1.5 bit: we can do even better (#5999)

ikawrakow · Iwan Kawrakow · web-flow · commit 44ca159faf4f · 2024-03-11T17:53:15.000+02:00
* iq1_s: we can do even better

Spent one of the 4 scale bits on a signs of a 0.125 shift.
I.e., quants are now -1 + delta, delta, 1 + delta, where delta
is +/- 0.125.

CUDA works, same performance as before.
PPL(LLaMA-v2-7B) is now 11.85!

* iq1_s: make scalar and AVX2 work with the new version

* iq1_s: make Neon work with new version.

~10% drop in performance, so will need some more work.

* iq1_s: make Metal work with new version

* iq1_s: very slightly faster dequantize on Metal

* iq1_s: fix dequantize on the CPU

---------

Co-authored-by: Iwan Kawrakow &lt;iwan.kawrakow@gmail.com&gt;
diff --git a/ggml-common.h b/ggml-common.h
@@ -645,6 +645,7 @@ GGML_TABLE_BEGIN(uint32_t, iq3s_grid, 512)
 GGML_TABLE_END()
 
 #define NGRID_IQ1S 2048
+#define IQ1S_DELTA 0.125f
 #if defined(GGML_COMMON_IMPL_C)
 GGML_TABLE_BEGIN(uint64_t, iq1s_grid, NGRID_IQ1S)
     0xffffffffffffffff, 0xffffffffffffff01, 0xffffffffffff0000, 0xffffffffffff01ff,
diff --git a/ggml-cuda.cu b/ggml-cuda.cu
@@ -1722,22 +1722,15 @@ static __global__ void dequantize_block_iq1_s(const void * __restrict__ vx, dst_
     const int il = tid/8; // 0...3
     const int ib = tid%8; // 0...7
     dst_t * y = yy + i*QK_K + 32*ib + 8*il;
-    const float d = (float)x[i].d * (2*((x[i].qh[ib] >> 12) & 0xf) + 1);
-#if __CUDA_ARCH__ >= MIN_CC_DP4A // lowest compute capability for integer intrinsics
-    int grid32[2]; const int8_t * q = (const int8_t *)grid32;
-    grid32[0] = *((const int *)(iq1s_grid_gpu + (x[i].qs[4*ib+il] | (((x[i].qh[ib] >> 3*il) & 7) << 8))));
-    grid32[1] = __vsub4((grid32[0] >>  4) & 0x0f0f0f0f, 0x01010101);
-    grid32[0] = __vsub4(grid32[0] & 0x0f0f0f0f, 0x01010101);
+    const float delta = x[i].qh[ib] & 0x8000 ? -1 - IQ1S_DELTA : -1 + IQ1S_DELTA;
+    const float d = (float)x[i].d * (2*((x[i].qh[ib] >> 12) & 7) + 1);
+    uint32_t grid32[2]; const int8_t * q = (const int8_t *)grid32;
+    grid32[0] = iq1s_grid_gpu[x[i].qs[4*ib+il] | (((x[i].qh[ib] >> 3*il) & 7) << 8)];
+    grid32[1] = (grid32[0] >> 4) & 0x0f0f0f0f;
+    grid32[0] &= 0x0f0f0f0f;
     for (int j = 0; j < 8; ++j) {
-        y[j] = d * q[j];
-    }
-#else
-    const uint8_t * grid = (const uint8_t *)(iq1s_grid_gpu + (x[i].qs[4*ib+il] | (((x[i].qh[ib] >> 3*il) & 7) << 8)));
-    for (int j = 0; j < 4; ++j) {
-        y[j+0] = d * ((grid[j] & 0xf) - 1);
-        y[j+4] = d * ((grid[j] >>  4) - 1);
+        y[j] = d * (q[j] + delta);
     }
-#endif
 #else
     assert(false);
 #endif
@@ -4560,22 +4553,25 @@ static __device__ __forceinline__ float vec_dot_iq1_s_q8_1(
     const int * q8 = (const int *)bq8_1[ib32].qs;
     for (int l = 0; l < 4; ++l) {
         const int * grid = (const int *)(iq1s_grid_gpu + (bq1->qs[4*ib32+l] | (((bq1->qh[ib32] >> 3*l) & 7) << 8)));
-        int grid0 = __vsub4(grid[0] & 0x0f0f0f0f, 0x01010101);
-        int grid1 = __vsub4((grid[0] >> 4) & 0x0f0f0f0f, 0x01010101);
+        int grid0 = grid[0] & 0x0f0f0f0f;
+        int grid1 = (grid[0] >> 4) & 0x0f0f0f0f;
         sumi = __dp4a(q8[2*l+1], grid1, __dp4a(q8[2*l+0], grid0, sumi));
     }
 #else
-    const int8_t   * q8 = bq8_1[ib32].qs;
+    const int8_t * q8 = bq8_1[ib32].qs;
     for (int l = 0; l < 4; ++l) {
         const uint8_t * grid = (const uint8_t *)(iq1s_grid_gpu + (bq1->qs[4*ib32+l] | (((bq1->qh[ib32] >> 3*l) & 7) << 8)));
         for (int j = 0; j < 4; ++j) {
-            sumi += q8[j] * ((grid[j] & 0xf) - 1) + q8[j+4] * ((grid[j] >>  4) - 1);
+            sumi += q8[j] * (grid[j] & 0xf) + q8[j+4] * (grid[j] >> 4);
         }
         q8 += 8;
     }
 #endif
-    const float d = (float)bq1->d * __low2float(bq8_1[ib32].ds);
-    return d * sumi * (2*(bq1->qh[ib32] >> 12) + 1);
+    const float delta = bq1->qh[ib32] & 0x8000 ? -1-IQ1S_DELTA : -1+IQ1S_DELTA;
+    const float d1q = (float)bq1->d * (2*((bq1->qh[ib32] >> 12) & 7) + 1);
+    const float d = d1q * __low2float (bq8_1[ib32].ds);
+    const float m = d1q * __high2float(bq8_1[ib32].ds);
+    return d * sumi + m * delta;
 #else
     assert(false);
     return 0.f;
diff --git a/ggml-metal.metal b/ggml-metal.metal
@@ -4377,7 +4377,7 @@ void kernel_mul_mv_iq1_s_f32_impl(
                      + yl[j+16] * (grid3[j] & 0xf) + yl[j+20] * (grid3[j] >> 4)
                      + yl[j+24] * (grid4[j] & 0xf) + yl[j+28] * (grid4[j] >> 4);
             }
-            sumf[row] += (float)dh[0] * (sum - sumy) * (2*(qh[0] >> 12) + 1);
+            sumf[row] += (float)dh[0] * (sum + sumy * (qh[0] & 0x8000 ? -1 - IQ1S_DELTA : -1 + IQ1S_DELTA)) * (2*((qh[0] >> 12) & 7) + 1);
 
