xref: /third_party/mesa3d/src/gallium/auxiliary/gallivm/lp_bld_arit.c

/**************************************************************************
 *
 * Copyright 2009-2010 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 above copyright notice and this permission notice (including the
 * next paragraph) shall be included in all copies or substantial portions
 * of the Software.
 *
 * 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 VMWARE 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.
 *
 **************************************************************************/


/**
 * @file
 * Helper
 *
 * LLVM IR doesn't support all basic arithmetic operations we care about (most
 * notably min/max and saturated operations), and it is often necessary to
 * resort machine-specific intrinsics directly. The functions here hide all
 * these implementation details from the other modules.
 *
 * We also do simple expressions simplification here. Reasons are:
 * - it is very easy given we have all necessary information readily available
 * - LLVM optimization passes fail to simplify several vector expressions
 * - We often know value constraints which the optimization passes have no way
 *   of knowing, such as when source arguments are known to be in [0, 1] range.
 *
 * @author Jose Fonseca <jfonseca@vmware.com>
 */


#include <float.h>

#include <llvm/Config/llvm-config.h>

#include "util/u_memory.h"
#include "util/u_debug.h"
#include "util/u_math.h"
#include "util/u_cpu_detect.h"

#include "lp_bld_type.h"
#include "lp_bld_const.h"
#include "lp_bld_init.h"
#include "lp_bld_intr.h"
#include "lp_bld_logic.h"
#include "lp_bld_pack.h"
#include "lp_bld_debug.h"
#include "lp_bld_bitarit.h"
#include "lp_bld_arit.h"
#include "lp_bld_flow.h"

#if defined(PIPE_ARCH_SSE)
#include <xmmintrin.h>
#endif

#ifndef _MM_DENORMALS_ZERO_MASK
#define _MM_DENORMALS_ZERO_MASK 0x0040
#endif

#ifndef _MM_FLUSH_ZERO_MASK
#define _MM_FLUSH_ZERO_MASK 0x8000
#endif

#define EXP_POLY_DEGREE 5

#define LOG_POLY_DEGREE 4


/**
 * Generate min(a, b)
 * No checks for special case values of a or b = 1 or 0 are done.
 * NaN's are handled according to the behavior specified by the
 * nan_behavior argument.
 */
static LLVMValueRef
lp_build_min_simple(struct lp_build_context *bld,
                    LLVMValueRef a,
                    LLVMValueRef b,
                    enum gallivm_nan_behavior nan_behavior)
{
   const struct lp_type type = bld->type;
   const char *intrinsic = NULL;
   unsigned intr_size = 0;
   LLVMValueRef cond;

   assert(lp_check_value(type, a));
   assert(lp_check_value(type, b));

   /* TODO: optimize the constant case */

   if (type.floating && util_get_cpu_caps()->has_sse) {
      if (type.width == 32) {
         if (type.length == 1) {
            intrinsic = "llvm.x86.sse.min.ss";
            intr_size = 128;
         }
         else if (type.length <= 4 || !util_get_cpu_caps()->has_avx) {
            intrinsic = "llvm.x86.sse.min.ps";
            intr_size = 128;
         }
         else {
            intrinsic = "llvm.x86.avx.min.ps.256";
            intr_size = 256;
         }
      }
      if (type.width == 64 && util_get_cpu_caps()->has_sse2) {
         if (type.length == 1) {
            intrinsic = "llvm.x86.sse2.min.sd";
            intr_size = 128;
         }
         else if (type.length == 2 || !util_get_cpu_caps()->has_avx) {
            intrinsic = "llvm.x86.sse2.min.pd";
            intr_size = 128;
         }
         else {
            intrinsic = "llvm.x86.avx.min.pd.256";
            intr_size = 256;
         }
      }
   }
   else if (type.floating && util_get_cpu_caps()->has_altivec) {
      if (nan_behavior == GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN) {
         debug_printf("%s: altivec doesn't support nan return nan behavior\n",
                      __FUNCTION__);
      }
      if (type.width == 32 && type.length == 4) {
         intrinsic = "llvm.ppc.altivec.vminfp";
         intr_size = 128;
      }
   } else if (util_get_cpu_caps()->has_altivec) {
      intr_size = 128;
      if (type.width == 8) {
         if (!type.sign) {
            intrinsic = "llvm.ppc.altivec.vminub";
         } else {
            intrinsic = "llvm.ppc.altivec.vminsb";
         }
      } else if (type.width == 16) {
         if (!type.sign) {
            intrinsic = "llvm.ppc.altivec.vminuh";
         } else {
            intrinsic = "llvm.ppc.altivec.vminsh";
         }
      } else if (type.width == 32) {
         if (!type.sign) {
            intrinsic = "llvm.ppc.altivec.vminuw";
         } else {
            intrinsic = "llvm.ppc.altivec.vminsw";
         }
      }
   }

   if (intrinsic) {
      /* We need to handle nan's for floating point numbers. If one of the
       * inputs is nan the other should be returned (required by both D3D10+
       * and OpenCL).
       * The sse intrinsics return the second operator in case of nan by
       * default so we need to special code to handle those.
       */
      if (util_get_cpu_caps()->has_sse && type.floating &&
          nan_behavior == GALLIVM_NAN_RETURN_OTHER) {
         LLVMValueRef isnan, min;
         min = lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
                                                   type,
                                                   intr_size, a, b);
         isnan = lp_build_isnan(bld, b);
         return lp_build_select(bld, isnan, a, min);
      } else {
         return lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
                                                    type,
                                                    intr_size, a, b);
      }
   }

   if (type.floating) {
      switch (nan_behavior) {
      case GALLIVM_NAN_RETURN_OTHER: {
         LLVMValueRef isnan = lp_build_isnan(bld, a);
         cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
         cond = LLVMBuildXor(bld->gallivm->builder, cond, isnan, "");
         return lp_build_select(bld, cond, a, b);
      }
         break;
      case GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN:
         cond = lp_build_cmp_ordered(bld, PIPE_FUNC_LESS, a, b);
         return lp_build_select(bld, cond, a, b);
      case GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN:
         cond = lp_build_cmp(bld, PIPE_FUNC_LESS, b, a);
         return lp_build_select(bld, cond, b, a);
      case GALLIVM_NAN_BEHAVIOR_UNDEFINED:
         cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
         return lp_build_select(bld, cond, a, b);
         break;
      default:
         assert(0);
         cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
         return lp_build_select(bld, cond, a, b);
      }
   } else {
      cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
      return lp_build_select(bld, cond, a, b);
   }
}


LLVMValueRef
lp_build_fmuladd(LLVMBuilderRef builder,
                 LLVMValueRef a,
                 LLVMValueRef b,
                 LLVMValueRef c)
{
   LLVMTypeRef type = LLVMTypeOf(a);
   assert(type == LLVMTypeOf(b));
   assert(type == LLVMTypeOf(c));

   char intrinsic[32];
   lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.fmuladd", type);
   LLVMValueRef args[] = { a, b, c };
   return lp_build_intrinsic(builder, intrinsic, type, args, 3, 0);
}


/**
 * Generate max(a, b)
 * No checks for special case values of a or b = 1 or 0 are done.
 * NaN's are handled according to the behavior specified by the
 * nan_behavior argument.
 */
static LLVMValueRef
lp_build_max_simple(struct lp_build_context *bld,
                    LLVMValueRef a,
                    LLVMValueRef b,
                    enum gallivm_nan_behavior nan_behavior)
{
   const struct lp_type type = bld->type;
   const char *intrinsic = NULL;
   unsigned intr_size = 0;
   LLVMValueRef cond;

   assert(lp_check_value(type, a));
   assert(lp_check_value(type, b));

   /* TODO: optimize the constant case */

   if (type.floating && util_get_cpu_caps()->has_sse) {
      if (type.width == 32) {
         if (type.length == 1) {
            intrinsic = "llvm.x86.sse.max.ss";
            intr_size = 128;
         }
         else if (type.length <= 4 || !util_get_cpu_caps()->has_avx) {
            intrinsic = "llvm.x86.sse.max.ps";
            intr_size = 128;
         }
         else {
            intrinsic = "llvm.x86.avx.max.ps.256";
            intr_size = 256;
         }
      }
      if (type.width == 64 && util_get_cpu_caps()->has_sse2) {
         if (type.length == 1) {
            intrinsic = "llvm.x86.sse2.max.sd";
            intr_size = 128;
         }
         else if (type.length == 2 || !util_get_cpu_caps()->has_avx) {
            intrinsic = "llvm.x86.sse2.max.pd";
            intr_size = 128;
         }
         else {
            intrinsic = "llvm.x86.avx.max.pd.256";
            intr_size = 256;
         }
      }
   }
   else if (type.floating && util_get_cpu_caps()->has_altivec) {
      if (nan_behavior == GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN) {
         debug_printf("%s: altivec doesn't support nan return nan behavior\n",
                      __FUNCTION__);
      }
      if (type.width == 32 || type.length == 4) {
         intrinsic = "llvm.ppc.altivec.vmaxfp";
         intr_size = 128;
      }
   } else if (util_get_cpu_caps()->has_altivec) {
     intr_size = 128;
     if (type.width == 8) {
       if (!type.sign) {
         intrinsic = "llvm.ppc.altivec.vmaxub";
       } else {
         intrinsic = "llvm.ppc.altivec.vmaxsb";
       }
     } else if (type.width == 16) {
       if (!type.sign) {
         intrinsic = "llvm.ppc.altivec.vmaxuh";
       } else {
         intrinsic = "llvm.ppc.altivec.vmaxsh";
       }
     } else if (type.width == 32) {
       if (!type.sign) {
         intrinsic = "llvm.ppc.altivec.vmaxuw";
       } else {
         intrinsic = "llvm.ppc.altivec.vmaxsw";
       }
     }
   }

   if (intrinsic) {
      if (util_get_cpu_caps()->has_sse && type.floating &&
          nan_behavior == GALLIVM_NAN_RETURN_OTHER) {
         LLVMValueRef isnan, max;
         max = lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
                                                   type,
                                                   intr_size, a, b);
         isnan = lp_build_isnan(bld, b);
         return lp_build_select(bld, isnan, a, max);
      } else {
         return lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
                                                    type,
                                                    intr_size, a, b);
      }
   }

   if (type.floating) {
      switch (nan_behavior) {
      case GALLIVM_NAN_RETURN_OTHER: {
         LLVMValueRef isnan = lp_build_isnan(bld, a);
         cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
         cond = LLVMBuildXor(bld->gallivm->builder, cond, isnan, "");
         return lp_build_select(bld, cond, a, b);
      }
         break;
      case GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN:
         cond = lp_build_cmp_ordered(bld, PIPE_FUNC_GREATER, a, b);
         return lp_build_select(bld, cond, a, b);
      case GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN:
         cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, b, a);
         return lp_build_select(bld, cond, b, a);
      case GALLIVM_NAN_BEHAVIOR_UNDEFINED:
         cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
         return lp_build_select(bld, cond, a, b);
         break;
      default:
         assert(0);
         cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
         return lp_build_select(bld, cond, a, b);
      }
   } else {
      cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
      return lp_build_select(bld, cond, a, b);
   }
}


/**
 * Generate 1 - a, or ~a depending on bld->type.
 */
LLVMValueRef
lp_build_comp(struct lp_build_context *bld,
              LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, a));

   if (a == bld->one)
      return bld->zero;
   if (a == bld->zero)
      return bld->one;

   if (type.norm && !type.floating && !type.fixed && !type.sign) {
      if (LLVMIsConstant(a))
         return LLVMConstNot(a);
      else
         return LLVMBuildNot(builder, a, "");
   }

   if (type.floating)
      return LLVMBuildFSub(builder, bld->one, a, "");
   else
      return LLVMBuildSub(builder, bld->one, a, "");
}


/**
 * Generate a + b
 */
LLVMValueRef
lp_build_add(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMValueRef res;

   assert(lp_check_value(type, a));
   assert(lp_check_value(type, b));

   if (a == bld->zero)
      return b;
   if (b == bld->zero)
      return a;
   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   if (type.norm) {
      const char *intrinsic = NULL;

      if (!type.sign && (a == bld->one || b == bld->one))
        return bld->one;

      if (!type.floating && !type.fixed) {
         if (LLVM_VERSION_MAJOR >= 8) {
            char intrin[32];
            intrinsic = type.sign ? "llvm.sadd.sat" : "llvm.uadd.sat";
            lp_format_intrinsic(intrin, sizeof intrin, intrinsic, bld->vec_type);
            return lp_build_intrinsic_binary(builder, intrin, bld->vec_type, a, b);
         }
         if (type.width * type.length == 128) {
            if (util_get_cpu_caps()->has_sse2) {
               if (type.width == 8)
                 intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
               if (type.width == 16)
                 intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
            } else if (util_get_cpu_caps()->has_altivec) {
               if (type.width == 8)
                  intrinsic = type.sign ? "llvm.ppc.altivec.vaddsbs" : "llvm.ppc.altivec.vaddubs";
               if (type.width == 16)
                  intrinsic = type.sign ? "llvm.ppc.altivec.vaddshs" : "llvm.ppc.altivec.vadduhs";
            }
         }
         if (type.width * type.length == 256) {
            if (util_get_cpu_caps()->has_avx2) {
               if (type.width == 8)
                  intrinsic = type.sign ? "llvm.x86.avx2.padds.b" : "llvm.x86.avx2.paddus.b";
               if (type.width == 16)
                  intrinsic = type.sign ? "llvm.x86.avx2.padds.w" : "llvm.x86.avx2.paddus.w";
            }
         }
      }

      if (intrinsic)
         return lp_build_intrinsic_binary(builder, intrinsic,
                       lp_build_vec_type(bld->gallivm, bld->type), a, b);
   }

   if (type.norm && !type.floating && !type.fixed) {
      if (type.sign) {
         uint64_t sign = (uint64_t)1 << (type.width - 1);
         LLVMValueRef max_val = lp_build_const_int_vec(bld->gallivm, type, sign - 1);
         LLVMValueRef min_val = lp_build_const_int_vec(bld->gallivm, type, sign);
         /* a_clamp_max is the maximum a for positive b,
            a_clamp_min is the minimum a for negative b. */
         LLVMValueRef a_clamp_max =
            lp_build_min_simple(bld, a, LLVMBuildSub(builder, max_val, b, ""),
                                GALLIVM_NAN_BEHAVIOR_UNDEFINED);
         LLVMValueRef a_clamp_min =
            lp_build_max_simple(bld, a, LLVMBuildSub(builder, min_val, b, ""),
                                GALLIVM_NAN_BEHAVIOR_UNDEFINED);
         a = lp_build_select(bld, lp_build_cmp(bld, PIPE_FUNC_GREATER, b,
                                     bld->zero), a_clamp_max, a_clamp_min);
      }
   }

   if (type.floating)
      res = LLVMBuildFAdd(builder, a, b, "");
   else
      res = LLVMBuildAdd(builder, a, b, "");

