path: root/src/gallium/auxiliary/gallivm/lp_bld_gather.c

/**************************************************************************
 *
 * Copyright 2010 VMware, Inc.
 * All Rights Reserved.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sub license, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL
 * THE COPYRIGHT HOLDERS, AUTHORS AND/OR ITS SUPPLIERS BE LIABLE FOR ANY CLAIM,
 * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
 * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
 * USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * The above copyright notice and this permission notice (including the
 * next paragraph) shall be included in all copies or substantial portions
 * of the Software.
 *
 **************************************************************************/


#include "util/u_debug.h"
#include "util/u_cpu_detect.h"
#include "util/u_math.h"
#include "lp_bld_debug.h"
#include "lp_bld_const.h"
#include "lp_bld_format.h"
#include "lp_bld_gather.h"
#include "lp_bld_swizzle.h"
#include "lp_bld_type.h"
#include "lp_bld_init.h"
#include "lp_bld_intr.h"
#include "lp_bld_pack.h"


/**
 * Get the pointer to one element from scatter positions in memory.
 *
 * @sa lp_build_gather()
 */
LLVMValueRef
lp_build_gather_elem_ptr(struct gallivm_state *gallivm,
                         unsigned length,
                         LLVMValueRef base_ptr,
                         LLVMValueRef offsets,
                         unsigned i)
{
   LLVMValueRef offset;
   LLVMValueRef ptr;

   assert(LLVMTypeOf(base_ptr) == LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0));

   if (length == 1) {
      assert(i == 0);
      offset = offsets;
   } else {
      LLVMValueRef index = lp_build_const_int32(gallivm, i);
      offset = LLVMBuildExtractElement(gallivm->builder, offsets, index, "");
   }

   ptr = LLVMBuildGEP(gallivm->builder, base_ptr, &offset, 1, "");

   return ptr;
}


/**
 * Gather one element from scatter positions in memory.
 *
 * @sa lp_build_gather()
 */
LLVMValueRef
lp_build_gather_elem(struct gallivm_state *gallivm,
                     unsigned length,
                     unsigned src_width,
                     unsigned dst_width,
                     boolean aligned,
                     LLVMValueRef base_ptr,
                     LLVMValueRef offsets,
                     unsigned i,
                     boolean vector_justify)
{
   LLVMTypeRef src_type = LLVMIntTypeInContext(gallivm->context, src_width);
   LLVMTypeRef src_ptr_type = LLVMPointerType(src_type, 0);
   LLVMTypeRef dst_elem_type = LLVMIntTypeInContext(gallivm->context, dst_width);
   LLVMValueRef ptr;
   LLVMValueRef res;

   assert(LLVMTypeOf(base_ptr) == LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0));

   ptr = lp_build_gather_elem_ptr(gallivm, length, base_ptr, offsets, i);
   ptr = LLVMBuildBitCast(gallivm->builder, ptr, src_ptr_type, "");
   res = LLVMBuildLoad(gallivm->builder, ptr, "");

   /* XXX
    * On some archs we probably really want to avoid having to deal
    * with alignments lower than 4 bytes (if fetch size is a power of
    * two >= 32). On x86 it doesn't matter, however.
    * We should be able to guarantee full alignment for any kind of texture
    * fetch (except ARB_texture_buffer_range, oops), but not vertex fetch
    * (there's PIPE_CAP_VERTEX_BUFFER_OFFSET_4BYTE_ALIGNED_ONLY and friends
    * but I don't think that's quite what we wanted).
    * For ARB_texture_buffer_range, PIPE_CAP_TEXTURE_BUFFER_OFFSET_ALIGNMENT
    * looks like a good fit, but it seems this cap bit (and OpenGL) aren't
    * enforcing what we want (which is what d3d10 does, the offset needs to
    * be aligned to element size, but GL has bytes regardless of element
    * size which would only leave us with minimum alignment restriction of 16
    * which doesn't make much sense if the type isn't 4x32bit). Due to
    * translation of offsets to first_elem in sampler_views it actually seems
    * gallium could not do anything else except 16 no matter what...
    */
   if (!aligned) {
      LLVMSetAlignment(res, 1);
   } else if (!util_is_power_of_two_or_zero(src_width)) {
      /*
       * Full alignment is impossible, assume the caller really meant
       * the individual elements were aligned (e.g. 3x32bit format).
       * And yes the generated code may otherwise crash, llvm will
       * really assume 128bit alignment with a 96bit fetch (I suppose
       * that makes sense as it can just assume the upper 32bit to be
       * whatever).
       * Maybe the caller should be able to explicitly set this, but
       * this should cover all the 3-channel formats.
       */
      if (((src_width / 24) * 24 == src_width) &&
           util_is_power_of_two_or_zero(src_width / 24)) {
          LLVMSetAlignment(res, src_width / 24);
      } else {
         LLVMSetAlignment(res, 1);
      }
   }

