MISTIC PROGRAMMING MANUAL Prepared by Computer Laboratory Staff COMPUTER LABORATORY MICHIGAN STATE UNIVERSITY EAST LANSING, MICHIGAN March 17, 1958 6.13 MISTIC LIBRARY CATEGORIES Programmed Arithmetic Miscellaneous --------------------- ------------- A. Floating Point Z. Miscellaneous complete B. Other programmed arithmetic programs Code Checking ------------- C. Post Mortem checks D. Dynamic code checks Integration ----------- E. Quadrature F. Ordinary differential equations G. Partial differential equations Operations on Functions ----------------------- H. Zeros and minima I. Interpolation J. Operations on polynomials and power series K. Approximations and statistics Linear Algebra -------------- L. Simultaneous linear equations M. Other operation son matrices and vectors Input and Output ---------------- N. Number input O. Scope Output P. Printing and punching Mathematical Logic ------------------ Q. Mathematical logic Particular Functions -------------------- R. Roots and fractional powers S. Logarithmic, exponential, and hyperbolic functions T. Trigonometric functions V. Other special functions Organizational -------------- W. Counting, sorting, and selecting X. Program preparation 6.14 PROGRAM LIBRARY INDEX LABEL TITLE ----- ----- A1 Floating Decimal Arithmetic Routine (168) A3 Convert a Number from Floating Decimal Representation to Normal Machine Form (27) A4 1.7 Precision Floating Decimal (279) A5 Complex Number Arithmetic (248) A6 Floating Decimal Routine and Auxiliaries (See Description) B2 Complex Number Operations (54) C1 Post Mortem of the Decimal Order Input [37+(25-DOI)] C3 Post Mortem of Fractions and Their Locations (31) C4 Post Mortem of Integers and Their Locations (38) C5 Print Sets of Order Pairs and Their Locations (32) C6 Address Search Routine (23) C9 Print Sets of Floating Decimal Numbers and Their Decimal Locations (36) C01 Post Mortem for Fractions and their Locations (63) D1 Check Point Routine [57+31+s+j (See Text)] D3 Sequence Checking Routine (30) D4 Control Transfer Check (41) E1 Integration fro f(x) Given at Equal Increments of x (45) E2 Integration by Simpson's Rule (Tabulated Values) (21) E3 Integration by Simpson's Rule (Fraction Values) (33) E4 Numerical Differentiation with Interpolation (103) E5 Quadrature by Gauss' Method (18+2n) E6 Integration over a Single Interval (Tabulated Values)(32) F1 Solution of a System of Ordinary Differential Equations (41) F2 Solutions of a System of Differential Equations by Milne's Method (80+46) F3 Integration of n Simultaneous 2nd Order Differential Equations with Initial Conditions Specified (40) F5 Integration of a System of Ordinary Differential Equations (60) FA1 Second Order Linear Differential Equations with Two Point Boundary Conditions (101) FA2 Floating Decimal Solution of a System of Ordinary Differential Equations. G1 LaPlace's Equation-Liebmann Method G2 Poisson's Equation-Liebmann-Frankel Method ---------------------------------------------------------------------- * Number after title is number of words in routine. 6.15 LABEL TITLE ----- ----- H1 Inverse Interpolation (33) H2 A Search for the Real Roots of f(x) = 0 (80) H3 Minimization of a Function of Two Variables (46) H4 " " " " " Four " (75) H5 " " " " " n " (89) H6 " " " " " n " Treating One Variable at a Time (46) HF1 Zero of a Solution of a Differential Equation (16) I1 Interpolation (51) J2 Roots of a Polynomial (Entire Program) K2 Product Moment Correlations, Means, Standard Deviations, Variances, and Covariances (Entire Program) K3 Least Squares (Entire Program) K4 Analysis and Intercorrelation of Scores Based on Paired Comparisons (Entire Program) K5 Autocorrelations (Entire Program) K6 Chi-Squared (23) K6M Chi-Squared K7 Interative Estimation of Communalities--Principle Axes Method of Factor Analysis (Entire Program) K9 Product Moment Correlation, Means, Standard Deviations, Variances in Logarithmic Scale (Entire Program) K10 Calculate Autocorrelations of a Time Series (85) K11 Quartimax Orthogonal Rotation of Factors (Entire Program) KA1 Polynomial Approximation (60) L1 Solution of a Set of Simultaneous Linear Algebraic Equations (83) L2 Automatic Linear Equation Solver L3 Complete Linear Equations Solver (Entire