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# Submit a comment to an "Available C++ Libraries FAQ" entry

## CategoryCommercial libraries (A-N)

### ExacMath - Quadruple Precision C++ Math Libraries

ExacMath is a quadruple and double quadruple C++ math library that supports the Borland C++ and Microsoft Visual C++ compilers. ExacMath supports real and complex arithmetic with three floating point data types. The epsilon real data type has a 128 bit mantissa. The dpepsilon real data type has a 256 bit mantissa. The cepsilon complex data type real and imaginary components each have a 128 bit mantissa.
ExacMath extends the capability of the Borland C++ and Microsoft Visual C++ math libraries, neither of which supports quadruple or double quadruple arithmetic. The ExacMath library of functions are the same ones found in the Borland C++ and Microsoft Visual C++ math libraries.

ExacMath libraries support DOS, Win16, Win32, 16 and 32 bit Windows Console Applications as well as MFC programs. ExacMath has an elaborate mecanism for exception handling that allows the programmer to trap an exception error message and continue executing the program after the exception occurred. ExacMath also has a library of functions that allow for processing of RMS and MRE errors automatically.

For pricing refer to the Floating Point Software Web Site

Licensing : Commercial

#### Comment from : STEPHEN TURATO on 2015-05-02

THE ORIGINAL VERSION OF EXACMATH HAS BEEN COMPLETELY REWRITTEN TO VERSION 7.0. THIS NEW VERSION HAS BEEN TESTED THROUGLY AND AT THIS POINT APPEARS TO HAVE NO PROBLEMS WITH IT. ANYONE USING VISUAL C++ KNOWS THE LONG DOUBLE DATA TYPE IS MISSING. THAT IS THE FLOATING POINT TYPE WITHA 64 BIT MANTISSA. MR. TURATO HAS FIGURED OUT A WAY TO OVERCOME THIS PROBLEM AND HAS CALLED THE NEW DATATYPE REAL80. IT HAS THE SAME FORMAT AS THE INTEL FPU WITH A 64 BIT MANTISSA. I WILL NOT DISCLOSE HOW I HAVE DONE THIS I WILL ONLY SAY IF YOU WANT TO KNOW HOW TO DO THIS YOU WILL HAVE PURCHASE THE SOURCE CODE WHICH IS WELL OVER 1 MILLION LINES OF CODE FOR ALL 4 RUN TIME LIBRARIES. IT WILL BE AVAILABLE ON EBAY AT FIRST AT A CHEAP PRICE OF $75.
THE RUNTIME MATH LIBARIES ARE THE FOLLOWING:
1) duad - 106 BITS OF PRECISION
2) quad - 128 BIT OF PRECISION
3) real80 - LONG DOUBLE 64 BITS OF PRECISION
4) mpad - MULTPLE PRECISION
EACH OF THE ABOVE RUNTIME MATH LIBRARIES HAS THE SAME FUNCTION AS THE VISUAL C++ MATH LIBRARIES AND SOME EXTRA ERROR COLLECTION FUNCTION AS THE MRE AND RMS ERRORS OR 2-NORMS.
INCLUDED IN THE LIST OF FUNCTIONS ARE TWO FUNCTIONS THAT COMPUTE MINMAX POLYNOMIALS. THE FUNCTIONS ARE WRITTEN WITH THE MPAD DATA TYPE TO MAXIMZE THE ACCURACY OF THE RESULTS.
ALONG WITH THE LIBRARIES IS AN EXCEPTION HANDLING MECHANISM THAT TEMPORARLY STOPS THE EXECUTION OF A VISUAL C++ PROGRAM WHEN SAY AN EXPONENT OVERFLOW OCCURS WHEN ADDING 2 NUMBERS.
INLCUED IN THE PACKAGE WILL BE A PROGRAMMERS REFERENCE MANUAL AND A FUNCTION REFERENCE NABUAL FOR EACH DATATYPE.
IF YOU ARE WONDERING HOW I COULD GET THE QUAD DATATYPE RTO WORK I USE DEKKERS ALGORITHM TO DOUBLE THE PRECISION OF A REAL80.
THE DUAD DATA TYPE IS DONE THE SAME WAY. THE REAL80 DATATYPE IS WRITTEN IN OPTIMIZED X60 FLOATING POINT ASSEMBLY CODE.
THE SOURCE CODE WILL BE AVAILABLE ALONG WITH THE DESIGN MANUALS FOR A PRICE OF AT LEAST $500.
I HOPE TO FINISH THIS UP SOMETIME IN 2015. I WILL NOTIFY ON FACEBOOK OR THIS WEBPAGE WHEN YOU CAN DOWNLOAD SAMPLE PROGRAMS TO SEE IF YOU LIKE THE ENTIRE SYSTEM. TYPPE IN STEPHEN TURATO ON FACEBOOK TO GET THIS INFORMATION.
THE SOFTWARE WILL BE AVAILABLE ON EBAY AT FIRST.
I HAVE USED AND TESTED MANY RUNTIME HIGH PRECISION MATH LIBRARIES ON THE INTERNET. THEY ALL HAVE THERE PROBLEMS SUCH AS INACCURACY AND SLOW RUNNING FUNCTIONS. THESE LIBRARIES ARE NOT ONLY FAST BUT EXTREMELY ACCURATE AND USE THE METHODS IN HTE BOOK BY CODY AND WAIT.