   assert(src_width <= dst_width);
   if (src_width < dst_width) {
      res = LLVMBuildZExt(gallivm->builder, res, dst_elem_type, "");
      if (vector_justify) {
#ifdef PIPE_ARCH_BIG_ENDIAN
         res = LLVMBuildShl(gallivm->builder, res,
                            LLVMConstInt(dst_elem_type, dst_width - src_width, 0), "");
#endif
      }
   }

   return res;
}


/**
 * Gather one element from scatter positions in memory.
 * Nearly the same as above, however the individual elements
 * may be vectors themselves, and fetches may be float type.
 * Can also do pad vector instead of ZExt.
 *
 * @sa lp_build_gather()
 */
static LLVMValueRef
lp_build_gather_elem_vec(struct gallivm_state *gallivm,
                         unsigned length,
                         unsigned src_width,
                         LLVMTypeRef src_type,
                         struct lp_type dst_type,
                         boolean aligned,
                         LLVMValueRef base_ptr,
                         LLVMValueRef offsets,
                         unsigned i,
                         boolean vector_justify)
{
   LLVMValueRef ptr, res;
   LLVMTypeRef src_ptr_type = LLVMPointerType(src_type, 0);
   assert(LLVMTypeOf(base_ptr) == LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0));

   ptr = lp_build_gather_elem_ptr(gallivm, length, base_ptr, offsets, i);
   ptr = LLVMBuildBitCast(gallivm->builder, ptr, src_ptr_type, "");
   res = LLVMBuildLoad(gallivm->builder, ptr, "");

   /* XXX
    * On some archs we probably really want to avoid having to deal
    * with alignments lower than 4 bytes (if fetch size is a power of
    * two >= 32). On x86 it doesn't matter, however.
    * We should be able to guarantee full alignment for any kind of texture
    * fetch (except ARB_texture_buffer_range, oops), but not vertex fetch
    * (there's PIPE_CAP_VERTEX_BUFFER_OFFSET_4BYTE_ALIGNED_ONLY and friends
    * but I don't think that's quite what we wanted).
    * For ARB_texture_buffer_range, PIPE_CAP_TEXTURE_BUFFER_OFFSET_ALIGNMENT
    * looks like a good fit, but it seems this cap bit (and OpenGL) aren't
    * enforcing what we want (which is what d3d10 does, the offset needs to
    * be aligned to element size, but GL has bytes regardless of element
    * size which would only leave us with minimum alignment restriction of 16
    * which doesn't make much sense if the type isn't 4x32bit). Due to
    * translation of offsets to first_elem in sampler_views it actually seems
    * gallium could not do anything else except 16 no matter what...
    */
   if (!aligned) {
      LLVMSetAlignment(res, 1);
   } else if (!util_is_power_of_two_or_zero(src_width)) {
      /*
       * Full alignment is impossible, assume the caller really meant
       * the individual elements were aligned (e.g. 3x32bit format).
       * And yes the generated code may otherwise crash, llvm will
       * really assume 128bit alignment with a 96bit fetch (I suppose
       * that makes sense as it can just assume the upper 32bit to be
       * whatever).
       * Maybe the caller should be able to explicitly set this, but
       * this should cover all the 3-channel formats.
       */
      if (((src_width / 24) * 24 == src_width) &&
           util_is_power_of_two_or_zero(src_width / 24)) {
          LLVMSetAlignment(res, src_width / 24);
      } else {
         LLVMSetAlignment(res, 1);
      }
   }