Program) L6 Solution of a Set of n Simultaneous Linear Algebraic Equations (162) L7 Automatic Linear Equation Solver with Programmed Checks and Calculation of Residues M0 Eigenvalues and Eigenvectors of a Symmetric Matrix (113) M2 Automatic Inversion of a Symmetric Matrix (Entire Program) M3 Automatic Eigenvalue-Eigenvector Program (Entire Program) M4 Closed Eigenvalues and Eigenvectors (163) M5 Solutions of the Determinantal Equation |A-yB| = 0 (Entire Program) M6 New Matrix Multiplication (88) M7 Principle Axes Factor Analysis (Entire Program) M8 Sums of Squares of Rows and Columns (Entire Program) M9 Square Root Factorization (See Description) ---------------------------------------------------------------------- * Number after title is number of words in routine. 6.16 LABEL TITLE ----- ----- M10 Estimation of Communalities by the Method of Maximum Likelihood (Entire Program) M11 Matrix Multiplication (77) M12 Triangularization of a Matrix and its Determinant (Entire Program) M13 Complete Linear Matrix Equation Solver and General Matrix Inversion (Entire Program) M14 Linear Matrix Equation Solver and General Matrix Inversion (115) M15 Linear Programming (Entire Program) M16 Matrix Multiplication when the Common Dimension is Large (Entire Program) M17 Post Multiplication of a Matrix or its Transpose by a Vector (45) MA1 Matrix Multiplication with Floating Decimal Auxiliary (21 or 26--See Description) N1 Input One Number From Tape, Integer or Fraction (19) N2 Input a Sequence of Decimal Fractions (26) N4 Input a Sequence of Integers (17) N8 Read One Number from Tape as Integer or Fraction (22) N9 Matrix Modifying Input (43+26 words of N2) N10 Input a Sequence of Integers with Sum Check (36) N11 Input a Sequence of Fractions or Integers (25) N12 Infraput (39) N13 Input a Sequence of Fractions all having the Same Number of Decimal Digits (21) N14 Input a Sequence of Integers P1 Print One Number Fractional or Integer in a Manner Determined by a Program Parameter (28) P2 Print (A) with or without Sign to n Places as Determined by a program Parameter (18) P3 Print n Digits of an Integer with or without Sign (20) P4 Zero Suppression Integer Print (27) P5 Print One Number in a Parameter Set Layout (24) P7 Letter Printing (32) P8 Tape Lettering (110) P9 Decimal Order Print Routine (23) P10 Print Headings Interlude P11 Rounded or Unrounded Print (18) P12 Single Column Print (Revised (13) P13 Combined Integer Print (35) P15 Multiple Precision Integer Conversion (32) P16 Infraprint (56) Q1 Logical Algebra (230) Q3 Complete Circuit Analyzer Q4 Single Circuit Analyzer ---------------------------------------------------------------------- * Number after title is number of words in routine. 6.17 LABEL TITLE ----- ----- R1 Square Root Routine (9) R2 Integral Root A 1/p (24) R3 Fractional Power Routine (18) R4 Cube Root (15) R5 Reciprocal (17) RA1 Floating Decimal Square Root Auxiliary (16) S1 Natural Logarithm (45) S2 Exponential (33) S3 Logarithm (14) S4 Exponential (21) SA2 Exponential Auxiliary for Floating Decimal (26) SA3 Natural Logarithm (30) S5 Natural Logarithm (60) T1 Sine-Cosine (30) T3 Arctangent in Degrees (15) T4 New Arctan X Routine (25) T5 Sine-cosine (21) TA1 Sine Auxiliary for Floating Decimal (26) TA2 Arc Tangent Auxiliary TO Floating Point Routine (48) V1 Legendre Polynomials (25) V2 Tchebyscheff Polynomials (15) V3 Sequence of Random Numbers with Optimal Preparatory Interlude (13) V4 Fourier Analysis (52) V5 Spherical Bessel Functions (59) V6 Associated Legendre Functions (80) V7 Provide Sets of Random Numbers from 1 to N (Entire Program) V8 Ordinary Bessel Functions (257) V9 Generate 40-bit Random Numbers (32) W1 Loop Cycling Control (21) W2 Word Sorting According to Ordering Relations (25) X1 Decimal Order Input (DOI) (25) X3 Constant-Listing Auxiliary (21) X7 Sum Check (11) X8 Assemble Blocks (4) X9 Program Interruption Routine (Without Sum Check) (34) X10 Program Interruption Routine (with Sum Check (49) X11 Data Tape Checking for Library Routines K2 and K9 (Entire Program) XA1 Constant-Listing Auxiliary for Floating Decimal (18) ---------------------------------------------------------------------- * Number after title is number of words in routine.