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Matt's Arbitrary Precision Math library

This is a wrapper for MAPM, an older but quite complete arbitrary math library. The wrapper is made to be as close to the Nim maths module as possible so that it can function as a drop-in replacement when you realise that you need better precision. The low-level wrapper is done through Futhark and both the libmapm.a and completed wrapper exists in this repo. If you want or need to rebuild libmapm.a you can run the Nimble task buildMapm. If you want Futhark to rebuild the wrapper you can compile with -d:useFuthark or -d:useFutharkForMapm.

Example:

import mapm

var x = initMapm(10) # Init a MAPM number from an existing int, float, or string
echo x / 6.4e+2'm # Or use the 'm literal specifier

Please note that MAPM accumulates precision when multiplying numbers, so rounding to your required precision should be done from time to time to avoid this. MAPM also handles errors by writing to stderr and return 0 in most cases. This wrapper could've wrapped the underlying functions in input checks and turned these into exceptions, but I opted not to do this for performance reasons.

The underlying C functions all take a MAPM number to store the result in. This is wrapped to put the result in a freshly initialized number for each operation. This is likely to give a performance penalty over using the library with the clever re-use of the result. If you want to squeeze the highest amount of performance out of this library you should use the low-level wrapper.

The rest of this documentation is more or less copied straight from the MAPM README.

MAPM library numerical limitations

A general floating point number is of the form:

Sn.nnnnnnnnE+yyyy        ex: -4.318384739357974916E+6215
Sn.nnnnnnnnE-yyyy        ex: +8.208237913789131096523645193E-12873

S is the sign, + or -.

In MAPM, a number (n.nnnn...) may contain up to ( INT_MAX - 1 ) digits.

For example, an MAPM number with a 16 bit integer may contain 2^15 or 32,767 digits. An MAPM number with a 32 bit integer may contain 2^31 or 2,147,483,647 digits. All MAPM numbers are stored in RAM, there is no "data on disk" option. So to represent the maximum number of digits on a 32 bit CPU will require greater than 2 Gig of RAM.

If you have a CPU with 64 bit ints, then the limitation is 2^63 or 9,223,372,036,854,775,807. It should be a very long time before computers have this much RAM in them.

For the exponent (yyyy), the limitations are also INT_MAX and INT_MIN.

For a 16 bit CPU, the largest number you can represent is approx 0.9999999....E+32767. (H)

For a 16 bit CPU, the smallest number you can represent (other than 0) is approx 0.1E-32767. (L)

For a 32 bit CPU, the largest number you can represent is approx 0.9999999....E+2147483647. (H)

For a 32 bit CPU, the smallest number you can represent (other than 0) is approx 0.1E-2147483647. (L)

The limitations for negative numbers are the same as positive numbers.

                            Real Number Axis

     +------------------------+    ---    +--------------------------+
     |                        |     |     |                          |
    -H                       -L    0.0   +L                         +H

MAPM can represent real numbers from -H to -L, 0.0, +L to +H.

The number of significant digits is typically only limited by available RAM.

In MAPM, numerical overflows and underflows are not handled very well (actually not at all). There really isn't a clean and portable way to detect integer overflow and underflow. Per K&R C, the result of integer overflow/underflow is implementation dependent. In assembly language, when you add two numbers, you have access to a "carry flag" to see if an overflow occurred. C has no analogous operator to a carry flag.

It is up to the user to decide if the results are valid for a given operation. In a 32 bit environment, the limit is so large that this is likely not an issue for most typical applications. However, it doesn't take much to overflow a 16 bit int so care should taken in a 16 bit environment.

The reaction to an integer overflow/underflow is unknown at run-time:

  • Adding 2 large positive numbers may silently roll over to a negative number.
  • In some embedded applications an integer overflow/underflow triggers a hardware exception.

Thread safety

Note that the default MAPM library is NOT thread safe. MAPM internal data structures could get corrupted if multiple MAPM functions are active at the same time. The user should guarantee that only one thread is performing MAPM functions. This can usually be achieved by a call to the operating system to obtain a 'semaphore', 'mutex', or 'critical code section' so the operating system will guarantee that only one MAPM thread will be active at a time.

This file is automatically generated from the documentation found in src/mapm.nim. Use nim doc src/mapm.nim to get the full documentation.