   assert(src_width <= dst_type.width * dst_type.length);
   if (src_width < dst_type.width * dst_type.length) {
      if (dst_type.length > 1) {
         res = lp_build_pad_vector(gallivm, res, dst_type.length);
         /*
          * vector_justify hopefully a non-issue since we only deal
          * with src_width >= 32 here?
          */
      } else {
         LLVMTypeRef dst_elem_type = lp_build_vec_type(gallivm, dst_type);

         /*
          * Only valid if src_ptr_type is int type...
          */
         res = LLVMBuildZExt(gallivm->builder, res, dst_elem_type, "");

#ifdef PIPE_ARCH_BIG_ENDIAN
         if (vector_justify) {
         res = LLVMBuildShl(gallivm->builder, res,
                            LLVMConstInt(dst_elem_type,
                                         dst_type.width - src_width, 0), "");
         }
         if (src_width == 48) {
            /* Load 3x16 bit vector.
             * The sequence of loads on big-endian hardware proceeds as follows.
             * 16-bit fields are denoted by X, Y, Z, and 0.  In memory, the sequence
             * of three fields appears in the order X, Y, Z.
             *
             * Load 32-bit word: 0.0.X.Y
             * Load 16-bit halfword: 0.0.0.Z
             * Rotate left: 0.X.Y.0
             * Bitwise OR: 0.X.Y.Z
             *
             * The order in which we need the fields in the result is 0.Z.Y.X,
             * the same as on little-endian; permute 16-bit fields accordingly
             * within 64-bit register:
             */
            LLVMValueRef shuffles[4] = {
               lp_build_const_int32(gallivm, 2),
               lp_build_const_int32(gallivm, 1),
               lp_build_const_int32(gallivm, 0),
               lp_build_const_int32(gallivm, 3),
            };
            res = LLVMBuildBitCast(gallivm->builder, res,
                                   lp_build_vec_type(gallivm, lp_type_uint_vec(16, 4*16)), "");
            res = LLVMBuildShuffleVector(gallivm->builder, res, res, LLVMConstVector(shuffles, 4), "");
            res = LLVMBuildBitCast(gallivm->builder, res, dst_elem_type, "");
         }
#endif
      }
   }
   return res;
}




static LLVMValueRef
lp_build_gather_avx2(struct gallivm_state *gallivm,
                     unsigned length,
                     unsigned src_width,
                     struct lp_type dst_type,
                     LLVMValueRef base_ptr,
                     LLVMValueRef offsets)
{
   LLVMBuilderRef builder = gallivm->builder;
   LLVMTypeRef src_type, src_vec_type;
   LLVMValueRef res;
   struct lp_type res_type = dst_type;
   res_type.length *= length;

   if (dst_type.floating) {
      src_type = src_width == 64 ? LLVMDoubleTypeInContext(gallivm->context) :
                                   LLVMFloatTypeInContext(gallivm->context);
   } else {
      src_type = LLVMIntTypeInContext(gallivm->context, src_width);
   }
   src_vec_type = LLVMVectorType(src_type, length);

   /* XXX should allow hw scaling (can handle i8, i16, i32, i64 for x86) */
   assert(LLVMTypeOf(base_ptr) == LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0));

   if (0) {
      /*
       * XXX: This will cause LLVM pre 3.7 to hang; it works on LLVM 3.8 but
       * will not use the AVX2 gather instrinsics (even with llvm 4.0), at
       * least with Haswell. See
       * http://lists.llvm.org/pipermail/llvm-dev/2016-January/094448.html
       * And the generated code doing the emulation is quite a bit worse
       * than what we get by doing it ourselves too.
       */
      LLVMTypeRef i32_type = LLVMIntTypeInContext(gallivm->context, 32);
      LLVMTypeRef i32_vec_type = LLVMVectorType(i32_type, length);
      LLVMTypeRef i1_type = LLVMIntTypeInContext(gallivm->context, 1);
      LLVMTypeRef i1_vec_type = LLVMVectorType(i1_type, length);
      LLVMTypeRef src_ptr_type = LLVMPointerType(src_type, 0);
      LLVMValueRef src_ptr;

      base_ptr = LLVMBuildBitCast(builder, base_ptr, src_ptr_type, "");