   /* clamp to ceiling of 1.0 */
   if (bld->type.norm && (bld->type.floating || bld->type.fixed))
      res = lp_build_min_simple(bld, res, bld->one, GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN);

   if (type.norm && !type.floating && !type.fixed) {
      if (!type.sign) {
         /*
          * newer llvm versions no longer support the intrinsics, but recognize
          * the pattern. Since auto-upgrade of intrinsics doesn't work for jit
          * code, it is important we match the pattern llvm uses (and pray llvm
          * doesn't change it - and hope they decide on the same pattern for
          * all backends supporting it...).
          * NOTE: cmp/select does sext/trunc of the mask. Does not seem to
          * interfere with llvm's ability to recognize the pattern but seems
          * a bit brittle.
          * NOTE: llvm 9+ always uses (non arch specific) intrinsic.
          */
         LLVMValueRef overflowed = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, res);
         res = lp_build_select(bld, overflowed,
                               LLVMConstAllOnes(bld->int_vec_type), res);
      }
   }

   /* XXX clamp to floor of -1 or 0??? */

   return res;
}


/** Return the scalar sum of the elements of a.
 * Should avoid this operation whenever possible.
 */
LLVMValueRef
lp_build_horizontal_add(struct lp_build_context *bld,
                        LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMValueRef index, res;
   unsigned i, length;
   LLVMValueRef shuffles1[LP_MAX_VECTOR_LENGTH / 2];
   LLVMValueRef shuffles2[LP_MAX_VECTOR_LENGTH / 2];
   LLVMValueRef vecres, elem2;

   assert(lp_check_value(type, a));

   if (type.length == 1) {
      return a;
   }

   assert(!bld->type.norm);

   /*
    * for byte vectors can do much better with psadbw.
    * Using repeated shuffle/adds here. Note with multiple vectors
    * this can be done more efficiently as outlined in the intel
    * optimization manual.
    * Note: could cause data rearrangement if used with smaller element
    * sizes.
    */

   vecres = a;
   length = type.length / 2;
   while (length > 1) {
      LLVMValueRef vec1, vec2;
      for (i = 0; i < length; i++) {
         shuffles1[i] = lp_build_const_int32(bld->gallivm, i);
         shuffles2[i] = lp_build_const_int32(bld->gallivm, i + length);
      }
      vec1 = LLVMBuildShuffleVector(builder, vecres, vecres,
                                    LLVMConstVector(shuffles1, length), "");
      vec2 = LLVMBuildShuffleVector(builder, vecres, vecres,
                                    LLVMConstVector(shuffles2, length), "");
      if (type.floating) {
         vecres = LLVMBuildFAdd(builder, vec1, vec2, "");
      }
      else {
         vecres = LLVMBuildAdd(builder, vec1, vec2, "");
      }
      length = length >> 1;
   }

   /* always have vector of size 2 here */
   assert(length == 1);

   index = lp_build_const_int32(bld->gallivm, 0);
   res = LLVMBuildExtractElement(builder, vecres, index, "");
   index = lp_build_const_int32(bld->gallivm, 1);
   elem2 = LLVMBuildExtractElement(builder, vecres, index, "");

   if (type.floating)
      res = LLVMBuildFAdd(builder, res, elem2, "");
    else
      res = LLVMBuildAdd(builder, res, elem2, "");

   return res;
}


/**
 * Return the horizontal sums of 4 float vectors as a float4 vector.
 * This uses the technique as outlined in Intel Optimization Manual.
 */
static LLVMValueRef
lp_build_horizontal_add4x4f(struct lp_build_context *bld,
                            LLVMValueRef src[4])
{
   struct gallivm_state *gallivm = bld->gallivm;
   LLVMBuilderRef builder = gallivm->builder;
   LLVMValueRef shuffles[4];
   LLVMValueRef tmp[4];
   LLVMValueRef sumtmp[2], shuftmp[2];

   /* lower half of regs */
   shuffles[0] = lp_build_const_int32(gallivm, 0);
   shuffles[1] = lp_build_const_int32(gallivm, 1);
   shuffles[2] = lp_build_const_int32(gallivm, 4);
   shuffles[3] = lp_build_const_int32(gallivm, 5);
   tmp[0] = LLVMBuildShuffleVector(builder, src[0], src[1],
                                   LLVMConstVector(shuffles, 4), "");
   tmp[2] = LLVMBuildShuffleVector(builder, src[2], src[3],
                                   LLVMConstVector(shuffles, 4), "");

   /* upper half of regs */
   shuffles[0] = lp_build_const_int32(gallivm, 2);
   shuffles[1] = lp_build_const_int32(gallivm, 3);
   shuffles[2] = lp_build_const_int32(gallivm, 6);
   shuffles[3] = lp_build_const_int32(gallivm, 7);
   tmp[1] = LLVMBuildShuffleVector(builder, src[0], src[1],
                                   LLVMConstVector(shuffles, 4), "");
   tmp[3] = LLVMBuildShuffleVector(builder, src[2], src[3],
                                   LLVMConstVector(shuffles, 4), "");

   sumtmp[0] = LLVMBuildFAdd(builder, tmp[0], tmp[1], "");
   sumtmp[1] = LLVMBuildFAdd(builder, tmp[2], tmp[3], "");

   shuffles[0] = lp_build_const_int32(gallivm, 0);
   shuffles[1] = lp_build_const_int32(gallivm, 2);
   shuffles[2] = lp_build_const_int32(gallivm, 4);
   shuffles[3] = lp_build_const_int32(gallivm, 6);
   shuftmp[0] = LLVMBuildShuffleVector(builder, sumtmp[0], sumtmp[1],
                                       LLVMConstVector(shuffles, 4), "");

   shuffles[0] = lp_build_const_int32(gallivm, 1);
   shuffles[1] = lp_build_const_int32(gallivm, 3);
   shuffles[2] = lp_build_const_int32(gallivm, 5);
   shuffles[3] = lp_build_const_int32(gallivm, 7);
   shuftmp[1] = LLVMBuildShuffleVector(builder, sumtmp[0], sumtmp[1],
                                       LLVMConstVector(shuffles, 4), "");

   return LLVMBuildFAdd(builder, shuftmp[0], shuftmp[1], "");
}


/*
 * partially horizontally add 2-4 float vectors with length nx4,
 * i.e. only four adjacent values in each vector will be added,
 * assuming values are really grouped in 4 which also determines
 * output order.
 *
 * Return a vector of the same length as the initial vectors,
 * with the excess elements (if any) being undefined.
 * The element order is independent of number of input vectors.
 * For 3 vectors x0x1x2x3x4x5x6x7, y0y1y2y3y4y5y6y7, z0z1z2z3z4z5z6z7
 * the output order thus will be
 * sumx0-x3,sumy0-y3,sumz0-z3,undef,sumx4-x7,sumy4-y7,sumz4z7,undef
 */
LLVMValueRef
lp_build_hadd_partial4(struct lp_build_context *bld,
                       LLVMValueRef vectors[],
                       unsigned num_vecs)
{
   struct gallivm_state *gallivm = bld->gallivm;
   LLVMBuilderRef builder = gallivm->builder;
   LLVMValueRef ret_vec;
   LLVMValueRef tmp[4];
   const char *intrinsic = NULL;

   assert(num_vecs >= 2 && num_vecs <= 4);
   assert(bld->type.floating);

   /* only use this with at least 2 vectors, as it is sort of expensive
    * (depending on cpu) and we always need two horizontal adds anyway,
    * so a shuffle/add approach might be better.
    */

   tmp[0] = vectors[0];
   tmp[1] = vectors[1];

   tmp[2] = num_vecs > 2 ? vectors[2] : vectors[0];
   tmp[3] = num_vecs > 3 ? vectors[3] : vectors[0];

   if (util_get_cpu_caps()->has_sse3 && bld->type.width == 32 &&
       bld->type.length == 4) {
      intrinsic = "llvm.x86.sse3.hadd.ps";
   }
   else if (util_get_cpu_caps()->has_avx && bld->type.width == 32 &&
            bld->type.length == 8) {
      intrinsic = "llvm.x86.avx.hadd.ps.256";
   }
   if (intrinsic) {
      tmp[0] = lp_build_intrinsic_binary(builder, intrinsic,
                                       lp_build_vec_type(gallivm, bld->type),
                                       tmp[0], tmp[1]);
      if (num_vecs > 2) {
         tmp[1] = lp_build_intrinsic_binary(builder, intrinsic,
                                          lp_build_vec_type(gallivm, bld->type),
                                          tmp[2], tmp[3]);
      }
      else {
         tmp[1] = tmp[0];
      }
      return lp_build_intrinsic_binary(builder, intrinsic,
                                       lp_build_vec_type(gallivm, bld->type),
                                       tmp[0], tmp[1]);
   }

   if (bld->type.length == 4) {
      ret_vec = lp_build_horizontal_add4x4f(bld, tmp);
   }
   else {
      LLVMValueRef partres[LP_MAX_VECTOR_LENGTH/4];
      unsigned j;
      unsigned num_iter = bld->type.length / 4;
      struct lp_type parttype = bld->type;
      parttype.length = 4;
      for (j = 0; j < num_iter; j++) {
         LLVMValueRef partsrc[4];
         unsigned i;
         for (i = 0; i < 4; i++) {
            partsrc[i] = lp_build_extract_range(gallivm, tmp[i], j*4, 4);
         }
         partres[j] = lp_build_horizontal_add4x4f(bld, partsrc);
      }
      ret_vec = lp_build_concat(gallivm, partres, parttype, num_iter);
   }
   return ret_vec;
}


/**
 * Generate a - b
 */
LLVMValueRef
lp_build_sub(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMValueRef res;

   assert(lp_check_value(type, a));
   assert(lp_check_value(type, b));

   if (b == bld->zero)
      return a;
   if (a == bld->undef || b == bld->undef)
      return bld->undef;
   if (a == b)
      return bld->zero;

   if (type.norm) {
      const char *intrinsic = NULL;

      if (!type.sign && b == bld->one)
        return bld->zero;

      if (!type.floating && !type.fixed) {
         if (LLVM_VERSION_MAJOR >= 8) {
            char intrin[32];
            intrinsic = type.sign ? "llvm.ssub.sat" : "llvm.usub.sat";
            lp_format_intrinsic(intrin, sizeof intrin, intrinsic, bld->vec_type);
            return lp_build_intrinsic_binary(builder, intrin, bld->vec_type, a, b);
         }
         if (type.width * type.length == 128) {
            if (util_get_cpu_caps()->has_sse2) {
               if (type.width == 8)
                  intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
               if (type.width == 16)
                  intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
            } else if (util_get_cpu_caps()->has_altivec) {
               if (type.width == 8)
                  intrinsic = type.sign ? "llvm.ppc.altivec.vsubsbs" : "llvm.ppc.altivec.vsububs";
               if (type.width == 16)
                  intrinsic = type.sign ? "llvm.ppc.altivec.vsubshs" : "llvm.ppc.altivec.vsubuhs";
            }
         }
         if (type.width * type.length == 256) {
            if (util_get_cpu_caps()->has_avx2) {
               if (type.width == 8)
                  intrinsic = type.sign ? "llvm.x86.avx2.psubs.b" : "llvm.x86.avx2.psubus.b";
               if (type.width == 16)
                  intrinsic = type.sign ? "llvm.x86.avx2.psubs.w" : "llvm.x86.avx2.psubus.w";
            }
         }
      }

      if (intrinsic)
         return lp_build_intrinsic_binary(builder, intrinsic,
                      lp_build_vec_type(bld->gallivm, bld->type), a, b);
   }

   if (type.norm && !type.floating && !type.fixed) {
      if (type.sign) {
         uint64_t sign = (uint64_t)1 << (type.width - 1);
         LLVMValueRef max_val =
            lp_build_const_int_vec(bld->gallivm, type, sign - 1);
         LLVMValueRef min_val =
            lp_build_const_int_vec(bld->gallivm, type, sign);
         /* a_clamp_max is the maximum a for negative b,
            a_clamp_min is the minimum a for positive b. */
         LLVMValueRef a_clamp_max =
            lp_build_min_simple(bld, a, LLVMBuildAdd(builder, max_val, b, ""),
                                GALLIVM_NAN_BEHAVIOR_UNDEFINED);
         LLVMValueRef a_clamp_min =
            lp_build_max_simple(bld, a, LLVMBuildAdd(builder, min_val, b, ""),
                                GALLIVM_NAN_BEHAVIOR_UNDEFINED);
         a = lp_build_select(bld, lp_build_cmp(bld, PIPE_FUNC_GREATER, b,
                                               bld->zero),
                             a_clamp_min, a_clamp_max);
      } else {
         /*
          * This must match llvm pattern for saturated unsigned sub.
          * (lp_build_max_simple actually does the job with its current
          * definition but do it explicitly here.)
          * NOTE: cmp/select does sext/trunc of the mask. Does not seem to
          * interfere with llvm's ability to recognize the pattern but seems
          * a bit brittle.
          * NOTE: llvm 9+ always uses (non arch specific) intrinsic.
          */
         LLVMValueRef no_ov = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
         a = lp_build_select(bld, no_ov, a, b);
      }
   }

   if (type.floating)
      res = LLVMBuildFSub(builder, a, b, "");
   else
      res = LLVMBuildSub(builder, a, b, "");

   if (bld->type.norm && (bld->type.floating || bld->type.fixed))
      res = lp_build_max_simple(bld, res, bld->zero, GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN);

   return res;
}


/**
 * Normalized multiplication.
 *
 * There are several approaches for (using 8-bit normalized multiplication as
 * an example):
 *
 * - alpha plus one
 *
 *     makes the following approximation to the division (Sree)
 *
 *       a*b/255 ~= (a*(b + 1)) >> 256
 *
 *     which is the fastest method that satisfies the following OpenGL
 *     criteria of
 *
 *       0*0 = 0 and 255*255 = 255
 *
 * - geometric series
 *
 *     takes the geometric series approximation to the division
 *
 *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 *
 *     in this case just the first two terms to fit in 16bit arithmetic
 *
 *       t/255 ~= (t + (t >> 8)) >> 8
 *
 *     note that just by itself it doesn't satisfies the OpenGL criteria,
 *     as 255*255 = 254, so the special case b = 255 must be accounted or
 *     roundoff must be used.
 *
 * - geometric series plus rounding
 *
 *     when using a geometric series division instead of truncating the result
 *     use roundoff in the approximation (Jim Blinn)
 *
 *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 *
 *     achieving the exact results.
 *
 *
 *
 * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 * @sa Michael Herf, The "double blend trick", May 2000,
 *     http://www.stereopsis.com/doubleblend.html
 */
LLVMValueRef
lp_build_mul_norm(struct gallivm_state *gallivm,
                  struct lp_type wide_type,
                  LLVMValueRef a, LLVMValueRef b)
{
   LLVMBuilderRef builder = gallivm->builder;
   struct lp_build_context bld;
   unsigned n;
   LLVMValueRef half;
   LLVMValueRef ab;

   assert(!wide_type.floating);
   assert(lp_check_value(wide_type, a));
   assert(lp_check_value(wide_type, b));

   lp_build_context_init(&bld, gallivm, wide_type);

   n = wide_type.width / 2;
   if (wide_type.sign) {
      --n;
   }

   /*
    * TODO: for 16bits normalized SSE2 vectors we could consider using PMULHUW
    * http://ssp.impulsetrain.com/2011/07/03/multiplying-normalized-16-bit-numbers-with-sse2/
    */

