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### D.7.1 `gslint` input parameters

The library functions `qng` and `qagx` take an argument of the form `(f,(a,b))`, where f is a function to be integrated, a is the lower limit, and b is the upper limit, both limits being floating point numbers as in `math`.

The `qng_tol` and `qagx_tol` functions take an argument of the form `((f,t),(a,b))`, where f, a, and b are as above, and t is a specified tolerance.

The `qagp` and `qagp_tol` functions take arguments of the form `(f,p)` and `((f,t),p)`, respectively, where f and t are as above, and p is an ordered list of real numbers specifying the limits of integration along with arbitrarily many intervening breakpoints.

The integrand f is expressed in virtual machine code, and takes a single real argument to a real result. The argument and result of f are required to be floating point numbers as described in `math`. Any expressible function of this type is acceptable, even one defined in terms of other integrals, so that a double or triple integral can be expressed easily, albeit a costly computation. However, a constant overhead in stack space is required for each nested library function call, and there is currently no mechanism to prevent segmentation faults due to a stack overflow.

When no tolerance is specified, as with `qng`, `qagx`, and `qagp`, the tightest attainable tolerance is chosen by default, currently `2e-14`, in order find the most accurate result possible. A selection of progressively looser tolerances is tried automatically if the tightest one is not successful, stopping when either a solution is found or ten orders of magnitude are covered.

If a tolerance is explicitly specified, as with `qng_tol`, `qagx_tol` or `qagp_tol`, only that tolerance is tried.

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