src/gallium/auxiliary/gallivm/lp_bld_arit.c

   1 /**************************************************************************
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   3  * Copyright 2009-2010 VMware, Inc.
   4  * All Rights Reserved.
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   7  * copy of this software and associated documentation files (the
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   9  * without limitation the rights to use, copy, modify, merge, publish,
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  11  * permit persons to whom the Software is furnished to do so, subject to
  12  * the following conditions:
  13  *
  14  * The above copyright notice and this permission notice (including the
  15  * next paragraph) shall be included in all copies or substantial portions
  16  * of the Software.
  17  *
  18  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  19  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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  23  * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
  24  * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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  27
  28
  29 /**
  30  * @file
  31  * Helper
  32  *
  33  * LLVM IR doesn't support all basic arithmetic operations we care about (most
  34  * notably min/max and saturated operations), and it is often necessary to
  35  * resort machine-specific intrinsics directly. The functions here hide all
  36  * these implementation details from the other modules.
  37  *
  38  * We also do simple expressions simplification here. Reasons are:
  39  * - it is very easy given we have all necessary information readily available
  40  * - LLVM optimization passes fail to simplify several vector expressions
  41  * - We often know value constraints which the optimization passes have no way
  42  *   of knowing, such as when source arguments are known to be in [0, 1] range.
  43  *
  44  * @author Jose Fonseca <jfonseca@vmware.com>
  45  */
  46
  47
  48 #include <float.h>
  49
  50 #include "util/u_memory.h"
  51 #include "util/u_debug.h"
  52 #include "util/u_math.h"
  53 #include "util/u_string.h"
  54 #include "util/u_cpu_detect.h"
  55
  56 #include "lp_bld_type.h"
  57 #include "lp_bld_const.h"
  58 #include "lp_bld_init.h"
  59 #include "lp_bld_intr.h"
  60 #include "lp_bld_logic.h"
  61 #include "lp_bld_pack.h"
  62 #include "lp_bld_debug.h"
  63 #include "lp_bld_bitarit.h"
  64 #include "lp_bld_arit.h"
  65 #include "lp_bld_flow.h"
  66
  67 #if defined(PIPE_ARCH_SSE)
  68 #include <xmmintrin.h>
  69 #endif
  70
  71 #ifndef _MM_DENORMALS_ZERO_MASK
  72 #define _MM_DENORMALS_ZERO_MASK 0x0040
  73 #endif
  74
  75 #ifndef _MM_FLUSH_ZERO_MASK
  76 #define _MM_FLUSH_ZERO_MASK 0x8000
  77 #endif
  78
  79 #define EXP_POLY_DEGREE 5
  80
  81 #define LOG_POLY_DEGREE 4
  82
  83
  84 /**
  85  * Generate min(a, b)
  86  * No checks for special case values of a or b = 1 or 0 are done.
  87  * NaN's are handled according to the behavior specified by the
  88  * nan_behavior argument.
  89  */
  90 static LLVMValueRef
  91 lp_build_min_simple(struct lp_build_context *bld,
  92                     LLVMValueRef a,
  93                     LLVMValueRef b,
  94                     enum gallivm_nan_behavior nan_behavior)
  95 {
  96    const struct lp_type type = bld->type;
  97    const char *intrinsic = NULL;
  98    unsigned intr_size = 0;
  99    LLVMValueRef cond;
 100
 101    assert(lp_check_value(type, a));
 102    assert(lp_check_value(type, b));
 103
 104    /* TODO: optimize the constant case */
 105
 106    if (type.floating && util_cpu_caps.has_sse) {
 107       if (type.width == 32) {
 108          if (type.length == 1) {
 109             intrinsic = "llvm.x86.sse.min.ss";
 110             intr_size = 128;
 111          }
 112          else if (type.length <= 4 || !util_cpu_caps.has_avx) {
 113             intrinsic = "llvm.x86.sse.min.ps";
 114             intr_size = 128;
 115          }
 116          else {
 117             intrinsic = "llvm.x86.avx.min.ps.256";
 118             intr_size = 256;
 119          }
 120       }
 121       if (type.width == 64 && util_cpu_caps.has_sse2) {
 122          if (type.length == 1) {
 123             intrinsic = "llvm.x86.sse2.min.sd";
 124             intr_size = 128;
 125          }
 126          else if (type.length == 2 || !util_cpu_caps.has_avx) {
 127             intrinsic = "llvm.x86.sse2.min.pd";
 128             intr_size = 128;
 129          }
 130          else {
 131             intrinsic = "llvm.x86.avx.min.pd.256";
 132             intr_size = 256;
 133          }
 134       }
 135    }
 136    else if (type.floating && util_cpu_caps.has_altivec) {
 137       if (nan_behavior == GALLIVM_NAN_RETURN_NAN ||
 138           nan_behavior == GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN) {
 139          debug_printf("%s: altivec doesn't support nan return nan behavior\n",
 140                       __FUNCTION__);
 141       }
 142       if (type.width == 32 && type.length == 4) {
 143          intrinsic = "llvm.ppc.altivec.vminfp";
 144          intr_size = 128;
 145       }
 146    } else if (util_cpu_caps.has_sse2 && type.length >= 2) {
 147       intr_size = 128;
 148       if ((type.width == 8 || type.width == 16) &&
 149           (type.width * type.length <= 64) &&
 150           (gallivm_debug & GALLIVM_DEBUG_PERF)) {
 151          debug_printf("%s: inefficient code, bogus shuffle due to packing\n",
 152                       __FUNCTION__);
 153       }
 154       if (type.width == 8 && !type.sign) {
 155          intrinsic = "llvm.x86.sse2.pminu.b";
 156       }
 157       else if (type.width == 16 && type.sign) {
 158          intrinsic = "llvm.x86.sse2.pmins.w";
 159       }
 160       if (util_cpu_caps.has_sse4_1) {
 161          if (type.width == 8 && type.sign) {
 162             intrinsic = "llvm.x86.sse41.pminsb";
 163          }
 164          if (type.width == 16 && !type.sign) {
 165             intrinsic = "llvm.x86.sse41.pminuw";
 166          }
 167          if (type.width == 32 && !type.sign) {
 168             intrinsic = "llvm.x86.sse41.pminud";
 169          }
 170          if (type.width == 32 && type.sign) {
 171             intrinsic = "llvm.x86.sse41.pminsd";
 172          }
 173       }
 174    } else if (util_cpu_caps.has_altivec) {
 175       intr_size = 128;
 176       if (type.width == 8) {
 177          if (!type.sign) {
 178             intrinsic = "llvm.ppc.altivec.vminub";
 179          } else {
 180             intrinsic = "llvm.ppc.altivec.vminsb";
 181          }
 182       } else if (type.width == 16) {
 183          if (!type.sign) {
 184             intrinsic = "llvm.ppc.altivec.vminuh";
 185          } else {
 186             intrinsic = "llvm.ppc.altivec.vminsh";
 187          }
 188       } else if (type.width == 32) {
 189          if (!type.sign) {
 190             intrinsic = "llvm.ppc.altivec.vminuw";
 191          } else {
 192             intrinsic = "llvm.ppc.altivec.vminsw";
 193          }
 194       }
 195    }
 196
 197    if(intrinsic) {
 198       /* We need to handle nan's for floating point numbers. If one of the
 199        * inputs is nan the other should be returned (required by both D3D10+
 200        * and OpenCL).
 201        * The sse intrinsics return the second operator in case of nan by
 202        * default so we need to special code to handle those.
 203        */
 204       if (util_cpu_caps.has_sse && type.floating &&
 205           nan_behavior != GALLIVM_NAN_BEHAVIOR_UNDEFINED &&
 206           nan_behavior != GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN &&
 207           nan_behavior != GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN) {
 208          LLVMValueRef isnan, min;
 209          min = lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
 210                                                    type,
 211                                                    intr_size, a, b);
 212          if (nan_behavior == GALLIVM_NAN_RETURN_OTHER) {
 213             isnan = lp_build_isnan(bld, b);
 214             return lp_build_select(bld, isnan, a, min);
 215          } else {
 216             assert(nan_behavior == GALLIVM_NAN_RETURN_NAN);
 217             isnan = lp_build_isnan(bld, a);
 218             return lp_build_select(bld, isnan, a, min);
 219          }
 220       } else {
 221          return lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
 222                                                     type,
 223                                                     intr_size, a, b);
 224       }
 225    }
 226
 227    if (type.floating) {
 228       switch (nan_behavior) {
 229       case GALLIVM_NAN_RETURN_NAN: {
 230          LLVMValueRef isnan = lp_build_isnan(bld, b);
 231          cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 232          cond = LLVMBuildXor(bld->gallivm->builder, cond, isnan, "");
 233          return lp_build_select(bld, cond, a, b);
 234       }
 235          break;
 236       case GALLIVM_NAN_RETURN_OTHER: {
 237          LLVMValueRef isnan = lp_build_isnan(bld, a);
 238          cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 239          cond = LLVMBuildXor(bld->gallivm->builder, cond, isnan, "");
 240          return lp_build_select(bld, cond, a, b);
 241       }
 242          break;
 243       case GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN:
 244          cond = lp_build_cmp_ordered(bld, PIPE_FUNC_LESS, a, b);
 245          return lp_build_select(bld, cond, a, b);
 246       case GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN:
 247          cond = lp_build_cmp(bld, PIPE_FUNC_LESS, b, a);
 248          return lp_build_select(bld, cond, b, a);
 249       case GALLIVM_NAN_BEHAVIOR_UNDEFINED:
 250          cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 251          return lp_build_select(bld, cond, a, b);
 252          break;
 253       default:
 254          assert(0);
 255          cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 256          return lp_build_select(bld, cond, a, b);
 257       }
 258    } else {
 259       cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 260       return lp_build_select(bld, cond, a, b);
 261    }
 262 }
 263
 264
 265 /**
 266  * Generate max(a, b)
 267  * No checks for special case values of a or b = 1 or 0 are done.
 268  * NaN's are handled according to the behavior specified by the
 269  * nan_behavior argument.
 270  */
 271 static LLVMValueRef
 272 lp_build_max_simple(struct lp_build_context *bld,
 273                     LLVMValueRef a,
 274                     LLVMValueRef b,
 275                     enum gallivm_nan_behavior nan_behavior)
 276 {
 277    const struct lp_type type = bld->type;
 278    const char *intrinsic = NULL;
 279    unsigned intr_size = 0;
 280    LLVMValueRef cond;
 281
 282    assert(lp_check_value(type, a));
 283    assert(lp_check_value(type, b));
 284
 285    /* TODO: optimize the constant case */
 286
 287    if (type.floating && util_cpu_caps.has_sse) {
 288       if (type.width == 32) {
 289          if (type.length == 1) {
 290             intrinsic = "llvm.x86.sse.max.ss";
 291             intr_size = 128;
 292          }
 293          else if (type.length <= 4 || !util_cpu_caps.has_avx) {
 294             intrinsic = "llvm.x86.sse.max.ps";
 295             intr_size = 128;
 296          }
 297          else {
 298             intrinsic = "llvm.x86.avx.max.ps.256";
 299             intr_size = 256;
 300          }
 301       }
 302       if (type.width == 64 && util_cpu_caps.has_sse2) {
 303          if (type.length == 1) {
 304             intrinsic = "llvm.x86.sse2.max.sd";
 305             intr_size = 128;
 306          }
 307          else if (type.length == 2 || !util_cpu_caps.has_avx) {
 308             intrinsic = "llvm.x86.sse2.max.pd";
 309             intr_size = 128;
 310          }
 311          else {
 312             intrinsic = "llvm.x86.avx.max.pd.256";
 313             intr_size = 256;
 314          }
 315       }
 316    }
 317    else if (type.floating && util_cpu_caps.has_altivec) {
 318       if (nan_behavior == GALLIVM_NAN_RETURN_NAN ||
 319           nan_behavior == GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN) {
 320          debug_printf("%s: altivec doesn't support nan return nan behavior\n",
 321                       __FUNCTION__);
 322       }
 323       if (type.width == 32 || type.length == 4) {
 324          intrinsic = "llvm.ppc.altivec.vmaxfp";
 325          intr_size = 128;
 326       }
 327    } else if (util_cpu_caps.has_sse2 && type.length >= 2) {
 328       intr_size = 128;
 329       if ((type.width == 8 || type.width == 16) &&
 330           (type.width * type.length <= 64) &&
 331           (gallivm_debug & GALLIVM_DEBUG_PERF)) {
 332          debug_printf("%s: inefficient code, bogus shuffle due to packing\n",
 333                       __FUNCTION__);
 334          }
 335       if (type.width == 8 && !type.sign) {
 336          intrinsic = "llvm.x86.sse2.pmaxu.b";
 337          intr_size = 128;
 338       }
 339       else if (type.width == 16 && type.sign) {
 340          intrinsic = "llvm.x86.sse2.pmaxs.w";
 341       }
 342       if (util_cpu_caps.has_sse4_1) {
 343          if (type.width == 8 && type.sign) {
 344             intrinsic = "llvm.x86.sse41.pmaxsb";
 345          }
 346          if (type.width == 16 && !type.sign) {
 347             intrinsic = "llvm.x86.sse41.pmaxuw";
 348          }
 349          if (type.width == 32 && !type.sign) {
 350             intrinsic = "llvm.x86.sse41.pmaxud";
 351         }
 352          if (type.width == 32 && type.sign) {
 353             intrinsic = "llvm.x86.sse41.pmaxsd";
 354          }
 355       }
 356    } else if (util_cpu_caps.has_altivec) {
 357      intr_size = 128;
 358      if (type.width == 8) {
 359        if (!type.sign) {
 360          intrinsic = "llvm.ppc.altivec.vmaxub";
 361        } else {
 362          intrinsic = "llvm.ppc.altivec.vmaxsb";
 363        }
 364      } else if (type.width == 16) {
 365        if (!type.sign) {
 366          intrinsic = "llvm.ppc.altivec.vmaxuh";
 367        } else {
 368          intrinsic = "llvm.ppc.altivec.vmaxsh";
 369        }
 370      } else if (type.width == 32) {
 371        if (!type.sign) {
 372          intrinsic = "llvm.ppc.altivec.vmaxuw";
 373        } else {
 374          intrinsic = "llvm.ppc.altivec.vmaxsw";
 375        }
 376      }
 377    }
 378
 379    if(intrinsic) {
 380       if (util_cpu_caps.has_sse && type.floating &&
 381           nan_behavior != GALLIVM_NAN_BEHAVIOR_UNDEFINED &&
 382           nan_behavior != GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN &&
 383           nan_behavior != GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN) {
 384          LLVMValueRef isnan, max;
 385          max = lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
 386                                                    type,
 387                                                    intr_size, a, b);
 388          if (nan_behavior == GALLIVM_NAN_RETURN_OTHER) {
 389             isnan = lp_build_isnan(bld, b);
 390             return lp_build_select(bld, isnan, a, max);
 391          } else {
 392             assert(nan_behavior == GALLIVM_NAN_RETURN_NAN);
 393             isnan = lp_build_isnan(bld, a);
 394             return lp_build_select(bld, isnan, a, max);
 395          }
 396       } else {
 397          return lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic,
 398                                                     type,
 399                                                     intr_size, a, b);
 400       }
 401    }
 402
 403    if (type.floating) {
 404       switch (nan_behavior) {
 405       case GALLIVM_NAN_RETURN_NAN: {
 406          LLVMValueRef isnan = lp_build_isnan(bld, b);
 407          cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 408          cond = LLVMBuildXor(bld->gallivm->builder, cond, isnan, "");
 409          return lp_build_select(bld, cond, a, b);
 410       }
 411          break;
 412       case GALLIVM_NAN_RETURN_OTHER: {
 413          LLVMValueRef isnan = lp_build_isnan(bld, a);
 414          cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 415          cond = LLVMBuildXor(bld->gallivm->builder, cond, isnan, "");
 416          return lp_build_select(bld, cond, a, b);
 417       }
 418          break;
 419       case GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN:
 420          cond = lp_build_cmp_ordered(bld, PIPE_FUNC_GREATER, a, b);
 421          return lp_build_select(bld, cond, a, b);
 422       case GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN:
 423          cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, b, a);
 424          return lp_build_select(bld, cond, b, a);
 425       case GALLIVM_NAN_BEHAVIOR_UNDEFINED:
 426          cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 427          return lp_build_select(bld, cond, a, b);
 428          break;
 429       default:
 430          assert(0);
 431          cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 432          return lp_build_select(bld, cond, a, b);
 433       }
 434    } else {
 435       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 436       return lp_build_select(bld, cond, a, b);
 437    }
 438 }
 439
 440
 441 /**
 442  * Generate 1 - a, or ~a depending on bld->type.
