vulkan: Implement SOLVE_TRI (#17486)

* vulkan: Implement SOLVE_TRI

* load B matrix through shared memory

* use FLOAT_TYPE

ggml/src/ggml-vulkan/vulkan-shaders/solve_tri.comp

@@ -0,0 +1,72 @@
+#version 450
+
+#include "types.glsl"
+#include "generic_binary_head.glsl"
+
+layout (constant_id = 1) const uint N = 64;
+layout (constant_id = 2) const uint K = 32;
+
+layout(local_size_x = 128, local_size_y = 1, local_size_z = 1) in;
+
+uint a_base, b_base, x_base;
+
+FLOAT_TYPE get_a(uint r, uint c) {
+    return FLOAT_TYPE(data_a[a_base + r * p.nb01 + c * p.nb00]);
+}
+
+FLOAT_TYPE get_b(uint r, uint c) {
+    return FLOAT_TYPE(data_b[b_base + r * p.nb11 + c * p.nb10]);
+}
+
+void store_x(uint r, uint c, FLOAT_TYPE v) {
+    data_d[x_base + r * p.nb21 + c * p.nb20] = D_TYPE(v);
+}
+
+shared FLOAT_TYPE shA[N * N];
+shared FLOAT_TYPE shB[N * K];
+
+void main() {
+    const uint batch = gl_WorkGroupID.z * 262144 + gl_WorkGroupID.y * 512 + gl_WorkGroupID.x;
+    const uint tid = gl_LocalInvocationID.x;
+
+    if (batch >= p.ne02 * p.ne03) {
+        return;
+    }
+
+    const uint i3 = batch / p.ne22;
+    const uint i2 = batch % p.ne22;
+    a_base = get_aoffset() + i2 * p.nb02 + i3 * p.nb03;
+    b_base = get_boffset() + i2 * p.nb12 + i3 * p.nb13;
+    x_base = get_doffset() + i2 * p.nb22 + i3 * p.nb23;
+
+    // Load the A matrix into shA
+    [[unroll]] for (uint i = 0; i < N * N; i += gl_WorkGroupSize.x) {
+        uint idx = i + tid;
+        if (((N * N) % gl_WorkGroupSize.x == 0) || idx < N * N) {
+            shA[idx] = get_a(idx / N, idx % N);
+        }
+    }
+    // Load the B matrix into shB
+    [[unroll]] for (uint i = 0; i < N * K; i += gl_WorkGroupSize.x) {
+        uint idx = i + tid;
+        if (((N * K) % gl_WorkGroupSize.x == 0) || idx < N * K) {
+            shB[idx] = get_b(idx / K, idx % K);
+        }
+    }
+    barrier();
+
+    FLOAT_TYPE X[N];
+    // Each thread solves one column
+    if (tid < K) {
+        [[unroll]] for (int r = 0; r < N; ++r) {
+            FLOAT_TYPE b = shB[r * K + tid];
+            // Compute x[r,c] = (b[r,c] - sum(a[r,c]*x[c])) / a[r,r]
+            [[unroll]] for (int c = 0; c < r; ++c) {
+                b -= shA[r * N + c] * X[c];
+            }
+            FLOAT_TYPE x = b / shA[r * N + r];
+            X[r] = x;
+            store_x(r, tid, x);
+        }
+    }
+}