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allaun
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This squashes all local history (768 commits) onto the scrubbed PR #90 baseline. Individual commits were lost during filter-repo corruption; the working tree content is preserved intact. Build: N/A (working tree state only)
59 lines
1.5 KiB
WebGPU Shading Language
59 lines
1.5 KiB
WebGPU Shading Language
// Q16_16 Arithmetic Theorems Verification Shader
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//
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// Depends on: q16_arithmetic.wgsl (shared include)
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//
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// This shader verifies the main arithmetic theorems from FixedPoint.lean:
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// 1. mul_one: mul q one = q
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// 2. div_one: div q one = q
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// 3. neg_involutive: neg (neg q) = q
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// 4. abs_nonNegative: (abs q).toInt >= 0
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//
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// Tests all 65,536 Q16_16 values in parallel on GPU.
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struct ArithmeticResult {
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mul_one_ok: u32,
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div_one_ok: u32,
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neg_involutive_ok: u32,
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abs_nonNegative_ok: u32,
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}
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@group(0) @binding(0) var<storage, read_write> results: array<ArithmeticResult>;
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const Q16_SPACE: u32 = 65536u;
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@compute @workgroup_size(64)
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fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
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let q = gid.x;
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if (q >= Q16_SPACE) {
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return;
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}
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// Lemma 1: mul_one
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// mul q one = q
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let mul_result = q16_mul(q, Q16_ONE);
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let mul_one_ok = select(0u, 1u, mul_result == q);
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// Lemma 2: div_one
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// div q one = q
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let div_result = q16_div(q, Q16_ONE);
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let div_one_ok = select(0u, 1u, div_result == q);
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// Lemma 3: neg_involutive
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// neg (neg q) = q
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let neg_once = q16_neg(q);
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let neg_twice = q16_neg(neg_once);
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let neg_involutive_ok = select(0u, 1u, neg_twice == q);
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// Lemma 4: abs_nonNegative
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// (abs q).toInt >= 0
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let abs_q = q16_abs(q);
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let abs_int = q16_to_int(abs_q);
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let abs_nonNegative_ok = select(0u, 1u, abs_int >= 0);
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results[q] = ArithmeticResult(
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mul_one_ok,
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div_one_ok,
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neg_involutive_ok,
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abs_nonNegative_ok
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);
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}
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