Application program interface (API) mapping is the key to the success of code migration. Leveraging API documentation to map APIs has been explored by previous studies, and recently, code-based learning approaches have become the mainstream approach and shown better results. However, learning approaches often require a large amount of training data (e.g., projects implemented using multiple languages or API mapping datasets), which are not widely available. In contrast, API documentation is usually available, but we have observed that much information in API documentation has been underexploited. Therefore, we develop a deep-dive approach to extensively explore API documentation to create improved API mapping methods. Our documentation exploration approach involves analyzing the functional description of APIs, and also considers the parameters and return values. The results of this analysis can be used to generate not only one-to-one API mapping, but also compatible API sequences, thereby enabling one-to-many API mapping. In addition, parameter-mapping relationships, which have often been ignored in previous approaches, can be produced. We apply this approach to map APIs from Java to Swift, and the experimental results indicate that our deep-dive analysis of API documentation leads to API mapping results that are superior to those generated by existing approaches.