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, 1LL << (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       char intrinsic[32];
1496       lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.fabs", vec_type);
1497       return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
1498    }
1499
1500    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
1501       switch(type.width) {
1502       case 8:
1503          return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
1504       case 16:
1505          return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
1506       case 32:
1507          return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
1508       }
1509    }
1510    else if (type.width*type.length == 256 && util_cpu_caps.has_ssse3 &&
1511             (gallivm_debug & GALLIVM_DEBUG_PERF) &&
1512             (type.width == 8 || type.width == 16 || type.width == 32)) {
1513       debug_printf("%s: inefficient code, should split vectors manually\n",
1514                    __FUNCTION__);
1515    }
1516
1517    return lp_build_max(bld, a, LLVMBuildNeg(builder, a, ""));
1518 }
1519
1520
1521 LLVMValueRef
1522 lp_build_negate(struct lp_build_context *bld,
1523                 LLVMValueRef a)
1524 {
1525    LLVMBuilderRef builder = bld->gallivm->builder;
1526
1527    assert(lp_check_value(bld->type, a));
1528
1529    if (bld->type.floating)
1530       a = LLVMBuildFNeg(builder, a, "");
1531    else
1532       a = LLVMBuildNeg(builder, a, "");
1533
1534    return a;
1535 }
1536
1537
1538 /** Return -1, 0 or +1 depending on the sign of a */
1539 LLVMValueRef
1540 lp_build_sgn(struct lp_build_context *bld,
1541              LLVMValueRef a)
1542 {
1543    LLVMBuilderRef builder = bld->gallivm->builder;
1544    const struct lp_type type = bld->type;
1545    LLVMValueRef cond;
1546    LLVMValueRef res;
1547
1548    assert(lp_check_value(type, a));
1549
1550    /* Handle non-zero case */
1551    if(!type.sign) {
1552       /* if not zero then sign must be positive */
1553       res = bld->one;
1554    }
1555    else if(type.floating) {
1556       LLVMTypeRef vec_type;
1557       LLVMTypeRef int_type;
1558       LLVMValueRef mask;
1559       LLVMValueRef sign;
1560       LLVMValueRef one;
1561       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
1562
1563       int_type = lp_build_int_vec_type(bld->gallivm, type);
1564       vec_type = lp_build_vec_type(bld->gallivm, type);
1565       mask = lp_build_const_int_vec(bld->gallivm, type, maskBit);
1566
1567       /* Take the sign bit and add it to 1 constant */
1568       sign = LLVMBuildBitCast(builder, a, int_type, "");
1569       sign = LLVMBuildAnd(builder, sign, mask, "");
1570       one = LLVMConstBitCast(bld->one, int_type);
1571       res = LLVMBuildOr(builder, sign, one, "");
1572       res = LLVMBuildBitCast(builder, res, vec_type, "");
1573    }
1574    else
1575    {
1576       /* signed int/norm/fixed point */
1577       /* could use psign with sse3 and appropriate vectors here */
1578       LLVMValueRef minus_one = lp_build_const_vec(bld->gallivm, type, -1.0);
1579       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
1580       res = lp_build_select(bld, cond, bld->one, minus_one);
1581    }
1582
1583    /* Handle zero */
1584    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
1585    res = lp_build_select(bld, cond, bld->zero, res);
1586
1587    return res;
1588 }
1589
1590
1591 /**
1592  * Set the sign of float vector 'a' according to 'sign'.
1593  * If sign==0, return abs(a).
1594  * If sign==1, return -abs(a);
1595  * Other values for sign produce undefined results.
1596  */
1597 LLVMValueRef
1598 lp_build_set_sign(struct lp_build_context *bld,
1599                   LLVMValueRef a, LLVMValueRef sign)
1600 {
1601    LLVMBuilderRef builder = bld->gallivm->builder;
1602    const struct lp_type type = bld->type;
1603    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
1604    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
1605    LLVMValueRef shift = lp_build_const_int_vec(bld->gallivm, type, type.width - 1);
1606    LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type,
1607                              ~((unsigned long long) 1 << (type.width - 1)));
1608    LLVMValueRef val, res;
1609
1610    assert(type.floating);
1611    assert(lp_check_value(type, a));
1612
1613    /* val = reinterpret_cast<int>(a) */
1614    val = LLVMBuildBitCast(builder, a, int_vec_type, "");
1615    /* val = val & mask */
1616    val = LLVMBuildAnd(builder, val, mask, "");
1617    /* sign = sign << shift */
1618    sign = LLVMBuildShl(builder, sign, shift, "");
1619    /* res = val | sign */
1620    res = LLVMBuildOr(builder, val, sign, "");
1621    /* res = reinterpret_cast<float>(res) */
1622    res = LLVMBuildBitCast(builder, res, vec_type, "");
1623
1624    return res;
1625 }
1626
1627
1628 /**
1629  * Convert vector of (or scalar) int to vector of (or scalar) float.
1630  */
1631 LLVMValueRef
1632 lp_build_int_to_float(struct lp_build_context *bld,
1633                       LLVMValueRef a)
1634 {
1635    LLVMBuilderRef builder = bld->gallivm->builder;
1636    const struct lp_type type = bld->type;
1637    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
1638
1639    assert(type.floating);
1640
1641    return LLVMBuildSIToFP(builder, a, vec_type, "");
1642 }
1643
1644 static boolean
1645 arch_rounding_available(const struct lp_type type)
1646 {
1647    if ((util_cpu_caps.has_sse4_1 &&
1648        (type.length == 1 || type.width*type.length == 128)) ||
1649        (util_cpu_caps.has_avx && type.width*type.length == 256))
1650       return TRUE;
1651    else if ((util_cpu_caps.has_altivec &&
1652             (type.width == 32 && type.length == 4)))
1653       return TRUE;
1654
1655    return FALSE;
1656 }
1657
1658 enum lp_build_round_mode
1659 {
1660    LP_BUILD_ROUND_NEAREST = 0,
1661    LP_BUILD_ROUND_FLOOR = 1,
1662    LP_BUILD_ROUND_CEIL = 2,
1663    LP_BUILD_ROUND_TRUNCATE = 3
1664 };
1665
1666 static inline LLVMValueRef
1667 lp_build_iround_nearest_sse2(struct lp_build_context *bld,
1668                              LLVMValueRef a)
1669 {
1670    LLVMBuilderRef builder = bld->gallivm->builder;
1671    const struct lp_type type = bld->type;
1672    LLVMTypeRef i32t = LLVMInt32TypeInContext(bld->gallivm->context);
1673    LLVMTypeRef ret_type = lp_build_int_vec_type(bld->gallivm, type);
1674    const char *intrinsic;
1675    LLVMValueRef res;
1676
1677    assert(type.floating);
1678    /* using the double precision conversions is a bit more complicated */
1679    assert(type.width == 32);
1680
1681    assert(lp_check_value(type, a));
1682    assert(util_cpu_caps.has_sse2);
1683
1684    /* This is relying on MXCSR rounding mode, which should always be nearest. */
1685    if (type.length == 1) {
1686       LLVMTypeRef vec_type;
1687       LLVMValueRef undef;
1688       LLVMValueRef arg;
1689       LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);
1690
1691       vec_type = LLVMVectorType(bld->elem_type, 4);
1692
1693       intrinsic = "llvm.x86.sse.cvtss2si";
1694
1695       undef = LLVMGetUndef(vec_type);
1696
1697       arg = LLVMBuildInsertElement(builder, undef, a, index0, "");
1698
1699       res = lp_build_intrinsic_unary(builder, intrinsic,
1700                                      ret_type, arg);
1701    }
1702    else {
1703       if (type.width* type.length == 128) {
1704          intrinsic = "llvm.x86.sse2.cvtps2dq";
1705       }
1706       else {
1707          assert(type.width*type.length == 256);
1708          assert(util_cpu_caps.has_avx);
1709
1710          intrinsic = "llvm.x86.avx.cvt.ps2dq.256";
1711       }
1712       res = lp_build_intrinsic_unary(builder, intrinsic,
1713                                      ret_type, a);
1714    }
1715
1716    return res;
1717 }
1718
1719
1720 /*
1721  */
1722 static inline LLVMValueRef
1723 lp_build_round_altivec(struct lp_build_context *bld,
1724                        LLVMValueRef a,
1725                        enum lp_build_round_mode mode)
1726 {
1727    LLVMBuilderRef builder = bld->gallivm->builder;
1728    const struct lp_type type = bld->type;
1729    const char *intrinsic = NULL;
1730
1731    assert(type.floating);
1732
1733    assert(lp_check_value(type, a));
1734    assert(util_cpu_caps.has_altivec);
1735
1736    (void)type;
1737
1738    switch (mode) {
1739    case LP_BUILD_ROUND_NEAREST:
1740       intrinsic = "llvm.ppc.altivec.vrfin";
1741       break;
1742    case LP_BUILD_ROUND_FLOOR:
1743       intrinsic = "llvm.ppc.altivec.vrfim";
1744       break;
1745    case LP_BUILD_ROUND_CEIL:
1746       intrinsic = "llvm.ppc.altivec.vrfip";
1747       break;
1748    case LP_BUILD_ROUND_TRUNCATE:
1749       intrinsic = "llvm.ppc.altivec.vrfiz";
1750       break;
1751    }
1752
1753    return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
1754 }
1755
1756 static inline LLVMValueRef
1757 lp_build_round_arch(struct lp_build_context *bld,
1758                     LLVMValueRef a,
1759                     enum lp_build_round_mode mode)
1760 {
1761    if (util_cpu_caps.has_sse4_1) {
1762       LLVMBuilderRef builder = bld->gallivm->builder;
1763       const struct lp_type type = bld->type;
1764       const char *intrinsic_root;
1765       char intrinsic[32];
1766
1767       assert(type.floating);
1768       assert(lp_check_value(type, a));
1769       (void)type;
1770
1771       switch (mode) {
1772       case LP_BUILD_ROUND_NEAREST:
1773          intrinsic_root = "llvm.nearbyint";
1774          break;
1775       case LP_BUILD_ROUND_FLOOR:
1776          intrinsic_root = "llvm.floor";
1777          break;
1778       case LP_BUILD_ROUND_CEIL:
1779          intrinsic_root = "llvm.ceil";
1780          break;
1781       case LP_BUILD_ROUND_TRUNCATE:
1782          intrinsic_root = "llvm.trunc";
1783          break;
1784       }
1785
1786       lp_format_intrinsic(intrinsic, sizeof intrinsic, intrinsic_root, bld->vec_type);
1787       return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
1788    }
1789    else /* (util_cpu_caps.has_altivec) */
1790      return lp_build_round_altivec(bld, a, mode);
1791 }
1792
1793 /**
1794  * Return the integer part of a float (vector) value (== round toward zero).
