0004107: Error in avg. spell school calculations for three-school spells.

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Category

Severity

Reproducibility

Date Submitted

Last Update

0004107

[DCSS] Bug Report

minor

always

2011-06-06 20:18

2011-11-09 17:56

Reporter

Caethan

View Status

public

Assigned To

galehar

Priority

normal

Resolution

done

Status

closed

Product Branch

0.8 ancient branch

Summary

0004107: Error in avg. spell school calculations for three-school spells.

Description

For spellpower calculations, twice the average skill level of all schools in the spell is calculated as part of the formula.

Due to rounding errors on integer arithmetic, this average skill level is calculated incorrectly for three-school spells.

This can be seen in-game using Wizard mode: set all skills to 2 and intelligence to 5 and compare the casting successes of Mephitic Cloud (a three-school level 3 spell) and any other level 3 spell, and you will see that Mephitic Cloud has a Very Poor success rate while all other level 3 spells have a Poor success rate.

This is because double the average is calculated as follows:

twice avg. = (2 * School 1 Skill) / (# of Schools) + (2 * School 2 Skill) / (# of Schools) + 2 * (2 * School 3 Skill) / (# of Schools)

For one- and two-school spells, this formula works correctly. Because this is done using integer arithmetic, three-school spells can have rounding errors that lead to an underestimate of the average school skill. For the example I gave above, it would be:

twice avg. = (2 * 2) / 3 + (2 * 2) / 3 + (2 * 2) / 3
                 = 4/3 + 4/3 + 4/3
                 = 1 + 1 + 1
                 = 3

The error in the code is found in spl-cast.cc, in the calc_spell_power function, in this section:

        unsigned int disciplines = get_spell_disciplines(spell);
        //jmf: evil evil evil -- exclude HOLY bit
        disciplines &= (~SPTYP_HOLY);
        int skillcount = count_bits(disciplines);
        if (skillcount)
        {
            for (int ndx = 0; ndx <= SPTYP_LAST_EXPONENT; ndx++)
            {	
                unsigned int bit = (1 << ndx);
                if (disciplines & bit)
                    power += (you.skill(spell_type2skill(bit)) * 2) / skillcount;
            }	
        }

This could be fixed by replacing the above code with:

        unsigned int disciplines = get_spell_disciplines(spell);
        //jmf: evil evil evil -- exclude HOLY bit
        disciplines &= (~SPTYP_HOLY);
        int skillcount = count_bits(disciplines);
        if (skillcount)
        {
            int tmp_power = 0;
            for (int ndx = 0; ndx <= SPTYP_LAST_EXPONENT; ndx++)
            {	
                unsigned int bit = (1 << ndx);
                if (disciplines & bit)
                    tmp_power += (you.skill(spell_type2skill(bit)) * 2);
            }
            power += tmp_power / skillcount;
        }

Additional Information

Issue History
Date Modified	Username	Field	Change
2011-06-06 20:18	Caethan	New Issue
2011-06-06 22:33	galehar	Note Added: 0013404
2011-06-06 22:33	galehar	Status	new => resolved
2011-06-06 22:33	galehar	Fixed in Branch	=> 0.9 development branch
2011-06-06 22:33	galehar	Resolution	open => done
2011-06-06 22:33	galehar	Assigned To	=> galehar
2011-11-09 17:56	Caethan	Status	resolved => closed

Notes
(0013404) galehar (administrator) 2011-06-06 22:33	Wow. I can't believe such an obvious bug has been going unnoticed for so long. Fixed. Thanks!

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