The CIPW Norm was developed in the early 1900s and named after its creators, the petrologists Charles Cross, Joseph Iddings, Louis Pirsson, and the geochemist Henry Washington. The CIPW normative mineralogy calculation is based on the typical minerals that may be precipitated from an anhydrous melt at low pressure, and simplifies the typical igneous geochemistry seen in nature with the following four constraints:
* The magma crystallizes under anhydrous conditions so that no hydrous minerals (hornblende, biotite) are formed.
* The ferromagnesian minerals are assumed to be free of AlO.
* The Fe/Mg ratio for all ferromagnesian minerals is assumed to be the same.
* Several minerals are assumed to be incompatible, thus nepheline and/or olivine never appear with quartz in the norm.
This is an artificial set of constraints, and therefore the results of the CIPW norm do not reflect the true course of igneous differentiation in nature.
The primary benefit of calculating a CIPW norm is determining what the ideal mineralogy of an aphanitic or porphyritic igneous rock is. Secondly, the degree of silica saturation of the melt that formed the rock can be assessed in the absence of diagnostic feldspathoid species.
The silica saturation of a rock varies not only with silica content but the proportion of the various alkalis and metal species within the melt. The silica saturation eutectic plane is thus different for various families of rocks and cannot be easily estimated, hence the requirement to calculate whether the rock is silica saturated or not.
This is achieved by assigning cations of the major elements within the rock to silica anions in modal proportion, to form solid solution minerals in the idealised mineral assemblage starting with phosphorus for apatite, chlorine and sodium for halite, sulfur and FeO into pyrite, FeO and CrO is allocated for chromite, FeO and equal molar amount of TiO for ilmenite, CaO and CO for calcite, to complete the most common non-silicate minerals. 
From the remaining chemical constituents, AlO and KO are allocated with silica for orthoclase; sodium, aluminium and potassium for albite, and so on until either there is no silica left (in which case feldspathoids are calculated) or excess, in which case the rock contains normative quartz.