 443  */
 444 LLVMValueRef
 445 lp_build_comp(struct lp_build_context *bld,
 446               LLVMValueRef a)
 447 {
 448    LLVMBuilderRef builder = bld->gallivm->builder;
 449    const struct lp_type type = bld->type;
 450
 451    assert(lp_check_value(type, a));
 452
 453    if(a == bld->one)
 454       return bld->zero;
 455    if(a == bld->zero)
 456       return bld->one;
 457
 458    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 459       if(LLVMIsConstant(a))
 460          return LLVMConstNot(a);
 461       else
 462          return LLVMBuildNot(builder, a, "");
 463    }
 464
 465    if(LLVMIsConstant(a))
 466       if (type.floating)
 467           return LLVMConstFSub(bld->one, a);
 468       else
 469           return LLVMConstSub(bld->one, a);
 470    else
 471       if (type.floating)
 472          return LLVMBuildFSub(builder, bld->one, a, "");
 473       else
 474          return LLVMBuildSub(builder, bld->one, a, "");
 475 }
 476
 477
 478 /**
 479  * Generate a + b
 480  */
 481 LLVMValueRef
 482 lp_build_add(struct lp_build_context *bld,
 483              LLVMValueRef a,
 484              LLVMValueRef b)
 485 {
 486    LLVMBuilderRef builder = bld->gallivm->builder;
 487    const struct lp_type type = bld->type;
 488    LLVMValueRef res;
 489
 490    assert(lp_check_value(type, a));
 491    assert(lp_check_value(type, b));
 492
 493    if(a == bld->zero)
 494       return b;
 495    if(b == bld->zero)
 496       return a;
 497    if(a == bld->undef || b == bld->undef)
 498       return bld->undef;
 499
 500    if(bld->type.norm) {
 501       const char *intrinsic = NULL;
 502
 503       if(a == bld->one || b == bld->one)
 504         return bld->one;
 505
 506       if (type.width * type.length == 128 &&
 507           !type.floating && !type.fixed) {
 508          if(util_cpu_caps.has_sse2) {
 509            if(type.width == 8)
 510              intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 511            if(type.width == 16)
 512              intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 513          } else if (util_cpu_caps.has_altivec) {
 514            if(type.width == 8)
 515               intrinsic = type.sign ? "llvm.ppc.altivec.vaddsbs" : "llvm.ppc.altivec.vaddubs";
 516            if(type.width == 16)
 517               intrinsic = type.sign ? "llvm.ppc.altivec.vaddshs" : "llvm.ppc.altivec.vadduhs";
 518          }
 519       }
 520
 521       if(intrinsic)
 522          return lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(bld->gallivm, bld->type), a, b);
 523    }
 524
 525    if(type.norm && !type.floating && !type.fixed) {
 526       if (type.sign) {
 527          uint64_t sign = (uint64_t)1 << (type.width - 1);
 528          LLVMValueRef max_val = lp_build_const_int_vec(bld->gallivm, type, sign - 1);
 529          LLVMValueRef min_val = lp_build_const_int_vec(bld->gallivm, type, sign);
 530          /* a_clamp_max is the maximum a for positive b,
 531             a_clamp_min is the minimum a for negative b. */
 532          LLVMValueRef a_clamp_max = lp_build_min_simple(bld, a, LLVMBuildSub(builder, max_val, b, ""), GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 533          LLVMValueRef a_clamp_min = lp_build_max_simple(bld, a, LLVMBuildSub(builder, min_val, b, ""), GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 534          a = lp_build_select(bld, lp_build_cmp(bld, PIPE_FUNC_GREATER, b, bld->zero), a_clamp_max, a_clamp_min);
 535       } else {
 536          a = lp_build_min_simple(bld, a, lp_build_comp(bld, b), GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 537       }
 538    }
 539
 540    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 541       if (type.floating)
 542          res = LLVMConstFAdd(a, b);
 543       else
 544          res = LLVMConstAdd(a, b);
 545    else
 546       if (type.floating)
 547          res = LLVMBuildFAdd(builder, a, b, "");
 548       else
 549          res = LLVMBuildAdd(builder, a, b, "");
 550
 551    /* clamp to ceiling of 1.0 */
 552    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 553       res = lp_build_min_simple(bld, res, bld->one, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 554
 555    /* XXX clamp to floor of -1 or 0??? */
 556
 557    return res;
 558 }
 559
 560
 561 /** Return the scalar sum of the elements of a.
 562  * Should avoid this operation whenever possible.
 563  */
 564 LLVMValueRef
 565 lp_build_horizontal_add(struct lp_build_context *bld,
 566                         LLVMValueRef a)
 567 {
 568    LLVMBuilderRef builder = bld->gallivm->builder;
 569    const struct lp_type type = bld->type;
 570    LLVMValueRef index, res;
 571    unsigned i, length;
 572    LLVMValueRef shuffles1[LP_MAX_VECTOR_LENGTH / 2];
 573    LLVMValueRef shuffles2[LP_MAX_VECTOR_LENGTH / 2];
 574    LLVMValueRef vecres, elem2;
 575
 576    assert(lp_check_value(type, a));
 577
 578    if (type.length == 1) {
 579       return a;
 580    }
 581
 582    assert(!bld->type.norm);
 583
 584    /*
 585     * for byte vectors can do much better with psadbw.
 586     * Using repeated shuffle/adds here. Note with multiple vectors
 587     * this can be done more efficiently as outlined in the intel
 588     * optimization manual.
 589     * Note: could cause data rearrangement if used with smaller element
 590     * sizes.
 591     */
 592
 593    vecres = a;
 594    length = type.length / 2;
 595    while (length > 1) {
 596       LLVMValueRef vec1, vec2;
 597       for (i = 0; i < length; i++) {
 598          shuffles1[i] = lp_build_const_int32(bld->gallivm, i);
 599          shuffles2[i] = lp_build_const_int32(bld->gallivm, i + length);
 600       }
 601       vec1 = LLVMBuildShuffleVector(builder, vecres, vecres,
 602                                     LLVMConstVector(shuffles1, length), "");
 603       vec2 = LLVMBuildShuffleVector(builder, vecres, vecres,
 604                                     LLVMConstVector(shuffles2, length), "");
 605       if (type.floating) {
 606          vecres = LLVMBuildFAdd(builder, vec1, vec2, "");
 607       }
 608       else {
 609          vecres = LLVMBuildAdd(builder, vec1, vec2, "");
 610       }
 611       length = length >> 1;
 612    }
 613
 614    /* always have vector of size 2 here */
 615    assert(length == 1);
 616
 617    index = lp_build_const_int32(bld->gallivm, 0);
 618    res = LLVMBuildExtractElement(builder, vecres, index, "");
 619    index = lp_build_const_int32(bld->gallivm, 1);
 620    elem2 = LLVMBuildExtractElement(builder, vecres, index, "");
 621
 622    if (type.floating)
 623       res = LLVMBuildFAdd(builder, res, elem2, "");
 624     else
 625       res = LLVMBuildAdd(builder, res, elem2, "");
 626
 627    return res;
 628 }
 629
 630 /**
 631  * Return the horizontal sums of 4 float vectors as a float4 vector.
 632  * This uses the technique as outlined in Intel Optimization Manual.
 633  */
 634 static LLVMValueRef
 635 lp_build_horizontal_add4x4f(struct lp_build_context *bld,
 636                             LLVMValueRef src[4])
 637 {
 638    struct gallivm_state *gallivm = bld->gallivm;
 639    LLVMBuilderRef builder = gallivm->builder;
 640    LLVMValueRef shuffles[4];
 641    LLVMValueRef tmp[4];
 642    LLVMValueRef sumtmp[2], shuftmp[2];
 643
 644    /* lower half of regs */
 645    shuffles[0] = lp_build_const_int32(gallivm, 0);
 646    shuffles[1] = lp_build_const_int32(gallivm, 1);
 647    shuffles[2] = lp_build_const_int32(gallivm, 4);
 648    shuffles[3] = lp_build_const_int32(gallivm, 5);
 649    tmp[0] = LLVMBuildShuffleVector(builder, src[0], src[1],
 650                                    LLVMConstVector(shuffles, 4), "");
 651    tmp[2] = LLVMBuildShuffleVector(builder, src[2], src[3],
 652                                    LLVMConstVector(shuffles, 4), "");
 653
 654    /* upper half of regs */
 655    shuffles[0] = lp_build_const_int32(gallivm, 2);
 656    shuffles[1] = lp_build_const_int32(gallivm, 3);
 657    shuffles[2] = lp_build_const_int32(gallivm, 6);
 658    shuffles[3] = lp_build_const_int32(gallivm, 7);
 659    tmp[1] = LLVMBuildShuffleVector(builder, src[0], src[1],
 660                                    LLVMConstVector(shuffles, 4), "");
 661    tmp[3] = LLVMBuildShuffleVector(builder, src[2], src[3],
 662                                    LLVMConstVector(shuffles, 4), "");
 663
 664    sumtmp[0] = LLVMBuildFAdd(builder, tmp[0], tmp[1], "");
 665    sumtmp[1] = LLVMBuildFAdd(builder, tmp[2], tmp[3], "");
 666
 667    shuffles[0] = lp_build_const_int32(gallivm, 0);
 668    shuffles[1] = lp_build_const_int32(gallivm, 2);
 669    shuffles[2] = lp_build_const_int32(gallivm, 4);
 670    shuffles[3] = lp_build_const_int32(gallivm, 6);
 671    shuftmp[0] = LLVMBuildShuffleVector(builder, sumtmp[0], sumtmp[1],
 672                                        LLVMConstVector(shuffles, 4), "");
 673
 674    shuffles[0] = lp_build_const_int32(gallivm, 1);
 675    shuffles[1] = lp_build_const_int32(gallivm, 3);
 676    shuffles[2] = lp_build_const_int32(gallivm, 5);
 677    shuffles[3] = lp_build_const_int32(gallivm, 7);
 678    shuftmp[1] = LLVMBuildShuffleVector(builder, sumtmp[0], sumtmp[1],
 679                                        LLVMConstVector(shuffles, 4), "");
 680
 681    return LLVMBuildFAdd(builder, shuftmp[0], shuftmp[1], "");
 682 }
 683
 684
 685 /*
 686  * partially horizontally add 2-4 float vectors with length nx4,
 687  * i.e. only four adjacent values in each vector will be added,
 688  * assuming values are really grouped in 4 which also determines
 689  * output order.
 690  *
 691  * Return a vector of the same length as the initial vectors,
 692  * with the excess elements (if any) being undefined.
 693  * The element order is independent of number of input vectors.
 694  * For 3 vectors x0x1x2x3x4x5x6x7, y0y1y2y3y4y5y6y7, z0z1z2z3z4z5z6z7
 695  * the output order thus will be
 696  * sumx0-x3,sumy0-y3,sumz0-z3,undef,sumx4-x7,sumy4-y7,sumz4z7,undef
 697  */
 698 LLVMValueRef
 699 lp_build_hadd_partial4(struct lp_build_context *bld,
 700                        LLVMValueRef vectors[],
 701                        unsigned num_vecs)
 702 {
 703    struct gallivm_state *gallivm = bld->gallivm;
 704    LLVMBuilderRef builder = gallivm->builder;
 705    LLVMValueRef ret_vec;
 706    LLVMValueRef tmp[4];
 707    const char *intrinsic = NULL;
 708
 709    assert(num_vecs >= 2 && num_vecs <= 4);
 710    assert(bld->type.floating);
 711
 712    /* only use this with at least 2 vectors, as it is sort of expensive
 713     * (depending on cpu) and we always need two horizontal adds anyway,
 714     * so a shuffle/add approach might be better.
 715     */
 716
 717    tmp[0] = vectors[0];
 718    tmp[1] = vectors[1];
 719
 720    tmp[2] = num_vecs > 2 ? vectors[2] : vectors[0];
 721    tmp[3] = num_vecs > 3 ? vectors[3] : vectors[0];
 722
 723    if (util_cpu_caps.has_sse3 && bld->type.width == 32 &&
 724        bld->type.length == 4) {
 725       intrinsic = "llvm.x86.sse3.hadd.ps";
 726    }
 727    else if (util_cpu_caps.has_avx && bld->type.width == 32 &&
 728             bld->type.length == 8) {
 729       intrinsic = "llvm.x86.avx.hadd.ps.256";
 730    }
 731    if (intrinsic) {
 732       tmp[0] = lp_build_intrinsic_binary(builder, intrinsic,
 733                                        lp_build_vec_type(gallivm, bld->type),
 734                                        tmp[0], tmp[1]);
 735       if (num_vecs > 2) {
 736          tmp[1] = lp_build_intrinsic_binary(builder, intrinsic,
 737                                           lp_build_vec_type(gallivm, bld->type),
 738                                           tmp[2], tmp[3]);
 739       }
 740       else {
 741          tmp[1] = tmp[0];
 742       }
 743       return lp_build_intrinsic_binary(builder, intrinsic,
 744                                        lp_build_vec_type(gallivm, bld->type),
 745                                        tmp[0], tmp[1]);
 746    }
 747
 748    if (bld->type.length == 4) {
 749       ret_vec = lp_build_horizontal_add4x4f(bld, tmp);
 750    }
 751    else {
 752       LLVMValueRef partres[LP_MAX_VECTOR_LENGTH/4];
 753       unsigned j;
 754       unsigned num_iter = bld->type.length / 4;
 755       struct lp_type parttype = bld->type;
 756       parttype.length = 4;
 757       for (j = 0; j < num_iter; j++) {
 758          LLVMValueRef partsrc[4];
 759          unsigned i;
 760          for (i = 0; i < 4; i++) {
 761             partsrc[i] = lp_build_extract_range(gallivm, tmp[i], j*4, 4);
 762          }
 763          partres[j] = lp_build_horizontal_add4x4f(bld, partsrc);
 764       }
 765       ret_vec = lp_build_concat(gallivm, partres, parttype, num_iter);
 766    }
 767    return ret_vec;
 768 }
 769
 770 /**
 771  * Generate a - b
 772  */
 773 LLVMValueRef
 774 lp_build_sub(struct lp_build_context *bld,
 775              LLVMValueRef a,
 776              LLVMValueRef b)
 777 {
 778    LLVMBuilderRef builder = bld->gallivm->builder;
 779    const struct lp_type type = bld->type;
 780    LLVMValueRef res;
 781
 782    assert(lp_check_value(type, a));
 783    assert(lp_check_value(type, b));
 784
 785    if(b == bld->zero)
 786       return a;
 787    if(a == bld->undef || b == bld->undef)
 788       return bld->undef;
 789    if(a == b)
 790       return bld->zero;
 791
 792    if(bld->type.norm) {
 793       const char *intrinsic = NULL;
 794
 795       if(b == bld->one)
 796         return bld->zero;
 797
 798       if (type.width * type.length == 128 &&
 799           !type.floating && !type.fixed) {
 800          if (util_cpu_caps.has_sse2) {
 801            if(type.width == 8)
 802               intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 803            if(type.width == 16)
 804               intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 805          } else if (util_cpu_caps.has_altivec) {
 806            if(type.width == 8)
 807               intrinsic = type.sign ? "llvm.ppc.altivec.vsubsbs" : "llvm.ppc.altivec.vsububs";
 808            if(type.width == 16)
 809               intrinsic = type.sign ? "llvm.ppc.altivec.vsubshs" : "llvm.ppc.altivec.vsubuhs";
 810          }
 811       }
 812
 813       if(intrinsic)
 814          return lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(bld->gallivm, bld->type), a, b);
 815    }
 816
 817    if(type.norm && !type.floating && !type.fixed) {
 818       if (type.sign) {
 819          uint64_t sign = (uint64_t)1 << (type.width - 1);
 820          LLVMValueRef max_val = lp_build_const_int_vec(bld->gallivm, type, sign - 1);
 821          LLVMValueRef min_val = lp_build_const_int_vec(bld->gallivm, type, sign);
 822          /* a_clamp_max is the maximum a for negative b,
 823             a_clamp_min is the minimum a for positive b. */
 824          LLVMValueRef a_clamp_max = lp_build_min_simple(bld, a, LLVMBuildAdd(builder, max_val, b, ""), GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 825          LLVMValueRef a_clamp_min = lp_build_max_simple(bld, a, LLVMBuildAdd(builder, min_val, b, ""), GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 826          a = lp_build_select(bld, lp_build_cmp(bld, PIPE_FUNC_GREATER, b, bld->zero), a_clamp_min, a_clamp_max);
 827       } else {
 828          a = lp_build_max_simple(bld, a, b, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 829       }
 830    }
 831
 832    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 833       if (type.floating)
 834          res = LLVMConstFSub(a, b);
 835       else
 836          res = LLVMConstSub(a, b);
 837    else
 838       if (type.floating)
 839          res = LLVMBuildFSub(builder, a, b, "");
 840       else
 841          res = LLVMBuildSub(builder, a, b, "");
 842
 843    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 844       res = lp_build_max_simple(bld, res, bld->zero, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
 845
 846    return res;
 847 }
 848
 849
 850
 851 /**
 852  * Normalized multiplication.
