diff --git a/ggml.c b/ggml.c
index 6e46c0e5ad1da..1b9f15aaf8b04 100644
--- a/ggml.c
+++ b/ggml.c
@@ -692,13 +692,17 @@ static void quantize_row_q4_0_reference(const float * restrict x, block_q4_0 * r
 
     for (int i = 0; i < nb; i++) {
         float amax = 0.0f; // absolute max
+        float max = 0.0f;
 
         for (int l = 0; l < QK4_0; l++) {
             const float v = x[i*QK4_0 + l];
-            amax = MAX(amax, fabsf(v));
+            if (amax < fabsf(v)) {
+                amax = fabsf(v);
+                max = v;
+            }
         }
 
-        const float d = amax / ((1 << 3) - 1);
+        const float d = max / -8;
         const float id = d ? 1.0f/d : 0.0f;
 
         y[i].d = d;
@@ -707,8 +711,8 @@ static void quantize_row_q4_0_reference(const float * restrict x, block_q4_0 * r
             const float v0 = x[i*QK4_0 + l + 0]*id;
             const float v1 = x[i*QK4_0 + l + 1]*id;
 
-            const uint8_t vi0 = (int8_t)roundf(v0) + 8;
-            const uint8_t vi1 = (int8_t)roundf(v1) + 8;
+            const uint8_t vi0 = MIN(15, (int8_t)roundf(v0) + 8);
+            const uint8_t vi1 = MIN(15, (int8_t)roundf(v1) + 8);
 
             assert(vi0 < 16);
             assert(vi1 < 16);
@@ -728,28 +732,42 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
 
 #if defined(__POWER9_VECTOR__)
     const vector float v85 = vec_splats(8.5f);
+    const vector signed int v15 = vec_splats(15);
     for (int i = 0; i < nb; i++) {
-        float amax = 0.0f; // absolute max
+        float max = 0.0f;
+        float min = 0.0f;
 
         vector float srcv [8];
-        vector float asrcv[8];
-        vector float amaxv[8];
+        vector float maxv[8];
+        vector float minv[8];
 
         for (int l = 0; l < 8; l++) srcv[l]  = *(vector float *)(x + i*32 + 4*l);
-        for (int l = 0; l < 8; l++) asrcv[l] = vec_abs(srcv[l]);
-
-        for (int l = 0; l < 4; l++) amaxv[2*l] = vec_max(asrcv[2*l], asrcv[2*l+1]);
-        //for (int l = 0; l < 2; l++) amaxv[4*l] = vec_max(amaxv[4*l], amaxv[4*l+2]);
-        amaxv[0] = vec_max(amaxv[0], amaxv[2]);
-        amaxv[4] = vec_max(amaxv[4], amaxv[6]);
-        //for (int l = 0; l < 1; l++) amaxv[8*l] = vec_max(amaxv[8*l], amaxv[8*l+4]);
-        amaxv[0] = vec_max(amaxv[0], amaxv[4]);
-
-        amax = MAX(
-                MAX(vec_extract(amaxv[0], 0), vec_extract(amaxv[0], 1)),
-                MAX(vec_extract(amaxv[0], 2), vec_extract(amaxv[0], 3)));
-
-        const float d = amax / ((1 << 3) - 1);
+        //for (int l = 0; l < 8; l++) asrcv[l] = vec_abs(srcv[l]);
+
+        for (int l = 0; l < 4; l++) maxv[2*l] = vec_max(asrcv[2*l], asrcv[2*l+1]);
+        //for (int l = 0; l < 2; l++) maxv[4*l] = vec_max(maxv[4*l], maxv[4*l+2]);
+        maxv[0] = vec_max(maxv[0], maxv[2]);
+        maxv[4] = vec_max(maxv[4], maxv[6]);
+        //for (int l = 0; l < 1; l++) maxv[8*l] = vec_max(maxv[8*l], maxv[8*l+4]);
+        maxv[0] = vec_max(maxv[0], maxv[4]);
+
+        for (int l = 0; l < 4; l++) minv[2*l] = vec_min(asrcv[2*l], asrcv[2*l+1]);
+        //for (int l = 0; l < 2; l++) minv[4*l] = vec_min(minv[4*l], minv[4*l+2]);
+        minv[0] = vec_min(minv[0], minv[2]);
+        minv[4] = vec_min(minv[4], minv[6]);
+        //for (int l = 0; l < 1; l++) minv[8*l] = vec_min(minv[8*l], minv[8*l+4]);
+        minv[0] = vec_min(minv[0], minv[4]);
+
+
+        max = MAX(
+                MAX(vec_extract(maxv[0], 0), vec_extract(maxv[0], 1)),
+                MAX(vec_extract(maxv[0], 2), vec_extract(maxv[0], 3)));
+        min = MIN(
+                MIN(vec_extract(minv[0], 0), vec_extract(minv[0], 1)),
+                MIN(vec_extract(minv[0], 2), vec_extract(minv[0], 3)));
+
+        const float magnitude = max >= fabsf(min) ? max : min;
+        const float d = magnitude / -8;
         const float id = d ? 1.0/d : 0.0;
 