      /* Rescale offsets from bytes to elements */
      LLVMValueRef scale = LLVMConstInt(i32_type, src_width/8, 0);
      scale = lp_build_broadcast(gallivm, i32_vec_type, scale);
      assert(LLVMTypeOf(offsets) == i32_vec_type);
      offsets = LLVMBuildSDiv(builder, offsets, scale, "");

      src_ptr = LLVMBuildGEP(builder, base_ptr, &offsets, 1, "vector-gep");

      char intrinsic[64];
      snprintf(intrinsic, sizeof intrinsic, "llvm.masked.gather.v%u%s%u",
               length, dst_type.floating ? "f" : "i", src_width);
      LLVMValueRef alignment = LLVMConstInt(i32_type, src_width/8, 0);
      LLVMValueRef mask = LLVMConstAllOnes(i1_vec_type);
      LLVMValueRef passthru = LLVMGetUndef(src_vec_type);

      LLVMValueRef args[] = { src_ptr, alignment, mask, passthru };

      res = lp_build_intrinsic(builder, intrinsic, src_vec_type, args, 4, 0);
   } else {
      LLVMTypeRef i8_type = LLVMIntTypeInContext(gallivm->context, 8);
      const char *intrinsic = NULL;
      unsigned l_idx = 0;

      assert(src_width == 32 || src_width == 64);
      if (src_width == 32) {
         assert(length == 4 || length == 8);
      } else {
         assert(length == 2 || length == 4);
      }

      static const char *intrinsics[2][2][2] = {

         {{"llvm.x86.avx2.gather.d.d",
           "llvm.x86.avx2.gather.d.d.256"},
          {"llvm.x86.avx2.gather.d.q",
           "llvm.x86.avx2.gather.d.q.256"}},

         {{"llvm.x86.avx2.gather.d.ps",
           "llvm.x86.avx2.gather.d.ps.256"},
          {"llvm.x86.avx2.gather.d.pd",
           "llvm.x86.avx2.gather.d.pd.256"}},
      };

      if ((src_width == 32 && length == 8) ||
          (src_width == 64 && length == 4)) {
         l_idx = 1;
      }
      intrinsic = intrinsics[dst_type.floating][src_width == 64][l_idx];

      LLVMValueRef passthru = LLVMGetUndef(src_vec_type);
      LLVMValueRef mask = LLVMConstAllOnes(src_vec_type);
      mask = LLVMConstBitCast(mask, src_vec_type);
      LLVMValueRef scale = LLVMConstInt(i8_type, 1, 0);

      LLVMValueRef args[] = { passthru, base_ptr, offsets, mask, scale };

      res = lp_build_intrinsic(builder, intrinsic, src_vec_type, args, 5, 0);
   }
   res = LLVMBuildBitCast(builder, res, lp_build_vec_type(gallivm, res_type), "");

   return res;
}


/**
 * Gather elements from scatter positions in memory into a single vector.
 * Use for fetching texels from a texture.
 * For SSE, typical values are length=4, src_width=32, dst_width=32.
 *
 * When src_width < dst_width, the return value can be justified in
 * one of two ways:
 * "integer justification" is used when the caller treats the destination
 * as a packed integer bitmask, as described by the channels' "shift" and
 * "width" fields;
 * "vector justification" is used when the caller casts the destination
 * to a vector and needs channel X to be in vector element 0.
 *
 * @param length length of the offsets
 * @param src_width src element width in bits
 * @param dst_type result element type (src will be expanded to fit,
 *        but truncation is not allowed)
 *        (this may be a vector, must be pot sized)
 * @param aligned whether the data is guaranteed to be aligned (to src_width)
 * @param base_ptr base pointer, needs to be a i8 pointer type.
 * @param offsets vector with offsets
 * @param vector_justify select vector rather than integer justification
 */
LLVMValueRef
lp_build_gather(struct gallivm_state *gallivm,
                unsigned length,
                unsigned src_width,
                struct lp_type dst_type,
                boolean aligned,
                LLVMValueRef base_ptr,
                LLVMValueRef offsets,
                boolean vector_justify)
{
   LLVMValueRef res;
   boolean need_expansion = src_width < dst_type.width * dst_type.length;
   boolean vec_fetch;
   struct lp_type fetch_type, fetch_dst_type;
   LLVMTypeRef src_type;