 853  *
 854  * There are several approaches for (using 8-bit normalized multiplication as
 855  * an example):
 856  *
 857  * - alpha plus one
 858  *
 859  *     makes the following approximation to the division (Sree)
 860  *
 861  *       a*b/255 ~= (a*(b + 1)) >> 256
 862  *
 863  *     which is the fastest method that satisfies the following OpenGL criteria of
 864  *
 865  *       0*0 = 0 and 255*255 = 255
 866  *
 867  * - geometric series
 868  *
 869  *     takes the geometric series approximation to the division
 870  *
 871  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 872  *
 873  *     in this case just the first two terms to fit in 16bit arithmetic
 874  *
 875  *       t/255 ~= (t + (t >> 8)) >> 8
 876  *
 877  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 878  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 879  *     must be used.
 880  *
 881  * - geometric series plus rounding
 882  *
 883  *     when using a geometric series division instead of truncating the result
 884  *     use roundoff in the approximation (Jim Blinn)
 885  *
 886  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 887  *
 888  *     achieving the exact results.
 889  *
 890  *
 891  *
 892  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 893  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 894  * @sa Michael Herf, The "double blend trick", May 2000,
 895  *     http://www.stereopsis.com/doubleblend.html
 896  */
 897 static LLVMValueRef
 898 lp_build_mul_norm(struct gallivm_state *gallivm,
 899                   struct lp_type wide_type,
 900                   LLVMValueRef a, LLVMValueRef b)
 901 {
 902    LLVMBuilderRef builder = gallivm->builder;
 903    struct lp_build_context bld;
 904    unsigned n;
 905    LLVMValueRef half;
 906    LLVMValueRef ab;
 907
 908    assert(!wide_type.floating);
 909    assert(lp_check_value(wide_type, a));
 910    assert(lp_check_value(wide_type, b));
 911
 912    lp_build_context_init(&bld, gallivm, wide_type);
 913
 914    n = wide_type.width / 2;
 915    if (wide_type.sign) {
 916       --n;
 917    }
 918
 919    /*
 920     * TODO: for 16bits normalized SSE2 vectors we could consider using PMULHUW
 921     * http://ssp.impulsetrain.com/2011/07/03/multiplying-normalized-16-bit-numbers-with-sse2/
 922     */
 923
 924    /*
 925     * a*b / (2**n - 1) ~= (a*b + (a*b >> n) + half) >> n
 926     */
 927
 928    ab = LLVMBuildMul(builder, a, b, "");
 929    ab = LLVMBuildAdd(builder, ab, lp_build_shr_imm(&bld, ab, n), "");
 930
 931    /*
 932     * half = sgn(ab) * 0.5 * (2 ** n) = sgn(ab) * (1 << (n - 1))
 933     */
 934
 935    half = lp_build_const_int_vec(gallivm, wide_type, 1 << (n - 1));
 936    if (wide_type.sign) {
 937       LLVMValueRef minus_half = LLVMBuildNeg(builder, half, "");
 938       LLVMValueRef sign = lp_build_shr_imm(&bld, ab, wide_type.width - 1);
 939       half = lp_build_select(&bld, sign, minus_half, half);
 940    }
 941    ab = LLVMBuildAdd(builder, ab, half, "");
 942
 943    /* Final division */
 944    ab = lp_build_shr_imm(&bld, ab, n);
 945
 946    return ab;
 947 }
 948
 949 /**
 950  * Generate a * b
 951  */
 952 LLVMValueRef
 953 lp_build_mul(struct lp_build_context *bld,
 954              LLVMValueRef a,
 955              LLVMValueRef b)
 956 {
 957    LLVMBuilderRef builder = bld->gallivm->builder;
 958    const struct lp_type type = bld->type;
 959    LLVMValueRef shift;
 960    LLVMValueRef res;
 961
 962    assert(lp_check_value(type, a));
 963    assert(lp_check_value(type, b));
 964
 965    if(a == bld->zero)
 966       return bld->zero;
 967    if(a == bld->one)
 968       return b;
 969    if(b == bld->zero)
 970       return bld->zero;
 971    if(b == bld->one)
 972       return a;
 973    if(a == bld->undef || b == bld->undef)
 974       return bld->undef;
 975
 976    if (!type.floating && !type.fixed && type.norm) {
 977       struct lp_type wide_type = lp_wider_type(type);
 978       LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 979
 980       lp_build_unpack2(bld->gallivm, type, wide_type, a, &al, &ah);
 981       lp_build_unpack2(bld->gallivm, type, wide_type, b, &bl, &bh);
 982
 983       /* PMULLW, PSRLW, PADDW */
 984       abl = lp_build_mul_norm(bld->gallivm, wide_type, al, bl);
 985       abh = lp_build_mul_norm(bld->gallivm, wide_type, ah, bh);
 986
 987       ab = lp_build_pack2(bld->gallivm, wide_type, type, abl, abh);
 988
 989       return ab;
 990    }
 991
 992    if(type.fixed)
 993       shift = lp_build_const_int_vec(bld->gallivm, type, type.width/2);
 994    else
 995       shift = NULL;
 996
 997    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 998       if (type.floating)
 999          res = LLVMConstFMul(a, b);
1000       else
1001          res = LLVMConstMul(a, b);
1002       if(shift) {
1003          if(type.sign)
1004             res = LLVMConstAShr(res, shift);
1005          else
1006             res = LLVMConstLShr(res, shift);
1007       }
1008    }
1009    else {
1010       if (type.floating)
1011          res = LLVMBuildFMul(builder, a, b, "");
1012       else
1013          res = LLVMBuildMul(builder, a, b, "");
1014       if(shift) {
1015          if(type.sign)
1016             res = LLVMBuildAShr(builder, res, shift, "");
1017          else
1018             res = LLVMBuildLShr(builder, res, shift, "");
1019       }
1020    }
1021
1022    return res;
1023 }
1024
1025
1026 /**
1027  * Small vector x scale multiplication optimization.
1028  */
1029 LLVMValueRef
1030 lp_build_mul_imm(struct lp_build_context *bld,
1031                  LLVMValueRef a,
1032                  int b)
1033 {
1034    LLVMBuilderRef builder = bld->gallivm->builder;
1035    LLVMValueRef factor;
1036
1037    assert(lp_check_value(bld->type, a));
1038
1039    if(b == 0)
1040       return bld->zero;
1041
1042    if(b == 1)
1043       return a;
1044
1045    if(b == -1)
1046       return lp_build_negate(bld, a);
1047
1048    if(b == 2 && bld->type.floating)
1049       return lp_build_add(bld, a, a);
1050
1051    if(util_is_power_of_two(b)) {
1052       unsigned shift = ffs(b) - 1;
1053
1054       if(bld->type.floating) {
1055 #if 0
1056          /*
1057           * Power of two multiplication by directly manipulating the exponent.
1058           *
1059           * XXX: This might not be always faster, it will introduce a small error
1060           * for multiplication by zero, and it will produce wrong results
1061           * for Inf and NaN.
1062           */
1063          unsigned mantissa = lp_mantissa(bld->type);
1064          factor = lp_build_const_int_vec(bld->gallivm, bld->type, (unsigned long long)shift << mantissa);
1065          a = LLVMBuildBitCast(builder, a, lp_build_int_vec_type(bld->type), "");
1066          a = LLVMBuildAdd(builder, a, factor, "");
1067          a = LLVMBuildBitCast(builder, a, lp_build_vec_type(bld->gallivm, bld->type), "");
1068          return a;
1069 #endif
1070       }
1071       else {
1072          factor = lp_build_const_vec(bld->gallivm, bld->type, shift);
1073          return LLVMBuildShl(builder, a, factor, "");
1074       }
1075    }
1076
1077    factor = lp_build_const_vec(bld->gallivm, bld->type, (double)b);
1078    return lp_build_mul(bld, a, factor);
1079 }
1080
1081
1082 /**
1083  * Generate a / b
1084  */
1085 LLVMValueRef
1086 lp_build_div(struct lp_build_context *bld,
1087              LLVMValueRef a,
1088              LLVMValueRef b)
1089 {
1090    LLVMBuilderRef builder = bld->gallivm->builder;
1091    const struct lp_type type = bld->type;
1092
1093    assert(lp_check_value(type, a));
1094    assert(lp_check_value(type, b));
1095
1096    if(a == bld->zero)
1097       return bld->zero;
1098    if(a == bld->one && type.floating)
1099       return lp_build_rcp(bld, b);
1100    if(b == bld->zero)
1101       return bld->undef;
1102    if(b == bld->one)
1103       return a;
1104    if(a == bld->undef || b == bld->undef)
1105       return bld->undef;
1106
1107    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
1108       if (type.floating)
1109          return LLVMConstFDiv(a, b);
1110       else if (type.sign)
1111          return LLVMConstSDiv(a, b);
1112       else
1113          return LLVMConstUDiv(a, b);
1114    }
1115
1116    if(((util_cpu_caps.has_sse && type.width == 32 && type.length == 4) ||
1117        (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) &&
1118       type.floating)
1119       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
1120
1121    if (type.floating)
1122       return LLVMBuildFDiv(builder, a, b, "");
1123    else if (type.sign)
1124       return LLVMBuildSDiv(builder, a, b, "");
1125    else
1126       return LLVMBuildUDiv(builder, a, b, "");
1127 }
1128
1129
1130 /**
1131  * Linear interpolation helper.
1132  *
1133  * @param normalized whether we are interpolating normalized values,
1134  *        encoded in normalized integers, twice as wide.
1135  *
1136  * @sa http://www.stereopsis.com/doubleblend.html
1137  */
1138 static INLINE LLVMValueRef
1139 lp_build_lerp_simple(struct lp_build_context *bld,
1140                      LLVMValueRef x,
1141                      LLVMValueRef v0,
1142                      LLVMValueRef v1,
1143                      unsigned flags)
1144 {
1145    unsigned half_width = bld->type.width/2;
1146    LLVMBuilderRef builder = bld->gallivm->builder;
1147    LLVMValueRef delta;
1148    LLVMValueRef res;
1149
1150    assert(lp_check_value(bld->type, x));
1151    assert(lp_check_value(bld->type, v0));
1152    assert(lp_check_value(bld->type, v1));
1153
1154    delta = lp_build_sub(bld, v1, v0);
1155
1156    if (flags & LP_BLD_LERP_WIDE_NORMALIZED) {
1157       if (!bld->type.sign) {
1158          if (!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS)) {
1159             /*
1160              * Scale x from [0, 2**n - 1] to [0, 2**n] by adding the
1161              * most-significant-bit to the lowest-significant-bit, so that
1162              * later we can just divide by 2**n instead of 2**n - 1.
1163              */
1164
1165             x = lp_build_add(bld, x, lp_build_shr_imm(bld, x, half_width - 1));
1166          }
1167
1168          /* (x * delta) >> n */
1169          res = lp_build_mul(bld, x, delta);
1170          res = lp_build_shr_imm(bld, res, half_width);
1171       } else {
1172          /*
1173           * The rescaling trick above doesn't work for signed numbers, so
1174           * use the 2**n - 1 divison approximation in lp_build_mul_norm
1175           * instead.
1176           */
1177          assert(!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS));
1178          res = lp_build_mul_norm(bld->gallivm, bld->type, x, delta);
1179       }
1180    } else {
1181       assert(!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS));
1182       res = lp_build_mul(bld, x, delta);
1183    }
1184
1185    res = lp_build_add(bld, v0, res);
1186
1187    if (((flags & LP_BLD_LERP_WIDE_NORMALIZED) && !bld->type.sign) ||
1188        bld->type.fixed) {
1189       /* We need to mask out the high order bits when lerping 8bit normalized colors stored on 16bits */
1190       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
1191        * but it will be wrong for true fixed point use cases. Basically we need
1192        * a more powerful lp_type, capable of further distinguishing the values
1193        * interpretation from the value storage. */
1194       res = LLVMBuildAnd(builder, res, lp_build_const_int_vec(bld->gallivm, bld->type, (1 << half_width) - 1), "");
1195    }
1196
1197    return res;
1198 }
1199
1200
1201 /**
1202  * Linear interpolation.
1203  */
1204 LLVMValueRef
1205 lp_build_lerp(struct lp_build_context *bld,
1206               LLVMValueRef x,
1207               LLVMValueRef v0,
1208               LLVMValueRef v1,
1209               unsigned flags)
1210 {
1211    const struct lp_type type = bld->type;
1212    LLVMValueRef res;
1213
1214    assert(lp_check_value(type, x));
1215    assert(lp_check_value(type, v0));
1216    assert(lp_check_value(type, v1));
1217
1218    assert(!(flags & LP_BLD_LERP_WIDE_NORMALIZED));
1219
1220    if (type.norm) {
1221       struct lp_type wide_type;
1222       struct lp_build_context wide_bld;
1223       LLVMValueRef xl, xh, v0l, v0h, v1l, v1h, resl, resh;
1224
1225       assert(type.length >= 2);
1226
1227       /*
1228        * Create a wider integer type, enough to hold the
1229        * intermediate result of the multiplication.
1230        */
1231       memset(&wide_type, 0, sizeof wide_type);
1232       wide_type.sign   = type.sign;
1233       wide_type.width  = type.width*2;
1234       wide_type.length = type.length/2;
1235
1236       lp_build_context_init(&wide_bld, bld->gallivm, wide_type);
1237
1238       lp_build_unpack2(bld->gallivm, type, wide_type, x,  &xl,  &xh);
1239       lp_build_unpack2(bld->gallivm, type, wide_type, v0, &v0l, &v0h);
1240       lp_build_unpack2(bld->gallivm, type, wide_type, v1, &v1l, &v1h);
1241
1242       /*
1243        * Lerp both halves.
1244        */
1245
1246       flags |= LP_BLD_LERP_WIDE_NORMALIZED;
1247
1248       resl = lp_build_lerp_simple(&wide_bld, xl, v0l, v1l, flags);
1249       resh = lp_build_lerp_simple(&wide_bld, xh, v0h, v1h, flags);
1250
1251       res = lp_build_pack2(bld->gallivm, wide_type, type, resl, resh);
1252    } else {
1253       res = lp_build_lerp_simple(bld, x, v0, v1, flags);
1254    }
1255
1256    return res;
1257 }
1258
1259
1260 /**
1261  * Bilinear interpolation.
1262  *
1263  * Values indices are in v_{yx}.
