Fixes a bug in msqrt when computing clearance value

[lin]

The formula to compute clearance in sqrt is contradicted with TeXBook definition. The result of this is that the base element is too close to the root bar. This might be a mistake in manual derivation as argued bellow unless this is purposely designed.

According to Rule 11 on TeXBook page 443 (Appendix G ).

The clearance value psi, which is q value in getPQ, is originally defined as psi = t + p / 4.

Under condition dy > bbox.h + bbox.d + psi, where dy = sbox.h + sbox.d - t, psi will be changed to a new value psi + (dy - (bbox.h + bbox.d + psi)) / 2 as stated in TeXBook.

The derivation for the condition dy > bbox.h + bbox.d + psi is right.

// since
dy = sbox.h + sbox.d - t
dy > bbox.h + bbox.d + psi
// so
sbox.h + sbox.d - t > bbox.h + bbox.d + psi
sbox.h + sbox.d  > bbox.h + bbox.d + psi + t
sbox.h + sbox.d  > bbox.h + bbox.d + t + p / 4 + t
// since
this.surdH = bbox.h + bbox.d + 2 * t + p / 4
// the condition is same as:
sbox.h + sbox.d  > this.surdH

However, the derivation for new assignment psi = psi + (dy - (bbox.h + bbox.d + psi)) / 2 is wrong.

// since
psi =  psi + (dy - (bbox.h + bbox.d + psi)) / 2
dy = sbox.h + sbox.d - t
// then
psi =  psi + ( sbox.h + sbox.d - t - (bbox.h + bbox.d + psi)) / 2
psi =  (sbox.h + sbox.d - t - (bbox.h + bbox.d - psi)) / 2
psi = (sbox.h + sbox.d - (bbox.h + bbox.d + t - psi)) / 2

Here is where I believe the derivation got wrong. If the last minus sign was a plus sign.

// if when wrong
psi = (sbox.h + sbox.d - (bbox.h + bbox.d + t + psi)) / 2
// since
this.surdH = bbox.h + bbox.d + 2 * t + p / 4
// then
psi = (sbox.h + sbox.d - (this.surdH - t)) / 2

This is the formula in the develop branch. The correct derivation should be

psi = (sbox.h + sbox.d - (bbox.h + bbox.d + t - psi)) / 2
// since
this.surdH = bbox.h + bbox.d + 2 * t + p / 4
// then
psi = (sbox.h + sbox.d - (this.surdH - 2 * psi)) / 2
psi = (sbox.h + sbox.d - (this.surdH - 2 * t - p / 2)) / 2

This is how this pull request computes psi, the clearance value.

[lin]

This is a comparison preview for this request. Other TeX libraries render similar results as in this pull request.

[dpvc]

I've had the chance to check this out, and your computations are correct. The results are much better. Thanks for the correction, and fo finding exactly where the error was!

[lin]

Thanks, wish I could contribute more. 😄