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README.md

Numerics

Overview

The CVM implements numerical operations similar to those available in typical programming languages. Most basic numerical operations are provided as Runtime Functions such as +, sqrt, max etc.

CVM numerical capabilities are primarily intended to support the kind of calculations likely to be required in on-chain decentralised applications. More sophisticated numerical calculations, particularly those that require significant computational power, should normally be performed off-chain.

Numeric Tower

The numeric Tower is defined as follows:

  • Double
  • Long

Operations that have arguments of different levels perform an implicit cast to the level of the highest argument.

Double

Doubles are 64-bit double precision floating point values as defined in the IEEE754 standard.

Certain special values are supported:

  • ##Inf is positive infinity (hex 0x7ff0000000000000)
  • ##-Inf is negative infinity (hex 0xfff0000000000000)
  • ##NaN is a unique "not a number" value (hex 0x7ff8000000000000)

Long

Longs are 64-bit signed integer values.

Numeric Equality

Numerical equality can be checked with the == Function.

This differs from Value equality = in several ways, and is consistent with the IEEE754 specification. In particular, Users should note that:

  • (== ##NaN ##NaN) => false
  • (== 0.0 -0.0) => true
  • (== 5 5.0) => true

Numeric Comparison

Numerical comparisons can be performed with <, >, <=, >=.

These generally behave in the expected way, support variadic arguments and are consistent with ==. Examples are given below:

  • (< 1 2 3) => true
  • (< 1 3 2) => false
  • (>= 3 3) => true

Explicit Casting to Numeric Values

Certain types can be explicitly cast to Numeric Values using Runtime Functions (long x) and (double x)

Recommendations

Users SHOULD perform checks on the validity of numeric arguments before executing numerical operations. In particular:

  • Be aware of the possibility of ##NaN, ##Inf or ##-Inf as a result from Double operations
  • Check for risk of 64-bit overflow with Long values.

If precise Long accuracy is not required, user SHOULD consider performing calculations on large numbers with Double to avoid overflow risks.

Users SHOULD NOT use the CVM for complex or intensive numerical computations, e.g. modelling fluid dynamics. Such computations are better performed off-chain.