Estimating software functional size is a crucial initial step before development, impacting costs and timelines. This involves applying standard Function Point Analysis (FPA) to the Software Requirements Specification (SRS). However, manual analysis by Function Point (FP) analysts during the splitting of FP entries from SRS remains inefficient and costly. To address this issue, for the first time, we propose an AI-based domain expert for FPA, named FPA-EX. It employs a large language model (LLM), intelligently extracts software FP entries from SRS, providing automated support to enhance efficiency. Specifically, we construct a multi-domain FPA dataset through collecting and annotating 778 question-answer pairs related to various SRS. Based on this dataset, we present a novel densely supervised fine-tuning (DSFT) on LLM, which performs entries-level optimization over the human augmented text, ensuring precise FPs outputs. Finally, we design a ConceptAct Promting (CAP) process for correct logical reasoning. Experiments demonstrate the superior performance of FPA-EX, particularly higher than GPT3.5 by 0.491 on F1 scores. Furthermore, in practical application, FPA-EX significantly enhances the productivity of FP analysts, contributing to a shift towards more intelligent work patterns.