1264  */
1265 LLVMValueRef
1266 lp_build_lerp_2d(struct lp_build_context *bld,
1267                  LLVMValueRef x,
1268                  LLVMValueRef y,
1269                  LLVMValueRef v00,
1270                  LLVMValueRef v01,
1271                  LLVMValueRef v10,
1272                  LLVMValueRef v11,
1273                  unsigned flags)
1274 {
1275    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01, flags);
1276    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11, flags);
1277    return lp_build_lerp(bld, y, v0, v1, flags);
1278 }
1279
1280
1281 LLVMValueRef
1282 lp_build_lerp_3d(struct lp_build_context *bld,
1283                  LLVMValueRef x,
1284                  LLVMValueRef y,
1285                  LLVMValueRef z,
1286                  LLVMValueRef v000,
1287                  LLVMValueRef v001,
1288                  LLVMValueRef v010,
1289                  LLVMValueRef v011,
1290                  LLVMValueRef v100,
1291                  LLVMValueRef v101,
1292                  LLVMValueRef v110,
1293                  LLVMValueRef v111,
1294                  unsigned flags)
1295 {
1296    LLVMValueRef v0 = lp_build_lerp_2d(bld, x, y, v000, v001, v010, v011, flags);
1297    LLVMValueRef v1 = lp_build_lerp_2d(bld, x, y, v100, v101, v110, v111, flags);
1298    return lp_build_lerp(bld, z, v0, v1, flags);
1299 }
1300
1301
1302 /**
1303  * Generate min(a, b)
1304  * Do checks for special cases but not for nans.
1305  */
1306 LLVMValueRef
1307 lp_build_min(struct lp_build_context *bld,
1308              LLVMValueRef a,
1309              LLVMValueRef b)
1310 {
1311    assert(lp_check_value(bld->type, a));
1312    assert(lp_check_value(bld->type, b));
1313
1314    if(a == bld->undef || b == bld->undef)
1315       return bld->undef;
1316
1317    if(a == b)
1318       return a;
1319
1320    if (bld->type.norm) {
1321       if (!bld->type.sign) {
1322          if (a == bld->zero || b == bld->zero) {
1323             return bld->zero;
1324          }
1325       }
1326       if(a == bld->one)
1327          return b;
1328       if(b == bld->one)
1329          return a;
1330    }
1331
1332    return lp_build_min_simple(bld, a, b, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
1333 }
1334
1335
1336 /**
1337  * Generate min(a, b)
1338  * NaN's are handled according to the behavior specified by the
1339  * nan_behavior argument.
1340  */
1341 LLVMValueRef
1342 lp_build_min_ext(struct lp_build_context *bld,
1343                  LLVMValueRef a,
1344                  LLVMValueRef b,
1345                  enum gallivm_nan_behavior nan_behavior)
1346 {
1347    assert(lp_check_value(bld->type, a));
1348    assert(lp_check_value(bld->type, b));
1349
1350    if(a == bld->undef || b == bld->undef)
1351       return bld->undef;
1352
1353    if(a == b)
1354       return a;
1355
1356    if (bld->type.norm) {
1357       if (!bld->type.sign) {
1358          if (a == bld->zero || b == bld->zero) {
1359             return bld->zero;
1360          }
1361       }
1362       if(a == bld->one)
1363          return b;
1364       if(b == bld->one)
1365          return a;
1366    }
1367
1368    return lp_build_min_simple(bld, a, b, nan_behavior);
1369 }
1370
1371 /**
1372  * Generate max(a, b)
1373  * Do checks for special cases, but NaN behavior is undefined.
1374  */
1375 LLVMValueRef
1376 lp_build_max(struct lp_build_context *bld,
1377              LLVMValueRef a,
1378              LLVMValueRef b)
1379 {
1380    assert(lp_check_value(bld->type, a));
1381    assert(lp_check_value(bld->type, b));
1382
1383    if(a == bld->undef || b == bld->undef)
1384       return bld->undef;
1385
1386    if(a == b)
1387       return a;
1388
1389    if(bld->type.norm) {
1390       if(a == bld->one || b == bld->one)
1391          return bld->one;
1392       if (!bld->type.sign) {
1393          if (a == bld->zero) {
1394             return b;
1395          }
1396          if (b == bld->zero) {
1397             return a;
1398          }
1399       }
1400    }
1401
1402    return lp_build_max_simple(bld, a, b, GALLIVM_NAN_BEHAVIOR_UNDEFINED);
1403 }
1404
1405
1406 /**
1407  * Generate max(a, b)
1408  * Checks for special cases.
1409  * NaN's are handled according to the behavior specified by the
1410  * nan_behavior argument.
1411  */
1412 LLVMValueRef
1413 lp_build_max_ext(struct lp_build_context *bld,
1414                   LLVMValueRef a,
1415                   LLVMValueRef b,
1416                   enum gallivm_nan_behavior nan_behavior)
1417 {
1418    assert(lp_check_value(bld->type, a));
1419    assert(lp_check_value(bld->type, b));
1420
1421    if(a == bld->undef || b == bld->undef)
1422       return bld->undef;
1423
1424    if(a == b)
1425       return a;
1426
1427    if(bld->type.norm) {
1428       if(a == bld->one || b == bld->one)
1429          return bld->one;
1430       if (!bld->type.sign) {
1431          if (a == bld->zero) {
1432             return b;
1433          }
1434          if (b == bld->zero) {
1435             return a;
1436          }
1437       }
1438    }
1439
1440    return lp_build_max_simple(bld, a, b, nan_behavior);
1441 }
1442
1443 /**
1444  * Generate clamp(a, min, max)
1445  * NaN behavior (for any of a, min, max) is undefined.
1446  * Do checks for special cases.
1447  */
1448 LLVMValueRef
1449 lp_build_clamp(struct lp_build_context *bld,
1450                LLVMValueRef a,
1451                LLVMValueRef min,
1452                LLVMValueRef max)
1453 {
1454    assert(lp_check_value(bld->type, a));
1455    assert(lp_check_value(bld->type, min));
1456    assert(lp_check_value(bld->type, max));
1457
1458    a = lp_build_min(bld, a, max);
1459    a = lp_build_max(bld, a, min);
1460    return a;
1461 }
1462
1463
1464 /**
1465  * Generate clamp(a, 0, 1)
1466  * A NaN will get converted to zero.
1467  */
1468 LLVMValueRef
1469 lp_build_clamp_zero_one_nanzero(struct lp_build_context *bld,
1470                                 LLVMValueRef a)
1471 {
1472    a = lp_build_max_ext(bld, a, bld->zero, GALLIVM_NAN_RETURN_OTHER_SECOND_NONNAN);
1473    a = lp_build_min(bld, a, bld->one);
1474    return a;
1475 }
1476
1477
1478 /**
1479  * Generate abs(a)
1480  */
1481 LLVMValueRef
1482 lp_build_abs(struct lp_build_context *bld,
1483              LLVMValueRef a)
1484 {
1485    LLVMBuilderRef builder = bld->gallivm->builder;
1486    const struct lp_type type = bld->type;
1487    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
1488
1489    assert(lp_check_value(type, a));
1490
1491    if(!type.sign)
1492       return a;
1493
1494    if(type.floating) {
1495       /* Mask out the sign bit */
1496       LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
1497       unsigned long long absMask = ~(1ULL << (type.width - 1));
1498       LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type, ((unsigned long long) absMask));
1499       a = LLVMBuildBitCast(builder, a, int_vec_type, "");
1500       a = LLVMBuildAnd(builder, a, mask, "");
1501       a = LLVMBuildBitCast(builder, a, vec_type, "");
1502       return a;
1503    }
1504
1505    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
1506       switch(type.width) {
1507       case 8:
1508          return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
1509       case 16:
1510          return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
1511       case 32:
1512          return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
1513       }
1514    }
1515    else if (type.width*type.length == 256 && util_cpu_caps.has_ssse3 &&
1516             (gallivm_debug & GALLIVM_DEBUG_PERF) &&
1517             (type.width == 8 || type.width == 16 || type.width == 32)) {
1518       debug_printf("%s: inefficient code, should split vectors manually\n",
1519                    __FUNCTION__);
1520    }
1521
1522    return lp_build_max(bld, a, LLVMBuildNeg(builder, a, ""));
1523 }
1524
1525
1526 LLVMValueRef
1527 lp_build_negate(struct lp_build_context *bld,
1528                 LLVMValueRef a)
1529 {
1530    LLVMBuilderRef builder = bld->gallivm->builder;
1531
1532    assert(lp_check_value(bld->type, a));
1533
1534    if (bld->type.floating)
1535       a = LLVMBuildFNeg(builder, a, "");
1536    else
1537       a = LLVMBuildNeg(builder, a, "");
1538
1539    return a;
1540 }
1541
1542
1543 /** Return -1, 0 or +1 depending on the sign of a */
1544 LLVMValueRef
1545 lp_build_sgn(struct lp_build_context *bld,
1546              LLVMValueRef a)
1547 {
1548    LLVMBuilderRef builder = bld->gallivm->builder;
1549    const struct lp_type type = bld->type;
1550    LLVMValueRef cond;
1551    LLVMValueRef res;
1552
1553    assert(lp_check_value(type, a));
1554
1555    /* Handle non-zero case */
1556    if(!type.sign) {
1557       /* if not zero then sign must be positive */
1558       res = bld->one;
1559    }
1560    else if(type.floating) {
1561       LLVMTypeRef vec_type;
1562       LLVMTypeRef int_type;
1563       LLVMValueRef mask;
1564       LLVMValueRef sign;
1565       LLVMValueRef one;
1566       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
1567
1568       int_type = lp_build_int_vec_type(bld->gallivm, type);
1569       vec_type = lp_build_vec_type(bld->gallivm, type);
1570       mask = lp_build_const_int_vec(bld->gallivm, type, maskBit);
1571
1572       /* Take the sign bit and add it to 1 constant */
1573       sign = LLVMBuildBitCast(builder, a, int_type, "");
1574       sign = LLVMBuildAnd(builder, sign, mask, "");
1575       one = LLVMConstBitCast(bld->one, int_type);
1576       res = LLVMBuildOr(builder, sign, one, "");
1577       res = LLVMBuildBitCast(builder, res, vec_type, "");
1578    }
1579    else
1580    {
1581       /* signed int/norm/fixed point */
1582       /* could use psign with sse3 and appropriate vectors here */
1583       LLVMValueRef minus_one = lp_build_const_vec(bld->gallivm, type, -1.0);
1584       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
1585       res = lp_build_select(bld, cond, bld->one, minus_one);
1586    }
1587
1588    /* Handle zero */
1589    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
1590    res = lp_build_select(bld, cond, bld->zero, res);
1591
1592    return res;
1593 }
1594
1595
1596 /**
1597  * Set the sign of float vector 'a' according to 'sign'.
1598  * If sign==0, return abs(a).
1599  * If sign==1, return -abs(a);
1600  * Other values for sign produce undefined results.
1601  */
1602 LLVMValueRef
1603 lp_build_set_sign(struct lp_build_context *bld,
1604                   LLVMValueRef a, LLVMValueRef sign)
1605 {
1606    LLVMBuilderRef builder = bld->gallivm->builder;
1607    const struct lp_type type = bld->type;
1608    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
1609    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
1610    LLVMValueRef shift = lp_build_const_int_vec(bld->gallivm, type, type.width - 1);
1611    LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type,
1612                              ~((unsigned long long) 1 << (type.width - 1)));
1613    LLVMValueRef val, res;
1614
1615    assert(type.floating);
1616    assert(lp_check_value(type, a));
1617
1618    /* val = reinterpret_cast<int>(a) */
1619    val = LLVMBuildBitCast(builder, a, int_vec_type, "");
1620    /* val = val & mask */
1621    val = LLVMBuildAnd(builder, val, mask, "");
1622    /* sign = sign << shift */
1623    sign = LLVMBuildShl(builder, sign, shift, "");
1624    /* res = val | sign */
1625    res = LLVMBuildOr(builder, val, sign, "");
1626    /* res = reinterpret_cast<float>(res) */
1627    res = LLVMBuildBitCast(builder, res, vec_type, "");
1628
1629    return res;
1630 }
1631
1632
1633 /**
1634  * Convert vector of (or scalar) int to vector of (or scalar) float.
1635  */
1636 LLVMValueRef
1637 lp_build_int_to_float(struct lp_build_context *bld,
1638                       LLVMValueRef a)
1639 {
1640    LLVMBuilderRef builder = bld->gallivm->builder;
1641    const struct lp_type type = bld->type;
1642    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
1643
1644    assert(type.floating);
1645
1646    return LLVMBuildSIToFP(builder, a, vec_type, "");
1647 }
1648
1649 static boolean
1650 arch_rounding_available(const struct lp_type type)
1651 {
1652    if ((util_cpu_caps.has_sse4_1 &&
1653        (type.length == 1 || type.width*type.length == 128)) ||
1654        (util_cpu_caps.has_avx && type.width*type.length == 256))
1655       return TRUE;
1656    else if ((util_cpu_caps.has_altivec &&
1657             (type.width == 32 && type.length == 4)))
1658       return TRUE;
1659
1660    return FALSE;
1661 }
1662
1663 enum lp_build_round_mode
1664 {
1665    LP_BUILD_ROUND_NEAREST = 0,
1666    LP_BUILD_ROUND_FLOOR = 1,
1667    LP_BUILD_ROUND_CEIL = 2,
1668    LP_BUILD_ROUND_TRUNCATE = 3
1669 };
1670
1671 /**
1672  * Helper for SSE4.1's ROUNDxx instructions.
1673  *
1674  * NOTE: In the SSE4.1's nearest mode, if two values are equally close, the
1675  * result is the even value.  That is, rounding 2.5 will be 2.0, and not 3.0.
