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Mathematical Expression Parser And JIT Compiler.


MathPresso is a C++ library designed to parse mathematical expressions and compile them into machine code. It's much faster than traditional AST or byte-code based evaluators, because there is basically no overhead in the expression's execution. The JIT compiler is based on AsmJit and works on X86 and X64 architectures.

This is an updated version of MathPresso that uses a stripped-off MPSL engine designed to work with scalar double precision floating points. It has many bugs fixed compared to the last version on google-code and contains improvements that can make execution of certain built-in functions (intrinsics) faster if the host CPU supports SSE4.1 (rounding, fraction, modulo, etc...).

This is also a transitional version that is available to users that want to use MathPresso and cannot wait for the new MPSL engine, which is a work in progress.


  • Unary operators:
    • Negate -(x)
    • Not !(x)
  • Arithmetic operators:
    • Assignment x = y
    • Addition x + y
    • Subtraction x - y
    • Multiplication x * y
    • Division x / y
    • Modulo x % y
  • Comparison operators:
    • Equal x == y
    • Not equal x != y
    • Greater x > y
    • Greater or equal x >= y
    • Lesser x < y
    • Lesser or equal x <= y
  • Functions defined by addBuiltIns():
    • Check for NaN isnan(x)
    • Check for infinity isinf(x)
    • Check for finite number isfinite(x)
    • Get a sign bit signbit(x)
    • Copy sign copysign(x, y)
    • Round to nearest round(x)
    • Round to even roundeven(x)
    • Truncate trunc(x)
    • Floor floor(x)
    • Ceil ceil(x)
    • Average value avg(x, y)
    • Minimum value min(x, y)
    • Maximum value max(x, y)
    • Absolute value abs(x)
    • Exponential exp(x)
    • Logarithm log(x)
    • Logarithm of base 2 log2(x)
    • Logarithm of base 10 log10(x)
    • Square root sqrt(x)
    • Fraction frac(x)
    • Reciprocal recip(x)
    • Power pow(x, y)
    • Sine sin(x)
    • Cosine cos(x)
    • Tangent tan(x)
    • Hyperbolic sine sinh(x)
    • Hyperbolic cosine cosh(x)
    • Hyperbolic tangent tanh(x)
    • Arcsine asin(x)
    • Arccosine acos(x)
    • Arctangent atan(x)
    • Arctangent atan2(x, y)
  • Constants defined by addBuiltIns():
    • Infinity INF
    • Not a Number NaN
    • Euler's constant E = 2.7182818284590452354
    • PI PI = 3.14159265358979323846


MathPresso's expression is always created around a mathpresso::Context, which defines an environment the expression can access and use. For example if you plan to extend MathPresso with your own function or constant the Context is the way to go. The Context also defines inputs and outputs of the expression as shown in the example below:

#include <mathpresso/mathpresso.h>
#include <stdio.h>

int main(int argc, char* argv[]) {
  mathpresso::Context ctx;
  mathpresso::Expression exp;

  // Initialize the context by adding MathPresso built-ins. Without this line
  // functions like round(), sin(), etc won't be available.

  // Let the context know the name of the variables we will refer to and
  // their positions in the data pointer. We will use an array of 3 doubles,
  // so index them by using `sizeof(double)`, like a normal C array.
  // The `addVariable()` also contains a third parameter that describes
  // variable flags, use `kVariableRO` to make a certain variable read-only.
  ctx.addVariable("x", 0 * sizeof(double));
  ctx.addVariable("y", 1 * sizeof(double));
  ctx.addVariable("z", 2 * sizeof(double));

  // Compile the expression.
  // The create parameters are:
  //   1. `mathpresso::Context&` - The expression's context / environment.
  //   2. `const char* body` - The expression body.
  //   3. `unsigned int` - Options, just pass `mathpresso::kNoOptions`.
  mathpresso::Error err = exp.compile(ctx, "(x*y) % z", mathpresso::kNoOptions);

  // Handle possible syntax or compilation error.
  if (err != mathpresso::kErrorOk) {
    printf("Expression Error: %u\n", err);
    return 1;

  // To evaluate the expression you need to create the `data` to be passed
  // to the expression and initialize it. Every expression returns `double`,
  // to return more members simply use the passed `data`.
  double data[] = {
    1.2, // 'x' - available at data[0]
    3.8, // 'y' - available at data[1]
    1.3  // 'z' - available at data[2]
  printf("Output: %f\n", exp.evaluate(data));

  return 0;

The example above should be self-explanatory. The next example does the same but by using a struct instead of an array to address the expression's data:

#include <mathpresso/mathpresso.h>
#include <stdio.h>

struct Data {
  inline Data(double x, double y, double z)
    : x(x), y(y), z(z) {}

  double x, y, z;

int main(int argc, char* argv[]) {
  mathpresso::Context ctx;
  mathpresso::Expression exp;

  ctx.addVariable("x", MATHPRESSO_OFFSET(Data, x));
  ctx.addVariable("y", MATHPRESSO_OFFSET(Data, y));
  ctx.addVariable("z", MATHPRESSO_OFFSET(Data, z));

  mathpresso::Error err = exp.compile(ctx, "(x*y) % z", mathpresso::kNoOptions);
  if (err != mathpresso::kErrorOk) {
    printf("Expression Error: %u\n", err);
    return 1;

  Data data(1.2, 3.8. 1.3);
  printf("Output: %f\n", exp.evaluate(&data));

  return 0;

Error Handling

MathPresso allows to attach an OutputLog instance to retrieve a human readable error message in case of error. It can output the following:

  • Errors, only one as MathPresso stops after the first error
  • Warnings
  • Abstract syntax tree (AST)
  • Assembly (ASM)

Here is the minimum working example that uses OutputLog to display errors. The interface is very simple, but extensible.