   /*
    * a*b / (2**n - 1) ~= (a*b + (a*b >> n) + half) >> n
    */

   ab = LLVMBuildMul(builder, a, b, "");
   ab = LLVMBuildAdd(builder, ab, lp_build_shr_imm(&bld, ab, n), "");

   /*
    * half = sgn(ab) * 0.5 * (2 ** n) = sgn(ab) * (1 << (n - 1))
    */

   half = lp_build_const_int_vec(gallivm, wide_type, 1LL << (n - 1));
   if (wide_type.sign) {
      LLVMValueRef minus_half = LLVMBuildNeg(builder, half, "");
      LLVMValueRef sign = lp_build_shr_imm(&bld, ab, wide_type.width - 1);
      half = lp_build_select(&bld, sign, minus_half, half);
   }
   ab = LLVMBuildAdd(builder, ab, half, "");

   /* Final division */
   ab = lp_build_shr_imm(&bld, ab, n);

   return ab;
}


/**
 * Generate a * b
 */
LLVMValueRef
lp_build_mul(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, a));
   assert(lp_check_value(type, b));

   if (a == bld->zero)
      return bld->zero;
   if (a == bld->one)
      return b;
   if (b == bld->zero)
      return bld->zero;
   if (b == bld->one)
      return a;
   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   if (!type.floating && !type.fixed && type.norm) {
      struct lp_type wide_type = lp_wider_type(type);
      LLVMValueRef al, ah, bl, bh, abl, abh, ab;

      lp_build_unpack2_native(bld->gallivm, type, wide_type, a, &al, &ah);
      lp_build_unpack2_native(bld->gallivm, type, wide_type, b, &bl, &bh);

      /* PMULLW, PSRLW, PADDW */
      abl = lp_build_mul_norm(bld->gallivm, wide_type, al, bl);
      abh = lp_build_mul_norm(bld->gallivm, wide_type, ah, bh);

      ab = lp_build_pack2_native(bld->gallivm, wide_type, type, abl, abh);

      return ab;
   }

   LLVMValueRef shift = type.fixed
      ? lp_build_const_int_vec(bld->gallivm, type, type.width/2) : NULL;

   LLVMValueRef res;
   if (type.floating)
      res = LLVMBuildFMul(builder, a, b, "");
   else
      res = LLVMBuildMul(builder, a, b, "");
   if (shift) {
      if (type.sign)
         res = LLVMBuildAShr(builder, res, shift, "");
      else
         res = LLVMBuildLShr(builder, res, shift, "");
   }

   return res;
}


/*
 * Widening mul, valid for 32x32 bit -> 64bit only.
 * Result is low 32bits, high bits returned in res_hi.
 *
 * Emits code that is meant to be compiled for the host CPU.
 */
LLVMValueRef
lp_build_mul_32_lohi_cpu(struct lp_build_context *bld,
                         LLVMValueRef a,
                         LLVMValueRef b,
                         LLVMValueRef *res_hi)
{
   struct gallivm_state *gallivm = bld->gallivm;
   LLVMBuilderRef builder = gallivm->builder;

   assert(bld->type.width == 32);
   assert(bld->type.floating == 0);
   assert(bld->type.fixed == 0);
   assert(bld->type.norm == 0);

   /*
    * XXX: for some reason, with zext/zext/mul/trunc the code llvm produces
    * for x86 simd is atrocious (even if the high bits weren't required),
    * trying to handle real 64bit inputs (which of course can't happen due
    * to using 64bit umul with 32bit numbers zero-extended to 64bit, but
    * apparently llvm does not recognize this widening mul). This includes 6
    * (instead of 2) pmuludq plus extra adds and shifts
    * The same story applies to signed mul, albeit fixing this requires sse41.
    * https://llvm.org/bugs/show_bug.cgi?id=30845
    * So, whip up our own code, albeit only for length 4 and 8 (which
    * should be good enough)...
    * FIXME: For llvm >= 7.0 we should match the autoupgrade pattern
    * (bitcast/and/mul/shuffle for unsigned, bitcast/shl/ashr/mul/shuffle
    * for signed), which the fallback code does not, without this llvm
    * will likely still produce atrocious code.
    */
   if (LLVM_VERSION_MAJOR < 7 &&
       (bld->type.length == 4 || bld->type.length == 8) &&
       ((util_get_cpu_caps()->has_sse2 && (bld->type.sign == 0)) ||
        util_get_cpu_caps()->has_sse4_1)) {
      const char *intrinsic = NULL;
      LLVMValueRef aeven, aodd, beven, bodd, muleven, mulodd;
      LLVMValueRef shuf[LP_MAX_VECTOR_WIDTH / 32], shuf_vec;
      struct lp_type type_wide = lp_wider_type(bld->type);
      LLVMTypeRef wider_type = lp_build_vec_type(gallivm, type_wide);
      unsigned i;
      for (i = 0; i < bld->type.length; i += 2) {
         shuf[i] = lp_build_const_int32(gallivm, i+1);
         shuf[i+1] = LLVMGetUndef(LLVMInt32TypeInContext(gallivm->context));
      }
      shuf_vec = LLVMConstVector(shuf, bld->type.length);
      aeven = a;
      beven = b;
      aodd = LLVMBuildShuffleVector(builder, aeven, bld->undef, shuf_vec, "");
      bodd = LLVMBuildShuffleVector(builder, beven, bld->undef, shuf_vec, "");

      if (util_get_cpu_caps()->has_avx2 && bld->type.length == 8) {
         if (bld->type.sign) {
            intrinsic = "llvm.x86.avx2.pmul.dq";
         } else {
            intrinsic = "llvm.x86.avx2.pmulu.dq";
         }
         muleven = lp_build_intrinsic_binary(builder, intrinsic,
                                             wider_type, aeven, beven);
         mulodd = lp_build_intrinsic_binary(builder, intrinsic,
                                            wider_type, aodd, bodd);
      }
      else {
         /* for consistent naming look elsewhere... */
         if (bld->type.sign) {
            intrinsic = "llvm.x86.sse41.pmuldq";
         } else {
            intrinsic = "llvm.x86.sse2.pmulu.dq";
         }
         /*
          * XXX If we only have AVX but not AVX2 this is a pain.
          * lp_build_intrinsic_binary_anylength() can't handle it
          * (due to src and dst type not being identical).
          */
         if (bld->type.length == 8) {
            LLVMValueRef aevenlo, aevenhi, bevenlo, bevenhi;
            LLVMValueRef aoddlo, aoddhi, boddlo, boddhi;
            LLVMValueRef muleven2[2], mulodd2[2];
            struct lp_type type_wide_half = type_wide;
            LLVMTypeRef wtype_half;
            type_wide_half.length = 2;
            wtype_half = lp_build_vec_type(gallivm, type_wide_half);
            aevenlo = lp_build_extract_range(gallivm, aeven, 0, 4);
            aevenhi = lp_build_extract_range(gallivm, aeven, 4, 4);
            bevenlo = lp_build_extract_range(gallivm, beven, 0, 4);
            bevenhi = lp_build_extract_range(gallivm, beven, 4, 4);
            aoddlo = lp_build_extract_range(gallivm, aodd, 0, 4);
            aoddhi = lp_build_extract_range(gallivm, aodd, 4, 4);
            boddlo = lp_build_extract_range(gallivm, bodd, 0, 4);
            boddhi = lp_build_extract_range(gallivm, bodd, 4, 4);
            muleven2[0] = lp_build_intrinsic_binary(builder, intrinsic,
                                                    wtype_half, aevenlo, bevenlo);
            mulodd2[0] = lp_build_intrinsic_binary(builder, intrinsic,
                                                   wtype_half, aoddlo, boddlo);
            muleven2[1] = lp_build_intrinsic_binary(builder, intrinsic,
                                                    wtype_half, aevenhi, bevenhi);
            mulodd2[1] = lp_build_intrinsic_binary(builder, intrinsic,
                                                   wtype_half, aoddhi, boddhi);
            muleven = lp_build_concat(gallivm, muleven2, type_wide_half, 2);
            mulodd = lp_build_concat(gallivm, mulodd2, type_wide_half, 2);

         }
         else {
            muleven = lp_build_intrinsic_binary(builder, intrinsic,
                                                wider_type, aeven, beven);
            mulodd = lp_build_intrinsic_binary(builder, intrinsic,
                                               wider_type, aodd, bodd);
         }
      }
      muleven = LLVMBuildBitCast(builder, muleven, bld->vec_type, "");
      mulodd = LLVMBuildBitCast(builder, mulodd, bld->vec_type, "");

      for (i = 0; i < bld->type.length; i += 2) {
         shuf[i] = lp_build_const_int32(gallivm, i + 1);
         shuf[i+1] = lp_build_const_int32(gallivm, i + 1 + bld->type.length);
      }
      shuf_vec = LLVMConstVector(shuf, bld->type.length);
      *res_hi = LLVMBuildShuffleVector(builder, muleven, mulodd, shuf_vec, "");

      for (i = 0; i < bld->type.length; i += 2) {
         shuf[i] = lp_build_const_int32(gallivm, i);
         shuf[i+1] = lp_build_const_int32(gallivm, i + bld->type.length);
      }
      shuf_vec = LLVMConstVector(shuf, bld->type.length);
      return LLVMBuildShuffleVector(builder, muleven, mulodd, shuf_vec, "");
   }
   else {
      return lp_build_mul_32_lohi(bld, a, b, res_hi);
   }
}


/*
 * Widening mul, valid for <= 32 (8, 16, 32) -> 64
 * Result is low N bits, high bits returned in res_hi.
 *
 * Emits generic code.
 */
LLVMValueRef
lp_build_mul_32_lohi(struct lp_build_context *bld,
                     LLVMValueRef a,
                     LLVMValueRef b,
                     LLVMValueRef *res_hi)
{
   struct gallivm_state *gallivm = bld->gallivm;
   LLVMBuilderRef builder = gallivm->builder;
   LLVMValueRef tmp, shift, res_lo;
   struct lp_type type_tmp;
   LLVMTypeRef wide_type, narrow_type;

   type_tmp = bld->type;
   narrow_type = lp_build_vec_type(gallivm, type_tmp);
   if (bld->type.width < 32)
      type_tmp.width = 32;
   else
      type_tmp.width *= 2;
   wide_type = lp_build_vec_type(gallivm, type_tmp);
   shift = lp_build_const_vec(gallivm, type_tmp, bld->type.width);

   if (bld->type.sign) {
      a = LLVMBuildSExt(builder, a, wide_type, "");
      b = LLVMBuildSExt(builder, b, wide_type, "");
   } else {
      a = LLVMBuildZExt(builder, a, wide_type, "");
      b = LLVMBuildZExt(builder, b, wide_type, "");
   }
   tmp = LLVMBuildMul(builder, a, b, "");

   res_lo = LLVMBuildTrunc(builder, tmp, narrow_type, "");

   /* Since we truncate anyway, LShr and AShr are equivalent. */
   tmp = LLVMBuildLShr(builder, tmp, shift, "");
   *res_hi = LLVMBuildTrunc(builder, tmp, narrow_type, "");

   return res_lo;
}


/* a * b + c */
LLVMValueRef
lp_build_mad(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b,
             LLVMValueRef c)
{
   const struct lp_type type = bld->type;
   if (type.floating) {
      return lp_build_fmuladd(bld->gallivm->builder, a, b, c);
   } else {
      return lp_build_add(bld, lp_build_mul(bld, a, b), c);
   }
}


/**
 * Small vector x scale multiplication optimization.
 */
LLVMValueRef
lp_build_mul_imm(struct lp_build_context *bld,
                 LLVMValueRef a,
                 int b)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef factor;

   assert(lp_check_value(bld->type, a));

   if (b == 0)
      return bld->zero;

   if (b == 1)
      return a;

   if (b == -1)
      return lp_build_negate(bld, a);

   if (b == 2 && bld->type.floating)
      return lp_build_add(bld, a, a);

   if (util_is_power_of_two_or_zero(b)) {
      unsigned shift = ffs(b) - 1;

      if (bld->type.floating) {
#if 0
         /*
          * Power of two multiplication by directly manipulating the exponent.
          *
          * XXX: This might not be always faster, it will introduce a small
          * error for multiplication by zero, and it will produce wrong results
          * for Inf and NaN.
          */
         unsigned mantissa = lp_mantissa(bld->type);
         factor = lp_build_const_int_vec(bld->gallivm, bld->type, (unsigned long long)shift << mantissa);
         a = LLVMBuildBitCast(builder, a, lp_build_int_vec_type(bld->type), "");
         a = LLVMBuildAdd(builder, a, factor, "");
         a = LLVMBuildBitCast(builder, a, lp_build_vec_type(bld->gallivm, bld->type), "");
         return a;
#endif
      }
      else {
         factor = lp_build_const_vec(bld->gallivm, bld->type, shift);
         return LLVMBuildShl(builder, a, factor, "");
      }
   }

   factor = lp_build_const_vec(bld->gallivm, bld->type, (double)b);
   return lp_build_mul(bld, a, factor);
}


/**
 * Generate a / b
 */
LLVMValueRef
lp_build_div(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, a));
   assert(lp_check_value(type, b));

   if (a == bld->zero)
      return bld->zero;
   if (a == bld->one && type.floating)
      return lp_build_rcp(bld, b);
   if (b == bld->zero)
      return bld->undef;
   if (b == bld->one)
      return a;
   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   /* fast rcp is disabled (just uses div), so makes no sense to try that */
   if (FALSE &&
      ((util_get_cpu_caps()->has_sse && type.width == 32 && type.length == 4) ||
       (util_get_cpu_caps()->has_avx && type.width == 32 && type.length == 8)) &&
      type.floating)
      return lp_build_mul(bld, a, lp_build_rcp(bld, b));

   if (type.floating)
      return LLVMBuildFDiv(builder, a, b, "");
   else if (type.sign)
      return LLVMBuildSDiv(builder, a, b, "");
   else
      return LLVMBuildUDiv(builder, a, b, "");
}