#### Comment from : STEPHEN TURATO on 2015-05-03

THE LATEST VERSION OF EXACMATH CAN BE RUN ON WINDOWS XP, WINDOWS Y7, AND WINDOWS 8. EXACMATH 7 IS THE LATEST VERSION. IT S UNACCURACY IS UNMATCHED DUE TO A NEW METHOD POSTED IN AN ARTICLE IN TOMS IN THE EARLY 1990'S. THE METHOD USES FOR TRANSCENDENTAL FUNCTION LIKE THE SIN FUNCTION A N ARGUMWENT REDUCTION FIRST FOR X OF THE COMPUTATION OF SIN(ZX). IT THEN CREATES AN INDEX THAT LOOKS UP A MINMAX POLYNOMIAL APPROXIMTION OCF THE REDUCED ARGUMENT. TEHE ANSWER FOR THE REDCUDED ARGUMENT IS THAN CALCULATED AND THE FINAL ANSWER FOR SIN(X) IS FOUND BY REVERSING THE STEPS USED TO CREATE THE REDUCED ARGUMENT. SOMETIMES IT IS ADVANTEGOUS TO USE AN IDENTITY TO COMPUTE THE REDUCED ARGUMENT. IN THAT CASE THAT IDENTITY IS USED IN THE REVERSING PROCEDURE TO CALCULATE THE FINAL ANSWER. ALGORITHMS EXISTS IN TOMS FOR SIN(X), COS(X), LOG(X), E^X AND MANY MORE FUNCTIONS.
THE OVERAL RESULT IS A RUNTIME LIBRARY THAT IS EXTREMELY FAST AND ACCURATE. ACCURACY PROGRAMS WILL BE AVAILABLE RTO SHOW THESE RESULTS IN 2015. MOST OF THE TIME THE FINAL RESULTS IS EITHER EXACT OR OFF BY ONE BIT.
DEKKERS ALGORITHM INVENTED BY A GERMAN MATHEMATCIAN IN 1970 IS USED FOR THE BASIC OPERATIONS SUCH AS THE SQRT(X) AND X/Y.
OVERALL THE RESULTING LIBRARY WILL BE VERY USEFUL FOR RESEARCHERS IN THE FIELD WHO NEED THE LONG DOUBLE LIBRARY AND QUAD PRECISION.
THE SOURCE CODE WILL BE AVAILABLE AT A HEFTY PRICE OF $500 BECAUSE THE OVERALL PRODUCT TOOK 20 YEARS OF RESEARCH, CODINFG AND DEVELOPEMENT.
THERE WILL BE SEVERAL BOOKS AVAILABLE THAT EXPLAIN HOW THE LOOKUP TABLE METHOD ACTUALLY WORKS.
ANY QUESTIONS ABOUT THE AVAILABILTY OF EXACMATH CAN BE OBTAINED BY WRITTING STEPHEN TURATO AT THE EMAIL ADDRESS s.turato@comcast.net

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