Do not rely on bash arithmetic in `bootstrap` (#625)

diff --git a/bootstrap b/bootstrap
index 2f43f50..7c7020d 100755
--- a/bootstrap
+++ b/bootstrap
@@ -1,19 +1,24 @@
 # !/bin/sh -e
 
+REQUIRED='is required, but not installed.'
+bc -v >/dev/null 2>&1 || { echo >&2 "'bc' $REQUIRED"; exit 1; }
+sed --version >/dev/null 2>&1 || { echo >&2 "'sed' $REQUIRED"; exit 1; }
+autoreconf --version >/dev/null 2>&1 || { echo >&2 "'autoconf' $REQUIRED"; exit 1; }
+
 mkdir m4 2>/dev/null
 
 BROTLI_ABI_HEX=`sed -n 's/#define BROTLI_ABI_VERSION 0x//p' c/common/version.h`
-BROTLI_ABI_INT=`echo $((16#$BROTLI_ABI_HEX))`
-BROTLI_ABI_CURRENT=$(($BROTLI_ABI_INT >> 24))
-BROTLI_ABI_REVISION=$((($BROTLI_ABI_INT >> 12) & 4095))
-BROTLI_ABI_AGE=$(($BROTLI_ABI_INT & 4095))
+BROTLI_ABI_INT=`echo "ibase=16;$BROTLI_ABI_HEX" | bc`
+BROTLI_ABI_CURRENT=`expr $BROTLI_ABI_INT / 16777216`
+BROTLI_ABI_REVISION=`expr $BROTLI_ABI_INT / 4096 % 4096`
+BROTLI_ABI_AGE=`expr $BROTLI_ABI_INT % 4096`
 BROTLI_ABI_INFO="$BROTLI_ABI_CURRENT:$BROTLI_ABI_REVISION:$BROTLI_ABI_AGE"
 
 BROTLI_VERSION_HEX=`sed -n 's/#define BROTLI_VERSION 0x//p' c/common/version.h`
-BROTLI_VERSION_INT=`echo $((16#$BROTLI_VERSION_HEX))`
-BROTLI_VERSION_MAJOR=$(($BROTLI_VERSION_INT >> 24))
-BROTLI_VERSION_MINOR=$((($BROTLI_VERSION_INT >> 12) & 4095))
-BROTLI_VERSION_PATCH=$(($BROTLI_VERSION_INT & 4095))
+BROTLI_VERSION_INT=`echo "ibase=16;$BROTLI_VERSION_HEX" | bc`
+BROTLI_VERSION_MAJOR=`expr $BROTLI_VERSION_INT / 16777216`
+BROTLI_VERSION_MINOR=`expr $BROTLI_VERSION_INT / 4096 % 4096`
+BROTLI_VERSION_PATCH=`expr $BROTLI_VERSION_INT % 4096`
 BROTLI_VERSION="$BROTLI_VERSION_MAJOR.$BROTLI_VERSION_MINOR.$BROTLI_VERSION_PATCH"
 
 sed -r "s/[0-9]+:[0-9]+:[0-9]+/$BROTLI_ABI_INFO/" Makefile.am -i