1676  */
1677 static INLINE LLVMValueRef
1678 lp_build_round_sse41(struct lp_build_context *bld,
1679                      LLVMValueRef a,
1680                      enum lp_build_round_mode mode)
1681 {
1682    LLVMBuilderRef builder = bld->gallivm->builder;
1683    const struct lp_type type = bld->type;
1684    LLVMTypeRef i32t = LLVMInt32TypeInContext(bld->gallivm->context);
1685    const char *intrinsic;
1686    LLVMValueRef res;
1687
1688    assert(type.floating);
1689
1690    assert(lp_check_value(type, a));
1691    assert(util_cpu_caps.has_sse4_1);
1692
1693    if (type.length == 1) {
1694       LLVMTypeRef vec_type;
1695       LLVMValueRef undef;
1696       LLVMValueRef args[3];
1697       LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);
1698
1699       switch(type.width) {
1700       case 32:
1701          intrinsic = "llvm.x86.sse41.round.ss";
1702          break;
1703       case 64:
1704          intrinsic = "llvm.x86.sse41.round.sd";
1705          break;
1706       default:
1707          assert(0);
1708          return bld->undef;
1709       }
1710
1711       vec_type = LLVMVectorType(bld->elem_type, 4);
1712
1713       undef = LLVMGetUndef(vec_type);
1714
1715       args[0] = undef;
1716       args[1] = LLVMBuildInsertElement(builder, undef, a, index0, "");
1717       args[2] = LLVMConstInt(i32t, mode, 0);
1718
1719       res = lp_build_intrinsic(builder, intrinsic,
1720                                vec_type, args, Elements(args));
1721
1722       res = LLVMBuildExtractElement(builder, res, index0, "");
1723    }
1724    else {
1725       if (type.width * type.length == 128) {
1726          switch(type.width) {
1727          case 32:
1728             intrinsic = "llvm.x86.sse41.round.ps";
1729             break;
1730          case 64:
1731             intrinsic = "llvm.x86.sse41.round.pd";
1732             break;
1733          default:
1734             assert(0);
1735             return bld->undef;
1736          }
1737       }
1738       else {
1739          assert(type.width * type.length == 256);
1740          assert(util_cpu_caps.has_avx);
1741
1742          switch(type.width) {
1743          case 32:
1744             intrinsic = "llvm.x86.avx.round.ps.256";
1745             break;
1746          case 64:
1747             intrinsic = "llvm.x86.avx.round.pd.256";
1748             break;
1749          default:
1750             assert(0);
1751             return bld->undef;
1752          }
1753       }
1754
1755       res = lp_build_intrinsic_binary(builder, intrinsic,
1756                                       bld->vec_type, a,
1757                                       LLVMConstInt(i32t, mode, 0));
1758    }
1759
1760    return res;
1761 }
1762
1763
1764 static INLINE LLVMValueRef
1765 lp_build_iround_nearest_sse2(struct lp_build_context *bld,
1766                              LLVMValueRef a)
1767 {
1768    LLVMBuilderRef builder = bld->gallivm->builder;
1769    const struct lp_type type = bld->type;
1770    LLVMTypeRef i32t = LLVMInt32TypeInContext(bld->gallivm->context);
1771    LLVMTypeRef ret_type = lp_build_int_vec_type(bld->gallivm, type);
1772    const char *intrinsic;
1773    LLVMValueRef res;
1774
1775    assert(type.floating);
1776    /* using the double precision conversions is a bit more complicated */
1777    assert(type.width == 32);
1778
1779    assert(lp_check_value(type, a));
1780    assert(util_cpu_caps.has_sse2);
1781
1782    /* This is relying on MXCSR rounding mode, which should always be nearest. */
1783    if (type.length == 1) {
1784       LLVMTypeRef vec_type;
1785       LLVMValueRef undef;
1786       LLVMValueRef arg;
1787       LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);
1788
1789       vec_type = LLVMVectorType(bld->elem_type, 4);
1790
1791       intrinsic = "llvm.x86.sse.cvtss2si";
1792
1793       undef = LLVMGetUndef(vec_type);
1794
1795       arg = LLVMBuildInsertElement(builder, undef, a, index0, "");
1796
1797       res = lp_build_intrinsic_unary(builder, intrinsic,
1798                                      ret_type, arg);
1799    }
1800    else {
1801       if (type.width* type.length == 128) {
1802          intrinsic = "llvm.x86.sse2.cvtps2dq";
1803       }
1804       else {
1805          assert(type.width*type.length == 256);
1806          assert(util_cpu_caps.has_avx);
1807
1808          intrinsic = "llvm.x86.avx.cvt.ps2dq.256";
1809       }
1810       res = lp_build_intrinsic_unary(builder, intrinsic,
1811                                      ret_type, a);
1812    }
1813
1814    return res;
1815 }
1816
1817
1818 /*
1819  */
1820 static INLINE LLVMValueRef
1821 lp_build_round_altivec(struct lp_build_context *bld,
1822                        LLVMValueRef a,
1823                        enum lp_build_round_mode mode)
1824 {
1825    LLVMBuilderRef builder = bld->gallivm->builder;
1826    const struct lp_type type = bld->type;
1827    const char *intrinsic = NULL;
1828
1829    assert(type.floating);
1830
1831    assert(lp_check_value(type, a));
1832    assert(util_cpu_caps.has_altivec);
1833
1834    switch (mode) {
1835    case LP_BUILD_ROUND_NEAREST:
1836       intrinsic = "llvm.ppc.altivec.vrfin";
1837       break;
1838    case LP_BUILD_ROUND_FLOOR:
1839       intrinsic = "llvm.ppc.altivec.vrfim";
1840       break;
1841    case LP_BUILD_ROUND_CEIL:
1842       intrinsic = "llvm.ppc.altivec.vrfip";
1843       break;
1844    case LP_BUILD_ROUND_TRUNCATE:
1845       intrinsic = "llvm.ppc.altivec.vrfiz";
1846       break;
1847    }
1848
1849    return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
1850 }
1851
1852 static INLINE LLVMValueRef
1853 lp_build_round_arch(struct lp_build_context *bld,
1854                     LLVMValueRef a,
1855                     enum lp_build_round_mode mode)
1856 {
1857    if (util_cpu_caps.has_sse4_1)
1858      return lp_build_round_sse41(bld, a, mode);
1859    else /* (util_cpu_caps.has_altivec) */
1860      return lp_build_round_altivec(bld, a, mode);
1861 }
1862
1863 /**
1864  * Return the integer part of a float (vector) value (== round toward zero).
1865  * The returned value is a float (vector).
1866  * Ex: trunc(-1.5) = -1.0
1867  */
1868 LLVMValueRef
1869 lp_build_trunc(struct lp_build_context *bld,
1870                LLVMValueRef a)
1871 {
1872    LLVMBuilderRef builder = bld->gallivm->builder;
1873    const struct lp_type type = bld->type;
1874
1875    assert(type.floating);
1876    assert(lp_check_value(type, a));
1877
1878    if (arch_rounding_available(type)) {
1879       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_TRUNCATE);
1880    }
1881    else {
1882       const struct lp_type type = bld->type;
1883       struct lp_type inttype;
1884       struct lp_build_context intbld;
1885       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1886       LLVMValueRef trunc, res, anosign, mask;
1887       LLVMTypeRef int_vec_type = bld->int_vec_type;
1888       LLVMTypeRef vec_type = bld->vec_type;
1889
1890       assert(type.width == 32); /* might want to handle doubles at some point */
1891
1892       inttype = type;
1893       inttype.floating = 0;
1894       lp_build_context_init(&intbld, bld->gallivm, inttype);
1895
1896       /* round by truncation */
1897       trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
1898       res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc");
1899
1900       /* mask out sign bit */
1901       anosign = lp_build_abs(bld, a);
1902       /*
1903        * mask out all values if anosign > 2^24
1904        * This should work both for large ints (all rounding is no-op for them
1905        * because such floats are always exact) as well as special cases like
1906        * NaNs, Infs (taking advantage of the fact they use max exponent).
1907        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
1908        */
1909       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
1910       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
1911       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
1912       return lp_build_select(bld, mask, a, res);
1913    }
1914 }
1915
1916
1917 /**
1918  * Return float (vector) rounded to nearest integer (vector).  The returned
1919  * value is a float (vector).
1920  * Ex: round(0.9) = 1.0
1921  * Ex: round(-1.5) = -2.0
1922  */
1923 LLVMValueRef
1924 lp_build_round(struct lp_build_context *bld,
1925                LLVMValueRef a)
1926 {
1927    LLVMBuilderRef builder = bld->gallivm->builder;
1928    const struct lp_type type = bld->type;
1929
1930    assert(type.floating);
1931    assert(lp_check_value(type, a));
1932
1933    if (arch_rounding_available(type)) {
1934       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST);
1935    }
1936    else {
1937       const struct lp_type type = bld->type;
1938       struct lp_type inttype;
1939       struct lp_build_context intbld;
1940       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1941       LLVMValueRef res, anosign, mask;
1942       LLVMTypeRef int_vec_type = bld->int_vec_type;
1943       LLVMTypeRef vec_type = bld->vec_type;
1944
1945       assert(type.width == 32); /* might want to handle doubles at some point */
1946
1947       inttype = type;
1948       inttype.floating = 0;
1949       lp_build_context_init(&intbld, bld->gallivm, inttype);
1950
1951       res = lp_build_iround(bld, a);
1952       res = LLVMBuildSIToFP(builder, res, vec_type, "");
1953
1954       /* mask out sign bit */
1955       anosign = lp_build_abs(bld, a);
1956       /*
1957        * mask out all values if anosign > 2^24
1958        * This should work both for large ints (all rounding is no-op for them
1959        * because such floats are always exact) as well as special cases like
1960        * NaNs, Infs (taking advantage of the fact they use max exponent).
1961        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
1962        */
1963       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
1964       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
1965       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
1966       return lp_build_select(bld, mask, a, res);
1967    }
1968 }
1969
1970
1971 /**
1972  * Return floor of float (vector), result is a float (vector)
1973  * Ex: floor(1.1) = 1.0
1974  * Ex: floor(-1.1) = -2.0
1975  */
1976 LLVMValueRef
1977 lp_build_floor(struct lp_build_context *bld,
1978                LLVMValueRef a)
1979 {
1980    LLVMBuilderRef builder = bld->gallivm->builder;
1981    const struct lp_type type = bld->type;
1982
1983    assert(type.floating);
1984    assert(lp_check_value(type, a));
1985
1986    if (arch_rounding_available(type)) {
1987       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR);
1988    }
1989    else {
1990       const struct lp_type type = bld->type;
1991       struct lp_type inttype;
1992       struct lp_build_context intbld;
1993       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1994       LLVMValueRef trunc, res, anosign, mask;
1995       LLVMTypeRef int_vec_type = bld->int_vec_type;
1996       LLVMTypeRef vec_type = bld->vec_type;
1997
1998       assert(type.width == 32); /* might want to handle doubles at some point */
1999
2000       inttype = type;
2001       inttype.floating = 0;
2002       lp_build_context_init(&intbld, bld->gallivm, inttype);
2003
2004       /* round by truncation */
2005       trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2006       res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc");
2007
2008       if (type.sign) {
2009          LLVMValueRef tmp;
2010
2011          /*
2012           * fix values if rounding is wrong (for non-special cases)
2013           * - this is the case if trunc > a
2014           */
2015          mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, res, a);
2016          /* tmp = trunc > a ? 1.0 : 0.0 */
2017          tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, "");
2018          tmp = lp_build_and(&intbld, mask, tmp);
2019          tmp = LLVMBuildBitCast(builder, tmp, vec_type, "");
2020          res = lp_build_sub(bld, res, tmp);
2021       }
2022
2023       /* mask out sign bit */
2024       anosign = lp_build_abs(bld, a);
2025       /*
2026        * mask out all values if anosign > 2^24
2027        * This should work both for large ints (all rounding is no-op for them
2028        * because such floats are always exact) as well as special cases like
2029        * NaNs, Infs (taking advantage of the fact they use max exponent).
2030        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
2031        */
2032       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
2033       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
2034       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
2035       return lp_build_select(bld, mask, a, res);
2036    }
2037 }
2038
2039
2040 /**
2041  * Return ceiling of float (vector), returning float (vector).
2042  * Ex: ceil( 1.1) = 2.0
2043  * Ex: ceil(-1.1) = -1.0
2044  */
2045 LLVMValueRef
2046 lp_build_ceil(struct lp_build_context *bld,
2047               LLVMValueRef a)
2048 {
2049    LLVMBuilderRef builder = bld->gallivm->builder;
2050    const struct lp_type type = bld->type;
2051
2052    assert(type.floating);
2053    assert(lp_check_value(type, a));
2054
2055    if (arch_rounding_available(type)) {
2056       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL);
2057    }
2058    else {
2059       const struct lp_type type = bld->type;
2060       struct lp_type inttype;
2061       struct lp_build_context intbld;
2062       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
2063       LLVMValueRef trunc, res, anosign, mask, tmp;
2064       LLVMTypeRef int_vec_type = bld->int_vec_type;
2065       LLVMTypeRef vec_type = bld->vec_type;
2066
2067       assert(type.width == 32); /* might want to handle doubles at some point */
2068
2069       inttype = type;
2070       inttype.floating = 0;
2071       lp_build_context_init(&intbld, bld->gallivm, inttype);
2072
2073       /* round by truncation */
2074       trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2075       trunc = LLVMBuildSIToFP(builder, trunc, vec_type, "ceil.trunc");
2076
2077       /*
2078        * fix values if rounding is wrong (for non-special cases)
2079        * - this is the case if trunc < a
2080        */
2081       mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a);
2082       /* tmp = trunc < a ? 1.0 : 0.0 */
2083       tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, "");
2084       tmp = lp_build_and(&intbld, mask, tmp);
2085       tmp = LLVMBuildBitCast(builder, tmp, vec_type, "");
2086       res = lp_build_add(bld, trunc, tmp);
2087
2088       /* mask out sign bit */
2089       anosign = lp_build_abs(bld, a);
2090       /*
2091        * mask out all values if anosign > 2^24
2092        * This should work both for large ints (all rounding is no-op for them
2093        * because such floats are always exact) as well as special cases like
2094        * NaNs, Infs (taking advantage of the fact they use max exponent).
2095        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
2096        */
2097       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
2098       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
2099       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
2100       return lp_build_select(bld, mask, a, res);
2101    }
2102 }
2103
2104
2105 /**
2106  * Return fractional part of 'a' computed as a - floor(a)
2107  * Typically used in texture coord arithmetic.
2108  */
2109 LLVMValueRef
2110 lp_build_fract(struct lp_build_context *bld,
2111                LLVMValueRef a)
2112 {
2113    assert(bld->type.floating);
2114    return lp_build_sub(bld, a, lp_build_floor(bld, a));
2115 }
2116
2117
2118 /**
2119  * Prevent returning a fractional part of 1.0 for very small negative values of
2120  * 'a' by clamping against 0.99999(9).
2121  */
2122 static inline LLVMValueRef
2123 clamp_fract(struct lp_build_context *bld, LLVMValueRef fract)
2124 {
2125    LLVMValueRef max;
2126
2127    /* this is the largest number smaller than 1.0 representable as float */
2128    max = lp_build_const_vec(bld->gallivm, bld->type,
2129                             1.0 - 1.0/(1LL << (lp_mantissa(bld->type) + 1)));
2130    return lp_build_min(bld, fract, max);
2131 }
2132
2133
2134 /**
2135  * Same as lp_build_fract, but guarantees that the result is always smaller
2136  * than one.
2137  */
2138 LLVMValueRef
2139 lp_build_fract_safe(struct lp_build_context *bld,
2140                     LLVMValueRef a)
2141 {
2142    return clamp_fract(bld, lp_build_fract(bld, a));
2143 }
2144
2145
2146 /**
2147  * Return the integer part of a float (vector) value (== round toward zero).
2148  * The returned value is an integer (vector).
2149  * Ex: itrunc(-1.5) = -1
2150  */
2151 LLVMValueRef
2152 lp_build_itrunc(struct lp_build_context *bld,
2153                 LLVMValueRef a)
2154 {
2155    LLVMBuilderRef builder = bld->gallivm->builder;
2156    const struct lp_type type = bld->type;
2157    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
2158
2159    assert(type.floating);
2160    assert(lp_check_value(type, a));
2161
2162    return LLVMBuildFPToSI(builder, a, int_vec_type, "");
2163 }
2164
2165
2166 /**
2167  * Return float (vector) rounded to nearest integer (vector).  The returned
2168  * value is an integer (vector).
2169  * Ex: iround(0.9) = 1
2170  * Ex: iround(-1.5) = -2
2171  */
2172 LLVMValueRef
2173 lp_build_iround(struct lp_build_context *bld,
2174                 LLVMValueRef a)
2175 {
2176    LLVMBuilderRef builder = bld->gallivm->builder;
2177    const struct lp_type type = bld->type;
2178    LLVMTypeRef int_vec_type = bld->int_vec_type;
2179    LLVMValueRef res;
2180
2181    assert(type.floating);
2182
2183    assert(lp_check_value(type, a));
2184
2185    if ((util_cpu_caps.has_sse2 &&
2186        ((type.width == 32) && (type.length == 1 || type.length == 4))) ||
2187        (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) {
2188       return lp_build_iround_nearest_sse2(bld, a);
2189    }
2190    if (arch_rounding_available(type)) {
2191       res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST);
2192    }
2193    else {
2194       LLVMValueRef half;
2195
2196       half = lp_build_const_vec(bld->gallivm, type, 0.5);
2197
2198       if (type.sign) {
2199          LLVMTypeRef vec_type = bld->vec_type;
2200          LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type,
2201                                     (unsigned long long)1 << (type.width - 1));
2202          LLVMValueRef sign;
2203
2204          /* get sign bit */
2205          sign = LLVMBuildBitCast(builder, a, int_vec_type, "");
2206          sign = LLVMBuildAnd(builder, sign, mask, "");
2207
2208          /* sign * 0.5 */
2209          half = LLVMBuildBitCast(builder, half, int_vec_type, "");
2210          half = LLVMBuildOr(builder, sign, half, "");
2211          half = LLVMBuildBitCast(builder, half, vec_type, "");
2212       }
2213
2214       res = LLVMBuildFAdd(builder, a, half, "");
2215    }
2216
2217    res = LLVMBuildFPToSI(builder, res, int_vec_type, "");
2218
2219    return res;
2220 }
2221
2222
2223 /**
2224  * Return floor of float (vector), result is an int (vector)
2225  * Ex: ifloor(1.1) = 1.0
2226  * Ex: ifloor(-1.1) = -2.0
2227  */
2228 LLVMValueRef
2229 lp_build_ifloor(struct lp_build_context *bld,
2230                 LLVMValueRef a)
2231 {
2232    LLVMBuilderRef builder = bld->gallivm->builder;
2233    const struct lp_type type = bld->type;
2234    LLVMTypeRef int_vec_type = bld->int_vec_type;
2235    LLVMValueRef res;
2236
2237    assert(type.floating);
2238    assert(lp_check_value(type, a));
2239
2240    res = a;
2241    if (type.sign) {
2242       if (arch_rounding_available(type)) {
2243          res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR);
2244       }
2245       else {
2246          struct lp_type inttype;
2247          struct lp_build_context intbld;
2248          LLVMValueRef trunc, itrunc, mask;
2249
2250          assert(type.floating);
2251          assert(lp_check_value(type, a));
2252
2253          inttype = type;
2254          inttype.floating = 0;
2255          lp_build_context_init(&intbld, bld->gallivm, inttype);
2256
2257          /* round by truncation */
2258          itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2259          trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "ifloor.trunc");
2260
2261          /*
2262           * fix values if rounding is wrong (for non-special cases)
2263           * - this is the case if trunc > a
2264           * The results of doing this with NaNs, very large values etc.
