4811252243247		0.4811252243247
+-0.2886751345948		0.2886751345948
+-0.0962250448649		0.0962250448649
+0.0962250448649		0.0962250448649
+0.2886751345948		0.2886751345948
+0.4811252243247		0.4811252243247
+0.6735753140546		0.6735753140546
+0.8660254037844		0.8660254037844
+
+
+"Time = 1.0000000000000
+-0.8660254037844		0.8660254037844
+-0.6735753140546		0.6735753140546
+-0.4811252243247		0.4811252243247
+-0.2886751345948		0.2886751345948
+-0.0962250448649		0.0962250448649
+0.0962250448649		0.0962250448649
+0.2886751345948		0.2886751345948
+0.4811252243247		0.4811252243247
+0.6735753140546		0.6735753140546
+0.8660254037844		0.8660254037844
+
+
+"Time = 2.0000000000000
+-0.8660254037844		0.8660254037844
+-0.6735753140546		0.6735753140546
+-0.4811252243247		0.4811252243247
+-0.2886751345948		0.2886751345948
+-0.0962250448649		0.0962250448649
+0.0962250448649		0.0962250448649
+0.2886751345948		0.2886751345948
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diff --git a/test/vectors/r_x_[5][5].xg b/test/vectors/r_x_[5][5].xg
new file mode 100644
index 0000000..4900394
--- /dev/null
+++ b/test/vectors/r_x_[5][5].xg
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diff --git a/test/vectors/r_y_[5][5].xg b/test/vectors/r_y_[5][5].xg
new file mode 100644
index 0000000..4900394
--- /dev/null
+++ b/test/vectors/r_y_[5][5].xg
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diff --git a/test/vectors/r_z_[5][5].xg b/test/vectors/r_z_[5][5].xg
new file mode 100644
index 0000000..4900394
--- /dev/null
+++ b/test/vectors/r_z_[5][5].xg
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+"Time = 7.0000000000000
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+-0.3888888888889		0.3967460238079
+-0.2777777777778		0.2886751345948
+-0.1666666666667		0.1842569327975
+-0.0555555555556		0.0962250448649
+0.0555555555556		0.0962250448649
+0.1666666666667		0.1842569327975
+0.2777777777778		0.2886751345948
+0.3888888888889		0.3967460238079
+0.5000000000000		0.5061351988413
+
+
+"Time = 8.0000000000000
+-0.5000000000000		0.5061351988413
+-0.3888888888889		0.3967460238079
+-0.2777777777778		0.2886751345948
+-0.1666666666667		0.1842569327975
+-0.0555555555556		0.0962250448649
+0.0555555555556		0.0962250448649
+0.1666666666667		0.1842569327975
+0.2777777777778		0.2886751345948
+0.3888888888889		0.3967460238079
+0.5000000000000		0.5061351988413
+
+
+"Time = 9.0000000000000
+-0.5000000000000		0.5061351988413
+-0.3888888888889		0.3967460238079
+-0.2777777777778		0.2886751345948
+-0.1666666666667		0.1842569327975
+-0.0555555555556		0.0962250448649
+0.0555555555556		0.0962250448649
+0.1666666666667		0.1842569327975
+0.2777777777778		0.2886751345948
+0.3888888888889		0.3967460238079
+0.5000000000000		0.5061351988413
+
+
+"Time = 10.0000000000000
+-0.5000000000000		0.5061351988413
+-0.3888888888889		0.3967460238079
+-0.2777777777778		0.2886751345948
+-0.1666666666667		0.1842569327975
+-0.0555555555556		0.0962250448649
+0.0555555555556		0.0962250448649
+0.1666666666667		0.1842569327975
+0.2777777777778		0.2886751345948
+0.3888888888889		0.3967460238079
+0.5000000000000		0.5061351988413