1795  * The returned value is a float (vector).
1796  * Ex: trunc(-1.5) = -1.0
1797  */
1798 LLVMValueRef
1799 lp_build_trunc(struct lp_build_context *bld,
1800                LLVMValueRef a)
1801 {
1802    LLVMBuilderRef builder = bld->gallivm->builder;
1803    const struct lp_type type = bld->type;
1804
1805    assert(type.floating);
1806    assert(lp_check_value(type, a));
1807
1808    if (arch_rounding_available(type)) {
1809       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_TRUNCATE);
1810    }
1811    else {
1812       const struct lp_type type = bld->type;
1813       struct lp_type inttype;
1814       struct lp_build_context intbld;
1815       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1816       LLVMValueRef trunc, res, anosign, mask;
1817       LLVMTypeRef int_vec_type = bld->int_vec_type;
1818       LLVMTypeRef vec_type = bld->vec_type;
1819
1820       assert(type.width == 32); /* might want to handle doubles at some point */
1821
1822       inttype = type;
1823       inttype.floating = 0;
1824       lp_build_context_init(&intbld, bld->gallivm, inttype);
1825
1826       /* round by truncation */
1827       trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
1828       res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc");
1829
1830       /* mask out sign bit */
1831       anosign = lp_build_abs(bld, a);
1832       /*
1833        * mask out all values if anosign > 2^24
1834        * This should work both for large ints (all rounding is no-op for them
1835        * because such floats are always exact) as well as special cases like
1836        * NaNs, Infs (taking advantage of the fact they use max exponent).
1837        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
1838        */
1839       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
1840       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
1841       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
1842       return lp_build_select(bld, mask, a, res);
1843    }
1844 }
1845
1846
1847 /**
1848  * Return float (vector) rounded to nearest integer (vector).  The returned
1849  * value is a float (vector).
1850  * Ex: round(0.9) = 1.0
1851  * Ex: round(-1.5) = -2.0
1852  */
1853 LLVMValueRef
1854 lp_build_round(struct lp_build_context *bld,
1855                LLVMValueRef a)
1856 {
1857    LLVMBuilderRef builder = bld->gallivm->builder;
1858    const struct lp_type type = bld->type;
1859
1860    assert(type.floating);
1861    assert(lp_check_value(type, a));
1862
1863    if (arch_rounding_available(type)) {
1864       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST);
1865    }
1866    else {
1867       const struct lp_type type = bld->type;
1868       struct lp_type inttype;
1869       struct lp_build_context intbld;
1870       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1871       LLVMValueRef res, anosign, mask;
1872       LLVMTypeRef int_vec_type = bld->int_vec_type;
1873       LLVMTypeRef vec_type = bld->vec_type;
1874
1875       assert(type.width == 32); /* might want to handle doubles at some point */
1876
1877       inttype = type;
1878       inttype.floating = 0;
1879       lp_build_context_init(&intbld, bld->gallivm, inttype);
1880
1881       res = lp_build_iround(bld, a);
1882       res = LLVMBuildSIToFP(builder, res, vec_type, "");
1883
1884       /* mask out sign bit */
1885       anosign = lp_build_abs(bld, a);
1886       /*
1887        * mask out all values if anosign > 2^24
1888        * This should work both for large ints (all rounding is no-op for them
1889        * because such floats are always exact) as well as special cases like
1890        * NaNs, Infs (taking advantage of the fact they use max exponent).
1891        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
1892        */
1893       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
1894       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
1895       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
1896       return lp_build_select(bld, mask, a, res);
1897    }
1898 }
1899
1900
1901 /**
1902  * Return floor of float (vector), result is a float (vector)
1903  * Ex: floor(1.1) = 1.0
1904  * Ex: floor(-1.1) = -2.0
1905  */
1906 LLVMValueRef
1907 lp_build_floor(struct lp_build_context *bld,
1908                LLVMValueRef a)
1909 {
1910    LLVMBuilderRef builder = bld->gallivm->builder;
1911    const struct lp_type type = bld->type;
1912
1913    assert(type.floating);
1914    assert(lp_check_value(type, a));
1915
1916    if (arch_rounding_available(type)) {
1917       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR);
1918    }
1919    else {
1920       const struct lp_type type = bld->type;
1921       struct lp_type inttype;
1922       struct lp_build_context intbld;
1923       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1924       LLVMValueRef trunc, res, anosign, mask;
1925       LLVMTypeRef int_vec_type = bld->int_vec_type;
1926       LLVMTypeRef vec_type = bld->vec_type;
1927
1928       if (type.width != 32) {
1929          char intrinsic[32];
1930          lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.floor", vec_type);
1931          return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
1932       }
1933
1934       assert(type.width == 32); /* might want to handle doubles at some point */
1935
1936       inttype = type;
1937       inttype.floating = 0;
1938       lp_build_context_init(&intbld, bld->gallivm, inttype);
1939
1940       /* round by truncation */
1941       trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
1942       res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc");
1943
1944       if (type.sign) {
1945          LLVMValueRef tmp;
1946
1947          /*
1948           * fix values if rounding is wrong (for non-special cases)
1949           * - this is the case if trunc > a
1950           */
1951          mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, res, a);
1952          /* tmp = trunc > a ? 1.0 : 0.0 */
1953          tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, "");
1954          tmp = lp_build_and(&intbld, mask, tmp);
1955          tmp = LLVMBuildBitCast(builder, tmp, vec_type, "");
1956          res = lp_build_sub(bld, res, tmp);
1957       }
1958
1959       /* mask out sign bit */
1960       anosign = lp_build_abs(bld, a);
1961       /*
1962        * mask out all values if anosign > 2^24
1963        * This should work both for large ints (all rounding is no-op for them
1964        * because such floats are always exact) as well as special cases like
1965        * NaNs, Infs (taking advantage of the fact they use max exponent).
1966        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
1967        */
1968       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
1969       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
1970       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
1971       return lp_build_select(bld, mask, a, res);
1972    }
1973 }
1974
1975
1976 /**
1977  * Return ceiling of float (vector), returning float (vector).