2265           * are undefined but this seems to be the case anyway.
2266           */
2267          mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, trunc, a);
2268          /* cheapie minus one with mask since the mask is minus one / zero */
2269          return lp_build_add(&intbld, itrunc, mask);
2270       }
2271    }
2272
2273    /* round to nearest (toward zero) */
2274    res = LLVMBuildFPToSI(builder, res, int_vec_type, "ifloor.res");
2275
2276    return res;
2277 }
2278
2279
2280 /**
2281  * Return ceiling of float (vector), returning int (vector).
2282  * Ex: iceil( 1.1) = 2
2283  * Ex: iceil(-1.1) = -1
2284  */
2285 LLVMValueRef
2286 lp_build_iceil(struct lp_build_context *bld,
2287                LLVMValueRef a)
2288 {
2289    LLVMBuilderRef builder = bld->gallivm->builder;
2290    const struct lp_type type = bld->type;
2291    LLVMTypeRef int_vec_type = bld->int_vec_type;
2292    LLVMValueRef res;
2293
2294    assert(type.floating);
2295    assert(lp_check_value(type, a));
2296
2297    if (arch_rounding_available(type)) {
2298       res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL);
2299    }
2300    else {
2301       struct lp_type inttype;
2302       struct lp_build_context intbld;
2303       LLVMValueRef trunc, itrunc, mask;
2304
2305       assert(type.floating);
2306       assert(lp_check_value(type, a));
2307
2308       inttype = type;
2309       inttype.floating = 0;
2310       lp_build_context_init(&intbld, bld->gallivm, inttype);
2311
2312       /* round by truncation */
2313       itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2314       trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "iceil.trunc");
2315
2316       /*
2317        * fix values if rounding is wrong (for non-special cases)
2318        * - this is the case if trunc < a
2319        * The results of doing this with NaNs, very large values etc.
2320        * are undefined but this seems to be the case anyway.
2321        */
2322       mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a);
2323       /* cheapie plus one with mask since the mask is minus one / zero */
2324       return lp_build_sub(&intbld, itrunc, mask);
2325    }
2326
2327    /* round to nearest (toward zero) */
2328    res = LLVMBuildFPToSI(builder, res, int_vec_type, "iceil.res");
2329
2330    return res;
2331 }
2332
2333
2334 /**
2335  * Combined ifloor() & fract().
2336  *
2337  * Preferred to calling the functions separately, as it will ensure that the
2338  * strategy (floor() vs ifloor()) that results in less redundant work is used.
2339  */
2340 void
2341 lp_build_ifloor_fract(struct lp_build_context *bld,
2342                       LLVMValueRef a,
2343                       LLVMValueRef *out_ipart,
2344                       LLVMValueRef *out_fpart)
2345 {
2346    LLVMBuilderRef builder = bld->gallivm->builder;
2347    const struct lp_type type = bld->type;
2348    LLVMValueRef ipart;
2349
2350    assert(type.floating);
2351    assert(lp_check_value(type, a));
2352
2353    if (arch_rounding_available(type)) {
2354       /*
2355        * floor() is easier.
2356        */
2357
2358       ipart = lp_build_floor(bld, a);
2359       *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart");
2360       *out_ipart = LLVMBuildFPToSI(builder, ipart, bld->int_vec_type, "ipart");
2361    }
2362    else {
2363       /*
2364        * ifloor() is easier.
2365        */
2366
2367       *out_ipart = lp_build_ifloor(bld, a);
2368       ipart = LLVMBuildSIToFP(builder, *out_ipart, bld->vec_type, "ipart");
2369       *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart");
2370    }
2371 }
2372
2373
2374 /**
2375  * Same as lp_build_ifloor_fract, but guarantees that the fractional part is
2376  * always smaller than one.
2377  */
2378 void
2379 lp_build_ifloor_fract_safe(struct lp_build_context *bld,
2380                            LLVMValueRef a,
2381                            LLVMValueRef *out_ipart,
2382                            LLVMValueRef *out_fpart)
2383 {
2384    lp_build_ifloor_fract(bld, a, out_ipart, out_fpart);
2385    *out_fpart = clamp_fract(bld, *out_fpart);
2386 }
2387
2388
2389 LLVMValueRef
2390 lp_build_sqrt(struct lp_build_context *bld,
2391               LLVMValueRef a)
2392 {
2393    LLVMBuilderRef builder = bld->gallivm->builder;
2394    const struct lp_type type = bld->type;
2395    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
2396    char intrinsic[32];
2397
2398    assert(lp_check_value(type, a));
2399
2400    /* TODO: optimize the constant case */
2401
2402    assert(type.floating);
2403    if (type.length == 1) {
2404       util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.f%u", type.width);
2405    }
2406    else {
2407       util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
2408    }
2409
2410    return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
2411 }
2412
2413
2414 /**
2415  * Do one Newton-Raphson step to improve reciprocate precision:
2416  *
2417  *   x_{i+1} = x_i * (2 - a * x_i)
2418  *
2419  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
2420  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
2421  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
2422  * halo. It would be necessary to clamp the argument to prevent this.
2423  *
2424  * See also:
2425  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
2426  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
2427  */
2428 static INLINE LLVMValueRef
2429 lp_build_rcp_refine(struct lp_build_context *bld,
2430                     LLVMValueRef a,
2431                     LLVMValueRef rcp_a)
2432 {
2433    LLVMBuilderRef builder = bld->gallivm->builder;
2434    LLVMValueRef two = lp_build_const_vec(bld->gallivm, bld->type, 2.0);
2435    LLVMValueRef res;
2436
2437    res = LLVMBuildFMul(builder, a, rcp_a, "");
2438    res = LLVMBuildFSub(builder, two, res, "");
2439    res = LLVMBuildFMul(builder, rcp_a, res, "");
2440
2441    return res;
2442 }
2443
2444
2445 LLVMValueRef
2446 lp_build_rcp(struct lp_build_context *bld,
2447              LLVMValueRef a)
2448 {
2449    LLVMBuilderRef builder = bld->gallivm->builder;
2450    const struct lp_type type = bld->type;
2451
2452    assert(lp_check_value(type, a));
2453
2454    if(a == bld->zero)
2455       return bld->undef;
2456    if(a == bld->one)
2457       return bld->one;
2458    if(a == bld->undef)
2459       return bld->undef;
2460
2461    assert(type.floating);
2462
2463    if(LLVMIsConstant(a))
2464       return LLVMConstFDiv(bld->one, a);
2465
2466    /*
2467     * We don't use RCPPS because:
2468     * - it only has 10bits of precision
2469     * - it doesn't even get the reciprocate of 1.0 exactly
2470     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
2471     * - for recent processors the benefit over DIVPS is marginal, a case
2472     *   dependent
2473     *
2474     * We could still use it on certain processors if benchmarks show that the
2475     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
2476     * particular uses that require less workarounds.
2477     */
2478
2479    if (FALSE && ((util_cpu_caps.has_sse && type.width == 32 && type.length == 4) ||
2480          (util_cpu_caps.has_avx && type.width == 32 && type.length == 8))){
2481       const unsigned num_iterations = 0;
2482       LLVMValueRef res;
2483       unsigned i;
2484       const char *intrinsic = NULL;
2485
2486       if (type.length == 4) {
2487          intrinsic = "llvm.x86.sse.rcp.ps";
2488       }
2489       else {
2490          intrinsic = "llvm.x86.avx.rcp.ps.256";
2491       }
2492
2493       res = lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
2494
2495       for (i = 0; i < num_iterations; ++i) {
2496          res = lp_build_rcp_refine(bld, a, res);
2497       }
2498
2499       return res;
2500    }
2501
2502    return LLVMBuildFDiv(builder, bld->one, a, "");
2503 }
2504
2505
2506 /**
2507  * Do one Newton-Raphson step to improve rsqrt precision:
2508  *
2509  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
2510  *
2511  * See also Intel 64 and IA-32 Architectures Optimization Manual.
2512  */
2513 static INLINE LLVMValueRef
2514 lp_build_rsqrt_refine(struct lp_build_context *bld,
2515                       LLVMValueRef a,
2516                       LLVMValueRef rsqrt_a)
2517 {
2518    LLVMBuilderRef builder = bld->gallivm->builder;
2519    LLVMValueRef half = lp_build_const_vec(bld->gallivm, bld->type, 0.5);
2520    LLVMValueRef three = lp_build_const_vec(bld->gallivm, bld->type, 3.0);
2521    LLVMValueRef res;
2522
2523    res = LLVMBuildFMul(builder, rsqrt_a, rsqrt_a, "");
2524    res = LLVMBuildFMul(builder, a, res, "");
2525    res = LLVMBuildFSub(builder, three, res, "");
2526    res = LLVMBuildFMul(builder, rsqrt_a, res, "");
2527    res = LLVMBuildFMul(builder, half, res, "");
2528
2529    return res;
2530 }
2531
2532
2533 /**
2534  * Generate 1/sqrt(a).
2535  * Result is undefined for values < 0, infinity for +0.
2536  */
2537 LLVMValueRef
2538 lp_build_rsqrt(struct lp_build_context *bld,
2539                LLVMValueRef a)
2540 {
2541    LLVMBuilderRef builder = bld->gallivm->builder;
2542    const struct lp_type type = bld->type;
2543
2544    assert(lp_check_value(type, a));
2545
2546    assert(type.floating);
2547
2548    /*
2549     * This should be faster but all denormals will end up as infinity.
2550     */
2551    if (0 && lp_build_fast_rsqrt_available(type)) {
2552       const unsigned num_iterations = 1;
2553       LLVMValueRef res;
2554       unsigned i;
2555
2556       /* rsqrt(1.0) != 1.0 here */
2557       res = lp_build_fast_rsqrt(bld, a);
2558
2559       if (num_iterations) {
2560          /*
2561           * Newton-Raphson will result in NaN instead of infinity for zero,
2562           * and NaN instead of zero for infinity.
2563           * Also, need to ensure rsqrt(1.0) == 1.0.
2564           * All numbers smaller than FLT_MIN will result in +infinity
2565           * (rsqrtps treats all denormals as zero).
2566           */
2567          /*
2568           * Certain non-c99 compilers don't know INFINITY and might not support
2569           * hacks to evaluate it at compile time neither.
2570           */
2571          const unsigned posinf_int = 0x7F800000;
2572          LLVMValueRef cmp;
2573          LLVMValueRef flt_min = lp_build_const_vec(bld->gallivm, type, FLT_MIN);
2574          LLVMValueRef inf = lp_build_const_int_vec(bld->gallivm, type, posinf_int);
2575
2576          inf = LLVMBuildBitCast(builder, inf, lp_build_vec_type(bld->gallivm, type), "");
2577
2578          for (i = 0; i < num_iterations; ++i) {
2579             res = lp_build_rsqrt_refine(bld, a, res);
2580          }
2581          cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_LESS, a, flt_min);
2582          res = lp_build_select(bld, cmp, inf, res);
2583          cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, inf);
2584          res = lp_build_select(bld, cmp, bld->zero, res);
2585          cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, bld->one);
2586          res = lp_build_select(bld, cmp, bld->one, res);
2587       }
2588
2589       return res;
2590    }
2591
2592    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
2593 }
2594
2595 /**
2596  * If there's a fast (inaccurate) rsqrt instruction available
2597  * (caller may want to avoid to call rsqrt_fast if it's not available,
2598  * i.e. for calculating x^0.5 it may do rsqrt_fast(x) * x but if
2599  * unavailable it would result in sqrt/div/mul so obviously
2600  * much better to just call sqrt, skipping both div and mul).
2601  */
2602 boolean
2603 lp_build_fast_rsqrt_available(struct lp_type type)
2604 {
2605    assert(type.floating);
2606
2607    if ((util_cpu_caps.has_sse && type.width == 32 && type.length == 4) ||
2608        (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) {
2609       return true;
2610    }
2611    return false;
2612 }
2613
2614
2615 /**
2616  * Generate 1/sqrt(a).
2617  * Result is undefined for values < 0, infinity for +0.
2618  * Precision is limited, only ~10 bits guaranteed
2619  * (rsqrt 1.0 may not be 1.0, denorms may be flushed to 0).
2620  */
2621 LLVMValueRef
2622 lp_build_fast_rsqrt(struct lp_build_context *bld,
2623                     LLVMValueRef a)
2624 {
2625    LLVMBuilderRef builder = bld->gallivm->builder;
2626    const struct lp_type type = bld->type;
2627
2628    assert(lp_check_value(type, a));
2629
2630    if (lp_build_fast_rsqrt_available(type)) {
2631       const char *intrinsic = NULL;
2632
2633       if (type.length == 4) {
2634          intrinsic = "llvm.x86.sse.rsqrt.ps";
2635       }
2636       else {
2637          intrinsic = "llvm.x86.avx.rsqrt.ps.256";
2638       }
2639       return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
2640    }
2641    else {
2642       debug_printf("%s: emulating fast rsqrt with rcp/sqrt\n", __FUNCTION__);
2643    }
2644    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
2645 }
2646
2647
2648 /**
2649  * Generate sin(a) or cos(a) using polynomial approximation.
2650  * TODO: it might be worth recognizing sin and cos using same source
2651  * (i.e. d3d10 sincos opcode). Obviously doing both at the same time
2652  * would be way cheaper than calculating (nearly) everything twice...
2653  * Not sure it's common enough to be worth bothering however, scs
2654  * opcode could also benefit from calculating both though.
2655  */
2656 static LLVMValueRef
2657 lp_build_sin_or_cos(struct lp_build_context *bld,
2658                     LLVMValueRef a,
2659                     boolean cos)
2660 {
2661    struct gallivm_state *gallivm = bld->gallivm;
2662    LLVMBuilderRef b = gallivm->builder;
2663    struct lp_type int_type = lp_int_type(bld->type);
2664
2665    /*
2666     *  take the absolute value,
2667     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
2668     */
2669
2670    LLVMValueRef inv_sig_mask = lp_build_const_int_vec(gallivm, bld->type, ~0x80000000);
2671    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, bld->int_vec_type, "a_v4si");
2672
2673    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
2674    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, bld->vec_type, "x_abs");
2675
2676    /*
2677     * scale by 4/Pi
2678     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
2679     */
2680
2681    LLVMValueRef FOPi = lp_build_const_vec(gallivm, bld->type, 1.27323954473516);
2682    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
2683
2684    /*
2685     * store the integer part of y in mm0
2686     * emm2 = _mm_cvttps_epi32(y);
2687     */
2688
2689    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, bld->int_vec_type, "emm2_i");
2690
2691    /*
2692     * j=(j+1) & (~1) (see the cephes sources)
2693     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
2694     */
2695
2696    LLVMValueRef all_one = lp_build_const_int_vec(gallivm, bld->type, 1);
2697    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
2698    /*
2699     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
2700     */
2701    LLVMValueRef inv_one = lp_build_const_int_vec(gallivm, bld->type, ~1);
2702    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
2703
2704    /*
2705     * y = _mm_cvtepi32_ps(emm2);
2706     */
2707    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, bld->vec_type, "y_2");
2708
2709    LLVMValueRef const_2 = lp_build_const_int_vec(gallivm, bld->type, 2);
2710    LLVMValueRef const_4 = lp_build_const_int_vec(gallivm, bld->type, 4);
2711    LLVMValueRef const_29 = lp_build_const_int_vec(gallivm, bld->type, 29);
2712    LLVMValueRef sign_mask = lp_build_const_int_vec(gallivm, bld->type, 0x80000000);
2713
2714    /*
2715     * Argument used for poly selection and sign bit determination
2716     * is different for sin vs. cos.
