SVG Animation Profile 3: Additive Composition

Status: Accepted source profile.

SVG Animation Profile 3 extends SVG Animation Profile 2 with typed addition between sandwich layers and terminal-value accumulation across repeat iterations. It is cumulative: every source accepted by Profile 2 is accepted by Profile 3 and produces the same sampled values, including the same binary32 bits.

All inherited source, timing, interpolation, priority, target, failure, and trust-boundary rules remain normative unless this document replaces them. Profile 3 replaces only the composition grammar and the replacement-only sampling procedure. It does not add by, lone-to animation, another target element, or another animated property.

The behavior follows SMIL's additive and cumulative animation model inside the deliberately bounded source and numeric domains of Profiles 0–2.

Composition vocabulary

Profile 3 admits these values on every otherwise admitted <animate>:

The attributes are orthogonal. All four combinations are admitted for x, y, width, height, and opacity. Unknown values are errors; a processor must not treat them as the absent defaults.

Effect composition and iteration composition have different operands:

• additive="replace" makes the effect replace its lower-priority underlying sandwich value.
• additive="sum" adds the effect to that underlying value.
• accumulate="none" uses the effect's simple value for the current iteration.
• accumulate="sum" first adds a multiple of the effect's terminal value to its current simple value. The resulting effect is then replaced or added as selected by additive.

The operations are typed property operations, not string concatenation and not a second untyped value channel. Each result projects back into the same property representation as its target.

Iteration accumulation

Let:

• V(p) be the inherited simple animation value at progress p, after keyframe selection, easing, and interpolation;
• T be the terminal simple value at the end of one simple duration; and
• k be the zero-based repeat index.

For from/to, T is to. For values, T is the last list item, regardless of which keyframe interval contains p. For a one-value animation, that one value is both V and T.

The effect value is:

E(p, k) = V(p)                         when accumulate = none
E(p, k) = V(p) + k × T                 when accumulate = sum

Accumulation uses the terminal value itself, not the change T - V(0) and not the value sampled immediately before a repeat boundary. When k = 0, both accumulation modes are bit-identical.

For an underlying sandwich value U, the four combinations are:

Iteration accumulation never changes sandwich priority. In particular, additive="replace" accumulate="sum" is still a replacement layer and is a cutoff; accumulation changes its value, not its relationship to lower layers.

Repeat and fill boundaries

Profile 0's begin-inclusive, end-exclusive active interval remains in force. At an exact internal repeat boundary, the next iteration has begun: k increments by one and p is exactly zero. An accumulated effect therefore contributes V(0) + k × T at that instant. Sampling just before the boundary still uses the preceding iteration and its progress.

At the final active end:

• fill="remove" contributes nothing and immediately falls through to the next contributing layer or the authored base; and
• fill="freeze" uses terminal progress with k = N - 1, where N is repeatCount.

Consequently a frozen accumulate="sum" effect has value N × T. A frozen additive effect continues to add that value at its unchanged sandwich priority. Direct seeking to the final end and arriving there through playback must agree.

Additive sandwich procedure

For each target/property pair, contributing effects are first ordered from lowest to highest priority by Profile 2. Active and frozen effects contribute; pre-begin and post-remove effects do not.

The result is then formed as follows:

1. Find the highest-priority contributing effect whose additive operation is replace.
2. Discard every contributing effect below that replacement. If a replacement exists, its accumulated effect value is the initial result. Otherwise the authored base value is the initial result.
3. Visit each remaining higher-priority effect in ascending priority. Compute its iteration-accumulated effect value, then replace or add it according to additive.
4. Project the final typed value back to the target property and emit at most one effective value for that target/property pair.

This is an ordered fold, not an algebraic reduction. Additions must not be reassociated, regrouped, or evaluated in document order after priority has been resolved. A replacement masks both the authored base and all lower effects, while higher additive effects still compose over it.

Every layer and live target is validated before sampling, including inactive and masked layers. Arithmetic below the highest contributing replacement cutoff is not evaluated, because it cannot influence the result. Thus a stale masked target is still an error, but numeric overflow in a masked lower effect's unused composition is not.

Typed domains and authored base

The source domains of Profile 0 remain unchanged:

An animation sandwich containing any additive="sum" layer requires the authored base to retain that exact numeric projection. An x or y base represented by a center pin, end pin, or two-edge span is not silently converted to a start-edge coordinate. An automatic size is not silently resolved into a fixed extent. The requirement is checked for the compiled source snapshot and again when sampled, so a later structural change cannot alter the meaning of addition.