/**
 * Linear interpolation helper.
 *
 * @param normalized whether we are interpolating normalized values,
 *        encoded in normalized integers, twice as wide.
 *
 * @sa http://www.stereopsis.com/doubleblend.html
 */
static inline LLVMValueRef
lp_build_lerp_simple(struct lp_build_context *bld,
                     LLVMValueRef x,
                     LLVMValueRef v0,
                     LLVMValueRef v1,
                     unsigned flags)
{
   unsigned half_width = bld->type.width/2;
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef delta;
   LLVMValueRef res;

   assert(lp_check_value(bld->type, x));
   assert(lp_check_value(bld->type, v0));
   assert(lp_check_value(bld->type, v1));

   delta = lp_build_sub(bld, v1, v0);

   if (bld->type.floating) {
      assert(flags == 0);
      return lp_build_mad(bld, x, delta, v0);
   }

   if (flags & LP_BLD_LERP_WIDE_NORMALIZED) {
      if (!bld->type.sign) {
         if (!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS)) {
            /*
             * Scale x from [0, 2**n - 1] to [0, 2**n] by adding the
             * most-significant-bit to the lowest-significant-bit, so that
             * later we can just divide by 2**n instead of 2**n - 1.
             */

            x = lp_build_add(bld, x, lp_build_shr_imm(bld, x, half_width - 1));
         }

         /* (x * delta) >> n */
         /*
          * For this multiply, higher internal precision is required to pass
          * CTS, the most efficient path to that is pmulhrsw on ssse3 and
          * above.  This could be opencoded on other arches if conformance was
          * required.
          */
         if (bld->type.width == 16 && bld->type.length == 8 && util_get_cpu_caps()->has_ssse3) {
            res = lp_build_intrinsic_binary(builder, "llvm.x86.ssse3.pmul.hr.sw.128", bld->vec_type, x, lp_build_shl_imm(bld, delta, 7));
            res = lp_build_and(bld, res, lp_build_const_int_vec(bld->gallivm, bld->type, 0xff));
         } else if (bld->type.width == 16 && bld->type.length == 16 && util_get_cpu_caps()->has_avx2) {
            res = lp_build_intrinsic_binary(builder, "llvm.x86.avx2.pmul.hr.sw", bld->vec_type, x, lp_build_shl_imm(bld, delta, 7));
            res = lp_build_and(bld, res, lp_build_const_int_vec(bld->gallivm, bld->type, 0xff));
         } else {
            res = lp_build_mul(bld, x, delta);
            res = lp_build_shr_imm(bld, res, half_width);
         }
      } else {
         /*
          * The rescaling trick above doesn't work for signed numbers, so
          * use the 2**n - 1 divison approximation in lp_build_mul_norm
          * instead.
          */
         assert(!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS));
         res = lp_build_mul_norm(bld->gallivm, bld->type, x, delta);
      }
   } else {
      assert(!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS));
      res = lp_build_mul(bld, x, delta);
   }

   if ((flags & LP_BLD_LERP_WIDE_NORMALIZED) && !bld->type.sign) {
      /*
       * At this point both res and v0 only use the lower half of the bits,
       * the rest is zero. Instead of add / mask, do add with half wide type.
       */
      struct lp_type narrow_type;
      struct lp_build_context narrow_bld;

      memset(&narrow_type, 0, sizeof narrow_type);
      narrow_type.sign   = bld->type.sign;
      narrow_type.width  = bld->type.width/2;
      narrow_type.length = bld->type.length*2;

      lp_build_context_init(&narrow_bld, bld->gallivm, narrow_type);
      res = LLVMBuildBitCast(builder, res, narrow_bld.vec_type, "");
      v0 = LLVMBuildBitCast(builder, v0, narrow_bld.vec_type, "");
      res = lp_build_add(&narrow_bld, v0, res);
      res = LLVMBuildBitCast(builder, res, bld->vec_type, "");
   } else {
      res = lp_build_add(bld, v0, res);

      if (bld->type.fixed) {
         /*
          * We need to mask out the high order bits when lerping 8bit
          * normalized colors stored on 16bits
          */
         /* XXX: This step is necessary for lerping 8bit colors stored on
          * 16bits, but it will be wrong for true fixed point use cases.
          * Basically we need a more powerful lp_type, capable of further
          * distinguishing the values interpretation from the value storage.
          */
         LLVMValueRef low_bits;
         low_bits = lp_build_const_int_vec(bld->gallivm, bld->type, (1 << half_width) - 1);
         res = LLVMBuildAnd(builder, res, low_bits, "");
      }
   }

   return res;
}


/**
 * Linear interpolation.
 */
LLVMValueRef
lp_build_lerp(struct lp_build_context *bld,
              LLVMValueRef x,
              LLVMValueRef v0,
              LLVMValueRef v1,
              unsigned flags)
{
   const struct lp_type type = bld->type;
   LLVMValueRef res;

   assert(lp_check_value(type, x));
   assert(lp_check_value(type, v0));
   assert(lp_check_value(type, v1));

   assert(!(flags & LP_BLD_LERP_WIDE_NORMALIZED));

   if (type.norm) {
      struct lp_type wide_type;
      struct lp_build_context wide_bld;
      LLVMValueRef xl, xh, v0l, v0h, v1l, v1h, resl, resh;

      assert(type.length >= 2);

      /*
       * Create a wider integer type, enough to hold the
       * intermediate result of the multiplication.
       */
      memset(&wide_type, 0, sizeof wide_type);
      wide_type.sign   = type.sign;
      wide_type.width  = type.width*2;
      wide_type.length = type.length/2;

      lp_build_context_init(&wide_bld, bld->gallivm, wide_type);

      lp_build_unpack2_native(bld->gallivm, type, wide_type, x,  &xl,  &xh);
      lp_build_unpack2_native(bld->gallivm, type, wide_type, v0, &v0l, &v0h);
      lp_build_unpack2_native(bld->gallivm, type, wide_type, v1, &v1l, &v1h);

      /*
       * Lerp both halves.
       */

      flags |= LP_BLD_LERP_WIDE_NORMALIZED;

      resl = lp_build_lerp_simple(&wide_bld, xl, v0l, v1l, flags);
      resh = lp_build_lerp_simple(&wide_bld, xh, v0h, v1h, flags);

      res = lp_build_pack2_native(bld->gallivm, wide_type, type, resl, resh);
   } else {
      res = lp_build_lerp_simple(bld, x, v0, v1, flags);
   }

   return res;
}


/**
 * Bilinear interpolation.
 *
 * Values indices are in v_{yx}.
 */
LLVMValueRef
lp_build_lerp_2d(struct lp_build_context *bld,
                 LLVMValueRef x,
                 LLVMValueRef y,
                 LLVMValueRef v00,
                 LLVMValueRef v01,
                 LLVMValueRef v10,
                 LLVMValueRef v11,
                 unsigned flags)
{
   LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01, flags);
   LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11, flags);
   return lp_build_lerp(bld, y, v0, v1, flags);
}


LLVMValueRef
lp_build_lerp_3d(struct lp_build_context *bld,
                 LLVMValueRef x,
                 LLVMValueRef y,
                 LLVMValueRef z,
                 LLVMValueRef v000,
                 LLVMValueRef v001,
                 LLVMValueRef v010,
                 LLVMValueRef v011,
                 LLVMValueRef v100,
                 LLVMValueRef v101,
                 LLVMValueRef v110,
                 LLVMValueRef v111,
                 unsigned flags)
{
   LLVMValueRef v0 = lp_build_lerp_2d(bld, x, y, v000, v001, v010, v011, flags);
   LLVMValueRef v1 = lp_build_lerp_2d(bld, x, y, v100, v101, v110, v111, flags);
   return lp_build_lerp(bld, z, v0, v1, flags);
}


/**
 * Generate min(a, b)
 * Do checks for special cases but not for nans.
 */
LLVMValueRef
lp_build_min(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b)
{
   assert(lp_check_value(bld->type, a));
   assert(lp_check_value(bld->type, b));

   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   if (a == b)
      return a;

   if (bld->type.norm) {
      if (!bld->type.sign) {
         if (a == bld->zero || b == bld->zero) {
            return bld->zero;
         }
      }
      if (a == bld->one)
         return b;
      if (b == bld->one)
         return a;
   }

   return lp_build_min_simple(bld, a, b, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
}


/**
 * Generate min(a, b)
 * NaN's are handled according to the behavior specified by the
 * nan_behavior argument.
 */
LLVMValueRef
lp_build_min_ext(struct lp_build_context *bld,
                 LLVMValueRef a,
                 LLVMValueRef b,
                 enum gallivm_nan_behavior nan_behavior)
{
   assert(lp_check_value(bld->type, a));
   assert(lp_check_value(bld->type, b));

   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   if (a == b)
      return a;

   if (bld->type.norm) {
      if (!bld->type.sign) {
         if (a == bld->zero || b == bld->zero) {
            return bld->zero;
         }
      }
      if (a == bld->one)
         return b;
      if (b == bld->one)
         return a;
   }

   return lp_build_min_simple(bld, a, b, nan_behavior);
}


/**
 * Generate max(a, b)
 * Do checks for special cases, but NaN behavior is undefined.
 */
LLVMValueRef
lp_build_max(struct lp_build_context *bld,
             LLVMValueRef a,
             LLVMValueRef b)
{
   assert(lp_check_value(bld->type, a));
   assert(lp_check_value(bld->type, b));

   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   if (a == b)
      return a;

   if (bld->type.norm) {
      if (a == bld->one || b == bld->one)
         return bld->one;
      if (!bld->type.sign) {
         if (a == bld->zero) {
            return b;
         }
         if (b == bld->zero) {
            return a;
         }
      }
   }

   return lp_build_max_simple(bld, a, b, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
}


/**
 * Generate max(a, b)
 * Checks for special cases.
 * NaN's are handled according to the behavior specified by the
 * nan_behavior argument.
 */
LLVMValueRef
lp_build_max_ext(struct lp_build_context *bld,
                  LLVMValueRef a,
                  LLVMValueRef b,
                  enum gallivm_nan_behavior nan_behavior)
{
   assert(lp_check_value(bld->type, a));
   assert(lp_check_value(bld->type, b));

   if (a == bld->undef || b == bld->undef)
      return bld->undef;

   if (a == b)
      return a;

   if (bld->type.norm) {
      if (a == bld->one || b == bld->one)
         return bld->one;
      if (!bld->type.sign) {
         if (a == bld->zero) {
            return b;
         }
         if (b == bld->zero) {
            return a;
         }
      }
   }

   return lp_build_max_simple(bld, a, b, nan_behavior);
}


/**
 * Generate clamp(a, min, max)
 * NaN behavior (for any of a, min, max) is undefined.
 * Do checks for special cases.
 */
LLVMValueRef
lp_build_clamp(struct lp_build_context *bld,
               LLVMValueRef a,
               LLVMValueRef min,
               LLVMValueRef max)
{
   assert(lp_check_value(bld->type, a));
   assert(lp_check_value(bld->type, min));
   assert(lp_check_value(bld->type, max));

   a = lp_build_min(bld, a, max);
   a = lp_build_max(bld, a, min);
   return a;
}


/**
 * Generate clamp(a, 0, 1)
 * A NaN will get converted to zero.
 */
LLVMValueRef
lp_build_clamp_zero_one_nanzero(struct lp_build_context *bld,
                                LLVMValueRef a)
{
   a = lp_build_max_ext(bld, a, bld->zero, GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN);
   a = lp_build_min(bld, a, bld->one);
   return a;
}


/**
 * Generate abs(a)
 */
LLVMValueRef
lp_build_abs(struct lp_build_context *bld,
             LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);

   assert(lp_check_value(type, a));

   if (!type.sign)
      return a;

   if (type.floating) {
      char intrinsic[32];
      lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.fabs", vec_type);
      return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
   }

   if (type.width*type.length == 128 && util_get_cpu_caps()->has_ssse3 && LLVM_VERSION_MAJOR < 6) {
      switch(type.width) {
      case 8:
         return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
      case 16:
         return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
      case 32:
         return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
      }
   }
   else if (type.width*type.length == 256 && util_get_cpu_caps()->has_avx2 && LLVM_VERSION_MAJOR < 6) {
      switch(type.width) {
      case 8:
         return lp_build_intrinsic_unary(builder, "llvm.x86.avx2.pabs.b", vec_type, a);
      case 16:
         return lp_build_intrinsic_unary(builder, "llvm.x86.avx2.pabs.w", vec_type, a);
      case 32:
         return lp_build_intrinsic_unary(builder, "llvm.x86.avx2.pabs.d", vec_type, a);
      }
   }

   return lp_build_select(bld, lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero),
                          a, LLVMBuildNeg(builder, a, ""));
}


LLVMValueRef
lp_build_negate(struct lp_build_context *bld,
                LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;

   assert(lp_check_value(bld->type, a));

   if (bld->type.floating)
      a = LLVMBuildFNeg(builder, a, "");
   else
      a = LLVMBuildNeg(builder, a, "");

   return a;
}


/** Return -1, 0 or +1 depending on the sign of a */
LLVMValueRef
lp_build_sgn(struct lp_build_context *bld,
             LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMValueRef cond;
   LLVMValueRef res;

   assert(lp_check_value(type, a));

   /* Handle non-zero case */
   if (!type.sign) {
      /* if not zero then sign must be positive */
      res = bld->one;
   }
   else if (type.floating) {
      LLVMTypeRef vec_type;
      LLVMTypeRef int_type;
      LLVMValueRef mask;
      LLVMValueRef sign;
      LLVMValueRef one;
      unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);

      int_type = lp_build_int_vec_type(bld->gallivm, type);
      vec_type = lp_build_vec_type(bld->gallivm, type);
      mask = lp_build_const_int_vec(bld->gallivm, type, maskBit);

      /* Take the sign bit and add it to 1 constant */
      sign = LLVMBuildBitCast(builder, a, int_type, "");
      sign = LLVMBuildAnd(builder, sign, mask, "");
      one = LLVMConstBitCast(bld->one, int_type);
      res = LLVMBuildOr(builder, sign, one, "");
      res = LLVMBuildBitCast(builder, res, vec_type, "");
   }
   else
   {
      /* signed int/norm/fixed point */
      /* could use psign with sse3 and appropriate vectors here */
      LLVMValueRef minus_one = lp_build_const_vec(bld->gallivm, type, -1.0);
      cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
      res = lp_build_select(bld, cond, bld->one, minus_one);
   }