         y[i].d = d;
@@ -759,27 +777,33 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
         for (int l = 0; l < 8; l++) {
             const vector float vf  = vec_madd(srcv[l], vid, v85);
             const vector signed int vi = vec_signed(vf);
+            const vector signed int vc = vec_min(vi, v15);
 
-            pb[2*l + 0] = vec_extract(vi, 0) | (vec_extract(vi, 1) << 4);
-            pb[2*l + 1] = vec_extract(vi, 2) | (vec_extract(vi, 3) << 4);
+            pb[2*l + 0] = vec_extract(vc, 0) | (vec_extract(vc, 1) << 4);
+            pb[2*l + 1] = vec_extract(vc, 2) | (vec_extract(vc, 3) << 4);
         }
     }
 #elif __ARM_NEON
     for (int i = 0; i < nb; i++) {
         float32x4_t srcv [8];
-        float32x4_t asrcv[8];
-        float32x4_t amaxv[8];
+        float32x4_t maxv[8];
+        float32x4_t minv[8];
 
         for (int l = 0; l < 8; l++) srcv[l]  = vld1q_f32(x + i*32 + 4*l);
-        for (int l = 0; l < 8; l++) asrcv[l] = vabsq_f32(srcv[l]);
 
-        for (int l = 0; l < 4; l++) amaxv[2*l] = vmaxq_f32(asrcv[2*l], asrcv[2*l+1]);
-        for (int l = 0; l < 2; l++) amaxv[4*l] = vmaxq_f32(amaxv[4*l], amaxv[4*l+2]);
-        for (int l = 0; l < 1; l++) amaxv[8*l] = vmaxq_f32(amaxv[8*l], amaxv[8*l+4]);
+        for (int l = 0; l < 4; l++) maxv[2*l] = vmaxq_f32(srcv[2*l], srcv[2*l+1]);
+        for (int l = 0; l < 2; l++) maxv[4*l] = vmaxq_f32(maxv[4*l], maxv[4*l+2]);
+        for (int l = 0; l < 1; l++) maxv[8*l] = vmaxq_f32(maxv[8*l], maxv[8*l+4]);
 
-        const float amax = vmaxvq_f32(amaxv[0]);
+        for (int l = 0; l < 4; l++) minv[2*l] = vminq_f32(srcv[2*l], srcv[2*l+1]);
+        for (int l = 0; l < 2; l++) minv[4*l] = vminq_f32(minv[4*l], minv[4*l+2]);
+        for (int l = 0; l < 1; l++) minv[8*l] = vminq_f32(minv[8*l], minv[8*l+4]);
 