The requirement applies even when the additive layer is inactive or happens to sit below a contributing replacement at one requested time. This keeps program validity independent from contribution state and prevents a masked source error from appearing only after a seek.

A replacement-only sandwich does not need the base as an arithmetic operand, but it still inherits Profile 0's target-identity and one-to-one materialization requirements.

Exact numeric contract

Profile 1's exact keyframe interpolation produces one stored binary32 simple value. Profile 3 adds two separately rounded operations:

1. Accumulation: interpret the stored V and T bits as exact values, evaluate V + k × T mathematically, then round once to finite IEEE 754 binary32 using round-to-nearest, ties-to-even.
2. Sandwich addition: interpret the current underlying bits and the already accumulated effect bits as exact values, add them mathematically, then round once by the same rule.

Every additive layer performs step 2 independently in low-to-high priority order. Accumulation and sandwich addition are never fused into one rounding, and several sandwich additions are never collapsed into a total. Replacement copies the accumulated effect bits without another arithmetic rounding.

An exact zero sum is negative zero only when both addends are negative zero; otherwise it is positive zero. Any accumulation or influential sandwich addition whose rounded result is non-finite is an error rather than a saturated value.

opacity is the one final projection clamp. Its composed binary32 values are not clamped between layers. After the complete sandwich has been folded, a value below zero projects to zero, a value above one projects to one, and a value already in [0, 1] is unchanged. This does not relax the inherited [0, 1] source-keyframe domain. Coordinates and extents have no corresponding final clamp.

Validation and diagnostics

Profile 3 inherits whole-document atomic validation. In addition to inherited failures, Sample rejects:

• an additive value other than replace or sum;
• an accumulate value other than none or sum;
• an additive sandwich whose authored base lacks the required typed numeric projection or violates that property's source domain, at compilation or after a later document change; or
• a non-finite result from influential accumulation or sandwich addition.

Diagnostics identify the source-located animation, target/property pair, and failed operation. An arithmetic failure identifies the failing effect and the already-applied prefix on which it depends; later effects that were never evaluated are not implicated. An unsupported authored-base shape names both the required numeric projection and the observed shape, while an invalid scalar names the violated domain. A masked or inactive stale target continues to identify all layers in its target sandwich. Failure produces neither a partial effective-value set nor a partial frame.

Conformance

Profile 3 adds these laws to the inherited conformance contract:

• every Profile 2 source samples bit-identically under Profile 3;
• all four additive/accumulate combinations are tested at the first keyframe, an interior sample, every repeat boundary, and the final end;
• accumulate="sum" uses the terminal keyframe value, including for a non-monotonic values list whose terminal differs from an earlier maximum;
• at an internal boundary, the result is the next iteration's first value plus its terminal-value accumulation;
• the frozen cumulative effect value is repeatCount × T, while remove falls through at the same exact end time;
• replace remains the sandwich cutoff when paired with accumulate="sum";
• additions above the cutoff run in low-to-high priority order with one binary32 rounding per operation;
• the authored base is used only when no contributing replacement cuts it off;
• an additive stack rejects unsupported authored-base projections even when the additive layer is currently inactive or masked;
• non-finite influential arithmetic rejects Sample, while unused arithmetic below a replacement cutoff is not evaluated;
• opacity is clamped once after the final composition rather than after each layer; and
• every accepted direct seek is independent of prior sample order.

A canonical scalar matrix uses authored base 10, from="20", to="30", dur="1s", repeatCount="3", and fill="freeze". At times 0, 0.5, 1, 1.5, 2, 2.5, and 3 seconds, the required results are:

These values are semantic vectors. Bit-level conformance additionally uses non-associative boundary operands that distinguish ordered per-layer rounding from regrouped arithmetic. Browser differential results remain separate from the profile's exact oracle because browser arithmetic and the wider SVG source domain are not this profile's numeric contract.

Deferred families

Profile 3 resolves addition and terminal-value repeat accumulation only for the inherited scalar property set. by, lone-to animation, calcMode="discrete", calcMode="paced", transforms, motion paths, colors, paint servers, lists and paths, additional SVG targets and properties, wider presentation-clamped source domains, begin lists, timing dependencies, restarts, indefinite timing, CSS/Web Animations interaction, and optimized or compositor execution remain outside this profile.