   /* Handle zero */
   cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
   res = lp_build_select(bld, cond, bld->zero, res);

   return res;
}


/**
 * Set the sign of float vector 'a' according to 'sign'.
 * If sign==0, return abs(a).
 * If sign==1, return -abs(a);
 * Other values for sign produce undefined results.
 */
LLVMValueRef
lp_build_set_sign(struct lp_build_context *bld,
                  LLVMValueRef a, LLVMValueRef sign)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
   LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
   LLVMValueRef shift = lp_build_const_int_vec(bld->gallivm, type, type.width - 1);
   LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type,
                             ~((unsigned long long) 1 << (type.width - 1)));
   LLVMValueRef val, res;

   assert(type.floating);
   assert(lp_check_value(type, a));

   /* val = reinterpret_cast<int>(a) */
   val = LLVMBuildBitCast(builder, a, int_vec_type, "");
   /* val = val & mask */
   val = LLVMBuildAnd(builder, val, mask, "");
   /* sign = sign << shift */
   sign = LLVMBuildShl(builder, sign, shift, "");
   /* res = val | sign */
   res = LLVMBuildOr(builder, val, sign, "");
   /* res = reinterpret_cast<float>(res) */
   res = LLVMBuildBitCast(builder, res, vec_type, "");

   return res;
}


/**
 * Convert vector of (or scalar) int to vector of (or scalar) float.
 */
LLVMValueRef
lp_build_int_to_float(struct lp_build_context *bld,
                      LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);

   assert(type.floating);

   return LLVMBuildSIToFP(builder, a, vec_type, "");
}


static boolean
arch_rounding_available(const struct lp_type type)
{
   if ((util_get_cpu_caps()->has_sse4_1 &&
       (type.length == 1 || type.width*type.length == 128)) ||
       (util_get_cpu_caps()->has_avx && type.width*type.length == 256) ||
       (util_get_cpu_caps()->has_avx512f && type.width*type.length == 512))
      return TRUE;
   else if ((util_get_cpu_caps()->has_altivec &&
            (type.width == 32 && type.length == 4)))
      return TRUE;
   else if (util_get_cpu_caps()->has_neon)
      return TRUE;
   else if (util_get_cpu_caps()->family == CPU_S390X)
      return TRUE;

   return FALSE;
}

enum lp_build_round_mode
{
   LP_BUILD_ROUND_NEAREST = 0,
   LP_BUILD_ROUND_FLOOR = 1,
   LP_BUILD_ROUND_CEIL = 2,
   LP_BUILD_ROUND_TRUNCATE = 3
};


static inline LLVMValueRef
lp_build_iround_nearest_sse2(struct lp_build_context *bld,
                             LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef i32t = LLVMInt32TypeInContext(bld->gallivm->context);
   LLVMTypeRef ret_type = lp_build_int_vec_type(bld->gallivm, type);
   const char *intrinsic;
   LLVMValueRef res;

   assert(type.floating);
   /* using the double precision conversions is a bit more complicated */
   assert(type.width == 32);

   assert(lp_check_value(type, a));
   assert(util_get_cpu_caps()->has_sse2);

   /* This is relying on MXCSR rounding mode, which should always be nearest. */
   if (type.length == 1) {
      LLVMTypeRef vec_type;
      LLVMValueRef undef;
      LLVMValueRef arg;
      LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);

      vec_type = LLVMVectorType(bld->elem_type, 4);

      intrinsic = "llvm.x86.sse.cvtss2si";

      undef = LLVMGetUndef(vec_type);

      arg = LLVMBuildInsertElement(builder, undef, a, index0, "");

      res = lp_build_intrinsic_unary(builder, intrinsic,
                                     ret_type, arg);
   }
   else {
      if (type.width* type.length == 128) {
         intrinsic = "llvm.x86.sse2.cvtps2dq";
      }
      else {
         assert(type.width*type.length == 256);
         assert(util_get_cpu_caps()->has_avx);

         intrinsic = "llvm.x86.avx.cvt.ps2dq.256";
      }
      res = lp_build_intrinsic_unary(builder, intrinsic,
                                     ret_type, a);
   }

   return res;
}


/*
 */
static inline LLVMValueRef
lp_build_round_altivec(struct lp_build_context *bld,
                       LLVMValueRef a,
                       enum lp_build_round_mode mode)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   const char *intrinsic = NULL;

   assert(type.floating);

   assert(lp_check_value(type, a));
   assert(util_get_cpu_caps()->has_altivec);

   (void)type;

   switch (mode) {
   case LP_BUILD_ROUND_NEAREST:
      intrinsic = "llvm.ppc.altivec.vrfin";
      break;
   case LP_BUILD_ROUND_FLOOR:
      intrinsic = "llvm.ppc.altivec.vrfim";
      break;
   case LP_BUILD_ROUND_CEIL:
      intrinsic = "llvm.ppc.altivec.vrfip";
      break;
   case LP_BUILD_ROUND_TRUNCATE:
      intrinsic = "llvm.ppc.altivec.vrfiz";
      break;
   }

   return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
}


static inline LLVMValueRef
lp_build_round_arch(struct lp_build_context *bld,
                    LLVMValueRef a,
                    enum lp_build_round_mode mode)
{
   if (util_get_cpu_caps()->has_sse4_1 || util_get_cpu_caps()->has_neon ||
       util_get_cpu_caps()->family == CPU_S390X) {
      LLVMBuilderRef builder = bld->gallivm->builder;
      const struct lp_type type = bld->type;
      const char *intrinsic_root;
      char intrinsic[32];

      assert(type.floating);
      assert(lp_check_value(type, a));
      (void)type;

      switch (mode) {
      case LP_BUILD_ROUND_NEAREST:
         intrinsic_root = "llvm.nearbyint";
         break;
      case LP_BUILD_ROUND_FLOOR:
         intrinsic_root = "llvm.floor";
         break;
      case LP_BUILD_ROUND_CEIL:
         intrinsic_root = "llvm.ceil";
         break;
      case LP_BUILD_ROUND_TRUNCATE:
         intrinsic_root = "llvm.trunc";
         break;
      default:
         unreachable("unhandled lp_build_round_mode");
      }

      lp_format_intrinsic(intrinsic, sizeof intrinsic, intrinsic_root, bld->vec_type);
      return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
   }
   else /* (util_get_cpu_caps()->has_altivec) */
     return lp_build_round_altivec(bld, a, mode);
}


/**
 * Return the integer part of a float (vector) value (== round toward zero).
 * The returned value is a float (vector).
 * Ex: trunc(-1.5) = -1.0
 */
LLVMValueRef
lp_build_trunc(struct lp_build_context *bld,
               LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(type.floating);
   assert(lp_check_value(type, a));

   if (type.width == 16) {
      char intrinsic[64];
      lp_format_intrinsic(intrinsic, 64, "llvm.trunc", bld->vec_type);
      return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
   }

   if (arch_rounding_available(type)) {
      return lp_build_round_arch(bld, a, LP_BUILD_ROUND_TRUNCATE);
   }
   else {
      const struct lp_type type = bld->type;
      struct lp_type inttype;
      struct lp_build_context intbld;
      LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
      LLVMValueRef trunc, res, anosign, mask;
      LLVMTypeRef int_vec_type = bld->int_vec_type;
      LLVMTypeRef vec_type = bld->vec_type;

      inttype = type;
      inttype.floating = 0;
      lp_build_context_init(&intbld, bld->gallivm, inttype);

      /* round by truncation */
      trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
      res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc");

      /* mask out sign bit */
      anosign = lp_build_abs(bld, a);
      /*
       * mask out all values if anosign > 2^24
       * This should work both for large ints (all rounding is no-op for them
       * because such floats are always exact) as well as special cases like
       * NaNs, Infs (taking advantage of the fact they use max exponent).
       * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
       */
      anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
      cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
      mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
      return lp_build_select(bld, mask, a, res);
   }
}


/**
 * Return float (vector) rounded to nearest integer (vector).  The returned
 * value is a float (vector).
 * Ex: round(0.9) = 1.0
 * Ex: round(-1.5) = -2.0
 */
LLVMValueRef
lp_build_round(struct lp_build_context *bld,
               LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(type.floating);
   assert(lp_check_value(type, a));

   if (type.width == 16) {
      char intrinsic[64];
      lp_format_intrinsic(intrinsic, 64, "llvm.round", bld->vec_type);
      return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
   }

   if (arch_rounding_available(type)) {
      return lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST);
   }
   else {
      const struct lp_type type = bld->type;
      struct lp_type inttype;
      struct lp_build_context intbld;
      LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
      LLVMValueRef res, anosign, mask;
      LLVMTypeRef int_vec_type = bld->int_vec_type;
      LLVMTypeRef vec_type = bld->vec_type;

      inttype = type;
      inttype.floating = 0;
      lp_build_context_init(&intbld, bld->gallivm, inttype);

      res = lp_build_iround(bld, a);
      res = LLVMBuildSIToFP(builder, res, vec_type, "");

      /* mask out sign bit */
      anosign = lp_build_abs(bld, a);
      /*
       * mask out all values if anosign > 2^24
       * This should work both for large ints (all rounding is no-op for them
       * because such floats are always exact) as well as special cases like
       * NaNs, Infs (taking advantage of the fact they use max exponent).
       * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
       */
      anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
      cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
      mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
      return lp_build_select(bld, mask, a, res);
   }
}


/**
 * Return floor of float (vector), result is a float (vector)
 * Ex: floor(1.1) = 1.0
 * Ex: floor(-1.1) = -2.0
 */
LLVMValueRef
lp_build_floor(struct lp_build_context *bld,
               LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(type.floating);
   assert(lp_check_value(type, a));

   if (arch_rounding_available(type)) {
      return lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR);
   }
   else {
      const struct lp_type type = bld->type;
      struct lp_type inttype;
      struct lp_build_context intbld;
      LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
      LLVMValueRef trunc, res, anosign, mask;
      LLVMTypeRef int_vec_type = bld->int_vec_type;
      LLVMTypeRef vec_type = bld->vec_type;

      if (type.width != 32) {
         char intrinsic[32];
         lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.floor", vec_type);
         return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
      }

      assert(type.width == 32); /* might want to handle doubles at some point */

      inttype = type;
      inttype.floating = 0;
      lp_build_context_init(&intbld, bld->gallivm, inttype);

      /* round by truncation */
      trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
      res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc");

      if (type.sign) {
         LLVMValueRef tmp;

         /*
          * fix values if rounding is wrong (for non-special cases)
          * - this is the case if trunc > a
          */
         mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, res, a);
         /* tmp = trunc > a ? 1.0 : 0.0 */
         tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, "");
         tmp = lp_build_and(&intbld, mask, tmp);
         tmp = LLVMBuildBitCast(builder, tmp, vec_type, "");
         res = lp_build_sub(bld, res, tmp);
      }

      /* mask out sign bit */
      anosign = lp_build_abs(bld, a);
      /*
       * mask out all values if anosign > 2^24
       * This should work both for large ints (all rounding is no-op for them
       * because such floats are always exact) as well as special cases like
       * NaNs, Infs (taking advantage of the fact they use max exponent).
       * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
       */
      anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
      cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
      mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
      return lp_build_select(bld, mask, a, res);
   }
}


/**
 * Return ceiling of float (vector), returning float (vector).
 * Ex: ceil( 1.1) = 2.0
 * Ex: ceil(-1.1) = -1.0
 */
LLVMValueRef
lp_build_ceil(struct lp_build_context *bld,
              LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(type.floating);
   assert(lp_check_value(type, a));

   if (arch_rounding_available(type)) {
      return lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL);
   }
   else {
      const struct lp_type type = bld->type;
      struct lp_type inttype;
      struct lp_build_context intbld;
      LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
      LLVMValueRef trunc, res, anosign, mask, tmp;
      LLVMTypeRef int_vec_type = bld->int_vec_type;
      LLVMTypeRef vec_type = bld->vec_type;

      if (type.width != 32) {
         char intrinsic[32];
         lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.ceil", vec_type);
         return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
      }

      assert(type.width == 32); /* might want to handle doubles at some point */

      inttype = type;
      inttype.floating = 0;
      lp_build_context_init(&intbld, bld->gallivm, inttype);

      /* round by truncation */
      trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
      trunc = LLVMBuildSIToFP(builder, trunc, vec_type, "ceil.trunc");

      /*
       * fix values if rounding is wrong (for non-special cases)
       * - this is the case if trunc < a
       */
      mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a);
      /* tmp = trunc < a ? 1.0 : 0.0 */
      tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, "");
      tmp = lp_build_and(&intbld, mask, tmp);
      tmp = LLVMBuildBitCast(builder, tmp, vec_type, "");
      res = lp_build_add(bld, trunc, tmp);

      /* mask out sign bit */
      anosign = lp_build_abs(bld, a);
      /*
       * mask out all values if anosign > 2^24
       * This should work both for large ints (all rounding is no-op for them
       * because such floats are always exact) as well as special cases like
       * NaNs, Infs (taking advantage of the fact they use max exponent).
       * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
       */
      anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
      cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
      mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
      return lp_build_select(bld, mask, a, res);
   }
}


/**
 * Return fractional part of 'a' computed as a - floor(a)
 * Typically used in texture coord arithmetic.
 */
LLVMValueRef
lp_build_fract(struct lp_build_context *bld,
               LLVMValueRef a)
{
   assert(bld->type.floating);
   return lp_build_sub(bld, a, lp_build_floor(bld, a));
}


/**
 * Prevent returning 1.0 for very small negative values of 'a' by clamping
 * against 0.99999(9). (Will also return that value for NaNs.)
 */
static inline LLVMValueRef
clamp_fract(struct lp_build_context *bld, LLVMValueRef fract)
{
   LLVMValueRef max;

   /* this is the largest number smaller than 1.0 representable as float */
   max = lp_build_const_vec(bld->gallivm, bld->type,
                            1.0 - 1.0/(1LL << (lp_mantissa(bld->type) + 1)));
   return lp_build_min_ext(bld, fract, max,
                           GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN);
}


/**
 * Same as lp_build_fract, but guarantees that the result is always smaller
 * than one. Will also return the smaller-than-one value for infs, NaNs.
 */
LLVMValueRef
lp_build_fract_safe(struct lp_build_context *bld,
                    LLVMValueRef a)
{
   return clamp_fract(bld, lp_build_fract(bld, a));
}