1978  * Ex: ceil( 1.1) = 2.0
1979  * Ex: ceil(-1.1) = -1.0
1980  */
1981 LLVMValueRef
1982 lp_build_ceil(struct lp_build_context *bld,
1983               LLVMValueRef a)
1984 {
1985    LLVMBuilderRef builder = bld->gallivm->builder;
1986    const struct lp_type type = bld->type;
1987
1988    assert(type.floating);
1989    assert(lp_check_value(type, a));
1990
1991    if (arch_rounding_available(type)) {
1992       return lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL);
1993    }
1994    else {
1995       const struct lp_type type = bld->type;
1996       struct lp_type inttype;
1997       struct lp_build_context intbld;
1998       LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 1<<24);
1999       LLVMValueRef trunc, res, anosign, mask, tmp;
2000       LLVMTypeRef int_vec_type = bld->int_vec_type;
2001       LLVMTypeRef vec_type = bld->vec_type;
2002
2003       if (type.width != 32) {
2004          char intrinsic[32];
2005          lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.ceil", vec_type);
2006          return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
2007       }
2008
2009       assert(type.width == 32); /* might want to handle doubles at some point */
2010
2011       inttype = type;
2012       inttype.floating = 0;
2013       lp_build_context_init(&intbld, bld->gallivm, inttype);
2014
2015       /* round by truncation */
2016       trunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2017       trunc = LLVMBuildSIToFP(builder, trunc, vec_type, "ceil.trunc");
2018
2019       /*
2020        * fix values if rounding is wrong (for non-special cases)
2021        * - this is the case if trunc < a
2022        */
2023       mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a);
2024       /* tmp = trunc < a ? 1.0 : 0.0 */
2025       tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, "");
2026       tmp = lp_build_and(&intbld, mask, tmp);
2027       tmp = LLVMBuildBitCast(builder, tmp, vec_type, "");
2028       res = lp_build_add(bld, trunc, tmp);
2029
2030       /* mask out sign bit */
2031       anosign = lp_build_abs(bld, a);
2032       /*
2033        * mask out all values if anosign > 2^24
2034        * This should work both for large ints (all rounding is no-op for them
2035        * because such floats are always exact) as well as special cases like
2036        * NaNs, Infs (taking advantage of the fact they use max exponent).
2037        * (2^24 is arbitrary anything between 2^24 and 2^31 should work.)
2038        */
2039       anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, "");
2040       cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, "");
2041       mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval);
2042       return lp_build_select(bld, mask, a, res);
2043    }
2044 }
2045
2046
2047 /**
2048  * Return fractional part of 'a' computed as a - floor(a)
2049  * Typically used in texture coord arithmetic.
2050  */
2051 LLVMValueRef
2052 lp_build_fract(struct lp_build_context *bld,
2053                LLVMValueRef a)
2054 {
2055    assert(bld->type.floating);
2056    return lp_build_sub(bld, a, lp_build_floor(bld, a));
2057 }
2058
2059
2060 /**
2061  * Prevent returning a fractional part of 1.0 for very small negative values of
2062  * 'a' by clamping against 0.99999(9).
2063  */
2064 static inline LLVMValueRef
2065 clamp_fract(struct lp_build_context *bld, LLVMValueRef fract)
2066 {
2067    LLVMValueRef max;
2068
2069    /* this is the largest number smaller than 1.0 representable as float */
2070    max = lp_build_const_vec(bld->gallivm, bld->type,
2071                             1.0 - 1.0/(1LL << (lp_mantissa(bld->type) + 1)));
2072    return lp_build_min(bld, fract, max);
2073 }
2074
2075
2076 /**
2077  * Same as lp_build_fract, but guarantees that the result is always smaller
2078  * than one.
2079  */
2080 LLVMValueRef
2081 lp_build_fract_safe(struct lp_build_context *bld,
2082                     LLVMValueRef a)
2083 {
2084    return clamp_fract(bld, lp_build_fract(bld, a));
2085 }
2086
2087
2088 /**
2089  * Return the integer part of a float (vector) value (== round toward zero).
2090  * The returned value is an integer (vector).
2091  * Ex: itrunc(-1.5) = -1
2092  */
2093 LLVMValueRef
2094 lp_build_itrunc(struct lp_build_context *bld,
2095                 LLVMValueRef a)
2096 {
2097    LLVMBuilderRef builder = bld->gallivm->builder;
2098    const struct lp_type type = bld->type;
2099    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
2100
2101    assert(type.floating);
2102    assert(lp_check_value(type, a));
2103
2104    return LLVMBuildFPToSI(builder, a, int_vec_type, "");
2105 }
2106
2107
2108 /**
2109  * Return float (vector) rounded to nearest integer (vector).  The returned
2110  * value is an integer (vector).
2111  * Ex: iround(0.9) = 1
2112  * Ex: iround(-1.5) = -2
2113  */
2114 LLVMValueRef
2115 lp_build_iround(struct lp_build_context *bld,
2116                 LLVMValueRef a)
2117 {
2118    LLVMBuilderRef builder = bld->gallivm->builder;
2119    const struct lp_type type = bld->type;
2120    LLVMTypeRef int_vec_type = bld->int_vec_type;
2121    LLVMValueRef res;
2122
2123    assert(type.floating);
2124
2125    assert(lp_check_value(type, a));
2126
2127    if ((util_cpu_caps.has_sse2 &&
2128        ((type.width == 32) && (type.length == 1 || type.length == 4))) ||
2129        (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) {
2130       return lp_build_iround_nearest_sse2(bld, a);
2131    }
2132    if (arch_rounding_available(type)) {
2133       res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST);
2134    }
2135    else {
2136       LLVMValueRef half;
2137
2138       half = lp_build_const_vec(bld->gallivm, type, 0.5);
2139
2140       if (type.sign) {
2141          LLVMTypeRef vec_type = bld->vec_type;
2142          LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type,
2143                                     (unsigned long long)1 << (type.width - 1));
2144          LLVMValueRef sign;
2145
2146          /* get sign bit */
2147          sign = LLVMBuildBitCast(builder, a, int_vec_type, "");
2148          sign = LLVMBuildAnd(builder, sign, mask, "");
2149
2150          /* sign * 0.5 */
2151          half = LLVMBuildBitCast(builder, half, int_vec_type, "");
2152          half = LLVMBuildOr(builder, sign, half, "");
2153          half = LLVMBuildBitCast(builder, half, vec_type, "");
2154       }
2155
2156       res = LLVMBuildFAdd(builder, a, half, "");
2157    }
2158
2159    res = LLVMBuildFPToSI(builder, res, int_vec_type, "");
2160
2161    return res;
2162 }
2163
2164
2165 /**
2166  * Return floor of float (vector), result is an int (vector)
2167  * Ex: ifloor(1.1) = 1.0
2168  * Ex: ifloor(-1.1) = -2.0
2169  */
2170 LLVMValueRef
2171 lp_build_ifloor(struct lp_build_context *bld,
2172                 LLVMValueRef a)
2173 {
2174    LLVMBuilderRef builder = bld->gallivm->builder;
2175    const struct lp_type type = bld->type;
2176    LLVMTypeRef int_vec_type = bld->int_vec_type;
2177    LLVMValueRef res;
2178
2179    assert(type.floating);
2180    assert(lp_check_value(type, a));
2181
2182    res = a;
2183    if (type.sign) {
2184       if (arch_rounding_available(type)) {
2185          res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR);
2186       }
2187       else {
2188          struct lp_type inttype;
2189          struct lp_build_context intbld;
2190          LLVMValueRef trunc, itrunc, mask;
2191
2192          assert(type.floating);
2193          assert(lp_check_value(type, a));
2194
2195          inttype = type;
2196          inttype.floating = 0;
2197          lp_build_context_init(&intbld, bld->gallivm, inttype);
2198
2199          /* round by truncation */
2200          itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2201          trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "ifloor.trunc");
2202
2203          /*
2204           * fix values if rounding is wrong (for non-special cases)
2205           * - this is the case if trunc > a
2206           * The results of doing this with NaNs, very large values etc.
2207           * are undefined but this seems to be the case anyway.
2208           */
2209          mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, trunc, a);
2210          /* cheapie minus one with mask since the mask is minus one / zero */
2211          return lp_build_add(&intbld, itrunc, mask);
2212       }
2213    }
2214
2215    /* round to nearest (toward zero) */
2216    res = LLVMBuildFPToSI(builder, res, int_vec_type, "ifloor.res");
2217
2218    return res;
2219 }
2220
2221
2222 /**
2223  * Return ceiling of float (vector), returning int (vector).
2224  * Ex: iceil( 1.1) = 2
2225  * Ex: iceil(-1.1) = -1
2226  */
2227 LLVMValueRef
2228 lp_build_iceil(struct lp_build_context *bld,
2229                LLVMValueRef a)
2230 {
2231    LLVMBuilderRef builder = bld->gallivm->builder;
2232    const struct lp_type type = bld->type;
2233    LLVMTypeRef int_vec_type = bld->int_vec_type;
2234    LLVMValueRef res;
2235
2236    assert(type.floating);
2237    assert(lp_check_value(type, a));
2238
2239    if (arch_rounding_available(type)) {
2240       res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL);
2241    }
2242    else {
2243       struct lp_type inttype;
2244       struct lp_build_context intbld;
2245       LLVMValueRef trunc, itrunc, mask;
2246
2247       assert(type.floating);
2248       assert(lp_check_value(type, a));
2249
2250       inttype = type;
2251       inttype.floating = 0;
2252       lp_build_context_init(&intbld, bld->gallivm, inttype);
2253
2254       /* round by truncation */
2255       itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, "");
2256       trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "iceil.trunc");
2257
2258       /*
2259        * fix values if rounding is wrong (for non-special cases)
2260        * - this is the case if trunc < a
2261        * The results of doing this with NaNs, very large values etc.
2262        * are undefined but this seems to be the case anyway.