   assert(src_width <= dst_type.width * dst_type.length);

   /*
    * This is quite a mess...
    * Figure out if the fetch should be done as:
    * a) scalar or vector
    * b) float or int
    *
    * As an example, for a 96bit fetch expanded into 4x32bit, it is better
    * to use (3x32bit) vector type (then pad the vector). Otherwise, the
    * zext will cause extra instructions.
    * However, the same isn't true for 3x16bit (the codegen for that is
    * completely worthless on x86 simd, and for 3x8bit is is way worse
    * still, don't try that... (To get really good code out of llvm for
    * these cases, the only way is to decompose the fetches manually
    * into 1x32bit/1x16bit, or 1x16/1x8bit respectively, although the latter
    * case requires sse41, otherwise simple scalar zext is way better.
    * But probably not important enough, so don't bother.)
    * Also, we try to honor the floating bit of destination (but isn't
    * possible if caller asks for instance for 2x32bit dst_type with
    * 48bit fetch - the idea would be to use 3x16bit fetch, pad and
    * cast to 2x32f type, so the fetch is always int and on top of that
    * we avoid the vec pad and use scalar zext due the above mentioned
    * issue).
    * Note this is optimized for x86 sse2 and up backend. Could be tweaked
    * for other archs if necessary...
    */
   if (((src_width % 32) == 0) && ((src_width % dst_type.width) == 0) &&
       (dst_type.length > 1)) {
      /* use vector fetch (if dst_type is vector) */
      vec_fetch = TRUE;
      if (dst_type.floating) {
         fetch_type = lp_type_float_vec(dst_type.width, src_width);
      } else {
         fetch_type = lp_type_int_vec(dst_type.width, src_width);
      }
      /* intentionally not using lp_build_vec_type here */
      src_type = LLVMVectorType(lp_build_elem_type(gallivm, fetch_type),
                                fetch_type.length);
      fetch_dst_type = fetch_type;
      fetch_dst_type.length = dst_type.length;
    } else {
      /* use scalar fetch */
      vec_fetch = FALSE;
      if (dst_type.floating && ((src_width == 32) || (src_width == 64))) {
         fetch_type = lp_type_float(src_width);
      } else {
         fetch_type = lp_type_int(src_width);
      }
      src_type = lp_build_vec_type(gallivm, fetch_type);
      fetch_dst_type = fetch_type;
      fetch_dst_type.width = dst_type.width * dst_type.length;
   }

   if (length == 1) {
      /* Scalar */
      res = lp_build_gather_elem_vec(gallivm, length,
                                     src_width, src_type, fetch_dst_type,
                                     aligned, base_ptr, offsets, 0,
                                     vector_justify);
      return LLVMBuildBitCast(gallivm->builder, res,
                              lp_build_vec_type(gallivm, dst_type), "");
      /*
       * Excluding expansion from these paths because if you need it for
       * 32bit/64bit fetches you're doing it wrong (this is gather, not
       * conversion) and it would be awkward for floats.
       */
   } else if (util_cpu_caps.has_avx2 && !need_expansion &&
              src_width == 32 && (length == 4 || length == 8)) {
      return lp_build_gather_avx2(gallivm, length, src_width, dst_type,
                                  base_ptr, offsets);
   /*
    * This looks bad on paper wrt throughtput/latency on Haswell.
    * Even on Broadwell it doesn't look stellar.
    * Albeit no measurements were done (but tested to work).
    * Should definitely enable on Skylake.
    * (In general, should be more of a win if the fetch is 256bit wide -
    * this is true for the 32bit case above too.)
    */
   } else if (0 && util_cpu_caps.has_avx2 && !need_expansion &&
              src_width == 64 && (length == 2 || length == 4)) {
      return lp_build_gather_avx2(gallivm, length, src_width, dst_type,
                                  base_ptr, offsets);
   } else {
      /* Vector */

