Most contacts were lost after iOS 7 Update - but they are available while texting

I have an iPhone 4 (32GB). After I updated to iOS 7, most of my Contact data was lost. About 10% of my contacts remain with no specific pattern.

I know the rest of the Contacts data is still in there somewhere because the names and numbers come up when I am in texting mode and I begin typing a letter in the addressee field. The missing names are available only during texting as input choices in grey, blue, or green letters.

What happened to my Contact data? How can I fix it?