-        const float d = amax / ((1 << 3) - 1);
+        const float max = vmaxvq_f32(maxv[0]);
+        const float min = vminvq_f32(minv[0]);
+
+        const float magnitude = max >= fabsf(min) ? max : min;
+        const float d = magnitude / -8;
         const float id = d ? 1.0f/d : 0.0f;
 
         y[i].d = d;
@@ -788,9 +812,10 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
             const float32x4_t v  = vmulq_n_f32(srcv[l], id);
             const float32x4_t vf = vaddq_f32(v, vdupq_n_f32(8.5f));
             const int32x4_t   vi = vcvtq_s32_f32(vf);
+            const int32x4_t   vc = vminq_s32(vi, vdupq_n_s32(15));
 
-            y[i].qs[2*l + 0] = vgetq_lane_s32(vi, 0) | (vgetq_lane_s32(vi, 1) << 4);
-            y[i].qs[2*l + 1] = vgetq_lane_s32(vi, 2) | (vgetq_lane_s32(vi, 3) << 4);
+            y[i].qs[2*l + 0] = vgetq_lane_s32(vc, 0) | (vgetq_lane_s32(vc, 1) << 4);
+            y[i].qs[2*l + 1] = vgetq_lane_s32(vc, 2) | (vgetq_lane_s32(vc, 3) << 4);
         }
     }
 #elif defined(__AVX2__)
@@ -802,22 +827,31 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
         __m256 v3 = _mm256_loadu_ps( x + 24 );
         x += 32;
 
-        // Compute max(abs(e)) for the block
-        const __m256 signBit = _mm256_set1_ps( -0.0f );
-        __m256 maxAbs = _mm256_andnot_ps( signBit, v0 );
-        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v1 ) );
-        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v2 ) );
-        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v3 ) );
+        // Compute max for the block
+        __m256 max  = _mm256_max_ps( v0, v1 );
+        __m256 maxTmp = _mm256_max_ps( v2, v3 );
+        max = _mm256_max_ps( max, maxTmp );
 
-        __m128 max4 = _mm_max_ps( _mm256_extractf128_ps( maxAbs, 1 ), _mm256_castps256_ps128( maxAbs ) );
+        __m128 max4 = _mm_max_ps( _mm256_extractf128_ps( max, 1 ), _mm256_castps256_ps128( max ) );
         max4 = _mm_max_ps( max4, _mm_movehl_ps( max4, max4 ) );
         max4 = _mm_max_ss( max4, _mm_movehdup_ps( max4 ) );
         const float maxScalar = _mm_cvtss_f32( max4 );
 
+        // Compute min for the block
+        __m256 min  = _mm256_min_ps( v0, v1 );
+        __m256 minTmp = _mm256_min_ps( v2, v3 );
+        min = _mm256_min_ps( min, minTmp );
+
+        __m128 min4 = _mm_min_ps( _mm256_extractf128_ps( min, 1 ), _mm256_castps256_ps128( min ) );
+        min4 = _mm_min_ps( min4, _mm_movehl_ps( min4, min4 ) );
+        min4 = _mm_min_ss( min4, _mm_movehdup_ps( min4 ) );
+        const float minScalar = _mm_cvtss_f32( min4 );
+
         // Quantize these floats
-        const float d = maxScalar / 7.0f;
+        const float magnitude = maxScalar >= fabsf(minScalar) ? maxScalar : minScalar;
+        const float d = magnitude / -8.0f;
         y[i].d = d;
-        const float id = ( maxScalar != 0.0f ) ? 7.0f / maxScalar : 0.0f;
+        const float id = ( magnitude != 0.0f ) ? -8.0f / magnitude : 0.0f;
         const __m256 mul = _mm256_set1_ps( id );
 
         // Apply the multiplier
@@ -850,9 +884,11 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
         const __m256i perm = _mm256_setr_epi32( 0, 4, 1, 5, 2, 6, 3, 7 );
         i0 = _mm256_permutevar8x32_epi32( i0, perm );
 