2263        */
2264       mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a);
2265       /* cheapie plus one with mask since the mask is minus one / zero */
2266       return lp_build_sub(&intbld, itrunc, mask);
2267    }
2268
2269    /* round to nearest (toward zero) */
2270    res = LLVMBuildFPToSI(builder, res, int_vec_type, "iceil.res");
2271
2272    return res;
2273 }
2274
2275
2276 /**
2277  * Combined ifloor() & fract().
2278  *
2279  * Preferred to calling the functions separately, as it will ensure that the
2280  * strategy (floor() vs ifloor()) that results in less redundant work is used.
2281  */
2282 void
2283 lp_build_ifloor_fract(struct lp_build_context *bld,
2284                       LLVMValueRef a,
2285                       LLVMValueRef *out_ipart,
2286                       LLVMValueRef *out_fpart)
2287 {
2288    LLVMBuilderRef builder = bld->gallivm->builder;
2289    const struct lp_type type = bld->type;
2290    LLVMValueRef ipart;
2291
2292    assert(type.floating);
2293    assert(lp_check_value(type, a));
2294
2295    if (arch_rounding_available(type)) {
2296       /*
2297        * floor() is easier.
2298        */
2299
2300       ipart = lp_build_floor(bld, a);
2301       *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart");
2302       *out_ipart = LLVMBuildFPToSI(builder, ipart, bld->int_vec_type, "ipart");
2303    }
2304    else {
2305       /*
2306        * ifloor() is easier.
2307        */
2308
2309       *out_ipart = lp_build_ifloor(bld, a);
2310       ipart = LLVMBuildSIToFP(builder, *out_ipart, bld->vec_type, "ipart");
2311       *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart");
2312    }
2313 }
2314
2315
2316 /**
2317  * Same as lp_build_ifloor_fract, but guarantees that the fractional part is
2318  * always smaller than one.
2319  */
2320 void
2321 lp_build_ifloor_fract_safe(struct lp_build_context *bld,
2322                            LLVMValueRef a,
2323                            LLVMValueRef *out_ipart,
2324                            LLVMValueRef *out_fpart)
2325 {
2326    lp_build_ifloor_fract(bld, a, out_ipart, out_fpart);
2327    *out_fpart = clamp_fract(bld, *out_fpart);
2328 }
2329
2330
2331 LLVMValueRef
2332 lp_build_sqrt(struct lp_build_context *bld,
2333               LLVMValueRef a)
2334 {
2335    LLVMBuilderRef builder = bld->gallivm->builder;
2336    const struct lp_type type = bld->type;
2337    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
2338    char intrinsic[32];
2339
2340    assert(lp_check_value(type, a));
2341
2342    assert(type.floating);
2343    lp_format_intrinsic(intrinsic, sizeof intrinsic, "llvm.sqrt", vec_type);
2344
2345    return lp_build_intrinsic_unary(builder, intrinsic, vec_type, a);
2346 }
2347
2348
2349 /**
2350  * Do one Newton-Raphson step to improve reciprocate precision:
2351  *
2352  *   x_{i+1} = x_i * (2 - a * x_i)
2353  *
2354  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
2355  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
2356  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
2357  * halo. It would be necessary to clamp the argument to prevent this.
2358  *
2359  * See also:
2360  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
2361  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
2362  */
2363 static inline LLVMValueRef
2364 lp_build_rcp_refine(struct lp_build_context *bld,
2365                     LLVMValueRef a,
2366                     LLVMValueRef rcp_a)
2367 {
2368    LLVMBuilderRef builder = bld->gallivm->builder;
2369    LLVMValueRef two = lp_build_const_vec(bld->gallivm, bld->type, 2.0);
2370    LLVMValueRef res;
2371
2372    res = LLVMBuildFMul(builder, a, rcp_a, "");
2373    res = LLVMBuildFSub(builder, two, res, "");
2374    res = LLVMBuildFMul(builder, rcp_a, res, "");
2375
2376    return res;
2377 }
2378
2379
2380 LLVMValueRef
2381 lp_build_rcp(struct lp_build_context *bld,
2382              LLVMValueRef a)
2383 {
2384    LLVMBuilderRef builder = bld->gallivm->builder;
2385    const struct lp_type type = bld->type;
2386
2387    assert(lp_check_value(type, a));
2388
2389    if(a == bld->zero)
2390       return bld->undef;
2391    if(a == bld->one)
2392       return bld->one;
2393    if(a == bld->undef)
2394       return bld->undef;
2395
2396    assert(type.floating);
2397
2398    if(LLVMIsConstant(a))
2399       return LLVMConstFDiv(bld->one, a);
2400
2401    /*
2402     * We don't use RCPPS because:
2403     * - it only has 10bits of precision
2404     * - it doesn't even get the reciprocate of 1.0 exactly
2405     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
2406     * - for recent processors the benefit over DIVPS is marginal, a case
2407     *   dependent
2408     *
2409     * We could still use it on certain processors if benchmarks show that the
2410     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
2411     * particular uses that require less workarounds.
2412     */
2413
2414    if (FALSE && ((util_cpu_caps.has_sse && type.width == 32 && type.length == 4) ||
2415          (util_cpu_caps.has_avx && type.width == 32 && type.length == 8))){
2416       const unsigned num_iterations = 0;
2417       LLVMValueRef res;
2418       unsigned i;
2419       const char *intrinsic = NULL;
2420
2421       if (type.length == 4) {
2422          intrinsic = "llvm.x86.sse.rcp.ps";
2423       }
2424       else {
2425          intrinsic = "llvm.x86.avx.rcp.ps.256";
2426       }
2427
2428       res = lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
2429
2430       for (i = 0; i < num_iterations; ++i) {
2431          res = lp_build_rcp_refine(bld, a, res);
2432       }
2433
2434       return res;
2435    }
2436
2437    return LLVMBuildFDiv(builder, bld->one, a, "");
2438 }
2439
2440
2441 /**
2442  * Do one Newton-Raphson step to improve rsqrt precision:
2443  *
2444  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
2445  *
2446  * See also Intel 64 and IA-32 Architectures Optimization Manual.
2447  */
2448 static inline LLVMValueRef
2449 lp_build_rsqrt_refine(struct lp_build_context *bld,
2450                       LLVMValueRef a,
2451                       LLVMValueRef rsqrt_a)
2452 {
2453    LLVMBuilderRef builder = bld->gallivm->builder;
2454    LLVMValueRef half = lp_build_const_vec(bld->gallivm, bld->type, 0.5);
2455    LLVMValueRef three = lp_build_const_vec(bld->gallivm, bld->type, 3.0);
2456    LLVMValueRef res;
2457
2458    res = LLVMBuildFMul(builder, rsqrt_a, rsqrt_a, "");
2459    res = LLVMBuildFMul(builder, a, res, "");
2460    res = LLVMBuildFSub(builder, three, res, "");
2461    res = LLVMBuildFMul(builder, rsqrt_a, res, "");
2462    res = LLVMBuildFMul(builder, half, res, "");
2463
2464    return res;
2465 }
2466
2467
2468 /**
2469  * Generate 1/sqrt(a).
2470  * Result is undefined for values < 0, infinity for +0.
2471  */
2472 LLVMValueRef
2473 lp_build_rsqrt(struct lp_build_context *bld,
2474                LLVMValueRef a)
2475 {
2476    const struct lp_type type = bld->type;
2477
2478    assert(lp_check_value(type, a));
2479
2480    assert(type.floating);
2481
2482    /*
2483     * This should be faster but all denormals will end up as infinity.
2484     */
2485    if (0 && lp_build_fast_rsqrt_available(type)) {
2486       const unsigned num_iterations = 1;
2487       LLVMValueRef res;
2488       unsigned i;
2489
2490       /* rsqrt(1.0) != 1.0 here */
2491       res = lp_build_fast_rsqrt(bld, a);
2492
2493       if (num_iterations) {
2494          /*
2495           * Newton-Raphson will result in NaN instead of infinity for zero,
2496           * and NaN instead of zero for infinity.
2497           * Also, need to ensure rsqrt(1.0) == 1.0.
2498           * All numbers smaller than FLT_MIN will result in +infinity
2499           * (rsqrtps treats all denormals as zero).
2500           */
2501          LLVMValueRef cmp;
2502          LLVMValueRef flt_min = lp_build_const_vec(bld->gallivm, type, FLT_MIN);
2503          LLVMValueRef inf = lp_build_const_vec(bld->gallivm, type, INFINITY);
2504
2505          for (i = 0; i < num_iterations; ++i) {
2506             res = lp_build_rsqrt_refine(bld, a, res);
2507          }
2508          cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_LESS, a, flt_min);
2509          res = lp_build_select(bld, cmp, inf, res);
2510          cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, inf);
2511          res = lp_build_select(bld, cmp, bld->zero, res);
2512          cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, bld->one);
2513          res = lp_build_select(bld, cmp, bld->one, res);
2514       }
2515
2516       return res;
2517    }
2518
2519    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
2520 }
2521
2522 /**
2523  * If there's a fast (inaccurate) rsqrt instruction available
2524  * (caller may want to avoid to call rsqrt_fast if it's not available,
2525  * i.e. for calculating x^0.5 it may do rsqrt_fast(x) * x but if
2526  * unavailable it would result in sqrt/div/mul so obviously
2527  * much better to just call sqrt, skipping both div and mul).
