The supplied operation catalogue supports arithmetic but lacks floor, remainder and conditional validation operations. It cannot calculate the required integer interval counts or reject every invalid combination of starting, target and reserved stitches. Defer activation pending engineering implementation and functional QA. The calculator below provides preliminary arithmetic only; it is not a completed decrease distribution calculator. Decimal display precision does not implement integer division or validate whole-stitch inputs.
Let S be the starting count, T the target count and E the total stitches reserved across both edges. Reserved stitches are included in S and T and are worked unchanged. Choose how E is split between the beginning and end before working the row.
Each decrease consumes two original working stitches and produces one stitch, reducing the count by one. A group of length L means work L − 2 stitches normally, then work one two-into-one decrease. Its length includes both stitches used by the decrease. This convention applies to a single row or round with single-stitch decreases; it does not describe double decreases or multi-row shaping.
Counts use the dimensionless unit 1, labelled as stitches, decreases or groups. Use whole numbers only. The proposed input cap is 100,000 stitches.
These formulas are derived directly from the stated stitch-consumption convention; no external formula source is claimed.
Required decreases: D = S − T. Available working stitches: W = S − E. Each decrease needs two original stitches, so a valid decrease row requires W ≥ 2D. The number worked normally is W − 2D.
For D > 0, use integer division: q = floor(W / D) and r = W − qD. Return D − r short groups consuming q original stitches each, and r long groups consuming q + 1 original stitches each. Work q − 2 plain stitches before each short-group decrease and q − 1 before each long-group decrease. These are scalar outputs; no generated stitch sequence is required.
The groups consume (D − r)q + r(q + 1) = W stitches and produce W − D stitches. Restoring the unchanged E edge stitches gives W − D + E = T.
For an evenly interspersed arrangement, number groups i from 1 through D. Group i is long when floor(ir / D) − floor((i − 1)r / D) equals 1; otherwise it is short. Group lengths differ by at most one stitch. This convention does not guarantee mirror symmetry at the row ends.
Engineering must register integer quotient/remainder and conditional validation capabilities, or a dedicated scalar decrease-distribution operation. This proposal does not introduce an unregistered operation.
The completed calculator must reject fractional inputs, values outside their bounds, T > S, E > T and W < 2D. It must not round fractional stitch counts into apparently valid instructions. For S = T, return zero decreases and zero group counts, leave group lengths unavailable and instruct the user to work all stitches unchanged. For valid D > 0, return q, q + 1, D − r, r and the associated plain-stitch counts. Mark an unused group size as unused when its count is zero.
The preliminary arithmetic does not enforce these cross-input checks. Negative results indicate invalid combinations, and a positive mean interval alone does not establish validity. When D = 0, division produces unavailable rather than a usable interval.
| Starting / target / reserved stitches | Calculation | Expected instructions or validation |
|---|---|---|
| 100 / 86 / 4 | D = 14; W = 96; q = 6; r = 12 | 2 short groups: work 4 plain stitches, then decrease. 12 long groups: work 5 plain stitches, then decrease. Distribute long groups throughout the row. With 2 reserved stitches at each edge, the final count is 2 + 2×5 + 12×6 + 2 = 86. |
| 30 / 24 / 0 | D = 6; W = 30; q = 5; r = 0 | 6 groups of work 3 plain stitches, then decrease. No long groups are used. Final count: 6×4 = 24. |
| 20 / 12 / 4 | D = 8; W = 16; q = 2; r = 0 | 8 consecutive decreases in the working section, with no plain stitches between them. Preserve all 4 reserved stitches. Final count: 8 + 4 = 12. |
| 20 / 11 / 4 | D = 9; W = 16; 2D = 18 | Reject: 9 decreases require 18 working stitches, but only 16 are available. |
| 20 / 20 / 4 | D = 0; W = 16 | No decreases needed. Work all 20 stitches unchanged; interval lengths are not applicable. |
| 20 / 22 / 0 | T > S | Reject: the target requires increases. |
No suitable registered thumbnail asset is identified in the supplied content. Before activation, create and register a 400×400 WebP thumbnail showing the cute yellow five-point star mascot with a cheerful face and hands, floating without separate legs or feet, on a white background with navy, blue and teal knitting graphics. Inspect neighboring thumbnails for style consistency. Add the registered asset as the first image block. Do not invent an asset ID or file path.