4 files changed, 99 insertions, 2 deletions
diff --git a/cov.awk b/cov.awk
index 92e92a8..e69ebf5 100644
--- a/cov.awk
+++ b/cov.awk
@@ -36,7 +36,6 @@ NF > 0 {
             meanx[x,y] += dx[x,y]/count[x,y]
             meany[x,y] += dy[x,y]/count[x,y]
             C[x,y] += dx[x,y]*dy[x,y]
-            # cov_pop[x,y] = C[x,y]/count[x,y]
             (count[x,y] > 1) ? cov_samp[x,y] = C[x,y]/(count[x,y] - 1) : cov_samp[x,y] = ""
         }
     }
diff --git a/diff.awk b/diff.awk
index 2b42a2d..1e6a882 100644
--- a/diff.awk
+++ b/diff.awk
@@ -2,6 +2,7 @@
 
 ### diff.awk
 # print numerical diff along columns
+# dy[n] = y[n] - y[n-1]
 
 
 BEGIN {
diff --git a/diff2.awk b/diff2.awk
new file mode 100644
index 0000000..6086254
--- /dev/null
+++ b/diff2.awk
@@ -0,0 +1,97 @@
+#!/usr/bin/awk -f
+
+### diff2.awk
+# print numerical second diff along columns
+#  dy[n]   =  y[n]   -  y[n-1]
+#  d2y[n]  =  dy[n]  -  dy[n-1]
+
+
+BEGIN {
+    OFS = FS
+    sign = "[+-]?"
+    decimal = "[0-9]+[.]?[0-9]*"
+    fraction = "[.][0-9]*"
+    exponent = "([Ee]" sign "[0-9]+)?"
+    number = "^" sign "(" decimal "|" fraction ")" exponent "$"
+}
+
+
+# column headers
+NR == 1 {
+    # orig data columns
+    for (n=1; n<=NF; n++) {
+        if ($n !~ number) {
+            header[n] = $n
+            dheader[n] = "d_" $n
+            d2header[n] = "d2_" $n
+        }
+        else {
+            header[n] = "col" n
+            dheader[n] = "d_col" n
+            d2header[n] = "d2_col" n
+        }
+        printf(header[n])
+        printf(OFS)
+    }
+
+    # new diff columns
+    for (n=1; n<=NF; n++) {
+        printf(dheader[n])
+        printf(OFS)
+    }
+
+    # new diff2 columns
+    for (n=1; n<=NF; n++) {
+        printf(d2header[n])
+        printf(n < NF ? OFS : ORS)
+    }
+}
+
+
+NF > 0 {
+    (NF > nf_max) ? nf_max = NF : nf_max = nf_max
+
+    # orig data columns
+    for (n=1; n<=nf_max; n++) {
+        if ($n == header[n] || $n == dheader[n])
+            continue
+        if ($n ~ number)
+            printf(OFMT, $n)
+        else
+            printf("")
+        printf(OFS)
+    }
+
+    # new diff columns
+    for (n=1; n<=nf_max; n++) {
+        if ($n == header[n] || $n == dheader[n])
+            continue
+        if ($n ~ number) {
+            data[n] = $n
+            if (data_prev[n] ~ number)
+                diff[n] = data[n] - data_prev[n]
+            else
+                diff[n] = ""
+            data_prev[n] = data[n]
+        }
+        printf(diff[n])
+        printf(OFS)
+    }
+
+    # new diff2 columns
+    for (n=1; n<=nf_max; n++) {
+        if ($n == header[n] || $n == d2header[n])
+            continue
+        if (diff[n] ~ number) {
+            #data[n] = $n
+            if (diff_prev[n] ~ number)
+                diff2[n] = diff[n] - diff_prev[n]
+            else
+                diff2[n] = ""
+            diff_prev[n] = diff[n]
+        }
+        printf(diff2[n])
+        printf(n < nf_max ? OFS : ORS)
+    }
+}
+
diff --git a/em.awk b/em.awk
index 2cc6a74..be84054 100644
--- a/em.awk
+++ b/em.awk
@@ -8,7 +8,7 @@ BEGIN {
     ARGV[1] ? OFMT = "%." ARGV[1] "g" : OFMT = "%.12g"
 
     # constants
-    pi = 4.0*atan2(1,1)         # rad
+    pi = 4.0*atan2(1.0,1.0)     # rad
     c0 = 299792458E0            # m/s, exact
     mu0 = (4.0E-7)*pi           # H/m = (T*m)/A = N/(A^2) = (kg*m)/(A*s)
     epsilon0 = (mu0*c0^2)^-1    # F/m = C/(V*m) = (A^2*s^4)/(kg*m^3)