2528  */
2529 boolean
2530 lp_build_fast_rsqrt_available(struct lp_type type)
2531 {
2532    assert(type.floating);
2533
2534    if ((util_cpu_caps.has_sse && type.width == 32 && type.length == 4) ||
2535        (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) {
2536       return true;
2537    }
2538    return false;
2539 }
2540
2541
2542 /**
2543  * Generate 1/sqrt(a).
2544  * Result is undefined for values < 0, infinity for +0.
2545  * Precision is limited, only ~10 bits guaranteed
2546  * (rsqrt 1.0 may not be 1.0, denorms may be flushed to 0).
2547  */
2548 LLVMValueRef
2549 lp_build_fast_rsqrt(struct lp_build_context *bld,
2550                     LLVMValueRef a)
2551 {
2552    LLVMBuilderRef builder = bld->gallivm->builder;
2553    const struct lp_type type = bld->type;
2554
2555    assert(lp_check_value(type, a));
2556
2557    if (lp_build_fast_rsqrt_available(type)) {
2558       const char *intrinsic = NULL;
2559
2560       if (type.length == 4) {
2561          intrinsic = "llvm.x86.sse.rsqrt.ps";
2562       }
2563       else {
2564          intrinsic = "llvm.x86.avx.rsqrt.ps.256";
2565       }
2566       return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a);
2567    }
2568    else {
2569       debug_printf("%s: emulating fast rsqrt with rcp/sqrt\n", __FUNCTION__);
2570    }
2571    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
2572 }
2573
2574
2575 /**
2576  * Generate sin(a) or cos(a) using polynomial approximation.
2577  * TODO: it might be worth recognizing sin and cos using same source
2578  * (i.e. d3d10 sincos opcode). Obviously doing both at the same time
2579  * would be way cheaper than calculating (nearly) everything twice...
2580  * Not sure it's common enough to be worth bothering however, scs
2581  * opcode could also benefit from calculating both though.
2582  */
2583 static LLVMValueRef
2584 lp_build_sin_or_cos(struct lp_build_context *bld,
2585                     LLVMValueRef a,
2586                     boolean cos)
2587 {
2588    struct gallivm_state *gallivm = bld->gallivm;
2589    LLVMBuilderRef b = gallivm->builder;
2590    struct lp_type int_type = lp_int_type(bld->type);
2591
2592    /*
2593     *  take the absolute value,
2594     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
2595     */
2596
2597    LLVMValueRef inv_sig_mask = lp_build_const_int_vec(gallivm, bld->type, ~0x80000000);
2598    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, bld->int_vec_type, "a_v4si");
2599
2600    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
2601    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, bld->vec_type, "x_abs");
2602
2603    /*
2604     * scale by 4/Pi
2605     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
2606     */
2607
2608    LLVMValueRef FOPi = lp_build_const_vec(gallivm, bld->type, 1.27323954473516);
2609    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
2610
2611    /*
2612     * store the integer part of y in mm0
2613     * emm2 = _mm_cvttps_epi32(y);
2614     */
2615
2616    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, bld->int_vec_type, "emm2_i");
2617
2618    /*
2619     * j=(j+1) & (~1) (see the cephes sources)
2620     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
2621     */
2622
2623    LLVMValueRef all_one = lp_build_const_int_vec(gallivm, bld->type, 1);
2624    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
2625    /*
2626     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
2627     */
2628    LLVMValueRef inv_one = lp_build_const_int_vec(gallivm, bld->type, ~1);
2629    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
2630
2631    /*
2632     * y = _mm_cvtepi32_ps(emm2);
2633     */
2634    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, bld->vec_type, "y_2");
2635
2636    LLVMValueRef const_2 = lp_build_const_int_vec(gallivm, bld->type, 2);
2637    LLVMValueRef const_4 = lp_build_const_int_vec(gallivm, bld->type, 4);
2638    LLVMValueRef const_29 = lp_build_const_int_vec(gallivm, bld->type, 29);
2639    LLVMValueRef sign_mask = lp_build_const_int_vec(gallivm, bld->type, 0x80000000);
2640
2641    /*
2642     * Argument used for poly selection and sign bit determination
2643     * is different for sin vs. cos.
2644     */
2645    LLVMValueRef emm2_2 = cos ? LLVMBuildSub(b, emm2_and, const_2, "emm2_2") :
2646                                emm2_and;
2647
2648    LLVMValueRef sign_bit = cos ? LLVMBuildShl(b, LLVMBuildAnd(b, const_4,
2649                                                               LLVMBuildNot(b, emm2_2, ""), ""),
2650                                               const_29, "sign_bit") :
2651                                  LLVMBuildAnd(b, LLVMBuildXor(b, a_v4si,
2652                                                               LLVMBuildShl(b, emm2_add,
2653                                                                            const_29, ""), ""),
2654                                               sign_mask, "sign_bit");
2655
2656    /*
2657     * get the polynom selection mask
2658     * there is one polynom for 0 <= x <= Pi/4
2659     * and another one for Pi/4<x<=Pi/2
2660     * Both branches will be computed.
2661     *
2662     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
2663     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
2664     */
2665
2666    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, const_2, "emm2_3");
2667    LLVMValueRef poly_mask = lp_build_compare(gallivm,
2668                                              int_type, PIPE_FUNC_EQUAL,
2669                                              emm2_3, lp_build_const_int_vec(gallivm, bld->type, 0));
2670
2671    /*
2672     * _PS_CONST(minus_cephes_DP1, -0.78515625);
2673     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
2674     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
2675     */
2676    LLVMValueRef DP1 = lp_build_const_vec(gallivm, bld->type, -0.78515625);
2677    LLVMValueRef DP2 = lp_build_const_vec(gallivm, bld->type, -2.4187564849853515625e-4);
2678    LLVMValueRef DP3 = lp_build_const_vec(gallivm, bld->type, -3.77489497744594108e-8);
2679
2680    /*
2681     * The magic pass: "Extended precision modular arithmetic"
2682     * x = ((x - y * DP1) - y * DP2) - y * DP3;
2683     * xmm1 = _mm_mul_ps(y, xmm1);
2684     * xmm2 = _mm_mul_ps(y, xmm2);
2685     * xmm3 = _mm_mul_ps(y, xmm3);
2686     */
2687    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
2688    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
2689    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
2690
2691    /*
2692     * x = _mm_add_ps(x, xmm1);
2693     * x = _mm_add_ps(x, xmm2);
2694     * x = _mm_add_ps(x, xmm3);
2695     */
2696
2697    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
2698    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
2699    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
2700
2701    /*
2702     * Evaluate the first polynom  (0 <= x <= Pi/4)
2703     *
2704     * z = _mm_mul_ps(x,x);
2705     */
2706    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
2707
2708    /*
2709     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
2710     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
2711     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
2712     */
2713    LLVMValueRef coscof_p0 = lp_build_const_vec(gallivm, bld->type, 2.443315711809948E-005);
2714    LLVMValueRef coscof_p1 = lp_build_const_vec(gallivm, bld->type, -1.388731625493765E-003);
2715    LLVMValueRef coscof_p2 = lp_build_const_vec(gallivm, bld->type, 4.166664568298827E-002);
2716
2717    /*
2718     * y = *(v4sf*)_ps_coscof_p0;
2719     * y = _mm_mul_ps(y, z);
2720     */
2721    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
2722    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
2723    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
2724    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
2725    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
2726    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
2727
2728
2729    /*
2730     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
2731     * y = _mm_sub_ps(y, tmp);
2732     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
2733     */
2734    LLVMValueRef half = lp_build_const_vec(gallivm, bld->type, 0.5);
2735    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
2736    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
2737    LLVMValueRef one = lp_build_const_vec(gallivm, bld->type, 1.0);
2738    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
2739
2740    /*
2741     * _PS_CONST(sincof_p0, -1.9515295891E-4);
2742     * _PS_CONST(sincof_p1,  8.3321608736E-3);
2743     * _PS_CONST(sincof_p2, -1.6666654611E-1);
2744     */
2745    LLVMValueRef sincof_p0 = lp_build_const_vec(gallivm, bld->type, -1.9515295891E-4);
2746    LLVMValueRef sincof_p1 = lp_build_const_vec(gallivm, bld->type, 8.3321608736E-3);
2747    LLVMValueRef sincof_p2 = lp_build_const_vec(gallivm, bld->type, -1.6666654611E-1);
2748
2749    /*
2750     * Evaluate the second polynom  (Pi/4 <= x <= 0)
2751     *
2752     * y2 = *(v4sf*)_ps_sincof_p0;
2753     * y2 = _mm_mul_ps(y2, z);
2754     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
2755     * y2 = _mm_mul_ps(y2, z);
2756     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