/**
 * Return the integer part of a float (vector) value (== round toward zero).
 * The returned value is an integer (vector).
 * Ex: itrunc(-1.5) = -1
 */
LLVMValueRef
lp_build_itrunc(struct lp_build_context *bld,
                LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);

   assert(type.floating);
   assert(lp_check_value(type, a));

   return LLVMBuildFPToSI(builder, a, int_vec_type, "");
}


/**
 * Return float (vector) rounded to nearest integer (vector).  The returned
 * value is an integer (vector).
 * Ex: iround(0.9) = 1
 * Ex: iround(-1.5) = -2
 */
LLVMValueRef
lp_build_iround(struct lp_build_context *bld,
                LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef int_vec_type = bld->int_vec_type;
   LLVMValueRef res;

   assert(type.floating);

   assert(lp_check_value(type, a));

   if ((util_get_cpu_caps()->has_sse2 &&
       ((type.width == 32) && (type.length == 1 || type.length == 4))) ||
       (util_get_cpu_caps()->has_avx && type.width == 32 && type.length == 8)) {
      return lp_build_iround_nearest_sse2(bld, a);
   }
   if (arch_rounding_available(type)) {
      res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST);
   }
   else {
      LLVMValueRef half;

      half = lp_build_const_vec(bld->gallivm, type, nextafterf(0.5, 0.0));

      if (type.sign) {
         LLVMTypeRef vec_type = bld->vec_type;
         LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type,
                                    (unsigned long long)1 << (type.width - 1));
         LLVMValueRef sign;

         /* get sign bit */
         sign = LLVMBuildBitCast(builder, a, int_vec_type, "");
         sign = LLVMBuildAnd(builder, sign, mask, "");

         /* sign * 0.5 */
         half = LLVMBuildBitCast(builder, half, int_vec_type, "");
         half = LLVMBuildOr(builder, sign, half, "");
         half = LLVMBuildBitCast(builder, half, vec_type, "");
      }

      res = LLVMBuildFAdd(builder, a, half, "");
   }

   res = LLVMBuildFPToSI(builder, res, int_vec_type, "");

   return res;
}


/**
 * Return floor of float (vector), result is an int (vector)
 * Ex: ifloor(1.1) = 1.0
 * Ex: ifloor(-1.1) = -2.0
 */
LLVMValueRef
lp_build_ifloor(struct lp_build_context *bld,
                LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef int_vec_type = bld->int_vec_type;
   LLVMValueRef res;

   assert(type.floating);
   assert(lp_check_value(type, a));

   res = a;
   if (type.sign) {
      if (arch_rounding_available(type)) {
         res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR);
      }
      else {
         struct lp_type inttype;
         struct lp_build_context intbld;
         LLVMValueRef trunc, itrunc, mask;

         assert(type.floating);
         assert(lp_check_value(type, a));

         inttype = type;
         inttype.floating = 0;
         lp_build_context_init(&intbld, bld->gallivm, inttype);

         /* round by truncation */
         itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
         trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "ifloor.trunc");

         /*
          * fix values if rounding is wrong (for non-special cases)
          * - this is the case if trunc > a
          * The results of doing this with NaNs, very large values etc.
          * are undefined but this seems to be the case anyway.
          */
         mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, trunc, a);
         /* cheapie minus one with mask since the mask is minus one / zero */
         return lp_build_add(&intbld, itrunc, mask);
      }
   }

   /* round to nearest (toward zero) */
   res = LLVMBuildFPToSI(builder, res, int_vec_type, "ifloor.res");

   return res;
}


/**
 * Return ceiling of float (vector), returning int (vector).
 * Ex: iceil( 1.1) = 2
 * Ex: iceil(-1.1) = -1
 */
LLVMValueRef
lp_build_iceil(struct lp_build_context *bld,
               LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef int_vec_type = bld->int_vec_type;
   LLVMValueRef res;

   assert(type.floating);
   assert(lp_check_value(type, a));

   if (arch_rounding_available(type)) {
      res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL);
   }
   else {
      struct lp_type inttype;
      struct lp_build_context intbld;
      LLVMValueRef trunc, itrunc, mask;

      assert(type.floating);
      assert(lp_check_value(type, a));

      inttype = type;
      inttype.floating = 0;
      lp_build_context_init(&intbld, bld->gallivm, inttype);

      /* round by truncation */
      itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
      trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "iceil.trunc");

      /*
       * fix values if rounding is wrong (for non-special cases)
       * - this is the case if trunc < a
       * The results of doing this with NaNs, very large values etc.
       * are undefined but this seems to be the case anyway.
       */
      mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a);
      /* cheapie plus one with mask since the mask is minus one / zero */
      return lp_build_sub(&intbld, itrunc, mask);
   }

   /* round to nearest (toward zero) */
   res = LLVMBuildFPToSI(builder, res, int_vec_type, "iceil.res");

   return res;
}


/**
 * Combined ifloor() & fract().
 *
 * Preferred to calling the functions separately, as it will ensure that the
 * strategy (floor() vs ifloor()) that results in less redundant work is used.
 */
void
lp_build_ifloor_fract(struct lp_build_context *bld,
                      LLVMValueRef a,
                      LLVMValueRef *out_ipart,
                      LLVMValueRef *out_fpart)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMValueRef ipart;

   assert(type.floating);
   assert(lp_check_value(type, a));

   if (arch_rounding_available(type)) {
      /*
       * floor() is easier.
       */

      ipart = lp_build_floor(bld, a);
      *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart");
      *out_ipart = LLVMBuildFPToSI(builder, ipart, bld->int_vec_type, "ipart");
   }
   else {
      /*
       * ifloor() is easier.
       */

      *out_ipart = lp_build_ifloor(bld, a);
      ipart = LLVMBuildSIToFP(builder, *out_ipart, bld->vec_type, "ipart");
      *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart");
   }
}


/**
 * Same as lp_build_ifloor_fract, but guarantees that the fractional part is
 * always smaller than one.
 */
void
lp_build_ifloor_fract_safe(struct lp_build_context *bld,
                           LLVMValueRef a,
                           LLVMValueRef *out_ipart,
                           LLVMValueRef *out_fpart)
{
   lp_build_ifloor_fract(bld, a, out_ipart, out_fpart);
   *out_fpart = clamp_fract(bld, *out_fpart);
}


LLVMValueRef
lp_build_sqrt(struct lp_build_context *bld,
              LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
   char intrinsic[32];

   assert(lp_check_value(type, a));

   assert(type.floating);
   lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.sqrt", vec_type);

   return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
}


/**
 * Do one Newton-Raphson step to improve reciprocate precision:
 *
 *   x_{i+1} = x_i + x_i * (1 - a * x_i)
 *
 * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
 * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
 * such as Google Earth, which does RCP(RSQRT(0.0)) when drawing the Earth's
 * halo. It would be necessary to clamp the argument to prevent this.
 *
 * See also:
 * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
 * - http://softwarecommunity.intel.com/articles/eng/1818.htm
 */
static inline LLVMValueRef
lp_build_rcp_refine(struct lp_build_context *bld,
                    LLVMValueRef a,
                    LLVMValueRef rcp_a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef neg_a;
   LLVMValueRef res;

   neg_a = LLVMBuildFNeg(builder, a, "");
   res = lp_build_fmuladd(builder, neg_a, rcp_a, bld->one);
   res = lp_build_fmuladd(builder, res, rcp_a, rcp_a);

   return res;
}


LLVMValueRef
lp_build_rcp(struct lp_build_context *bld,
             LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, a));

   if (a == bld->zero)
      return bld->undef;
   if (a == bld->one)
      return bld->one;
   if (a == bld->undef)
      return bld->undef;

   assert(type.floating);

   if (LLVMIsConstant(a))
      return LLVMBuildFDiv(builder, bld->one, a, "");

   /*
    * We don't use RCPPS because:
    * - it only has 10bits of precision
    * - it doesn't even get the reciprocate of 1.0 exactly
    * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
    * - for recent processors the benefit over DIVPS is marginal, a case
    *   dependent
    *
    * We could still use it on certain processors if benchmarks show that the
    * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
    * particular uses that require less workarounds.
    */

   if (FALSE && ((util_get_cpu_caps()->has_sse && type.width == 32 && type.length == 4) ||
         (util_get_cpu_caps()->has_avx && type.width == 32 && type.length == 8))){
      const unsigned num_iterations = 0;
      LLVMValueRef res;
      unsigned i;
      const char *intrinsic = NULL;

      if (type.length == 4) {
         intrinsic = "llvm.x86.sse.rcp.ps";
      }
      else {
         intrinsic = "llvm.x86.avx.rcp.ps.256";
      }

      res = lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);

      for (i = 0; i < num_iterations; ++i) {
         res = lp_build_rcp_refine(bld, a, res);
      }

      return res;
   }

   return LLVMBuildFDiv(builder, bld->one, a, "");
}


/**
 * Do one Newton-Raphson step to improve rsqrt precision:
 *
 *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
 *
 * See also Intel 64 and IA-32 Architectures Optimization Manual.
 */
static inline LLVMValueRef
lp_build_rsqrt_refine(struct lp_build_context *bld,
                      LLVMValueRef a,
                      LLVMValueRef rsqrt_a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef half = lp_build_const_vec(bld->gallivm, bld->type, 0.5);
   LLVMValueRef three = lp_build_const_vec(bld->gallivm, bld->type, 3.0);
   LLVMValueRef res;

   res = LLVMBuildFMul(builder, rsqrt_a, rsqrt_a, "");
   res = LLVMBuildFMul(builder, a, res, "");
   res = LLVMBuildFSub(builder, three, res, "");
   res = LLVMBuildFMul(builder, rsqrt_a, res, "");
   res = LLVMBuildFMul(builder, half, res, "");

   return res;
}


/**
 * Generate 1/sqrt(a).
 * Result is undefined for values < 0, infinity for +0.
 */
LLVMValueRef
lp_build_rsqrt(struct lp_build_context *bld,
               LLVMValueRef a)
{
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, a));

   assert(type.floating);

   /*
    * This should be faster but all denormals will end up as infinity.
    */
   if (0 && lp_build_fast_rsqrt_available(type)) {
      const unsigned num_iterations = 1;
      LLVMValueRef res;
      unsigned i;

      /* rsqrt(1.0) != 1.0 here */
      res = lp_build_fast_rsqrt(bld, a);

      if (num_iterations) {
         /*
          * Newton-Raphson will result in NaN instead of infinity for zero,
          * and NaN instead of zero for infinity.
          * Also, need to ensure rsqrt(1.0) == 1.0.
          * All numbers smaller than FLT_MIN will result in +infinity
          * (rsqrtps treats all denormals as zero).
          */
         LLVMValueRef cmp;
         LLVMValueRef flt_min = lp_build_const_vec(bld->gallivm, type, FLT_MIN);
         LLVMValueRef inf = lp_build_const_vec(bld->gallivm, type, INFINITY);

         for (i = 0; i < num_iterations; ++i) {
            res = lp_build_rsqrt_refine(bld, a, res);
         }
         cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_LESS, a, flt_min);
         res = lp_build_select(bld, cmp, inf, res);
         cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, inf);
         res = lp_build_select(bld, cmp, bld->zero, res);
         cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, bld->one);
         res = lp_build_select(bld, cmp, bld->one, res);
      }

      return res;
   }

   return lp_build_rcp(bld, lp_build_sqrt(bld, a));
}


/**
 * If there's a fast (inaccurate) rsqrt instruction available
 * (caller may want to avoid to call rsqrt_fast if it's not available,
 * i.e. for calculating x^0.5 it may do rsqrt_fast(x) * x but if
 * unavailable it would result in sqrt/div/mul so obviously
 * much better to just call sqrt, skipping both div and mul).
 */
boolean
lp_build_fast_rsqrt_available(struct lp_type type)
{
   assert(type.floating);

   if ((util_get_cpu_caps()->has_sse && type.width == 32 && type.length == 4) ||
       (util_get_cpu_caps()->has_avx && type.width == 32 && type.length == 8)) {
      return true;
   }
   return false;
}


/**
 * Generate 1/sqrt(a).
 * Result is undefined for values < 0, infinity for +0.
 * Precision is limited, only ~10 bits guaranteed
 * (rsqrt 1.0 may not be 1.0, denorms may be flushed to 0).
 */
LLVMValueRef
lp_build_fast_rsqrt(struct lp_build_context *bld,
                    LLVMValueRef a)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, a));

   if (lp_build_fast_rsqrt_available(type)) {
      const char *intrinsic = NULL;

      if (type.length == 4) {
         intrinsic = "llvm.x86.sse.rsqrt.ps";
      }
      else {
         intrinsic = "llvm.x86.avx.rsqrt.ps.256";
      }
      return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
   }
   else {
      debug_printf("%s: emulating fast rsqrt with rcp/sqrt\n", __FUNCTION__);
   }
   return lp_build_rcp(bld, lp_build_sqrt(bld, a));
}


/**
 * Generate sin(a) or cos(a) using polynomial approximation.
 * TODO: it might be worth recognizing sin and cos using same source
 * (i.e. d3d10 sincos opcode). Obviously doing both at the same time
 * would be way cheaper than calculating (nearly) everything twice...
 * Not sure it's common enough to be worth bothering however, scs
 * opcode could also benefit from calculating both though.
 */
static LLVMValueRef
lp_build_sin_or_cos(struct lp_build_context *bld,
                    LLVMValueRef a,
                    boolean cos)
{
   struct gallivm_state *gallivm = bld->gallivm;
   LLVMBuilderRef b = gallivm->builder;
   struct lp_type int_type = lp_int_type(bld->type);

   /*
    *  take the absolute value,
    *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
    */

   LLVMValueRef inv_sig_mask = lp_build_const_int_vec(gallivm, bld->type, ~0x80000000);
   LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, bld->int_vec_type, "a_v4si");

   LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
   LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, bld->vec_type, "x_abs");

   /*
    * scale by 4/Pi
    * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
    */

   LLVMValueRef FOPi = lp_build_const_vec(gallivm, bld->type, 1.27323954473516);
   LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");

   /*
    * store the integer part of y in mm0
    * emm2 = _mm_cvttps_epi32(y);
    */

   LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, bld->int_vec_type, "emm2_i");

   /*
    * j=(j+1) & (~1) (see the cephes sources)
    * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
    */

   LLVMValueRef all_one = lp_build_const_int_vec(gallivm, bld->type, 1);
   LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
   /*
    * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
    */
   LLVMValueRef inv_one = lp_build_const_int_vec(gallivm, bld->type, ~1);
   LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");

   /*
    * y = _mm_cvtepi32_ps(emm2);
    */
   LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, bld->vec_type, "y_2");

   LLVMValueRef const_2 = lp_build_const_int_vec(gallivm, bld->type, 2);
   LLVMValueRef const_4 = lp_build_const_int_vec(gallivm, bld->type, 4);
   LLVMValueRef const_29 = lp_build_const_int_vec(gallivm, bld->type, 29);
   LLVMValueRef sign_mask = lp_build_const_int_vec(gallivm, bld->type, 0x80000000);

   /*
    * Argument used for poly selection and sign bit determination
    * is different for sin vs. cos.
    */
   LLVMValueRef emm2_2 = cos ? LLVMBuildSub(b, emm2_and, const_2, "emm2_2") :
                               emm2_and;