             dh += nb*sizeof(block_iq1_s)/2;
             qs += nb*sizeof(block_iq1_s);
@@ -5076,14 +5076,16 @@ void dequantize_iq1_s(device const block_iq1_s * xb, short il, thread type4x4 &
     const float d = xb->d;
     device const uint8_t  * qs = xb->qs + 4*ib32 + 2*il;
     device const uint16_t * qh = xb->qh;
-    const float dl = d * (2*(qh[ib32] >> 12) + 1);
-    constant uint8_t * grid1 = (constant uint8_t *)(iq1s_grid_gpu + (qs[0] | (((qh[ib32] >> (6*il+0)) & 7) << 8)));
-    constant uint8_t * grid2 = (constant uint8_t *)(iq1s_grid_gpu + (qs[1] | (((qh[ib32] >> (6*il+3)) & 7) << 8)));
+    const float dl = d * (2*((qh[ib32] >> 12) & 7) + 1);
+    const float ml = dl * (qh[ib32] & 0x8000 ? -1 - IQ1S_DELTA : -1 + IQ1S_DELTA);
+    const uint16_t h = qh[ib32] >> 6*il;
+    constant uint8_t * grid1 = (constant uint8_t *)(iq1s_grid_gpu + (qs[0] | ((h << 8) & 0x700)));
+    constant uint8_t * grid2 = (constant uint8_t *)(iq1s_grid_gpu + (qs[1] | ((h << 5) & 0x700)));
     for (int i = 0; i < 4; ++i) {
-        reg[0][i] = dl * (grid1[i] & 0xf) - dl;
-        reg[1][i] = dl * (grid1[i] >>  4) - dl;
-        reg[2][i] = dl * (grid2[i] & 0xf) - dl;
-        reg[3][i] = dl * (grid2[i] >>  4) - dl;
+        reg[0][i] = dl * (grid1[i] & 0xf) + ml;
+        reg[1][i] = dl * (grid1[i] >>  4) + ml;
+        reg[2][i] = dl * (grid2[i] & 0xf) + ml;
+        reg[3][i] = dl * (grid2[i] >>  4) + ml;
     }
 }
 
