Analytics Software

It seems to me you'd be better off encapsulating such methods in a descendant object type, but anyway...
Code seems ok, but a couple of points :
Replace power(..), with a squaring multiplication. Power is great, has its place, but it's relatively slow.
You seem to be overly assigning everything to variables. Whilst that's good for instrumentation if you're outputting everything, it slows code down as values need to be loaded in registers, range and type checked and it makes code more verbose.
I think your code can be rewritten as this :

with
    function pythagoras(x1 in number, y1 in number, x2 in number, y2 in number) return number is
    begin
      return round(sqrt( (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)), 2);  -- Power is a slow function
    end;
   
    function m_as_length(shape in sde.st_geometry) return varchar2
    is
        result              varchar2(32767);
        vertex_set          varchar2(32767);
        oldX                number;
        oldY                number;
        newX                number;
        newY                number;
        line_len            number := 0;
    begin       
        for vPartIndex in 1..sde.st_geometry_operators.st_numgeometries_f(shape)
        loop
            vertex_set      := null;
            for vPointIndex in 1..sde.st_geometry_operators.st_numpoints_f(sde.st_geometry_operators.ST_GeometryN_f(shape,vPartIndex))
            loop
                newX        := sde.st_geometry_operators.st_x_f(sde.st_geometry_operators.st_pointn_f(sde.st_geometry_operators.st_geometryn_f(shape,vPartIndex),vPointIndex));
                newY        := sde.st_geometry_operators.st_y_f(sde.st_geometry_operators.st_pointn_f(sde.st_geometry_operators.st_geometryn_f(shape,vPartIndex),vPointIndex));
                if vPointIndex <> 1 then
                   line_len := line_len + pythagoras(oldX, oldY, newX, newY);
                end if;
                oldX        := newX;
                oldY        := newY;
                vertex_set  := vertex_set || newX || ' ' || newY || ' ' || line_len || ', ';
            end loop;
            result          := result || '(' || rtrim((vertex_set),', ') || '),';
        end loop;
        return 'MULTILINESTRING M (' || rtrim((result),',') || ')';
    end;
select
    m_as_length(shape)
from
    polylines

Have a look at the fine article"How to calculate cumulative length of a linestring" by The Spatial Database Advisor
How to calculate cumulative length of a linestring, or the truck tonnage that accumulates across a set of roads - The Spatial Database Advisor (0 Bytes)

Paulzip Thanks! That helps. And of course, your revised function produces the correct result:

MULTILINESTRING M ((0 5 0, 10 10 11.18, 30 0 33.54),(50 10 33.54, 60 10 43.54))

Side question:
Regarding your comment "It seems to me you'd be better off encapsulating such methods in a descendant object type...". Is there any chance you could elaborate on that?
Related:
Link: More succinct SDE.ST_GEOMETRY function calls in PL/SQL
Link: ST_Geometry data type and its subclasses
Thanks again.

If you use (free) LRS-functions you can directly achieve the result:

SELECT SDO_LRS.CONVERT_TO_LRS_GEOM(
        SDO_CS.make_2d(
           SDO_UTIL.FROM_WKTGEOMETRY('MULTILINESTRING (( 0.0 5.0 -100000.0, 10.0 10.0 -100000.0, 30.0 0.0 -100000.0),( 50.0 10.0 -100000.0, 60.0 10.0 -100000.0))')
         )) lrsline 
   FROM dual;

{ "spatialdimension" : 2,
"geometrycollection" : {"geometries" :
 [{"line" : {"datapoints" : [[0,5,0],[10,10,11.180339887499],[30,0,33.5410196624969]]}},
  {"line" : {"datapoints" : [[50,10,33.5410196624969],[60,10,43.5410196624969]]}}]}
} 

Btw. if you code a function DETERMINISTIC clause could improve perfomance.

I don't have that spatial library installed, but can assume ST_GEOMETRY appears to be an object type. As such, you could inherit from it and add a method "m_as_length" to that object type.

@jum3 Nice! That LRS-function solution is very simple. I like it.
Out of curiosity, how did you output the geometry to JSON? Just curious what technique you used...

Tested it with https://livesql.oracle.com

Side note:
In my original function (and in Paulzip 's code review), we defined the variables as:

result       varchar2(32767);
vertex_set   varchar2(32767);

Alternatively, I suppose we could have defined those variables a CLOBs:

result       clob;
vertex_set   clob;