genann: Use reciprocal interval value to strength reduce divide to multiply

This gives a reduction of roughly 2.5 million instructions in the execution
trace of example4.

genann_act_sigmoid_cached() previously divided by interval to calculate the
lookup index. Divide is a expensive operation, so instead use the reciprocal of
the existing interval calculation to reduce the divide to a multiply.

Building with the following configuration:

```
$ head /proc/cpuinfo
processor       : 0
vendor_id       : GenuineIntel
cpu family      : 6
model           : 61
model name      : Intel(R) Core(TM) i7-5600U CPU @ 2.60GHz
stepping        : 4
microcode       : 0x25
cpu MHz         : 2593.871
cache size      : 4096 KB
physical id     : 0
$ cat /etc/os-release
NAME="Ubuntu"
VERSION="17.10 (Artful Aardvark)"
ID=ubuntu
ID_LIKE=debian
PRETTY_NAME="Ubuntu 17.10"
VERSION_ID="17.10"
HOME_URL="https://www.ubuntu.com/"
SUPPORT_URL="https://help.ubuntu.com/"
BUG_REPORT_URL="https://bugs.launchpad.net/ubuntu/"
PRIVACY_POLICY_URL="https://www.ubuntu.com/legal/terms-and-policies/privacy-policy"
VERSION_CODENAME=artful
UBUNTU_CODENAME=artful
$ cc --version
gcc (Ubuntu 7.2.0-8ubuntu3) 7.2.0
Copyright (C) 2017 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
```

on my Lenovo X1 Carbon Gen 3 machine sees the following:

```
$ make CFLAGS="-g -O3 -march=native -DNDEBUG"
cc -g -O3 -march=native -DNDEBUG   -c -o test.o test.c
cc -g -O3 -march=native -DNDEBUG   -c -o genann.o genann.c
cc -g -O3 -march=native -DNDEBUG   -c -o example1.o example1.c
cc -g -O3 -march=native -DNDEBUG   -c -o example2.o example2.c
cc -g -O3 -march=native -DNDEBUG   -c -o example3.o example3.c
cc -g -O3 -march=native -DNDEBUG   -c -o example4.o example4.c
cc -g -O3 -march=native -DNDEBUG   -c -o strings.o strings.c
cc   test.o genann.o  -lm -o test
cc   example1.o genann.o  -lm -o example1
cc   example4.o genann.o  -lm -o example4
cc   example3.o genann.o  -lm -o example3
cc   example2.o genann.o  -lm -o example2
cc   strings.o genann.o  -lm -o strings
$ for i in `seq 0 10`; do ./example4 > /dev/null; done; sudo perf stat record ./example4
GENANN example 4.
Train an ANN on the IRIS dataset using backpropagation.
Loading 150 data points from example/iris.data
Training for 5000 loops over data.
147/150 correct (98.0%).

 Performance counter stats for './example4':

        101.369081      task-clock (msec)         #    0.998 CPUs utilized
                 1      context-switches          #    0.010 K/sec
                 0      cpu-migrations            #    0.000 K/sec
                79      page-faults               #    0.779 K/sec
       320,197,883      cycles                    #    3.159 GHz
     1,121,174,423      instructions              #    3.50  insn per cycle
       223,257,752      branches                  # 2202.425 M/sec
            62,680      branch-misses             #    0.03% of all branches

       0.101595114 seconds time elapsed
```

Prior to the change, we see something like:

```
$ make CFLAGS="-g -O3 -march=native"
cc -g -O3 -march=native   -c -o test.o test.c
cc -g -O3 -march=native   -c -o genann.o genann.c
cc -g -O3 -march=native   -c -o example1.o example1.c
cc -g -O3 -march=native   -c -o example2.o example2.c
cc -g -O3 -march=native   -c -o example3.o example3.c
cc -g -O3 -march=native   -c -o example4.o example4.c
cc -g -O3 -march=native   -c -o strings.o strings.c
cc   test.o genann.o  -lm -o test
cc   example1.o genann.o  -lm -o example1
cc   example3.o genann.o  -lm -o example3
cc   example4.o genann.o  -lm -o example4
cc   strings.o genann.o  -lm -o strings
cc   example2.o genann.o  -lm -o example2
$ for i in `seq 0 10`; do ./example4 > /dev/null; done; sudo perf stat record ./example4
GENANN example 4.
Train an ANN on the IRIS dataset using backpropagation.
Loading 150 data points from example/iris.data
Training for 5000 loops over data.
147/150 correct (98.0%).

 Performance counter stats for './example4':

        104.644198      task-clock (msec)         #    0.998 CPUs utilized
                 0      context-switches          #    0.000 K/sec
                 0      cpu-migrations            #    0.000 K/sec
                79      page-faults               #    0.755 K/sec
       330,340,554      cycles                    #    3.157 GHz
     1,123,669,767      instructions              #    3.40  insn per cycle
       215,441,809      branches                  # 2058.803 M/sec
            62,406      branch-misses             #    0.03% of all branches

       0.104891323 seconds time elapsed
```

Signed-off-by: Andrew Jeffery <andrew@aj.id.au>

genann.c

@@ -54,20 +54,27 @@ double genann_act_sigmoid_cached(double a) {
 
     /* Calculate entire lookup table on first run. */
     if (!initialized) {
-        interval = (max - min) / LOOKUP_SIZE;
+        const double f = (max - min) / LOOKUP_SIZE;
         int i;
+        interval = LOOKUP_SIZE / (max - min);
         for (i = 0; i < LOOKUP_SIZE; ++i) {
-            lookup[i] = genann_act_sigmoid(min + interval * i);
+            lookup[i] = genann_act_sigmoid(min + f * i);
         }
         /* This is down here to make this thread safe. */
         initialized = 1;
     }
 
-    int i;
+    assert(!isnan(a));
-    i = (int)((a-min)/interval+0.5);
+
-    if (i <= 0) return lookup[0];
+    if (a < min) return lookup[0];
-    if (i >= LOOKUP_SIZE) return lookup[LOOKUP_SIZE-1];
+    if (a >= max) return lookup[LOOKUP_SIZE - 1];
-    return lookup[i];
+
+    size_t j = (size_t)((a-min)*interval+0.5);
+
+    if (j < 0) return lookup[0];
+    if (j >= LOOKUP_SIZE) return lookup[LOOKUP_SIZE - 1];
+
+    return lookup[j];
 }