diff --git a/ggml-quants.c b/ggml-quants.c
@@ -3456,11 +3456,12 @@ void dequantize_row_iq1_s(const block_iq1_s * restrict x, float * restrict y, in
         const uint16_t * qh = x[i].qh;
 
         for (int ib = 0; ib < QK_K/32; ++ib) {
-            const float dl = d * (2*(qh[ib] >> 12) + 1);
+            const float dl = d * (2*((qh[ib] >> 12) & 7) + 1);
+            const float delta = qh[ib] & 0x8000 ? -IQ1S_DELTA : IQ1S_DELTA;
             for (int l = 0; l < 4; ++l) {
                 const int8_t * grid = (const int8_t *)(iq1s_grid + (qs[l] | (((qh[ib] >> 3*l) & 7) << 8)));
                 for (int j = 0; j < 8; ++j) {
-                    y[j] = dl * grid[j];
+                    y[j] = dl * (grid[j] + delta);
                 }
                 y += 8;
             }
@@ -9582,7 +9583,7 @@ void ggml_vec_dot_iq1_s_q8_K  (int n, float * restrict s, size_t bs, const void
         const uint8_t  * qs = x[i].qs;
         const uint16_t * qh = x[i].qh;
 
-        int sumi1 = 0, sumi2 = 0;
+        int sumi1 = 0, sumi2 = 0, sumi3 = 0;
 
         for (int ib = 0; ib < QK_K/32; ib += 2) {
 
@@ -9601,26 +9602,32 @@ void ggml_vec_dot_iq1_s_q8_K  (int n, float * restrict s, size_t bs, const void
             const int32x4_t p1 = ggml_vdotq_s32(ggml_vdotq_s32(vdupq_n_s32(0), q1b.val[0], q8b.val[0]), q1b.val[1], q8b.val[1]);
             const int32x4_t p2 = ggml_vdotq_s32(ggml_vdotq_s32(vdupq_n_s32(0), q1b.val[2], q8b.val[2]), q1b.val[3], q8b.val[3]);
 
-            sumi1 += vaddvq_s32(p1) * (2*(qh[ib+0] >> 12) + 1);
-            sumi2 += vaddvq_s32(p2) * (2*(qh[ib+1] >> 12) + 1);
+            const int ls1 = 2*((qh[ib+0] >> 12) & 7) + 1;
+            const int ls2 = 2*((qh[ib+1] >> 12) & 7) + 1;
+            sumi1 += vaddvq_s32(p1) * ls1;
+            sumi2 += vaddvq_s32(p2) * ls2;
+            sumi3 += (y[i].bsums[2*ib+0] + y[i].bsums[2*ib+1]) * ls1 * (qh[ib+0] & 0x8000 ? -1 : 1)
+                   + (y[i].bsums[2*ib+2] + y[i].bsums[2*ib+3]) * ls2 * (qh[ib+1] & 0x8000 ? -1 : 1);
 
         }
 
-        sumf += y[i].d * GGML_FP16_TO_FP32(x[i].d) * (sumi1 + sumi2);
+        sumf += y[i].d * GGML_FP16_TO_FP32(x[i].d) * (sumi1 + sumi2 + IQ1S_DELTA * sumi3);
     }
 
     *s = sumf;
 
 #elif defined __AVX2__
 
     __m256 accum = _mm256_setzero_ps();
+    float accum1 = 0;
     for (int i = 0; i < nb; ++i) {
 
         const int8_t   * q8 = y[i].qs;
         const uint8_t  * qs = x[i].qs;
         const uint16_t * qh = x[i].qh;
 
