OpenVMS VAX RTL Mathematics (MTH$) Manual

This manual, published in May 1993, documents the mathematics routines available in the MTH$ facility of the OpenVMS Run-Time Library for VAX systems. It is intended for system and application programmers using languages such as VAX MACRO, Ada, BASIC, FORTRAN, and Pascal.

The document is structured into two main parts:

1. Introduction to MTH$: This section covers general guidelines for using scalar mathematics routines, including entry point naming conventions, calling conventions, algorithms, condition handling (error signaling and recovery), and the representation of complex numbers. It also lists additional mathematics routines not fully detailed in the main reference section.
2. Vector Routines in MTH$: This section focuses on routines designed for vector processing, which are optimized for VAX vector hardware. It details four categories:
   • Basic Linear Algebra Subroutines (BLAS) Level 1: Routines for vector operations like copying, swapping, scaling, dot products, and generating Givens plane rotations. Both scalar and vectorized versions are described.
   • First Order Linear Recurrence (FOLR) routines: Provide vectorized algorithms for linear recurrence relations to improve performance.
   • Vector versions of existing scalar routines: Vectorized counterparts of many scalar MTH$ routines, maintaining bit-for-bit identical results where possible.
   • Fast-Vector math routines: Offer higher performance with slightly reduced accuracy and may have restricted input argument domains.

The manual includes extensive reference sections for both scalar and vector MTH$ routines, providing detailed descriptions of each function.