// This is a minimum working example that uses most of MathPresso features. It
// shows how to compile and evaluate expressions and how to handle errors. It
// also shows how to print the generated AST and machine code.
#include <mathpresso/mathpresso.h>
#include <stdio.h>

// The data passed to the expression.
struct Data {
  double x, y, z;

// By inheriting `OutputLog` one can create a way how to handle possible errors
// and report them to humans. The most interesting and used message type is
// `kMessageError`, because it signalizes an invalid expression. Other message
// types are used mostly for debugging.
struct MyOutputLog : public mathpresso::OutputLog {
  MyOutputLog() {}
  virtual ~MyOutputLog() {}
  virtual void log(unsigned int type, unsigned int line, unsigned int column, const char* message, size_t size) {
    switch (type) {
      case kMessageError:
        printf("[ERROR]: %s (line %u, column %u)\n", message, line, column);

      case kMessageWarning:
        printf("[WARNING]: %s (line %u, column %u)\n", message, line, column);

      case kMessageAstInitial:
        printf("[AST-INITIAL]\n%s", message);

      case kMessageAstFinal:
        printf("[AST-FINAL]\n%s", message);

      case kMessageAsm:
        printf("[ASSEMBLY]\n%s", message);

        printf("[UNKNOWN]\n%s", message);

int main(int argc, char* argv[]) {
  MyOutputLog outputLog;

  // Create the context, add builtins and define the `Data` layout.
  mathpresso::Context ctx;
  ctx.addVariable("x"  , MATHPRESSO_OFFSET(Data, x));
  ctx.addVariable("y"  , MATHPRESSO_OFFSET(Data, y));
  ctx.addVariable("z"  , MATHPRESSO_OFFSET(Data, z));

  // The following options will cause that MathPresso will send everything
  // it does to `OutputLog`.
  unsigned int options =
    mathpresso::kOptionVerbose         | // Enable warnings, not just errors.
    mathpresso::kOptionDebugAst        | // Enable AST dumps.
    mathpresso::kOptionDebugMachineCode; // Enable ASM dumps.

  mathpresso::Expression exp;
  mathpresso::Error err = exp.compile(ctx,
    "-(-(abs(x * y - floor(x)))) * z * (12.9 - 3)", options, &outputLog);

  // Handle possible syntax or compilation error. The OutputLog has already
  // received and printed the reason in a human readable form.
  if (err) {
    printf("ERROR %u\n", err);
    return 1;

  // Evaluate the expression, if compiled.
  Data data = { 12.2, 9.2, -1.9 };
  double result = exp.evaluate(&data);

  printf("RESULT: %f\n", result);
  return 0;

When executed the output of the application would be something like:

* [Binary]
  * [Binary]
    - [Unary]
      - [Unary]
        abs [Unary]
          - [Binary]
            * [Binary]
            floor [Unary]
  - [Binary]

* [Binary]
  * [Binary]
    abs [Unary]
      - [Binary]
        * [Binary]
        floor [Unary]

L0:                                 ;                     |                           ..
lea rax, [L2]                       ; 488D05........      | lea pConst, [L2]          ..w
movsd xmm0, [rdx]                   ; F20F1002            | movsd v3, [pVariables]    .r.w
mulsd xmm0, [rdx+8]                 ; F20F594208          | mulsd v3, [pVariables+8]  .r.x
movsd xmm1, [rdx]                   ; F20F100A            | movsd v4, [pVariables]    .r..w
roundsd xmm1, xmm1, 9               ; 660F3A0BC909        | roundsd v4, v4, 9         ....x
subsd xmm0, xmm1                    ; F20F5CC1            | subsd v3, v4              ...xR
xorpd xmm1, xmm1                    ; 660F57C9            | xorpd v5, v5              .... w
subsd xmm1, xmm0                    ; F20F5CC8            | subsd v5, v3              ...r x
maxsd xmm1, xmm0                    ; F20F5FC8            | maxsd v5, v3              ...R x
mulsd xmm1, [rdx+16]                ; F20F594A10          | mulsd v5, [pVariables+16] .R.  x
mulsd xmm1, [rax]                   ; F20F5908            | mulsd v5, [pConst]        . R  x
movsd [rcx], xmm1                   ; F20F1109            | movsd [pResult], v5       R    R
L1:                                 ;                     |
ret                                 ; C3                  |
.align 8
L2:                                 ;                     |

RESULT: -1885.514400


  • AsmJit


MathPresso is an open-source library released under a permissive ZLIB license, which makes it possible to use it freely in any open-source or commercial product. Free support is available through issues and gitter channel.

If you use MathPresso in a non-commercial project and would like to appreciate the library in the form of a donation you are welcome to support us. Donations are anonymous unless the donor lets us know otherwise. The order and format of listed donors is not guaranteed and may change in the future. Additionally, donations should be considered as an appreciation of past work and not used to gain special privileges in terms of future development. MathPresso authors reserve the right to remove a donor from the list in extreme cases of disruptive behavior against other community members. Diversity of opinions and constructive criticism will always be welcome in the MathPresso community.

Donation Addresses:

  • BTC: 14dEp5h8jYSxgXB9vcjE8eh78uweD76o7W
  • ETH: 0xd4f0b9424cF31DF5a5359D029CF3A65c500a581E
  • Please contact us if you would like to donate through a different channel or to use a different crypto-currency. Wire transfers and SEPA payments are both possible.

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