2757     * y2 = _mm_mul_ps(y2, z);
2758     * y2 = _mm_mul_ps(y2, x);
2759     * y2 = _mm_add_ps(y2, x);
2760     */
2761
2762    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
2763    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
2764    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
2765    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
2766    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
2767    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
2768    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
2769
2770    /*
2771     * select the correct result from the two polynoms
2772     * xmm3 = poly_mask;
2773     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
2774     * y = _mm_andnot_ps(xmm3, y);
2775     * y = _mm_or_ps(y,y2);
2776     */
2777    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, bld->int_vec_type, "y2_i");
2778    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, bld->int_vec_type, "y_i");
2779    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
2780    LLVMValueRef poly_mask_inv = LLVMBuildNot(b, poly_mask, "poly_mask_inv");
2781    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
2782    LLVMValueRef y_combine = LLVMBuildOr(b, y_and, y2_and, "y_combine");
2783
2784    /*
2785     * update the sign
2786     * y = _mm_xor_ps(y, sign_bit);
2787     */
2788    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sign");
2789    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, bld->vec_type, "y_result");
2790
2791    LLVMValueRef isfinite = lp_build_isfinite(bld, a);
2792
2793    /* clamp output to be within [-1, 1] */
2794    y_result = lp_build_clamp(bld, y_result,
2795                              lp_build_const_vec(bld->gallivm, bld->type,  -1.f),
2796                              lp_build_const_vec(bld->gallivm, bld->type,  1.f));
2797    /* If a is -inf, inf or NaN then return NaN */
2798    y_result = lp_build_select(bld, isfinite, y_result,
2799                               lp_build_const_vec(bld->gallivm, bld->type,  NAN));
2800    return y_result;
2801 }
2802
2803
2804 /**
2805  * Generate sin(a)
2806  */
2807 LLVMValueRef
2808 lp_build_sin(struct lp_build_context *bld,
2809              LLVMValueRef a)
2810 {
2811    return lp_build_sin_or_cos(bld, a, FALSE);
2812 }
2813
2814
2815 /**
2816  * Generate cos(a)
2817  */
2818 LLVMValueRef
2819 lp_build_cos(struct lp_build_context *bld,
2820              LLVMValueRef a)
2821 {
2822    return lp_build_sin_or_cos(bld, a, TRUE);
2823 }
2824
2825
2826 /**
2827  * Generate pow(x, y)
2828  */
2829 LLVMValueRef
2830 lp_build_pow(struct lp_build_context *bld,
2831              LLVMValueRef x,
2832              LLVMValueRef y)
2833 {
2834    /* TODO: optimize the constant case */
2835    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2836        LLVMIsConstant(x) && LLVMIsConstant(y)) {
2837       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2838                    __FUNCTION__);
2839    }
2840
2841    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
2842 }
2843
2844
2845 /**
2846  * Generate exp(x)
2847  */
2848 LLVMValueRef
2849 lp_build_exp(struct lp_build_context *bld,
2850              LLVMValueRef x)
2851 {
2852    /* log2(e) = 1/log(2) */
2853    LLVMValueRef log2e = lp_build_const_vec(bld->gallivm, bld->type,
2854                                            1.4426950408889634);
2855
2856    assert(lp_check_value(bld->type, x));
2857
2858    return lp_build_exp2(bld, lp_build_mul(bld, log2e, x));
2859 }
2860
2861
2862 /**
2863  * Generate log(x)
2864  * Behavior is undefined with infs, 0s and nans
2865  */
2866 LLVMValueRef
2867 lp_build_log(struct lp_build_context *bld,
2868              LLVMValueRef x)
2869 {
2870    /* log(2) */
2871    LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type,
2872                                           0.69314718055994529);
2873
2874    assert(lp_check_value(bld->type, x));
2875
2876    return lp_build_mul(bld, log2, lp_build_log2(bld, x));
2877 }
2878
2879 /**
2880  * Generate log(x) that handles edge cases (infs, 0s and nans)
2881  */
2882 LLVMValueRef
2883 lp_build_log_safe(struct lp_build_context *bld,
2884                   LLVMValueRef x)
2885 {
2886    /* log(2) */
2887    LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type,
2888                                           0.69314718055994529);
2889
2890    assert(lp_check_value(bld->type, x));
2891
2892    return lp_build_mul(bld, log2, lp_build_log2_safe(bld, x));
2893 }
2894
2895
2896 /**
2897  * Generate polynomial.
2898  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
2899  */
2900 LLVMValueRef
2901 lp_build_polynomial(struct lp_build_context *bld,
2902                     LLVMValueRef x,
2903                     const double *coeffs,
2904                     unsigned num_coeffs)
2905 {
2906    const struct lp_type type = bld->type;
2907    LLVMValueRef even = NULL, odd = NULL;
2908    LLVMValueRef x2;
2909    unsigned i;
2910
2911    assert(lp_check_value(bld->type, x));
2912
2913    /* TODO: optimize the constant case */
2914    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2915        LLVMIsConstant(x)) {
2916       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2917                    __FUNCTION__);
2918    }
2919
2920    /*
2921     * Calculate odd and even terms seperately to decrease data dependency
2922     * Ex:
2923     *     c[0] + x^2 * c[2] + x^4 * c[4] ...
2924     *     + x * (c[1] + x^2 * c[3] + x^4 * c[5]) ...
2925     */
2926    x2 = lp_build_mul(bld, x, x);
2927
2928    for (i = num_coeffs; i--; ) {
2929       LLVMValueRef coeff;
2930
2931       coeff = lp_build_const_vec(bld->gallivm, type, coeffs[i]);
2932
2933       if (i % 2 == 0) {
2934          if (even)
2935             even = lp_build_add(bld, coeff, lp_build_mul(bld, x2, even));
2936          else
2937             even = coeff;
2938       } else {
2939          if (odd)
2940             odd = lp_build_add(bld, coeff, lp_build_mul(bld, x2, odd));
2941          else
2942             odd = coeff;
2943       }
2944    }
2945
2946    if (odd)
2947       return lp_build_add(bld, lp_build_mul(bld, odd, x), even);
2948    else if (even)
2949       return even;
2950    else
2951       return bld->undef;
2952 }
2953
2954
2955 /**
2956  * Minimax polynomial fit of 2**x, in range [0, 1[
2957  */
2958 const double lp_build_exp2_polynomial[] = {
2959 #if EXP_POLY_DEGREE == 5
2960    1.000000000000000000000, /*XXX: was 0.999999925063526176901, recompute others */
2961    0.693153073200168932794,
2962    0.240153617044375388211,
2963    0.0558263180532956664775,
2964    0.00898934009049466391101,
2965    0.00187757667519147912699
2966 #elif EXP_POLY_DEGREE == 4
2967    1.00000259337069434683,
2968    0.693003834469974940458,
2969    0.24144275689150793076,
2970    0.0520114606103070150235,
2971    0.0135341679161270268764
2972 #elif EXP_POLY_DEGREE == 3
2973    0.999925218562710312959,
2974    0.695833540494823811697,
2975    0.226067155427249155588,
2976    0.0780245226406372992967
2977 #elif EXP_POLY_DEGREE == 2
2978    1.00172476321474503578,
2979    0.657636275736077639316,
2980    0.33718943461968720704
2981 #else
2982 #error
2983 #endif
2984 };
2985
2986
2987 LLVMValueRef
2988 lp_build_exp2(struct lp_build_context *bld,
2989               LLVMValueRef x)
2990 {
2991    LLVMBuilderRef builder = bld->gallivm->builder;
2992    const struct lp_type type = bld->type;
2993    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
2994    LLVMValueRef ipart = NULL;
2995    LLVMValueRef fpart = NULL;
2996    LLVMValueRef expipart = NULL;
2997    LLVMValueRef expfpart = NULL;
2998    LLVMValueRef res = NULL;
2999
3000    assert(lp_check_value(bld->type, x));
3001
3002    /* TODO: optimize the constant case */
3003    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
3004        LLVMIsConstant(x)) {
3005       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
3006                    __FUNCTION__);
3007    }
3008
3009    assert(type.floating && type.width == 32);
3010
3011    /* We want to preserve NaN and make sure than for exp2 if x > 128,
3012     * the result is INF  and if it's smaller than -126.9 the result is 0 */
3013    x = lp_build_min_ext(bld, lp_build_const_vec(bld->gallivm, type,  128.0), x,
3014                         GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN);
3015    x = lp_build_max_ext(bld, lp_build_const_vec(bld->gallivm, type, -126.99999),
3016                         x, GALLIVM_NAN_RETURN_NAN_FIRST_NONNAN);
3017
3018    /* ipart = floor(x) */
3019    /* fpart = x - ipart */
3020    lp_build_ifloor_fract(bld, x, &ipart, &fpart);
3021
3022    /* expipart = (float) (1 << ipart) */
3023    expipart = LLVMBuildAdd(builder, ipart,
3024                            lp_build_const_int_vec(bld->gallivm, type, 127), "");
3025    expipart = LLVMBuildShl(builder, expipart,
3026                            lp_build_const_int_vec(bld->gallivm, type, 23), "");
3027    expipart = LLVMBuildBitCast(builder, expipart, vec_type, "");
3028
3029    expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
3030                                   Elements(lp_build_exp2_polynomial));
3031
3032    res = LLVMBuildFMul(builder, expipart, expfpart, "");
3033
3034    return res;
3035 }
3036
3037
3038
3039 /**
3040  * Extract the exponent of a IEEE-754 floating point value.