-        // Apply offset to translate the range from [ -7 .. +7 ] into [ +1 .. +15 ]
+        // Apply offset and clamp to translate the range from [ -8 .. +8 ] into [ +0 .. +15 ]
         const __m256i off = _mm256_set1_epi8( 8 );
         i0 = _mm256_add_epi8( i0, off );
+        const __m256i maxNibble = _mm256_set1_epi8( 15 );
+        i0 = _mm256_min_epi8( i0, maxNibble );
 
         // Compress the vector into 4 bit/value, and store
         __m128i res = packNibbles( i0 );
@@ -867,22 +903,31 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
         __m256 v3 = _mm256_loadu_ps( x + 24 );
         x += 32;
 
-        // Compute max(abs(e)) for the block
-        const __m256 signBit = _mm256_set1_ps( -0.0f );
-        __m256 maxAbs = _mm256_andnot_ps( signBit, v0 );
-        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v1 ) );
-        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v2 ) );
-        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v3 ) );
+        // Compute max for the block
+        __m256 max  = _mm256_max_ps( v0, v1 );
+        __m256 maxTmp = _mm256_max_ps( v2, v3 );
+        max = _mm256_max_ps( max, maxTmp );
 
-        __m128 max4 = _mm_max_ps( _mm256_extractf128_ps( maxAbs, 1 ), _mm256_castps256_ps128( maxAbs ) );
+        __m128 max4 = _mm_max_ps( _mm256_extractf128_ps( max, 1 ), _mm256_castps256_ps128( max ) );
         max4 = _mm_max_ps( max4, _mm_movehl_ps( max4, max4 ) );
         max4 = _mm_max_ss( max4, _mm_movehdup_ps( max4 ) );
         const float maxScalar = _mm_cvtss_f32( max4 );
 
+        // Compute min for the block
+        __m256 min  = _mm256_min_ps( v0, v1 );
+        __m256 minTmp = _mm256_min_ps( v2, v3 );
+        min = _mm256_min_ps( min, minTmp );
+
+        __m128 min4 = _mm_min_ps( _mm256_extractf128_ps( min, 1 ), _mm256_castps256_ps128( min ) );
+        min4 = _mm_min_ps( min4, _mm_movehl_ps( min4, min4 ) );
+        min4 = _mm_min_ss( min4, _mm_movehdup_ps( min4 ) );
+        const float minScalar = _mm_cvtss_f32( min4 );
+
         // Quantize these floats
-        const float d = maxScalar / 7.0f;
+        const float magnitude = maxScalar >= fabsf(minScalar) ? maxScalar : minScalar;
+        const float d = magnitude / -8.0f;
         y[i].d = d;
-        const float id = ( maxScalar != 0.0f ) ? 7.0f / maxScalar : 0.0f;
+        const float id = ( magnitude != 0.0f ) ? -8.0f / magnitude : 0.0f;
         const __m256 mul = _mm256_set1_ps( id );
 
         // Apply the multiplier
@@ -923,10 +968,13 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
         ni0 = _mm_packs_epi16( ni0, ni2 );
         ni4 = _mm_packs_epi16( ni4, ni6 );
 
-        // Apply offset to translate the range from [ -7 .. +7 ] into [ +1 .. +15 ]
-        const __m128i off = _mm_set1_epi8( 8);
+        // Apply offset and clamp to translate the range from [ -8 .. +8 ] into [ +0 .. +15 ]
+        const __m128i off = _mm_set1_epi8( 8 );
         ni0 = _mm_add_epi8( ni0, off );
         ni4 = _mm_add_epi8( ni4, off );
+        const __m128i maxNibble = _mm_set1_epi8( 15 );
+        ni0 = _mm_min_epi8( ni0, maxNibble );
+        ni4 = _mm_min_epi8( ni4, maxNibble );
 
