stillwater-sc / universal / 32548418546

85%

master: 84%

Build Type

push

github

Committed by web-flow

Commit Message

fix(elreal): stop infsum dropping a term when the accumulator cancels to zero (#1375)

infsumRec_step's null-sum branch advanced the input cursor to rest1.tail(),
discarding `bs` along with `as`. `bs` had not been consumed, so whenever a term
summed the accumulator to exactly zero, the FOLLOWING term was silently dropped
from the sum.

The branch was written as defensive dead code -- "full cancellation ... McCleeary's
pattern match assumes this cannot occur (prev dominates as)". It is not dead. Zero
blocks are legitimate ZBCL blocks, the streaming multiply emits an all-zero term
whenever an operand block is zero, and add(zero, zero) is empty.

The consequence was that mul_online silently truncated against any operand carrying
interior zero blocks. Two expansions holding the EXACT SAME VALUE gave different
products:

    [1@0, Z@-100, Z@-150, Z@-200, 1@-1700] * sqrt(2,8) ->  9 blocks, stops 2^-588
    [1@0,                        1@-1700] * sqrt(2,8) -> 16 blocks, reaches 2^-2088

Newton's reciprocal walked straight into it: the cancellation in 2 - b*r emits a
growing run of zero blocks as it converges (1, 2, 6, 14, 31 ...), so past a certain
depth the correction term r*e was discarded whole and the iteration fixed-pointed.
That is what capped dense division at ~513 decimal digits on a double host and ~62
on float, at any requested depth (#1373).

Fixed, div_online tracks its divisor's own accuracy at every depth on both hosts:

    depth        8     16     32     48     72    150
    double     131    265    524    784   1175   1240      (was 513 from d=32 on)
    float       60    123    246    369    552   1147      (was  62 from d=16 on)

matching sqrt(2,d) digit for digit. A float host now reaches 1147 digits through
division where it previously managed 62.

Consume only `as`, and set the accumulator to the empty (zero) ZBCL -- which is what
prevs + as actually is here; the old code set it to `as`, correct only because `as`
happened to be zero in... (continued)

Coverage Stats

2 of 2 new or added lines in 1 file covered. (100.0%)

8 existing lines in 1 file now uncovered.

43085 of 50469 relevant lines covered (85.37%)

7296820.4 hits per line