2717     */
2718    LLVMValueRef emm2_2 = cos ? LLVMBuildSub(b, emm2_and, const_2, "emm2_2") :
2719                                emm2_and;
2720
2721    LLVMValueRef sign_bit = cos ? LLVMBuildShl(b, LLVMBuildAnd(b, const_4,
2722                                                               LLVMBuildNot(b, emm2_2, ""), ""),
2723                                               const_29, "sign_bit") :
2724                                  LLVMBuildAnd(b, LLVMBuildXor(b, a_v4si,
2725                                                               LLVMBuildShl(b, emm2_add,
2726                                                                            const_29, ""), ""),
2727                                               sign_mask, "sign_bit");
2728
2729    /*
2730     * get the polynom selection mask
2731     * there is one polynom for 0 <= x <= Pi/4
2732     * and another one for Pi/4<x<=Pi/2
2733     * Both branches will be computed.
2734     *
2735     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
2736     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
2737     */
2738
2739    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, const_2, "emm2_3");
2740    LLVMValueRef poly_mask = lp_build_compare(gallivm,
2741                                              int_type, PIPE_FUNC_EQUAL,
2742                                              emm2_3, lp_build_const_int_vec(gallivm, bld->type, 0));
2743
2744    /*
2745     * _PS_CONST(minus_cephes_DP1, -0.78515625);
2746     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
2747     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
2748     */
2749    LLVMValueRef DP1 = lp_build_const_vec(gallivm, bld->type, -0.78515625);
2750    LLVMValueRef DP2 = lp_build_const_vec(gallivm, bld->type, -2.4187564849853515625e-4);
2751    LLVMValueRef DP3 = lp_build_const_vec(gallivm, bld->type, -3.77489497744594108e-8);
2752
2753    /*
2754     * The magic pass: "Extended precision modular arithmetic"
2755     * x = ((x - y * DP1) - y * DP2) - y * DP3;
2756     * xmm1 = _mm_mul_ps(y, xmm1);
2757     * xmm2 = _mm_mul_ps(y, xmm2);
2758     * xmm3 = _mm_mul_ps(y, xmm3);
2759     */
2760    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
2761    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
2762    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
2763
2764    /*
2765     * x = _mm_add_ps(x, xmm1);
2766     * x = _mm_add_ps(x, xmm2);
2767     * x = _mm_add_ps(x, xmm3);
2768     */
2769
2770    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
2771    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
2772    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
2773
2774    /*
2775     * Evaluate the first polynom  (0 <= x <= Pi/4)
2776     *
2777     * z = _mm_mul_ps(x,x);
2778     */
2779    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
2780
2781    /*
2782     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
2783     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
2784     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
2785     */
2786    LLVMValueRef coscof_p0 = lp_build_const_vec(gallivm, bld->type, 2.443315711809948E-005);
2787    LLVMValueRef coscof_p1 = lp_build_const_vec(gallivm, bld->type, -1.388731625493765E-003);
2788    LLVMValueRef coscof_p2 = lp_build_const_vec(gallivm, bld->type, 4.166664568298827E-002);
2789
2790    /*
2791     * y = *(v4sf*)_ps_coscof_p0;
2792     * y = _mm_mul_ps(y, z);
2793     */
2794    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
2795    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
2796    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
2797    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
2798    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
2799    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
2800
2801
2802    /*
2803     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
2804     * y = _mm_sub_ps(y, tmp);
2805     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
2806     */
2807    LLVMValueRef half = lp_build_const_vec(gallivm, bld->type, 0.5);
2808    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
2809    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
2810    LLVMValueRef one = lp_build_const_vec(gallivm, bld->type, 1.0);
2811    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
2812
2813    /*
2814     * _PS_CONST(sincof_p0, -1.9515295891E-4);
2815     * _PS_CONST(sincof_p1,  8.3321608736E-3);
2816     * _PS_CONST(sincof_p2, -1.6666654611E-1);
2817     */
2818    LLVMValueRef sincof_p0 = lp_build_const_vec(gallivm, bld->type, -1.9515295891E-4);
2819    LLVMValueRef sincof_p1 = lp_build_const_vec(gallivm, bld->type, 8.3321608736E-3);
2820    LLVMValueRef sincof_p2 = lp_build_const_vec(gallivm, bld->type, -1.6666654611E-1);
2821
2822    /*
2823     * Evaluate the second polynom  (Pi/4 <= x <= 0)
2824     *
2825     * y2 = *(v4sf*)_ps_sincof_p0;
2826     * y2 = _mm_mul_ps(y2, z);
2827     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
2828     * y2 = _mm_mul_ps(y2, z);
2829     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
2830     * y2 = _mm_mul_ps(y2, z);
2831     * y2 = _mm_mul_ps(y2, x);
2832     * y2 = _mm_add_ps(y2, x);
2833     */
2834
2835    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
2836    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
2837    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
2838    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
2839    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
2840    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
2841    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
2842
2843    /*
2844     * select the correct result from the two polynoms
2845     * xmm3 = poly_mask;
2846     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
2847     * y = _mm_andnot_ps(xmm3, y);
2848     * y = _mm_or_ps(y,y2);
2849     */
2850    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, bld->int_vec_type, "y2_i");
2851    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, bld->int_vec_type, "y_i");
2852    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
2853    LLVMValueRef poly_mask_inv = LLVMBuildNot(b, poly_mask, "poly_mask_inv");
2854    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
2855    LLVMValueRef y_combine = LLVMBuildOr(b, y_and, y2_and, "y_combine");
2856
2857    /*
2858     * update the sign
2859     * y = _mm_xor_ps(y, sign_bit);
2860     */
2861    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sign");
2862    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, bld->vec_type, "y_result");
2863
2864    LLVMValueRef isfinite = lp_build_isfinite(bld, a);
2865
2866    /* clamp output to be within [-1, 1] */
2867    y_result = lp_build_clamp(bld, y_result,
2868                              lp_build_const_vec(bld->gallivm, bld->type,  -1.f),
2869                              lp_build_const_vec(bld->gallivm, bld->type,  1.f));
2870    /* If a is -inf, inf or NaN then return NaN */
2871    y_result = lp_build_select(bld, isfinite, y_result,
2872                               lp_build_const_vec(bld->gallivm, bld->type,  NAN));
2873    return y_result;
2874 }
2875
2876
2877 /**
2878  * Generate sin(a)
2879  */
2880 LLVMValueRef
2881 lp_build_sin(struct lp_build_context *bld,
2882              LLVMValueRef a)
2883 {
2884    return lp_build_sin_or_cos(bld, a, FALSE);
2885 }
2886
2887
2888 /**
2889  * Generate cos(a)
2890  */
2891 LLVMValueRef
2892 lp_build_cos(struct lp_build_context *bld,
2893              LLVMValueRef a)
2894 {
2895    return lp_build_sin_or_cos(bld, a, TRUE);
2896 }
2897
2898
2899 /**
2900  * Generate pow(x, y)
2901  */
2902 LLVMValueRef
2903 lp_build_pow(struct lp_build_context *bld,
2904              LLVMValueRef x,
2905              LLVMValueRef y)
2906 {
2907    /* TODO: optimize the constant case */
2908    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2909        LLVMIsConstant(x) && LLVMIsConstant(y)) {
2910       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2911                    __FUNCTION__);
2912    }
2913
2914    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
2915 }
2916
2917
2918 /**
2919  * Generate exp(x)
2920  */
2921 LLVMValueRef
2922 lp_build_exp(struct lp_build_context *bld,
2923              LLVMValueRef x)
2924 {
2925    /* log2(e) = 1/log(2) */
2926    LLVMValueRef log2e = lp_build_const_vec(bld->gallivm, bld->type,
2927                                            1.4426950408889634);
2928
2929    assert(lp_check_value(bld->type, x));
2930
2931    return lp_build_exp2(bld, lp_build_mul(bld, log2e, x));
2932 }
2933
2934
2935 /**
2936  * Generate log(x)
2937  * Behavior is undefined with infs, 0s and nans
2938  */
2939 LLVMValueRef
2940 lp_build_log(struct lp_build_context *bld,
2941              LLVMValueRef x)
2942 {
2943    /* log(2) */
2944    LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type,
2945                                           0.69314718055994529);
2946
2947    assert(lp_check_value(bld->type, x));
2948
2949    return lp_build_mul(bld, log2, lp_build_log2(bld, x));
2950 }
2951
2952 /**
2953  * Generate log(x) that handles edge cases (infs, 0s and nans)
2954  */
2955 LLVMValueRef
2956 lp_build_log_safe(struct lp_build_context *bld,
2957                   LLVMValueRef x)
2958 {
2959    /* log(2) */
2960    LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type,
2961                                           0.69314718055994529);
2962
2963    assert(lp_check_value(bld->type, x));
2964
2965    return lp_build_mul(bld, log2, lp_build_log2_safe(bld, x));
2966 }
2967
2968
2969 /**
2970  * Generate polynomial.
2971  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
2972  */
2973 LLVMValueRef
2974 lp_build_polynomial(struct lp_build_context *bld,
2975                     LLVMValueRef x,
2976                     const double *coeffs,
2977                     unsigned num_coeffs)
2978 {
2979    const struct lp_type type = bld->type;
2980    LLVMValueRef even = NULL, odd = NULL;
2981    LLVMValueRef x2;
2982    unsigned i;
2983
2984    assert(lp_check_value(bld->type, x));
2985
2986    /* TODO: optimize the constant case */
2987    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2988        LLVMIsConstant(x)) {
2989       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2990                    __FUNCTION__);
2991    }
2992
2993    /*
2994     * Calculate odd and even terms seperately to decrease data dependency
2995     * Ex:
2996     *     c[0] + x^2 * c[2] + x^4 * c[4] ...
2997     *     + x * (c[1] + x^2 * c[3] + x^4 * c[5]) ...
2998     */
2999    x2 = lp_build_mul(bld, x, x);
3000
3001    for (i = num_coeffs; i--; ) {
3002       LLVMValueRef coeff;
3003
3004       coeff = lp_build_const_vec(bld->gallivm, type, coeffs[i]);
3005
3006       if (i % 2 == 0) {
3007          if (even)
3008             even = lp_build_add(bld, coeff, lp_build_mul(bld, x2, even));
3009          else
3010             even = coeff;
3011       } else {
3012          if (odd)
3013             odd = lp_build_add(bld, coeff, lp_build_mul(bld, x2, odd));
3014          else
3015             odd = coeff;
3016       }
3017    }
3018
3019    if (odd)
3020       return lp_build_add(bld, lp_build_mul(bld, odd, x), even);
3021    else if (even)
3022       return even;
3023    else
3024       return bld->undef;
3025 }
3026
3027
3028 /**
3029  * Minimax polynomial fit of 2**x, in range [0, 1[
3030  */
3031 const double lp_build_exp2_polynomial[] = {
3032 #if EXP_POLY_DEGREE == 5
3033    1.000000000000000000000, /*XXX: was 0.999999925063526176901, recompute others */
3034    0.693153073200168932794,
3035    0.240153617044375388211,
3036    0.0558263180532956664775,
3037    0.00898934009049466391101,
3038    0.00187757667519147912699
3039 #elif EXP_POLY_DEGREE == 4
3040    1.00000259337069434683,
3041    0.693003834469974940458,
3042    0.24144275689150793076,
3043    0.0520114606103070150235,
3044    0.0135341679161270268764
3045 #elif EXP_POLY_DEGREE == 3
3046    0.999925218562710312959,
3047    0.695833540494823811697,
3048    0.226067155427249155588,
3049    0.0780245226406372992967
3050 #elif EXP_POLY_DEGREE == 2
3051    1.00172476321474503578,
3052    0.657636275736077639316,
3053    0.33718943461968720704
3054 #else
3055 #error
3056 #endif
3057 };
3058
3059
3060 LLVMValueRef
3061 lp_build_exp2(struct lp_build_context *bld,
3062               LLVMValueRef x)
3063 {
3064    LLVMBuilderRef builder = bld->gallivm->builder;
3065    const struct lp_type type = bld->type;
3066    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
3067    LLVMValueRef ipart = NULL;
3068    LLVMValueRef fpart = NULL;
3069    LLVMValueRef expipart = NULL;
3070    LLVMValueRef expfpart = NULL;
3071    LLVMValueRef res = NULL;
3072
3073    assert(lp_check_value(bld->type, x));
3074
3075    /* TODO: optimize the constant case */
3076    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
3077        LLVMIsConstant(x)) {
3078       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
3079                    __FUNCTION__);
3080    }
3081
3082    assert(type.floating && type.width == 32);
3083
3084    /* We want to preserve NaN and make sure than for exp2 if x > 128,
3085     * the result is INF  and if it's smaller than -126.9 the result is 0 */
3086    x = lp_build_min_ext(bld, lp_build_const_vec(bld->gallivm, type,  128.0), x,
3087                         GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN);
3088    x = lp_build_max_ext(bld, lp_build_const_vec(bld->gallivm, type, -126.99999),
3089                         x, GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN);
3090
3091    /* ipart = floor(x) */
3092    /* fpart = x - ipart */
3093    lp_build_ifloor_fract(bld, x, &ipart, &fpart);
3094
3095    /* expipart = (float) (1 << ipart) */
3096    expipart = LLVMBuildAdd(builder, ipart,
3097                            lp_build_const_int_vec(bld->gallivm, type, 127), "");
3098    expipart = LLVMBuildShl(builder, expipart,
3099                            lp_build_const_int_vec(bld->gallivm, type, 23), "");
3100    expipart = LLVMBuildBitCast(builder, expipart, vec_type, "");
3101
3102    expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
3103                                   Elements(lp_build_exp2_polynomial));
3104
3105    res = LLVMBuildFMul(builder, expipart, expfpart, "");
3106
3107    return res;
3108 }
3109
3110
3111
3112 /**
3113  * Extract the exponent of a IEEE-754 floating point value.
3114  *
3115  * Optionally apply an integer bias.
3116  *
3117  * Result is an integer value with
3118  *
3119  *   ifloor(log2(x)) + bias
3120  */
3121 LLVMValueRef
3122 lp_build_extract_exponent(struct lp_build_context *bld,
3123                           LLVMValueRef x,
3124                           int bias)
3125 {
3126    LLVMBuilderRef builder = bld->gallivm->builder;
3127    const struct lp_type type = bld->type;
3128    unsigned mantissa = lp_mantissa(type);
3129    LLVMValueRef res;
3130
3131    assert(type.floating);
3132
3133    assert(lp_check_value(bld->type, x));
3134
3135    x = LLVMBuildBitCast(builder, x, bld->int_vec_type, "");
3136
3137    res = LLVMBuildLShr(builder, x,
3138                        lp_build_const_int_vec(bld->gallivm, type, mantissa), "");
3139    res = LLVMBuildAnd(builder, res,
3140                       lp_build_const_int_vec(bld->gallivm, type, 255), "");
3141    res = LLVMBuildSub(builder, res,
3142                       lp_build_const_int_vec(bld->gallivm, type, 127 - bias), "");
3143
3144    return res;
3145 }
3146
3147
3148 /**
3149  * Extract the mantissa of the a floating.
3150  *
3151  * Result is a floating point value with
3152  *
3153  *   x / floor(log2(x))
3154  */
3155 LLVMValueRef
3156 lp_build_extract_mantissa(struct lp_build_context *bld,
3157                           LLVMValueRef x)
3158 {
3159    LLVMBuilderRef builder = bld->gallivm->builder;
3160    const struct lp_type type = bld->type;
3161    unsigned mantissa = lp_mantissa(type);
3162    LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type,
3163                                                   (1ULL << mantissa) - 1);
3164    LLVMValueRef one = LLVMConstBitCast(bld->one, bld->int_vec_type);
3165    LLVMValueRef res;
3166
3167    assert(lp_check_value(bld->type, x));
3168
3169    assert(type.floating);
3170
3171    x = LLVMBuildBitCast(builder, x, bld->int_vec_type, "");
3172
3173    /* res = x / 2**ipart */
3174    res = LLVMBuildAnd(builder, x, mantmask, "");
3175    res = LLVMBuildOr(builder, res, one, "");
3176    res = LLVMBuildBitCast(builder, res, bld->vec_type, "");
3177
3178    return res;
3179 }
3180
3181
3182
3183 /**
3184  * Minimax polynomial fit of log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x) ,for x in range of [0, 1/9[
3185  * These coefficients can be generate with
3186  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
3187  */
3188 const double lp_build_log2_polynomial[] = {
3189 #if LOG_POLY_DEGREE == 5
3190    2.88539008148777786488L,
3191    0.961796878841293367824L,
3192    0.577058946784739859012L,
3193    0.412914355135828735411L,
3194    0.308591899232910175289L,
3195    0.352376952300281371868L,
3196 #elif LOG_POLY_DEGREE == 4
3197    2.88539009343309178325L,
3198    0.961791550404184197881L,
3199    0.577440339438736392009L,
3200    0.403343858251329912514L,
3201    0.406718052498846252698L,
3202 #elif LOG_POLY_DEGREE == 3
3203    2.88538959748872753838L,
3204    0.961932915889597772928L,
3205    0.571118517972136195241L,
3206    0.493997535084709500285L,
3207 #else
3208 #error
3209 #endif
3210 };
3211
3212 /**
3213  * See http://www.devmaster.net/forums/showthread.php?p=43580
3214  * http://en.wikipedia.org/wiki/Logarithm#Calculation
3215  * http://www.nezumi.demon.co.uk/consult/logx.htm
3216  *
3217  * If handle_edge_cases is true the function will perform computations
3218  * to match the required D3D10+ behavior for each of the edge cases.