3041  *
3042  * Optionally apply an integer bias.
3043  *
3044  * Result is an integer value with
3045  *
3046  *   ifloor(log2(x)) + bias
3047  */
3048 LLVMValueRef
3049 lp_build_extract_exponent(struct lp_build_context *bld,
3050                           LLVMValueRef x,
3051                           int bias)
3052 {
3053    LLVMBuilderRef builder = bld->gallivm->builder;
3054    const struct lp_type type = bld->type;
3055    unsigned mantissa = lp_mantissa(type);
3056    LLVMValueRef res;
3057
3058    assert(type.floating);
3059
3060    assert(lp_check_value(bld->type, x));
3061
3062    x = LLVMBuildBitCast(builder, x, bld->int_vec_type, "");
3063
3064    res = LLVMBuildLShr(builder, x,
3065                        lp_build_const_int_vec(bld->gallivm, type, mantissa), "");
3066    res = LLVMBuildAnd(builder, res,
3067                       lp_build_const_int_vec(bld->gallivm, type, 255), "");
3068    res = LLVMBuildSub(builder, res,
3069                       lp_build_const_int_vec(bld->gallivm, type, 127 - bias), "");
3070
3071    return res;
3072 }
3073
3074
3075 /**
3076  * Extract the mantissa of the a floating.
3077  *
3078  * Result is a floating point value with
3079  *
3080  *   x / floor(log2(x))
3081  */
3082 LLVMValueRef
3083 lp_build_extract_mantissa(struct lp_build_context *bld,
3084                           LLVMValueRef x)
3085 {
3086    LLVMBuilderRef builder = bld->gallivm->builder;
3087    const struct lp_type type = bld->type;
3088    unsigned mantissa = lp_mantissa(type);
3089    LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type,
3090                                                   (1ULL << mantissa) - 1);
3091    LLVMValueRef one = LLVMConstBitCast(bld->one, bld->int_vec_type);
3092    LLVMValueRef res;
3093
3094    assert(lp_check_value(bld->type, x));
3095
3096    assert(type.floating);
3097
3098    x = LLVMBuildBitCast(builder, x, bld->int_vec_type, "");
3099
3100    /* res = x / 2**ipart */
3101    res = LLVMBuildAnd(builder, x, mantmask, "");
3102    res = LLVMBuildOr(builder, res, one, "");
3103    res = LLVMBuildBitCast(builder, res, bld->vec_type, "");
3104
3105    return res;
3106 }
3107
3108
3109
3110 /**
3111  * Minimax polynomial fit of log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x) ,for x in range of [0, 1/9[
3112  * These coefficients can be generate with
3113  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
3114  */
3115 const double lp_build_log2_polynomial[] = {
3116 #if LOG_POLY_DEGREE == 5
3117    2.88539008148777786488L,
3118    0.961796878841293367824L,
3119    0.577058946784739859012L,
3120    0.412914355135828735411L,
3121    0.308591899232910175289L,
3122    0.352376952300281371868L,
3123 #elif LOG_POLY_DEGREE == 4
3124    2.88539009343309178325L,
3125    0.961791550404184197881L,
3126    0.577440339438736392009L,
3127    0.403343858251329912514L,
3128    0.406718052498846252698L,
3129 #elif LOG_POLY_DEGREE == 3
3130    2.88538959748872753838L,
3131    0.961932915889597772928L,
3132    0.571118517972136195241L,
3133    0.493997535084709500285L,
3134 #else
3135 #error
3136 #endif
3137 };
3138
3139 /**
3140  * See http://www.devmaster.net/forums/showthread.php?p=43580
3141  * http://en.wikipedia.org/wiki/Logarithm#Calculation
3142  * http://www.nezumi.demon.co.uk/consult/logx.htm
3143  *
3144  * If handle_edge_cases is true the function will perform computations
3145  * to match the required D3D10+ behavior for each of the edge cases.
3146  * That means that if input is:
3147  * - less than zero (to and including -inf) then NaN will be returned
3148  * - equal to zero (-denorm, -0, +0 or +denorm), then -inf will be returned
3149  * - +infinity, then +infinity will be returned
3150  * - NaN, then NaN will be returned
3151  *
3152  * Those checks are fairly expensive so if you don't need them make sure
3153  * handle_edge_cases is false.
3154  */
3155 void
3156 lp_build_log2_approx(struct lp_build_context *bld,
3157                      LLVMValueRef x,
3158                      LLVMValueRef *p_exp,
3159                      LLVMValueRef *p_floor_log2,
3160                      LLVMValueRef *p_log2,
3161                      boolean handle_edge_cases)
3162 {
3163    LLVMBuilderRef builder = bld->gallivm->builder;
3164    const struct lp_type type = bld->type;
3165    LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type);
3166    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type);
3167
3168    LLVMValueRef expmask = lp_build_const_int_vec(bld->gallivm, type, 0x7f800000);
3169    LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type, 0x007fffff);
3170    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
3171
3172    LLVMValueRef i = NULL;
3173    LLVMValueRef y = NULL;
3174    LLVMValueRef z = NULL;
3175    LLVMValueRef exp = NULL;
3176    LLVMValueRef mant = NULL;
3177    LLVMValueRef logexp = NULL;
3178    LLVMValueRef logmant = NULL;
3179    LLVMValueRef res = NULL;
3180
3181    assert(lp_check_value(bld->type, x));
3182
3183    if(p_exp || p_floor_log2 || p_log2) {
3184       /* TODO: optimize the constant case */
3185       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
3186           LLVMIsConstant(x)) {
3187          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
3188                       __FUNCTION__);
3189       }
3190
3191       assert(type.floating && type.width == 32);
3192
3193       /*
3194        * We don't explicitly handle denormalized numbers. They will yield a
3195        * result in the neighbourhood of -127, which appears to be adequate
3196        * enough.
3197        */
3198
3199       i = LLVMBuildBitCast(builder, x, int_vec_type, "");
3200
3201       /* exp = (float) exponent(x) */
3202       exp = LLVMBuildAnd(builder, i, expmask, "");
3203    }
3204
3205    if(p_floor_log2 || p_log2) {
3206       logexp = LLVMBuildLShr(builder, exp, lp_build_const_int_vec(bld->gallivm, type, 23), "");
3207       logexp = LLVMBuildSub(builder, logexp, lp_build_const_int_vec(bld->gallivm, type, 127), "");
3208       logexp = LLVMBuildSIToFP(builder, logexp, vec_type, "");
3209    }
3210
3211    if (p_log2) {
3212       /* mant = 1 + (float) mantissa(x) */
3213       mant = LLVMBuildAnd(builder, i, mantmask, "");
3214       mant = LLVMBuildOr(builder, mant, one, "");
3215       mant = LLVMBuildBitCast(builder, mant, vec_type, "");
3216
3217       /* y = (mant - 1) / (mant + 1) */
3218       y = lp_build_div(bld,
3219          lp_build_sub(bld, mant, bld->one),
3220          lp_build_add(bld, mant, bld->one)
3221       );
3222
3223       /* z = y^2 */
3224       z = lp_build_mul(bld, y, y);
3225
3226       /* compute P(z) */
3227       logmant = lp_build_polynomial(bld, z, lp_build_log2_polynomial,
3228                                     Elements(lp_build_log2_polynomial));
3229
3230       /* logmant = y * P(z) */
3231       logmant = lp_build_mul(bld, y, logmant);
3232
3233       res = lp_build_add(bld, logmant, logexp);
3234
3235       if (type.floating && handle_edge_cases) {
3236          LLVMValueRef negmask, infmask,  zmask;
3237          negmask = lp_build_cmp(bld, PIPE_FUNC_LESS, x,
3238                                 lp_build_const_vec(bld->gallivm, type,  0.0f));
3239          zmask = lp_build_cmp(bld, PIPE_FUNC_EQUAL, x,
3240                               lp_build_const_vec(bld->gallivm, type,  0.0f));
3241          infmask = lp_build_cmp(bld, PIPE_FUNC_GEQUAL, x,
3242                                 lp_build_const_vec(bld->gallivm, type,  INFINITY));
3243
3244          /* If x is qual to inf make sure we return inf */
3245          res = lp_build_select(bld, infmask,
3246                                lp_build_const_vec(bld->gallivm, type,  INFINITY),
3247                                res);
3248          /* If x is qual to 0, return -inf */
3249          res = lp_build_select(bld, zmask,
3250                                lp_build_const_vec(bld->gallivm, type,  -INFINITY),
3251                                res);
3252          /* If x is nan or less than 0, return nan */
3253          res = lp_build_select(bld, negmask,
3254                                lp_build_const_vec(bld->gallivm, type,  NAN),
3255                                res);
3256       }
3257    }
3258
3259    if (p_exp) {
3260       exp = LLVMBuildBitCast(builder, exp, vec_type, "");
3261       *p_exp = exp;
3262    }
3263
3264    if (p_floor_log2)
3265       *p_floor_log2 = logexp;
3266
3267    if (p_log2)
3268       *p_log2 = res;
3269 }
3270
3271
3272 /*
3273  * log2 implementation which doesn't have special code to
3274  * handle edge cases (-inf, 0, inf, NaN). It's faster but
3275  * the results for those cases are undefined.
