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doc/utils/eval: review and extend, clarify ld/st index meaning
Prefer idx in place of id for functions accessing the internal variables, and add a short introduction to mention them.
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@ -801,6 +801,11 @@ The following binary operators are available: @code{+}, @code{-},
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The following unary operators are available: @code{+}, @code{-}.
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Some internal variables can be used to store and load intermediary
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results. They can be accessed using the @code{ld} and @code{st}
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functions with an index argument varying from 0 to 9 to specify which
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internal variable to access.
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The following functions are available:
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@table @option
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@item abs(x)
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@ -898,9 +903,9 @@ Return 1.0 if @var{x} is +/-INFINITY, 0.0 otherwise.
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@item isnan(x)
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Return 1.0 if @var{x} is NAN, 0.0 otherwise.
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@item ld(var)
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Load the value of the internal variable with number
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@var{var}, which was previously stored with st(@var{var}, @var{expr}).
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@item ld(idx)
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Load the value of the internal variable with index @var{idx}, which was
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previously stored with st(@var{idx}, @var{expr}).
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The function returns the loaded value.
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@item lerp(x, y, z)
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@ -933,16 +938,14 @@ Compute the power of @var{x} elevated @var{y}, it is equivalent to
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@item print(t)
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@item print(t, l)
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Print the value of expression @var{t} with loglevel @var{l}. If
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@var{l} is not specified then a default log level is used.
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Returns the value of the expression printed.
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Prints t with loglevel l
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Print the value of expression @var{t} with loglevel @var{l}. If @var{l} is not
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specified then a default log level is used.
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Return the value of the expression printed.
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@item random(idx)
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Return a pseudo random value between 0.0 and 1.0. @var{idx} is the
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index of the internal variable which will be used to save the
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seed/state.
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index of the internal variable used to save the seed/state, which can be
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previously stored with @code{st(idx)}.
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To initialize the seed, you need to store the seed value as a 64-bit
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unsigned integer in the internal variable with index @var{idx}.
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@ -955,8 +958,8 @@ st(0,42); print(random(0)); print(random(0)); print(random(0))
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@item randomi(idx, min, max)
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Return a pseudo random value in the interval between @var{min} and
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@var{max}. @var{idx} is the index of the internal variable which will
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be used to save the seed/state.
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@var{max}. @var{idx} is the index of the internal variable which will be used to
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save the seed/state, which can be previously stored with @code{st(idx)}.
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To initialize the seed, you need to store the seed value as a 64-bit
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unsigned integer in the internal variable with index @var{idx}.
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@ -968,14 +971,14 @@ with argument @var{ld(0)} is 0 in the interval 0..@var{max}.
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The expression in @var{expr} must denote a continuous function or the
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result is undefined.
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@var{ld(0)} is used to represent the function input value, which means
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that the given expression will be evaluated multiple times with
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various input values that the expression can access through
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@code{ld(0)}. When the expression evaluates to 0 then the
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corresponding input value will be returned.
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@var{ld(0)} is used to represent the function input value, which means that the
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given expression will be evaluated multiple times with various input values that
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the expression can access through @code{ld(0)}. When the expression evaluates to
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0 then the corresponding input value will be returned.
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@item round(expr)
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Round the value of expression @var{expr} to the nearest integer. For example, "round(1.5)" is "2.0".
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Round the value of expression @var{expr} to the nearest integer. For example,
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"round(1.5)" is "2.0".
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@item sgn(x)
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Compute sign of @var{x}.
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@ -993,12 +996,15 @@ Compute the square root of @var{expr}. This is equivalent to
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@item squish(x)
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Compute expression @code{1/(1 + exp(4*x))}.
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@item st(var, expr)
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@item st(idx, expr)
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Store the value of the expression @var{expr} in an internal
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variable. @var{var} specifies the number of the variable where to
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store the value, and it is a value ranging from 0 to 9. The function
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returns the value stored in the internal variable.
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Note, Variables are currently not shared between expressions.
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variable. @var{idx} specifies the index of the variable where to store
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the value, and it is a value ranging from 0 to 9. The function returns
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the value stored in the internal variable.
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The stored value can be retrieved with @code{ld(var)}.
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Note: variables are currently not shared between expressions.
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@item tan(x)
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Compute tangent of @var{x}.
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@ -1007,16 +1013,16 @@ Compute tangent of @var{x}.
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Compute hyperbolic tangent of @var{x}.
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@item taylor(expr, x)
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@item taylor(expr, x, id)
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@item taylor(expr, x, idx)
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Evaluate a Taylor series at @var{x}, given an expression representing
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the @code{ld(id)}-th derivative of a function at 0.
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the @code{ld(idx)}-th derivative of a function at 0.
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When the series does not converge the result is undefined.
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@var{ld(id)} is used to represent the derivative order in @var{expr},
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@var{ld(idx)} is used to represent the derivative order in @var{expr},
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which means that the given expression will be evaluated multiple times
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with various input values that the expression can access through
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@code{ld(id)}. If @var{id} is not specified then 0 is assumed.
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@code{ld(idx)}. If @var{idx} is not specified then 0 is assumed.
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Note, when you have the derivatives at y instead of 0,
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@code{taylor(expr, x-y)} can be used.
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