      LLVMValueRef elems[LP_MAX_VECTOR_WIDTH / 8];
      unsigned i;
      boolean vec_zext = FALSE;
      struct lp_type res_type, gather_res_type;
      LLVMTypeRef res_t, gather_res_t;

      res_type = fetch_dst_type;
      res_type.length *= length;
      gather_res_type = res_type;

      if (src_width == 16 && dst_type.width == 32 && dst_type.length == 1) {
         /*
          * Note that llvm is never able to optimize zext/insert combos
          * directly (i.e. zero the simd reg, then place the elements into
          * the appropriate place directly). (I think this has to do with
          * scalar/vector transition.) And scalar 16->32bit zext simd loads
          * aren't possible (instead loading to scalar reg first).
          * No idea about other archs...
          * We could do this manually, but instead we just use a vector
          * zext, which is simple enough (and, in fact, llvm might optimize
          * this away).
          * (We're not trying that with other bit widths as that might not be
          * easier, in particular with 8 bit values at least with only sse2.)
          */
         assert(vec_fetch == FALSE);
         gather_res_type.width /= 2;
         fetch_dst_type = fetch_type;
         src_type = lp_build_vec_type(gallivm, fetch_type);
         vec_zext = TRUE;
      }
      res_t = lp_build_vec_type(gallivm, res_type);
      gather_res_t = lp_build_vec_type(gallivm, gather_res_type);
      res = LLVMGetUndef(gather_res_t);
      for (i = 0; i < length; ++i) {
         LLVMValueRef index = lp_build_const_int32(gallivm, i);
         elems[i] = lp_build_gather_elem_vec(gallivm, length,
                                             src_width, src_type, fetch_dst_type,
                                             aligned, base_ptr, offsets, i,
                                             vector_justify);
         if (!vec_fetch) {
            res = LLVMBuildInsertElement(gallivm->builder, res, elems[i], index, "");
         }
      }
      if (vec_zext) {
         res = LLVMBuildZExt(gallivm->builder, res, res_t, "");
         if (vector_justify) {
#ifdef PIPE_ARCH_BIG_ENDIAN
            unsigned sv = dst_type.width - src_width;
            res = LLVMBuildShl(gallivm->builder, res,
                               lp_build_const_int_vec(gallivm, res_type, sv), "");
#endif
         }
      }
      if (vec_fetch) {
         /*
          * Do bitcast now otherwise llvm might get some funny ideas wrt
          * float/int types...
          */
         for (i = 0; i < length; i++) {
            elems[i] = LLVMBuildBitCast(gallivm->builder, elems[i],
                                        lp_build_vec_type(gallivm, dst_type), "");
         }
         res = lp_build_concat(gallivm, elems, dst_type, length);
      } else {
         struct lp_type really_final_type = dst_type;
         assert(res_type.length * res_type.width ==
                dst_type.length * dst_type.width * length);
         really_final_type.length *= length;
         res = LLVMBuildBitCast(gallivm->builder, res,
                                lp_build_vec_type(gallivm, really_final_type), "");
      }
   }

   return res;
}

LLVMValueRef
lp_build_gather_values(struct gallivm_state * gallivm,
                       LLVMValueRef * values,
                       unsigned value_count)
{
   LLVMTypeRef vec_type = LLVMVectorType(LLVMTypeOf(values[0]), value_count);
   LLVMBuilderRef builder = gallivm->builder;
   LLVMValueRef vec = LLVMGetUndef(vec_type);
   unsigned i;

   for (i = 0; i < value_count; i++) {
      LLVMValueRef index = lp_build_const_int32(gallivm, i);
      vec = LLVMBuildInsertElement(builder, vec, values[i], index, "");
   }
   return vec;
}