   LLVMValueRef sign_bit = cos ? LLVMBuildShl(b, LLVMBuildAnd(b, const_4,
                                                              LLVMBuildNot(b, emm2_2, ""), ""),
                                              const_29, "sign_bit") :
                                 LLVMBuildAnd(b, LLVMBuildXor(b, a_v4si,
                                                              LLVMBuildShl(b, emm2_add,
                                                                           const_29, ""), ""),
                                              sign_mask, "sign_bit");

   /*
    * get the polynom selection mask
    * there is one polynom for 0 <= x <= Pi/4
    * and another one for Pi/4<x<=Pi/2
    * Both branches will be computed.
    *
    * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
    * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
    */

   LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, const_2, "emm2_3");
   LLVMValueRef poly_mask = lp_build_compare(gallivm,
                                             int_type, PIPE_FUNC_EQUAL,
                                             emm2_3, lp_build_const_int_vec(gallivm, bld->type, 0));

   /*
    * _PS_CONST(minus_cephes_DP1, -0.78515625);
    * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
    * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
    */
   LLVMValueRef DP1 = lp_build_const_vec(gallivm, bld->type, -0.78515625);
   LLVMValueRef DP2 = lp_build_const_vec(gallivm, bld->type, -2.4187564849853515625e-4);
   LLVMValueRef DP3 = lp_build_const_vec(gallivm, bld->type, -3.77489497744594108e-8);

   /*
    * The magic pass: "Extended precision modular arithmetic"
    * x = ((x - y * DP1) - y * DP2) - y * DP3;
    */
   LLVMValueRef x_1 = lp_build_fmuladd(b, y_2, DP1, x_abs);
   LLVMValueRef x_2 = lp_build_fmuladd(b, y_2, DP2, x_1);
   LLVMValueRef x_3 = lp_build_fmuladd(b, y_2, DP3, x_2);

   /*
    * Evaluate the first polynom  (0 <= x <= Pi/4)
    *
    * z = _mm_mul_ps(x,x);
    */
   LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");

   /*
    * _PS_CONST(coscof_p0,  2.443315711809948E-005);
    * _PS_CONST(coscof_p1, -1.388731625493765E-003);
    * _PS_CONST(coscof_p2,  4.166664568298827E-002);
    */
   LLVMValueRef coscof_p0 = lp_build_const_vec(gallivm, bld->type, 2.443315711809948E-005);
   LLVMValueRef coscof_p1 = lp_build_const_vec(gallivm, bld->type, -1.388731625493765E-003);
   LLVMValueRef coscof_p2 = lp_build_const_vec(gallivm, bld->type, 4.166664568298827E-002);

   /*
    * y = *(v4sf*)_ps_coscof_p0;
    * y = _mm_mul_ps(y, z);
    */
   LLVMValueRef y_4 = lp_build_fmuladd(b, z, coscof_p0, coscof_p1);
   LLVMValueRef y_6 = lp_build_fmuladd(b, y_4, z, coscof_p2);
   LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
   LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");


   /*
    * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
    * y = _mm_sub_ps(y, tmp);
    * y = _mm_add_ps(y, *(v4sf*)_ps_1);
    */
   LLVMValueRef half = lp_build_const_vec(gallivm, bld->type, 0.5);
   LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
   LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
   LLVMValueRef one = lp_build_const_vec(gallivm, bld->type, 1.0);
   LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");

   /*
    * _PS_CONST(sincof_p0, -1.9515295891E-4);
    * _PS_CONST(sincof_p1,  8.3321608736E-3);
    * _PS_CONST(sincof_p2, -1.6666654611E-1);
    */
   LLVMValueRef sincof_p0 = lp_build_const_vec(gallivm, bld->type, -1.9515295891E-4);
   LLVMValueRef sincof_p1 = lp_build_const_vec(gallivm, bld->type, 8.3321608736E-3);
   LLVMValueRef sincof_p2 = lp_build_const_vec(gallivm, bld->type, -1.6666654611E-1);

   /*
    * Evaluate the second polynom  (Pi/4 <= x <= 0)
    *
    * y2 = *(v4sf*)_ps_sincof_p0;
    * y2 = _mm_mul_ps(y2, z);
    * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
    * y2 = _mm_mul_ps(y2, z);
    * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
    * y2 = _mm_mul_ps(y2, z);
    * y2 = _mm_mul_ps(y2, x);
    * y2 = _mm_add_ps(y2, x);
    */

   LLVMValueRef y2_4 = lp_build_fmuladd(b, z, sincof_p0, sincof_p1);
   LLVMValueRef y2_6 = lp_build_fmuladd(b, y2_4, z, sincof_p2);
   LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
   LLVMValueRef y2_9 = lp_build_fmuladd(b, y2_7, x_3, x_3);

   /*
    * select the correct result from the two polynoms
    * xmm3 = poly_mask;
    * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
    * y = _mm_andnot_ps(xmm3, y);
    * y = _mm_or_ps(y,y2);
    */
   LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, bld->int_vec_type, "y2_i");
   LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, bld->int_vec_type, "y_i");
   LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
   LLVMValueRef poly_mask_inv = LLVMBuildNot(b, poly_mask, "poly_mask_inv");
   LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
   LLVMValueRef y_combine = LLVMBuildOr(b, y_and, y2_and, "y_combine");

   /*
    * update the sign
    * y = _mm_xor_ps(y, sign_bit);
    */
   LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sign");
   LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, bld->vec_type, "y_result");

   LLVMValueRef isfinite = lp_build_isfinite(bld, a);

   /* clamp output to be within [-1, 1] */
   y_result = lp_build_clamp(bld, y_result,
                             lp_build_const_vec(bld->gallivm, bld->type,  -1.f),
                             lp_build_const_vec(bld->gallivm, bld->type,  1.f));
   /* If a is -inf, inf or NaN then return NaN */
   y_result = lp_build_select(bld, isfinite, y_result,
                              lp_build_const_vec(bld->gallivm, bld->type,  NAN));
   return y_result;
}


/**
 * Generate sin(a)
 */
LLVMValueRef
lp_build_sin(struct lp_build_context *bld,
             LLVMValueRef a)
{
   const struct lp_type type = bld->type;

   if (type.width == 16) {
      LLVMBuilderRef builder = bld->gallivm->builder;
      LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
      char intrinsic[32];
      lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.sin", vec_type);
      LLVMValueRef args[] = { a };
      return lp_build_intrinsic(builder, intrinsic, vec_type, args, 1, 0);
   }

   return lp_build_sin_or_cos(bld, a, FALSE);
}


/**
 * Generate cos(a)
 */
LLVMValueRef
lp_build_cos(struct lp_build_context *bld,
             LLVMValueRef a)
{
   const struct lp_type type = bld->type;

   if (type.width == 16) {
      LLVMBuilderRef builder = bld->gallivm->builder;
      LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
      char intrinsic[32];
      lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.cos", vec_type);
      LLVMValueRef args[] = { a };
      return lp_build_intrinsic(builder, intrinsic, vec_type, args, 1, 0);
   }

   return lp_build_sin_or_cos(bld, a, TRUE);
}


/**
 * Generate pow(x, y)
 */
LLVMValueRef
lp_build_pow(struct lp_build_context *bld,
             LLVMValueRef x,
             LLVMValueRef y)
{
   /* TODO: optimize the constant case */
   if (gallivm_debug & GALLIVM_DEBUG_PERF &&
       LLVMIsConstant(x) && LLVMIsConstant(y)) {
      debug_printf("%s: inefficient/imprecise constant arithmetic\n",
                   __FUNCTION__);
   }

   LLVMValueRef cmp = lp_build_cmp(bld, PIPE_FUNC_EQUAL, x, lp_build_const_vec(bld->gallivm, bld->type, 0.0f));
   LLVMValueRef res = lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2_safe(bld, x), y));

   res = lp_build_select(bld, cmp, lp_build_const_vec(bld->gallivm, bld->type, 0.0f), res);
   return res;
}


/**
 * Generate exp(x)
 */
LLVMValueRef
lp_build_exp(struct lp_build_context *bld,
             LLVMValueRef x)
{
   /* log2(e) = 1/log(2) */
   LLVMValueRef log2e = lp_build_const_vec(bld->gallivm, bld->type,
                                           1.4426950408889634);

   assert(lp_check_value(bld->type, x));

   return lp_build_exp2(bld, lp_build_mul(bld, log2e, x));
}


/**
 * Generate log(x)
 * Behavior is undefined with infs, 0s and nans
 */
LLVMValueRef
lp_build_log(struct lp_build_context *bld,
             LLVMValueRef x)
{
   /* log(2) */
   LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type,
                                          0.69314718055994529);

   assert(lp_check_value(bld->type, x));

   return lp_build_mul(bld, log2, lp_build_log2(bld, x));
}


/**
 * Generate log(x) that handles edge cases (infs, 0s and nans)
 */
LLVMValueRef
lp_build_log_safe(struct lp_build_context *bld,
                  LLVMValueRef x)
{
   /* log(2) */
   LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type,
                                          0.69314718055994529);

   assert(lp_check_value(bld->type, x));

   return lp_build_mul(bld, log2, lp_build_log2_safe(bld, x));
}


/**
 * Generate polynomial.
 * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
 */
LLVMValueRef
lp_build_polynomial(struct lp_build_context *bld,
                    LLVMValueRef x,
                    const double *coeffs,
                    unsigned num_coeffs)
{
   const struct lp_type type = bld->type;
   LLVMValueRef even = NULL, odd = NULL;
   LLVMValueRef x2;
   unsigned i;

   assert(lp_check_value(bld->type, x));

   /* TODO: optimize the constant case */
   if (gallivm_debug & GALLIVM_DEBUG_PERF &&
       LLVMIsConstant(x)) {
      debug_printf("%s: inefficient/imprecise constant arithmetic\n",
                   __FUNCTION__);
   }

   /*
    * Calculate odd and even terms seperately to decrease data dependency
    * Ex:
    *     c[0] + x^2 * c[2] + x^4 * c[4] ...
    *     + x * (c[1] + x^2 * c[3] + x^4 * c[5]) ...
    */
   x2 = lp_build_mul(bld, x, x);

   for (i = num_coeffs; i--; ) {
      LLVMValueRef coeff;

      coeff = lp_build_const_vec(bld->gallivm, type, coeffs[i]);

      if (i % 2 == 0) {
         if (even)
            even = lp_build_mad(bld, x2, even, coeff);
         else
            even = coeff;
      } else {
         if (odd)
            odd = lp_build_mad(bld, x2, odd, coeff);
         else
            odd = coeff;
      }
   }

   if (odd)
      return lp_build_mad(bld, odd, x, even);
   else if (even)
      return even;
   else
      return bld->undef;
}


/**
 * Minimax polynomial fit of 2**x, in range [0, 1[
 */
static const double lp_build_exp2_polynomial[] = {
#if EXP_POLY_DEGREE == 5
   1.000000000000000000000, /*XXX: was 0.999999925063526176901, recompute others */
   0.693153073200168932794,
   0.240153617044375388211,
   0.0558263180532956664775,
   0.00898934009049466391101,
   0.00187757667519147912699
#elif EXP_POLY_DEGREE == 4
   1.00000259337069434683,
   0.693003834469974940458,
   0.24144275689150793076,
   0.0520114606103070150235,
   0.0135341679161270268764
#elif EXP_POLY_DEGREE == 3
   0.999925218562710312959,
   0.695833540494823811697,
   0.226067155427249155588,
   0.0780245226406372992967
#elif EXP_POLY_DEGREE == 2
   1.00172476321474503578,
   0.657636275736077639316,
   0.33718943461968720704
#else
#error
#endif
};


LLVMValueRef
lp_build_exp2(struct lp_build_context *bld,
              LLVMValueRef x)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
   LLVMValueRef ipart = NULL;
   LLVMValueRef fpart = NULL;
   LLVMValueRef expipart = NULL;
   LLVMValueRef expfpart = NULL;
   LLVMValueRef res = NULL;

   if (type.floating && type.width == 16) {
      char intrinsic[32];
      lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.exp2", vec_type);
      LLVMValueRef args[] = { x };
      return lp_build_intrinsic(builder, intrinsic, vec_type, args, 1, 0);
   }

   assert(lp_check_value(bld->type, x));

   /* TODO: optimize the constant case */
   if (gallivm_debug & GALLIVM_DEBUG_PERF &&
       LLVMIsConstant(x)) {
      debug_printf("%s: inefficient/imprecise constant arithmetic\n",
                   __FUNCTION__);
   }

   assert(type.floating && type.width == 32);

   /* We want to preserve NaN and make sure than for exp2 if x > 128,
    * the result is INF  and if it's smaller than -126.9 the result is 0 */
   x = lp_build_min_ext(bld, lp_build_const_vec(bld->gallivm, type,  128.0), x,
                        GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN);
   x = lp_build_max_ext(bld, lp_build_const_vec(bld->gallivm, type, -126.99999),
                        x, GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN);

   /* ipart = floor(x) */
   /* fpart = x - ipart */
   lp_build_ifloor_fract(bld, x, &ipart, &fpart);

   /* expipart = (float) (1 << ipart) */
   expipart = LLVMBuildAdd(builder, ipart,
                           lp_build_const_int_vec(bld->gallivm, type, 127), "");
   expipart = LLVMBuildShl(builder, expipart,
                           lp_build_const_int_vec(bld->gallivm, type, 23), "");
   expipart = LLVMBuildBitCast(builder, expipart, vec_type, "");

   expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
                                  ARRAY_SIZE(lp_build_exp2_polynomial));

   res = LLVMBuildFMul(builder, expipart, expfpart, "");

   return res;
}


/**
 * Extract the exponent of a IEEE-754 floating point value.
 *
 * Optionally apply an integer bias.
 *
 * Result is an integer value with
 *
 *   ifloor(log2(x)) + bias
 */
LLVMValueRef
lp_build_extract_exponent(struct lp_build_context *bld,
                          LLVMValueRef x,
                          int bias)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   unsigned mantissa = lp_mantissa(type);
   LLVMValueRef res;

   assert(type.floating);

   assert(lp_check_value(bld->type, x));

   x = LLVMBuildBitCast(builder, x, bld->int_vec_type, "");

   res = LLVMBuildLShr(builder, x,
                       lp_build_const_int_vec(bld->gallivm, type, mantissa), "");
   res = LLVMBuildAnd(builder, res,
                      lp_build_const_int_vec(bld->gallivm, type, 255), "");
   res = LLVMBuildSub(builder, res,
                      lp_build_const_int_vec(bld->gallivm, type, 127 - bias), "");

   return res;
}


/**
 * Extract the mantissa of the a floating.
 *
 * Result is a floating point value with
 *
 *   x / floor(log2(x))
 */
LLVMValueRef
lp_build_extract_mantissa(struct lp_build_context *bld,
                          LLVMValueRef x)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   unsigned mantissa = lp_mantissa(type);
   LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type,
                                                  (1ULL << mantissa) - 1);
   LLVMValueRef one = LLVMConstBitCast(bld->one, bld->int_vec_type);
   LLVMValueRef res;

   assert(lp_check_value(bld->type, x));

   assert(type.floating);

   x = LLVMBuildBitCast(builder, x, bld->int_vec_type, "");