         __m256i sumi = _mm256_setzero_si256();
+        int sumi1 = 0;
         for (int ib = 0; ib < QK_K/32; ib += 2) {
             const __m256i q1b_1 = _mm256_set_epi64x(iq1s_grid[qs[3] | ((qh[ib+0] >> 1) & 0x700)], iq1s_grid[qs[2] | ((qh[ib+0] << 2) & 0x700)],
                                                     iq1s_grid[qs[1] | ((qh[ib+0] << 5) & 0x700)], iq1s_grid[qs[0] | ((qh[ib+0] << 8) & 0x700)]);
@@ -9632,17 +9639,23 @@ void ggml_vec_dot_iq1_s_q8_K  (int n, float * restrict s, size_t bs, const void
 
             const __m256i dot1 = mul_add_epi8(q1b_1, q8b_1);
             const __m256i dot2 = mul_add_epi8(q1b_2, q8b_2);
-            const __m256i p1 = _mm256_madd_epi16(dot1, _mm256_set1_epi16(2*(qh[ib+0] >> 12) + 1));
-            const __m256i p2 = _mm256_madd_epi16(dot2, _mm256_set1_epi16(2*(qh[ib+1] >> 12) + 1));
+            const int16_t ls1 = 2*((qh[ib+0] >> 12) & 7) + 1;
+            const int16_t ls2 = 2*((qh[ib+1] >> 12) & 7) + 1;
+            const __m256i p1 = _mm256_madd_epi16(dot1, _mm256_set1_epi16(ls1));
+            const __m256i p2 = _mm256_madd_epi16(dot2, _mm256_set1_epi16(ls2));
 
             sumi = _mm256_add_epi32(sumi, _mm256_add_epi32(p1, p2));
+            sumi1 += (y[i].bsums[2*ib+0] + y[i].bsums[2*ib+1]) * (qh[ib+0] & 0x8000 ? -1 : 1) * ls1
+                   + (y[i].bsums[2*ib+2] + y[i].bsums[2*ib+3]) * (qh[ib+1] & 0x8000 ? -1 : 1) * ls2;
         }
 
-        accum = _mm256_fmadd_ps(_mm256_set1_ps(y[i].d * GGML_FP16_TO_FP32(x[i].d)), _mm256_cvtepi32_ps(sumi), accum);
+        const float d = y[i].d * GGML_FP16_TO_FP32(x[i].d);
+        accum = _mm256_fmadd_ps(_mm256_set1_ps(d), _mm256_cvtepi32_ps(sumi), accum);
+        accum1 += d * sumi1;
 
     }
 
-    *s = hsum_float_8(accum);
+    *s = hsum_float_8(accum) + IQ1S_DELTA * accum1;
 
 #else
 
@@ -9653,9 +9666,10 @@ void ggml_vec_dot_iq1_s_q8_K  (int n, float * restrict s, size_t bs, const void
         const uint8_t  * qs = x[i].qs;
         const uint16_t * qh = x[i].qh;
 
-        int sumi = 0;
+        int sumi = 0, sumi1 = 0;
         for (int ib = 0; ib < QK_K/32; ++ib) {
-            const int ls = 2*(qh[ib] >> 12) + 1;
+            const int ls = 2*((qh[ib] >> 12) & 7) + 1;
+            const int delta = qh[ib] & 0x8000 ? -1 : 1;
             int lsum = 0;
             for (int l = 0; l < 4; ++l) {
                 const int8_t * grid = (const int8_t *)(iq1s_grid + (qs[l] | (((qh[ib] >> 3*l) & 7) << 8)));
@@ -9664,11 +9678,12 @@ void ggml_vec_dot_iq1_s_q8_K  (int n, float * restrict s, size_t bs, const void
                 }
                 q8 += 8;
             }
-            sumi += ls * lsum;
+            sumi  += ls * lsum;
+            sumi1 += ls * delta * (y[i].bsums[2*ib+0] + y[i].bsums[2*ib+1]);
             qs += 4;
         }
 
-        sumf += GGML_FP16_TO_FP32(x[i].d) * y[i].d * sumi;
+        sumf += GGML_FP16_TO_FP32(x[i].d) * y[i].d * (sumi + IQ1S_DELTA * sumi1);
     }
 
