Customizing the wordpress tag-cloud output

This is how the links are created in wp_generate_tag_cloud (wp-includes/category-template.php)

foreach ( $tags as $key => $tag ) {
    $count = $counts[ $key ];
    $real_count = $real_counts[ $key ];
    $tag_link = '#' != $tag->link ? esc_url( $tag->link ) : '#';
    $tag_id = isset($tags[ $key ]->id) ? $tags[ $key ]->id : $key;
    $tag_name = $tags[ $key ]->name;
    $a[] = "<a href="https://wordpress.stackexchange.com/questions/17090/$tag_link" class="tag-link-$tag_id" title="" . esc_attr( call_user_func( $topic_count_text_callback, $real_count ) ) . "" style="font-size: " .
        ( $smallest + ( ( $count - $min_count ) * $font_step ) )
        . "$unit;">$tag_name</a>";
}

There seems not to be a way to do what you need. Maybe copying all wp_generate_tag_cloud and modifying it to your needs in your functions.php?

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