   /* res = x / 2**ipart */
   res = LLVMBuildAnd(builder, x, mantmask, "");
   res = LLVMBuildOr(builder, res, one, "");
   res = LLVMBuildBitCast(builder, res, bld->vec_type, "");

   return res;
}



/**
 * Minimax polynomial fit of log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x) ,for x in range of [0, 1/9[
 * These coefficients can be generate with
 * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
 */
static const double lp_build_log2_polynomial[] = {
#if LOG_POLY_DEGREE == 5
   2.88539008148777786488L,
   0.961796878841293367824L,
   0.577058946784739859012L,
   0.412914355135828735411L,
   0.308591899232910175289L,
   0.352376952300281371868L,
#elif LOG_POLY_DEGREE == 4
   2.88539009343309178325L,
   0.961791550404184197881L,
   0.577440339438736392009L,
   0.403343858251329912514L,
   0.406718052498846252698L,
#elif LOG_POLY_DEGREE == 3
   2.88538959748872753838L,
   0.961932915889597772928L,
   0.571118517972136195241L,
   0.493997535084709500285L,
#else
#error
#endif
};


/**
 * See http://www.devmaster.net/forums/showthread.php?p=43580
 * http://en.wikipedia.org/wiki/Logarithm#Calculation
 * http://www.nezumi.demon.co.uk/consult/logx.htm
 *
 * If handle_edge_cases is true the function will perform computations
 * to match the required D3D10+ behavior for each of the edge cases.
 * That means that if input is:
 * - less than zero (to and including -inf) then NaN will be returned
 * - equal to zero (-denorm, -0, +0 or +denorm), then -inf will be returned
 * - +infinity, then +infinity will be returned
 * - NaN, then NaN will be returned
 *
 * Those checks are fairly expensive so if you don't need them make sure
 * handle_edge_cases is false.
 */
void
lp_build_log2_approx(struct lp_build_context *bld,
                     LLVMValueRef x,
                     LLVMValueRef *p_exp,
                     LLVMValueRef *p_floor_log2,
                     LLVMValueRef *p_log2,
                     boolean handle_edge_cases)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   const struct lp_type type = bld->type;
   LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
   LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);

   LLVMValueRef expmask = lp_build_const_int_vec(bld->gallivm, type, 0x7f800000);
   LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type, 0x007fffff);
   LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);

   LLVMValueRef i = NULL;
   LLVMValueRef y = NULL;
   LLVMValueRef z = NULL;
   LLVMValueRef exp = NULL;
   LLVMValueRef mant = NULL;
   LLVMValueRef logexp = NULL;
   LLVMValueRef p_z = NULL;
   LLVMValueRef res = NULL;

   if (bld->type.width == 16) {
      char intrinsic[32];
      lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.log2", bld->vec_type);
      LLVMValueRef args[] = { x };
      if (p_log2)
         *p_log2 = lp_build_intrinsic(builder, intrinsic, bld->vec_type, args, 1, 0);
      return;
   }

   assert(lp_check_value(bld->type, x));

   if (p_exp || p_floor_log2 || p_log2) {
      /* TODO: optimize the constant case */
      if (gallivm_debug & GALLIVM_DEBUG_PERF &&
          LLVMIsConstant(x)) {
         debug_printf("%s: inefficient/imprecise constant arithmetic\n",
                      __FUNCTION__);
      }

      assert(type.floating && type.width == 32);

      /*
       * We don't explicitly handle denormalized numbers. They will yield a
       * result in the neighbourhood of -127, which appears to be adequate
       * enough.
       */

      i = LLVMBuildBitCast(builder, x, int_vec_type, "");

      /* exp = (float) exponent(x) */
      exp = LLVMBuildAnd(builder, i, expmask, "");
   }

   if (p_floor_log2 || p_log2) {
      logexp = LLVMBuildLShr(builder, exp, lp_build_const_int_vec(bld->gallivm, type, 23), "");
      logexp = LLVMBuildSub(builder, logexp, lp_build_const_int_vec(bld->gallivm, type, 127), "");
      logexp = LLVMBuildSIToFP(builder, logexp, vec_type, "");
   }

   if (p_log2) {
      /* mant = 1 + (float) mantissa(x) */
      mant = LLVMBuildAnd(builder, i, mantmask, "");
      mant = LLVMBuildOr(builder, mant, one, "");
      mant = LLVMBuildBitCast(builder, mant, vec_type, "");

      /* y = (mant - 1) / (mant + 1) */
      y = lp_build_div(bld,
         lp_build_sub(bld, mant, bld->one),
         lp_build_add(bld, mant, bld->one));

      /* z = y^2 */
      z = lp_build_mul(bld, y, y);

      /* compute P(z) */
      p_z = lp_build_polynomial(bld, z, lp_build_log2_polynomial,
                                ARRAY_SIZE(lp_build_log2_polynomial));

      /* y * P(z) + logexp */
      res = lp_build_mad(bld, y, p_z, logexp);

      if (type.floating && handle_edge_cases) {
         LLVMValueRef negmask, infmask,  zmask;
         negmask = lp_build_cmp(bld, PIPE_FUNC_LESS, x,
                                lp_build_const_vec(bld->gallivm, type,  0.0f));
         zmask = lp_build_cmp(bld, PIPE_FUNC_EQUAL, x,
                              lp_build_const_vec(bld->gallivm, type,  0.0f));
         infmask = lp_build_cmp(bld, PIPE_FUNC_GEQUAL, x,
                                lp_build_const_vec(bld->gallivm, type,  INFINITY));

         /* If x is qual to inf make sure we return inf */
         res = lp_build_select(bld, infmask,
                               lp_build_const_vec(bld->gallivm, type,  INFINITY),
                               res);
         /* If x is qual to 0, return -inf */
         res = lp_build_select(bld, zmask,
                               lp_build_const_vec(bld->gallivm, type,  -INFINITY),
                               res);
         /* If x is nan or less than 0, return nan */
         res = lp_build_select(bld, negmask,
                               lp_build_const_vec(bld->gallivm, type,  NAN),
                               res);
      }
   }

   if (p_exp) {
      exp = LLVMBuildBitCast(builder, exp, vec_type, "");
      *p_exp = exp;
   }

   if (p_floor_log2)
      *p_floor_log2 = logexp;

   if (p_log2)
      *p_log2 = res;
}


/*
 * log2 implementation which doesn't have special code to
 * handle edge cases (-inf, 0, inf, NaN). It's faster but
 * the results for those cases are undefined.
 */
LLVMValueRef
lp_build_log2(struct lp_build_context *bld,
              LLVMValueRef x)
{
   LLVMValueRef res;
   lp_build_log2_approx(bld, x, NULL, NULL, &res, FALSE);
   return res;
}


/*
 * Version of log2 which handles all edge cases.
 * Look at documentation of lp_build_log2_approx for
 * description of the behavior for each of the edge cases.
 */
LLVMValueRef
lp_build_log2_safe(struct lp_build_context *bld,
                   LLVMValueRef x)
{
   LLVMValueRef res;
   lp_build_log2_approx(bld, x, NULL, NULL, &res, TRUE);
   return res;
}


/**
 * Faster (and less accurate) log2.
 *
 *    log2(x) = floor(log2(x)) - 1 + x / 2**floor(log2(x))
 *
 * Piece-wise linear approximation, with exact results when x is a
 * power of two.
 *
 * See http://www.flipcode.com/archives/Fast_log_Function.shtml
 */
LLVMValueRef
lp_build_fast_log2(struct lp_build_context *bld,
                   LLVMValueRef x)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef ipart;
   LLVMValueRef fpart;

   assert(lp_check_value(bld->type, x));

   assert(bld->type.floating);

   /* ipart = floor(log2(x)) - 1 */
   ipart = lp_build_extract_exponent(bld, x, -1);
   ipart = LLVMBuildSIToFP(builder, ipart, bld->vec_type, "");

   /* fpart = x / 2**ipart */
   fpart = lp_build_extract_mantissa(bld, x);

   /* ipart + fpart */
   return LLVMBuildFAdd(builder, ipart, fpart, "");
}


/**
 * Fast implementation of iround(log2(x)).
 *
 * Not an approximation -- it should give accurate results all the time.
 */
LLVMValueRef
lp_build_ilog2(struct lp_build_context *bld,
               LLVMValueRef x)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef sqrt2 = lp_build_const_vec(bld->gallivm, bld->type, M_SQRT2);
   LLVMValueRef ipart;

   assert(bld->type.floating);

   assert(lp_check_value(bld->type, x));

   /* x * 2^(0.5)   i.e., add 0.5 to the log2(x) */
   x = LLVMBuildFMul(builder, x, sqrt2, "");

   /* ipart = floor(log2(x) + 0.5)  */
   ipart = lp_build_extract_exponent(bld, x, 0);

   return ipart;
}

LLVMValueRef
lp_build_mod(struct lp_build_context *bld,
             LLVMValueRef x,
             LLVMValueRef y)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMValueRef res;
   const struct lp_type type = bld->type;

   assert(lp_check_value(type, x));
   assert(lp_check_value(type, y));

   if (type.floating)
      res = LLVMBuildFRem(builder, x, y, "");
   else if (type.sign)
      res = LLVMBuildSRem(builder, x, y, "");
   else
      res = LLVMBuildURem(builder, x, y, "");
   return res;
}


/*
 * For floating inputs it creates and returns a mask
 * which is all 1's for channels which are NaN.
 * Channels inside x which are not NaN will be 0.
 */
LLVMValueRef
lp_build_isnan(struct lp_build_context *bld,
               LLVMValueRef x)
{
   LLVMValueRef mask;
   LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, bld->type);

   assert(bld->type.floating);
   assert(lp_check_value(bld->type, x));

   mask = LLVMBuildFCmp(bld->gallivm->builder, LLVMRealOEQ, x, x,
                        "isnotnan");
   mask = LLVMBuildNot(bld->gallivm->builder, mask, "");
   mask = LLVMBuildSExt(bld->gallivm->builder, mask, int_vec_type, "isnan");
   return mask;
}


/* Returns all 1's for floating point numbers that are
 * finite numbers and returns all zeros for -inf,
 * inf and nan's */
LLVMValueRef
lp_build_isfinite(struct lp_build_context *bld,
                  LLVMValueRef x)
{
   LLVMBuilderRef builder = bld->gallivm->builder;
   LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, bld->type);
   struct lp_type int_type = lp_int_type(bld->type);
   LLVMValueRef intx = LLVMBuildBitCast(builder, x, int_vec_type, "");
   LLVMValueRef infornan32 = lp_build_const_int_vec(bld->gallivm, bld->type,
                                                    0x7f800000);

   if (!bld->type.floating) {
      return lp_build_const_int_vec(bld->gallivm, bld->type, 0);
   }
   assert(bld->type.floating);
   assert(lp_check_value(bld->type, x));
   assert(bld->type.width == 32);

   intx = LLVMBuildAnd(builder, intx, infornan32, "");
   return lp_build_compare(bld->gallivm, int_type, PIPE_FUNC_NOTEQUAL,
                           intx, infornan32);
}


/*
 * Returns true if the number is nan or inf and false otherwise.
 * The input has to be a floating point vector.
 */
LLVMValueRef
lp_build_is_inf_or_nan(struct gallivm_state *gallivm,
                       const struct lp_type type,
                       LLVMValueRef x)
{
   LLVMBuilderRef builder = gallivm->builder;
   struct lp_type int_type = lp_int_type(type);
   LLVMValueRef const0 = lp_build_const_int_vec(gallivm, int_type,
                                                0x7f800000);
   LLVMValueRef ret;

   assert(type.floating);

   ret = LLVMBuildBitCast(builder, x, lp_build_vec_type(gallivm, int_type), "");
   ret = LLVMBuildAnd(builder, ret, const0, "");
   ret = lp_build_compare(gallivm, int_type, PIPE_FUNC_EQUAL,
                          ret, const0);

   return ret;
}


LLVMValueRef
lp_build_fpstate_get(struct gallivm_state *gallivm)
{
   if (util_get_cpu_caps()->has_sse) {
      LLVMBuilderRef builder = gallivm->builder;
      LLVMValueRef mxcsr_ptr = lp_build_alloca(
         gallivm,
         LLVMInt32TypeInContext(gallivm->context),
         "mxcsr_ptr");
      LLVMValueRef mxcsr_ptr8 = LLVMBuildPointerCast(builder, mxcsr_ptr,
          LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0), "");
      lp_build_intrinsic(builder,
                         "llvm.x86.sse.stmxcsr",
                         LLVMVoidTypeInContext(gallivm->context),
                         &mxcsr_ptr8, 1, 0);
      return mxcsr_ptr;
   }
   return 0;
}

void
lp_build_fpstate_set_denorms_zero(struct gallivm_state *gallivm,
                                  boolean zero)
{
   if (util_get_cpu_caps()->has_sse) {
      /* turn on DAZ (64) | FTZ (32768) = 32832 if available */
      int daz_ftz = _MM_FLUSH_ZERO_MASK;

      LLVMBuilderRef builder = gallivm->builder;
      LLVMValueRef mxcsr_ptr = lp_build_fpstate_get(gallivm);
      LLVMValueRef mxcsr =
         LLVMBuildLoad2(builder, LLVMInt32TypeInContext(gallivm->context), mxcsr_ptr, "mxcsr");

      if (util_get_cpu_caps()->has_daz) {
         /* Enable denormals are zero mode */
         daz_ftz |= _MM_DENORMALS_ZERO_MASK;
      }
      if (zero) {
         mxcsr = LLVMBuildOr(builder, mxcsr,
                             LLVMConstInt(LLVMTypeOf(mxcsr), daz_ftz, 0), "");
      } else {
         mxcsr = LLVMBuildAnd(builder, mxcsr,
                              LLVMConstInt(LLVMTypeOf(mxcsr), ~daz_ftz, 0), "");
      }

      LLVMBuildStore(builder, mxcsr, mxcsr_ptr);
      lp_build_fpstate_set(gallivm, mxcsr_ptr);
   }
}


void
lp_build_fpstate_set(struct gallivm_state *gallivm,
                     LLVMValueRef mxcsr_ptr)
{
   if (util_get_cpu_caps()->has_sse) {
      LLVMBuilderRef builder = gallivm->builder;
      mxcsr_ptr = LLVMBuildPointerCast(builder, mxcsr_ptr,
                     LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0), "");
      lp_build_intrinsic(builder,
                         "llvm.x86.sse.ldmxcsr",
                         LLVMVoidTypeInContext(gallivm->context),
                         &mxcsr_ptr, 1, 0);
   }
}