     *s = sumf;
@@ -11438,7 +11453,7 @@ static int iq1_find_best_neighbour(const uint16_t * restrict neighbours, const u
 }
 
 static int iq1_find_best_neighbour2(const uint16_t * restrict neighbours, const uint64_t * restrict grid,
-        const float * restrict xval, const float * restrict weight, float scale, int8_t * restrict L, int ngrid) {
+        const float * restrict xval, const float * restrict weight, float scale, const float * restrict xg, int8_t * restrict L, int ngrid) {
     int num_neighbors = neighbours[0];
     GGML_ASSERT(num_neighbors > 0);
     float best_score = FLT_MAX;
@@ -11447,7 +11462,7 @@ static int iq1_find_best_neighbour2(const uint16_t * restrict neighbours, const
         const int8_t * pg = (const int8_t *)(grid + neighbours[j]);
         float d2 = 0;
         for (int i = 0; i < 8; ++i) {
-            float q = (pg[i] - 3)/2;
+            float q = xg[(pg[i] - 1)/2];
             float w = weight[i];
             float diff = scale*q - xval[i];
             d2 += w*diff*diff;
@@ -11463,7 +11478,7 @@ static int iq1_find_best_neighbour2(const uint16_t * restrict neighbours, const
             float d2 = 0;
             for (int j = 0; j < 8; ++j) {
                 float w = weight[j];
-                float q = (grid_i[j] - 3)/2;
+                float q = xg[(grid_i[j] - 1)/2];
                 float diff = scale*q - xval[i];
                 d2 += w*diff*diff;
             }
@@ -11480,7 +11495,7 @@ static int iq1_find_best_neighbour2(const uint16_t * restrict neighbours, const
             const int8_t * pg = (const int8_t *)(grid + neighbours[j]);
             float sumqx = 0, sumq2 = 0;
             for (int i = 0; i < 8; ++i) {
-                float q = (pg[i] - 3)/2;
+                float q = xg[(pg[i] - 1)/2];
                 float w = weight[i];
                 sumqx += w*q*xval[i];
                 sumq2 += w*q*q;
@@ -11519,6 +11534,9 @@ static void quantize_row_iq1_s_impl(const float * restrict x, void * restrict vy
 
     block_iq1_s * y = vy;
 
+    const float x_p[3] = {-1 + IQ1S_DELTA,  IQ1S_DELTA, 1 + IQ1S_DELTA};
+    const float x_m[3] = {-1 - IQ1S_DELTA, -IQ1S_DELTA, 1 - IQ1S_DELTA};
+
     float  scales[QK_K/IQ1S_BLOCK_SIZE];
     float  weight[IQ1S_BLOCK_SIZE];
     int8_t L[IQ1S_BLOCK_SIZE];
@@ -11527,6 +11545,7 @@ static void quantize_row_iq1_s_impl(const float * restrict x, void * restrict vy
     float  pairs[2*IQ1S_BLOCK_SIZE];
     int * idx = (int *)(pairs + 1);
     uint16_t index[IQ1S_BLOCK_SIZE/8];
+    int8_t shifts[QK_K/IQ1S_BLOCK_SIZE];
 