         // Compress the vector into 4 bit/value, and store
         __m128i res = packNibbles( ni0, ni4 );
@@ -934,24 +982,32 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
     }
 #elif defined(__wasm_simd128__)
     for (int i = 0; i < nb; i++) {
-        float amax = 0.0f; // absolute max
+        float max = 0.0f;
+        float min = 0.0f;
 
         v128_t srcv [8];
-        v128_t asrcv[8];
-        v128_t amaxv[8];
+        v128_t maxv[8];
+        v128_t minv[8];
 
         for (int l = 0; l < 8; l++) srcv[l]  = wasm_v128_load(x + i*32 + 4*l);
-        for (int l = 0; l < 8; l++) asrcv[l] = wasm_f32x4_abs(srcv[l]);
 
-        for (int l = 0; l < 4; l++) amaxv[2*l] = wasm_f32x4_max(asrcv[2*l], asrcv[2*l+1]);
-        for (int l = 0; l < 2; l++) amaxv[4*l] = wasm_f32x4_max(amaxv[4*l], amaxv[4*l+2]);
-        for (int l = 0; l < 1; l++) amaxv[8*l] = wasm_f32x4_max(amaxv[8*l], amaxv[8*l+4]);
+        for (int l = 0; l < 4; l++) maxv[2*l] = wasm_f32x4_max(srcv[2*l], srcv[2*l+1]);
+        for (int l = 0; l < 2; l++) maxv[4*l] = wasm_f32x4_max(maxv[4*l], maxv[4*l+2]);
+        for (int l = 0; l < 1; l++) maxv[8*l] = wasm_f32x4_max(maxv[8*l], maxv[8*l+4]);
 
-        amax = MAX(
-                MAX(wasm_f32x4_extract_lane(amaxv[0], 0), wasm_f32x4_extract_lane(amaxv[0], 1)),
-                MAX(wasm_f32x4_extract_lane(amaxv[0], 2), wasm_f32x4_extract_lane(amaxv[0], 3)));
+        for (int l = 0; l < 4; l++) minv[2*l] = wasm_f32x4_min(srcv[2*l], srcv[2*l+1]);
+        for (int l = 0; l < 2; l++) minv[4*l] = wasm_f32x4_min(minv[4*l], minv[4*l+2]);
+        for (int l = 0; l < 1; l++) minv[8*l] = wasm_f32x4_min(minv[8*l], minv[8*l+4]);
 
-        const float d = amax / ((1 << 3) - 1);
+        max = MAX(
+                MAX(wasm_f32x4_extract_lane(maxv[0], 0), wasm_f32x4_extract_lane(maxv[0], 1)),
+                MAX(wasm_f32x4_extract_lane(maxv[0], 2), wasm_f32x4_extract_lane(maxv[0], 3)));
+        min = MIN(
+                MIN(wasm_f32x4_extract_lane(minv[0], 0), wasm_f32x4_extract_lane(minv[0], 1)),
+                MIN(wasm_f32x4_extract_lane(minv[0], 2), wasm_f32x4_extract_lane(minv[0], 3)));
+
+        const float magnitude = max >= fabsf(min) ? max : min;
+        const float d = magnitude / -8;
         const float id = d ? 1.0/d : 0.0;
 
         y[i].d = d;
@@ -960,9 +1016,10 @@ static void quantize_row_q4_0(const float * restrict x, void * restrict vy, int
             const v128_t v  = wasm_f32x4_mul(srcv[l], wasm_f32x4_splat(id));
             const v128_t vf = wasm_f32x4_add(v, wasm_f32x4_splat(8.5f));
             const v128_t vi = wasm_i32x4_trunc_sat_f32x4(vf);
+            const v128_t vc = wasm_i32x4_min_u(vi, wasm_i32x4_splat(15));
 