3219  * That means that if input is:
3220  * - less than zero (to and including -inf) then NaN will be returned
3221  * - equal to zero (-denorm, -0, +0 or +denorm), then -inf will be returned
3222  * - +infinity, then +infinity will be returned
3223  * - NaN, then NaN will be returned
3224  *
3225  * Those checks are fairly expensive so if you don't need them make sure
3226  * handle_edge_cases is false.
3227  */
3228 void
3229 lp_build_log2_approx(struct lp_build_context *bld,
3230                      LLVMValueRef x,
3231                      LLVMValueRef *p_exp,
3232                      LLVMValueRef *p_floor_log2,
3233                      LLVMValueRef *p_log2,
3234                      boolean handle_edge_cases)
3235 {
3236    LLVMBuilderRef builder = bld->gallivm->builder;
3237    const struct lp_type type = bld->type;
3238    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
3239    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
3240
3241    LLVMValueRef expmask = lp_build_const_int_vec(bld->gallivm, type, 0x7f800000);
3242    LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type, 0x007fffff);
3243    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
3244
3245    LLVMValueRef i = NULL;
3246    LLVMValueRef y = NULL;
3247    LLVMValueRef z = NULL;
3248    LLVMValueRef exp = NULL;
3249    LLVMValueRef mant = NULL;
3250    LLVMValueRef logexp = NULL;
3251    LLVMValueRef logmant = NULL;
3252    LLVMValueRef res = NULL;
3253
3254    assert(lp_check_value(bld->type, x));
3255
3256    if(p_exp || p_floor_log2 || p_log2) {
3257       /* TODO: optimize the constant case */
3258       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
3259           LLVMIsConstant(x)) {
3260          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
3261                       __FUNCTION__);
3262       }
3263
3264       assert(type.floating && type.width == 32);
3265
3266       /*
3267        * We don't explicitly handle denormalized numbers. They will yield a
3268        * result in the neighbourhood of -127, which appears to be adequate
3269        * enough.
3270        */
3271
3272       i = LLVMBuildBitCast(builder, x, int_vec_type, "");
3273
3274       /* exp = (float) exponent(x) */
3275       exp = LLVMBuildAnd(builder, i, expmask, "");
3276    }
3277
3278    if(p_floor_log2 || p_log2) {
3279       logexp = LLVMBuildLShr(builder, exp, lp_build_const_int_vec(bld->gallivm, type, 23), "");
3280       logexp = LLVMBuildSub(builder, logexp, lp_build_const_int_vec(bld->gallivm, type, 127), "");
3281       logexp = LLVMBuildSIToFP(builder, logexp, vec_type, "");
3282    }
3283
3284    if(p_log2) {
3285       /* mant = 1 + (float) mantissa(x) */
3286       mant = LLVMBuildAnd(builder, i, mantmask, "");
3287       mant = LLVMBuildOr(builder, mant, one, "");
3288       mant = LLVMBuildBitCast(builder, mant, vec_type, "");
3289
3290       /* y = (mant - 1) / (mant + 1) */
3291       y = lp_build_div(bld,
3292          lp_build_sub(bld, mant, bld->one),
3293          lp_build_add(bld, mant, bld->one)
3294       );
3295
3296       /* z = y^2 */
3297       z = lp_build_mul(bld, y, y);
3298
3299       /* compute P(z) */
3300       logmant = lp_build_polynomial(bld, z, lp_build_log2_polynomial,
3301                                     Elements(lp_build_log2_polynomial));
3302
3303       /* logmant = y * P(z) */
3304       logmant = lp_build_mul(bld, y, logmant);
3305
3306       res = lp_build_add(bld, logmant, logexp);
3307
3308       if (type.floating && handle_edge_cases) {
3309          LLVMValueRef negmask, infmask,  zmask;
3310          negmask = lp_build_cmp(bld, PIPE_FUNC_LESS, x,
3311                                 lp_build_const_vec(bld->gallivm, type,  0.0f));
3312          zmask = lp_build_cmp(bld, PIPE_FUNC_EQUAL, x,
3313                               lp_build_const_vec(bld->gallivm, type,  0.0f));
3314          infmask = lp_build_cmp(bld, PIPE_FUNC_GEQUAL, x,
3315                                 lp_build_const_vec(bld->gallivm, type,  INFINITY));
3316
3317          /* If x is qual to inf make sure we return inf */
3318          res = lp_build_select(bld, infmask,
3319                                lp_build_const_vec(bld->gallivm, type,  INFINITY),
3320                                res);
3321          /* If x is qual to 0, return -inf */
3322          res = lp_build_select(bld, zmask,
3323                                lp_build_const_vec(bld->gallivm, type,  -INFINITY),
3324                                res);
3325          /* If x is nan or less than 0, return nan */
3326          res = lp_build_select(bld, negmask,
3327                                lp_build_const_vec(bld->gallivm, type,  NAN),
3328                                res);
3329       }
3330    }
3331
3332    if(p_exp) {
3333       exp = LLVMBuildBitCast(builder, exp, vec_type, "");
3334       *p_exp = exp;
3335    }
3336
3337    if(p_floor_log2)
3338       *p_floor_log2 = logexp;
3339
3340    if(p_log2)
3341       *p_log2 = res;
3342 }
3343
3344
3345 /*
3346  * log2 implementation which doesn't have special code to
3347  * handle edge cases (-inf, 0, inf, NaN). It's faster but
3348  * the results for those cases are undefined.
3349  */
3350 LLVMValueRef
3351 lp_build_log2(struct lp_build_context *bld,
3352               LLVMValueRef x)
3353 {
3354    LLVMValueRef res;
3355    lp_build_log2_approx(bld, x, NULL, NULL, &res, FALSE);
3356    return res;
3357 }
3358
3359 /*
3360  * Version of log2 which handles all edge cases.
3361  * Look at documentation of lp_build_log2_approx for
3362  * description of the behavior for each of the edge cases.
3363  */
3364 LLVMValueRef
3365 lp_build_log2_safe(struct lp_build_context *bld,
3366                    LLVMValueRef x)
3367 {
3368    LLVMValueRef res;
3369    lp_build_log2_approx(bld, x, NULL, NULL, &res, TRUE);
3370    return res;
3371 }
3372
3373
3374 /**
3375  * Faster (and less accurate) log2.
3376  *
3377  *    log2(x) = floor(log2(x)) - 1 + x / 2**floor(log2(x))
3378  *
3379  * Piece-wise linear approximation, with exact results when x is a
3380  * power of two.
3381  *
3382  * See http://www.flipcode.com/archives/Fast_log_Function.shtml
3383  */
3384 LLVMValueRef
3385 lp_build_fast_log2(struct lp_build_context *bld,
3386                    LLVMValueRef x)
3387 {
3388    LLVMBuilderRef builder = bld->gallivm->builder;
3389    LLVMValueRef ipart;
3390    LLVMValueRef fpart;
3391
3392    assert(lp_check_value(bld->type, x));
3393
3394    assert(bld->type.floating);
3395
3396    /* ipart = floor(log2(x)) - 1 */
3397    ipart = lp_build_extract_exponent(bld, x, -1);
3398    ipart = LLVMBuildSIToFP(builder, ipart, bld->vec_type, "");
3399
3400    /* fpart = x / 2**ipart */
3401    fpart = lp_build_extract_mantissa(bld, x);
3402
3403    /* ipart + fpart */
3404    return LLVMBuildFAdd(builder, ipart, fpart, "");
3405 }
3406
3407
3408 /**
3409  * Fast implementation of iround(log2(x)).
3410  *
3411  * Not an approximation -- it should give accurate results all the time.
3412  */
3413 LLVMValueRef
3414 lp_build_ilog2(struct lp_build_context *bld,
3415                LLVMValueRef x)
3416 {
3417    LLVMBuilderRef builder = bld->gallivm->builder;
3418    LLVMValueRef sqrt2 = lp_build_const_vec(bld->gallivm, bld->type, M_SQRT2);
3419    LLVMValueRef ipart;
3420
3421    assert(bld->type.floating);
3422
3423    assert(lp_check_value(bld->type, x));
3424
3425    /* x * 2^(0.5)   i.e., add 0.5 to the log2(x) */
3426    x = LLVMBuildFMul(builder, x, sqrt2, "");
3427
3428    /* ipart = floor(log2(x) + 0.5)  */
3429    ipart = lp_build_extract_exponent(bld, x, 0);
3430
3431    return ipart;
3432 }
3433
3434 LLVMValueRef
3435 lp_build_mod(struct lp_build_context *bld,
3436              LLVMValueRef x,
3437              LLVMValueRef y)
3438 {
3439    LLVMBuilderRef builder = bld->gallivm->builder;
3440    LLVMValueRef res;
3441    const struct lp_type type = bld->type;
3442
3443    assert(lp_check_value(type, x));
3444    assert(lp_check_value(type, y));
3445
3446    if (type.floating)
3447       res = LLVMBuildFRem(builder, x, y, "");
3448    else if (type.sign)
3449       res = LLVMBuildSRem(builder, x, y, "");
3450    else
3451       res = LLVMBuildURem(builder, x, y, "");
3452    return res;
3453 }
3454
3455
3456 /*
3457  * For floating inputs it creates and returns a mask
3458  * which is all 1's for channels which are NaN.
3459  * Channels inside x which are not NaN will be 0.
3460  */
3461 LLVMValueRef
3462 lp_build_isnan(struct lp_build_context *bld,
3463                LLVMValueRef x)
3464 {
3465    LLVMValueRef mask;
3466    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, bld->type);
3467
3468    assert(bld->type.floating);
3469    assert(lp_check_value(bld->type, x));
3470
3471    mask = LLVMBuildFCmp(bld->gallivm->builder, LLVMRealOEQ, x, x,
3472                         "isnotnan");
3473    mask = LLVMBuildNot(bld->gallivm->builder, mask, "");
3474    mask = LLVMBuildSExt(bld->gallivm->builder, mask, int_vec_type, "isnan");
3475    return mask;
3476 }
3477
3478 /* Returns all 1's for floating point numbers that are
3479  * finite numbers and returns all zeros for -inf,
3480  * inf and nan's */
3481 LLVMValueRef
3482 lp_build_isfinite(struct lp_build_context *bld,
3483                   LLVMValueRef x)
3484 {
3485    LLVMBuilderRef builder = bld->gallivm->builder;
3486    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, bld->type);
3487    struct lp_type int_type = lp_int_type(bld->type);
3488    LLVMValueRef intx = LLVMBuildBitCast(builder, x, int_vec_type, "");
3489    LLVMValueRef infornan32 = lp_build_const_int_vec(bld->gallivm, bld->type,
3490                                                     0x7f800000);
3491
3492    if (!bld->type.floating) {
3493       return lp_build_const_int_vec(bld->gallivm, bld->type, 0);
3494    }
3495    assert(bld->type.floating);
3496    assert(lp_check_value(bld->type, x));
3497    assert(bld->type.width == 32);
3498
3499    intx = LLVMBuildAnd(builder, intx, infornan32, "");
3500    return lp_build_compare(bld->gallivm, int_type, PIPE_FUNC_NOTEQUAL,
3501                            intx, infornan32);
3502 }
3503
3504 /*
3505  * Returns true if the number is nan or inf and false otherwise.
3506  * The input has to be a floating point vector.
3507  */
3508 LLVMValueRef
3509 lp_build_is_inf_or_nan(struct gallivm_state *gallivm,
3510                        const struct lp_type type,
3511                        LLVMValueRef x)
3512 {
3513    LLVMBuilderRef builder = gallivm->builder;
3514    struct lp_type int_type = lp_int_type(type);
3515    LLVMValueRef const0 = lp_build_const_int_vec(gallivm, int_type,
3516                                                 0x7f800000);
3517    LLVMValueRef ret;
3518
3519    assert(type.floating);
3520
3521    ret = LLVMBuildBitCast(builder, x, lp_build_vec_type(gallivm, int_type), "");
3522    ret = LLVMBuildAnd(builder, ret, const0, "");
3523    ret = lp_build_compare(gallivm, int_type, PIPE_FUNC_EQUAL,
3524                           ret, const0);
3525
3526    return ret;
3527 }
3528
3529
3530 LLVMValueRef
3531 lp_build_fpstate_get(struct gallivm_state *gallivm)
3532 {
3533    if (util_cpu_caps.has_sse) {
3534       LLVMBuilderRef builder = gallivm->builder;
3535       LLVMValueRef mxcsr_ptr = lp_build_alloca(
3536          gallivm,
3537          LLVMInt32TypeInContext(gallivm->context),
3538          "mxcsr_ptr");
3539       LLVMValueRef mxcsr_ptr8 = LLVMBuildPointerCast(builder, mxcsr_ptr,
3540           LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0), "");
3541       lp_build_intrinsic(builder,
3542                          "llvm.x86.sse.stmxcsr",
3543                          LLVMVoidTypeInContext(gallivm->context),
3544                          &mxcsr_ptr8, 1);
3545       return mxcsr_ptr;
3546    }
3547    return 0;
3548 }
3549
3550 void
3551 lp_build_fpstate_set_denorms_zero(struct gallivm_state *gallivm,
3552                                   boolean zero)
3553 {
3554    if (util_cpu_caps.has_sse) {
3555       /* turn on DAZ (64) | FTZ (32768) = 32832 if available */
3556       int daz_ftz = _MM_FLUSH_ZERO_MASK;
3557
3558       LLVMBuilderRef builder = gallivm->builder;
3559       LLVMValueRef mxcsr_ptr = lp_build_fpstate_get(gallivm);
3560       LLVMValueRef mxcsr =
3561          LLVMBuildLoad(builder, mxcsr_ptr, "mxcsr");
3562
3563       if (util_cpu_caps.has_daz) {
3564          /* Enable denormals are zero mode */
3565          daz_ftz |= _MM_DENORMALS_ZERO_MASK;
3566       }
3567       if (zero) {
3568          mxcsr = LLVMBuildOr(builder, mxcsr,
3569                              LLVMConstInt(LLVMTypeOf(mxcsr), daz_ftz, 0), "");
3570       } else {
3571          mxcsr = LLVMBuildAnd(builder, mxcsr,
3572                               LLVMConstInt(LLVMTypeOf(mxcsr), ~daz_ftz, 0), "");
3573       }
3574
3575       LLVMBuildStore(builder, mxcsr, mxcsr_ptr);
3576       lp_build_fpstate_set(gallivm, mxcsr_ptr);
3577    }
3578 }
3579
3580 void
3581 lp_build_fpstate_set(struct gallivm_state *gallivm,
3582                      LLVMValueRef mxcsr_ptr)
3583 {
3584    if (util_cpu_caps.has_sse) {
3585       LLVMBuilderRef builder = gallivm->builder;
3586       mxcsr_ptr = LLVMBuildPointerCast(builder, mxcsr_ptr,
3587                      LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0), "");
3588       lp_build_intrinsic(builder,
3589                          "llvm.x86.sse.ldmxcsr",
3590                          LLVMVoidTypeInContext(gallivm->context),
3591                          &mxcsr_ptr, 1);
3592    }
3593 }