     for (int ibl = 0; ibl < nbl; ++ibl) {
 
@@ -11572,33 +11591,41 @@ static void quantize_row_iq1_s_impl(const float * restrict x, void * restrict vy
                 }
             }
             float best_score = 0, scale = max;
-            int besti1 = 0, besti2 = 0;
+            int besti1 = -1, besti2 = -1, best_shift = 0;
             for (int i1 = 0; i1 <= IQ1S_BLOCK_SIZE; ++i1) {
                 for (int i2 = i1; i2 <= IQ1S_BLOCK_SIZE; ++i2) {
-                    float sumqx = -(sumx[i1] - sumx[0]) + (sumx[IQ1S_BLOCK_SIZE] - sumx[i2]);
-                    float sumq2 =  (sumw[i1] - sumw[0]) + (sumw[IQ1S_BLOCK_SIZE] - sumw[i2]);
+                    float sumqx = (sumx[i1] - sumx[0])*x_p[0] + (sumx[i2] - sumx[i1])*x_p[1] + (sumx[IQ1S_BLOCK_SIZE] - sumx[i2])*x_p[2];
+                    float sumq2 = (sumw[i1] - sumw[0])*x_p[0]*x_p[0] + (sumw[i2] - sumw[i1])*x_p[1]*x_p[1] + (sumw[IQ1S_BLOCK_SIZE] - sumw[i2])*x_p[2]*x_p[2];
+                    if (sumq2 > 0 && sumqx*sumqx > best_score*sumq2) {
+                        scale = sumqx/sumq2; best_score = scale*sumqx;
+                        besti1 = i1; besti2 = i2; best_shift = 1;
+                    }
+                    sumqx = (sumx[i1] - sumx[0])*x_m[0] + (sumx[i2] - sumx[i1])*x_m[1] + (sumx[IQ1S_BLOCK_SIZE] - sumx[i2])*x_m[2];
+                    sumq2 = (sumw[i1] - sumw[0])*x_m[0]*x_m[0] + (sumw[i2] - sumw[i1])*x_m[1]*x_m[1] + (sumw[IQ1S_BLOCK_SIZE] - sumw[i2])*x_m[2]*x_m[2];
                     if (sumq2 > 0 && sumqx*sumqx > best_score*sumq2) {
                         scale = sumqx/sumq2; best_score = scale*sumqx;
-                        besti1 = i1; besti2 = i2;
+                        besti1 = i1; besti2 = i2; best_shift = -1;
                     }
                 }
             }
+            GGML_ASSERT(besti1 >= 0 && besti2 >= 0 && best_shift != 0);
             for (int j =      0; j < besti1; ++j) L[idx[2*j]] = 0;
             for (int j = besti1; j < besti2; ++j) L[idx[2*j]] = 1;
             for (int j = besti2; j < IQ1S_BLOCK_SIZE; ++j) L[idx[2*j]] = 2;
             if (scale < 0) {
                 for (int j = 0; j < IQ1S_BLOCK_SIZE; ++j) L[j] = 2 - L[j];
-                scale = -scale;
+                scale = -scale; best_shift = -best_shift;
             }
             bool all_on_grid = true;
+            const float * xx = best_shift == 1 ? x_p : x_m;
             for (int k = 0; k < IQ1S_BLOCK_SIZE/8; ++k) {
                 uint16_t u = 0;
                 for (int j = 0; j < 8; ++j) u |= (L[8*k+j] << 2*j);
                 int grid_index = kmap_q2xs[u];
                 if (grid_index < 0) {
                     all_on_grid = false;
                     const uint16_t * neighbours = kneighbors_q2xs - kmap_q2xs[u] - 1;
-                    grid_index = iq1_find_best_neighbour2(neighbours, kgrid_q2xs, xb + 8*k, weight + 8*k, scale, L + 8*k, NGRID_IQ1S);
+                    grid_index = iq1_find_best_neighbour2(neighbours, kgrid_q2xs, xb + 8*k, weight + 8*k, scale, xx, L + 8*k, NGRID_IQ1S);
                     GGML_ASSERT(grid_index >= 0);
                 }
                 index[k] = grid_index;
@@ -11609,7 +11636,7 @@ static void quantize_row_iq1_s_impl(const float * restrict x, void * restrict vy
                     const int8_t * pg = (const int8_t *)(kgrid_q2xs + index[k]);
                     for (int j = 0; j < 8; ++j) {
                         float w = weight[8*k + j];
-                        float q = (pg[j] - 3)/2;
+                        float q = xx[(pg[j] - 1)/2];
                         sumqx += w*q*xb[8*k+j];
                         sumq2 += w*q*q;
                     }
@@ -11624,6 +11651,7 @@ static void quantize_row_iq1_s_impl(const float * restrict x, void * restrict vy
             y[ibl].qh[ib] = h;
             GGML_ASSERT(scale >= 0);
             scales[ib] = scale;
+            shifts[ib] = best_shift;
             max_scale = MAX(max_scale, scale);
         }
 
@@ -11632,12 +11660,13 @@ static void quantize_row_iq1_s_impl(const float * restrict x, void * restrict vy
             continue;
         }
 
-        float d = max_scale/31;
+        float d = max_scale/15;
         y[ibl].d = GGML_FP32_TO_FP16(d*1.125f); // 1.085f is another fudge factor. Don't ask me why it is needed.
         float id = 1/d;
         for (int ib = 0; ib < QK_K/IQ1S_BLOCK_SIZE; ++ib) {
             int l = nearest_int(0.5f*(id*scales[ib]-1));
-            l = MAX(0, MIN(15, l));
+            l = MAX(0, MIN(7, l));
+            if (shifts[ib] == -1) l |= 8;
             y[ibl].qh[ib] |= (l << 12);
         }
     }