-            y[i].qs[2*l + 0] = wasm_i32x4_extract_lane(vi, 0) | (wasm_i32x4_extract_lane(vi, 1) << 4);
-            y[i].qs[2*l + 1] = wasm_i32x4_extract_lane(vi, 2) | (wasm_i32x4_extract_lane(vi, 3) << 4);
+            y[i].qs[2*l + 0] = wasm_i32x4_extract_lane(vc, 0) | (wasm_i32x4_extract_lane(vc, 1) << 4);
+            y[i].qs[2*l + 1] = wasm_i32x4_extract_lane(vc, 2) | (wasm_i32x4_extract_lane(vc, 3) << 4);
         }
     }
 #else
@@ -1143,13 +1200,17 @@ static void quantize_row_q4_2_reference(const float * restrict x, block_q4_2 * r
 
     for (int i = 0; i < nb; i++) {
         float amax = 0.0f; // absolute max
+        float max = 0.0f;
 
         for (int l = 0; l < QK4_2; l++) {
             const float v = x[i*QK4_2 + l];
-            amax = MAX(amax, fabsf(v));
+            if (amax < fabsf(v)) {
+                amax = fabsf(v);
+                max = v;
+            }
         }
 
-        const float d = amax / ((1 << 3) - 1);
+        const float d = max / -8;
 
         const float id = d ? 1.0f/d : 0.0f;
 
@@ -1159,8 +1220,8 @@ static void quantize_row_q4_2_reference(const float * restrict x, block_q4_2 * r
             const float v0 = x[i*QK4_2 + l + 0]*id;
             const float v1 = x[i*QK4_2 + l + 1]*id;
 
-            const uint8_t vi0 = (uint8_t)(v0 + 8.5f);
-            const uint8_t vi1 = (uint8_t)(v1 + 8.5f);
+            const uint8_t vi0 = MIN(15, (uint8_t)(v0 + 8.5f));
+            const uint8_t vi1 = MIN(15, (uint8_t)(v1 + 8.5f));
 
             assert(vi0 < 16);
             assert(vi1 < 16);
@@ -1254,9 +1315,7 @@ static void quantize_row_q4_2(const float * restrict x, void * restrict vy, int
 
     block_q4_2 * restrict y = vy;
 
-    //quantize_row_q4_2_reference(x, y, k);
-    // This produces the exact same format, just better match to the input floats ("better" as measured by RMSE)
-    quantize_row_q4_2_rmse(x, y, k);
+    quantize_row_q4_2_reference(x, y, k);
 }
 
 static void quantize_row_q4_3_reference(const float * restrict x, block_q4_3 * restrict y, int k) {
@@ -1807,7 +1866,7 @@ static const quantize_fns_t quantize_fns[GGML_TYPE_COUNT] = {
     [GGML_TYPE_Q4_2] = {
         .dequantize_row_q         = dequantize_row_q4_2,
         .quantize_row_q           = quantize_row_q4_2,
-        .quantize_row_q_reference = (quantize_row_q_t) quantize_row_q4_2_rmse, //quantize_row_q4_2_reference,
+        .quantize_row_q_reference = (quantize_row_q_t) quantize_row_q4_2_reference,
         .quantize_row_q_dot       = quantize_row_q8_0,
         .vec_dot_q                = ggml_vec_dot_q4_2_q8_0,
     },
@@ -12139,8 +12198,7 @@ size_t ggml_quantize_q4_2(const float * src, void * dst, int n, int k, int64_t *
     for (int j = 0; j < n; j += k) {
         block_q4_2 * restrict y = (block_q4_2 *)dst + j/QK4_2;
 
-        //quantize_row_q4_2_reference(src + j, y, k);
-        quantize_row_q4_2_rmse(src + j, y, k);
+        quantize_row_q4_2_reference(src + j, y, k);
 
         for (int i = 0; i < nb; i++) {
             for (int l = 0; l < QK4_2; l += 2) {