3276  */
3277 LLVMValueRef
3278 lp_build_log2(struct lp_build_context *bld,
3279               LLVMValueRef x)
3280 {
3281    LLVMValueRef res;
3282    lp_build_log2_approx(bld, x, NULL, NULL, &res, FALSE);
3283    return res;
3284 }
3285
3286 /*
3287  * Version of log2 which handles all edge cases.
3288  * Look at documentation of lp_build_log2_approx for
3289  * description of the behavior for each of the edge cases.
3290  */
3291 LLVMValueRef
3292 lp_build_log2_safe(struct lp_build_context *bld,
3293                    LLVMValueRef x)
3294 {
3295    LLVMValueRef res;
3296    lp_build_log2_approx(bld, x, NULL, NULL, &res, TRUE);
3297    return res;
3298 }
3299
3300
3301 /**
3302  * Faster (and less accurate) log2.
3303  *
3304  *    log2(x) = floor(log2(x)) - 1 + x / 2**floor(log2(x))
3305  *
3306  * Piece-wise linear approximation, with exact results when x is a
3307  * power of two.
3308  *
3309  * See http://www.flipcode.com/archives/Fast_log_Function.shtml
3310  */
3311 LLVMValueRef
3312 lp_build_fast_log2(struct lp_build_context *bld,
3313                    LLVMValueRef x)
3314 {
3315    LLVMBuilderRef builder = bld->gallivm->builder;
3316    LLVMValueRef ipart;
3317    LLVMValueRef fpart;
3318
3319    assert(lp_check_value(bld->type, x));
3320
3321    assert(bld->type.floating);
3322
3323    /* ipart = floor(log2(x)) - 1 */
3324    ipart = lp_build_extract_exponent(bld, x, -1);
3325    ipart = LLVMBuildSIToFP(builder, ipart, bld->vec_type, "");
3326
3327    /* fpart = x / 2**ipart */
3328    fpart = lp_build_extract_mantissa(bld, x);
3329
3330    /* ipart + fpart */
3331    return LLVMBuildFAdd(builder, ipart, fpart, "");
3332 }
3333
3334
3335 /**
3336  * Fast implementation of iround(log2(x)).
3337  *
3338  * Not an approximation -- it should give accurate results all the time.
3339  */
3340 LLVMValueRef
3341 lp_build_ilog2(struct lp_build_context *bld,
3342                LLVMValueRef x)
3343 {
3344    LLVMBuilderRef builder = bld->gallivm->builder;
3345    LLVMValueRef sqrt2 = lp_build_const_vec(bld->gallivm, bld->type, M_SQRT2);
3346    LLVMValueRef ipart;
3347
3348    assert(bld->type.floating);
3349
3350    assert(lp_check_value(bld->type, x));
3351
3352    /* x * 2^(0.5)   i.e., add 0.5 to the log2(x) */
3353    x = LLVMBuildFMul(builder, x, sqrt2, "");
3354
3355    /* ipart = floor(log2(x) + 0.5)  */
3356    ipart = lp_build_extract_exponent(bld, x, 0);
3357
3358    return ipart;
3359 }
3360
3361 LLVMValueRef
3362 lp_build_mod(struct lp_build_context *bld,
3363              LLVMValueRef x,
3364              LLVMValueRef y)
3365 {
3366    LLVMBuilderRef builder = bld->gallivm->builder;
3367    LLVMValueRef res;
3368    const struct lp_type type = bld->type;
3369
3370    assert(lp_check_value(type, x));
3371    assert(lp_check_value(type, y));
3372
3373    if (type.floating)
3374       res = LLVMBuildFRem(builder, x, y, "");
3375    else if (type.sign)
3376       res = LLVMBuildSRem(builder, x, y, "");
3377    else
3378       res = LLVMBuildURem(builder, x, y, "");
3379    return res;
3380 }
3381
3382
3383 /*
3384  * For floating inputs it creates and returns a mask
3385  * which is all 1's for channels which are NaN.
3386  * Channels inside x which are not NaN will be 0.
3387  */
3388 LLVMValueRef
3389 lp_build_isnan(struct lp_build_context *bld,
3390                LLVMValueRef x)
3391 {
3392    LLVMValueRef mask;
3393    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, bld->type);
3394
3395    assert(bld->type.floating);
3396    assert(lp_check_value(bld->type, x));
3397
3398    mask = LLVMBuildFCmp(bld->gallivm->builder, LLVMRealOEQ, x, x,
3399                         "isnotnan");
3400    mask = LLVMBuildNot(bld->gallivm->builder, mask, "");
3401    mask = LLVMBuildSExt(bld->gallivm->builder, mask, int_vec_type, "isnan");
3402    return mask;
3403 }
3404
3405 /* Returns all 1's for floating point numbers that are
3406  * finite numbers and returns all zeros for -inf,
3407  * inf and nan's */
3408 LLVMValueRef
3409 lp_build_isfinite(struct lp_build_context *bld,
3410                   LLVMValueRef x)
3411 {
3412    LLVMBuilderRef builder = bld->gallivm->builder;
3413    LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, bld->type);
3414    struct lp_type int_type = lp_int_type(bld->type);
3415    LLVMValueRef intx = LLVMBuildBitCast(builder, x, int_vec_type, "");
3416    LLVMValueRef infornan32 = lp_build_const_int_vec(bld->gallivm, bld->type,
3417                                                     0x7f800000);
3418
3419    if (!bld->type.floating) {
3420       return lp_build_const_int_vec(bld->gallivm, bld->type, 0);
3421    }
3422    assert(bld->type.floating);
3423    assert(lp_check_value(bld->type, x));
3424    assert(bld->type.width == 32);
3425
3426    intx = LLVMBuildAnd(builder, intx, infornan32, "");
3427    return lp_build_compare(bld->gallivm, int_type, PIPE_FUNC_NOTEQUAL,
3428                            intx, infornan32);
3429 }
3430
3431 /*
3432  * Returns true if the number is nan or inf and false otherwise.
3433  * The input has to be a floating point vector.
3434  */
3435 LLVMValueRef
3436 lp_build_is_inf_or_nan(struct gallivm_state *gallivm,
3437                        const struct lp_type type,
3438                        LLVMValueRef x)
3439 {
3440    LLVMBuilderRef builder = gallivm->builder;
3441    struct lp_type int_type = lp_int_type(type);
3442    LLVMValueRef const0 = lp_build_const_int_vec(gallivm, int_type,
3443                                                 0x7f800000);
3444    LLVMValueRef ret;
3445
3446    assert(type.floating);
3447
3448    ret = LLVMBuildBitCast(builder, x, lp_build_vec_type(gallivm, int_type), "");
3449    ret = LLVMBuildAnd(builder, ret, const0, "");
3450    ret = lp_build_compare(gallivm, int_type, PIPE_FUNC_EQUAL,
3451                           ret, const0);
3452
3453    return ret;
3454 }
3455
3456
3457 LLVMValueRef
3458 lp_build_fpstate_get(struct gallivm_state *gallivm)
3459 {
3460    if (util_cpu_caps.has_sse) {
3461       LLVMBuilderRef builder = gallivm->builder;
3462       LLVMValueRef mxcsr_ptr = lp_build_alloca(
3463          gallivm,
3464          LLVMInt32TypeInContext(gallivm->context),
3465          "mxcsr_ptr");
3466       LLVMValueRef mxcsr_ptr8 = LLVMBuildPointerCast(builder, mxcsr_ptr,
3467           LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0), "");
3468       lp_build_intrinsic(builder,
3469                          "llvm.x86.sse.stmxcsr",
3470                          LLVMVoidTypeInContext(gallivm->context),
3471                          &mxcsr_ptr8, 1, 0);
3472       return mxcsr_ptr;
3473    }
3474    return 0;
3475 }
3476
3477 void
3478 lp_build_fpstate_set_denorms_zero(struct gallivm_state *gallivm,
3479                                   boolean zero)
3480 {
3481    if (util_cpu_caps.has_sse) {
3482       /* turn on DAZ (64) | FTZ (32768) = 32832 if available */
3483       int daz_ftz = _MM_FLUSH_ZERO_MASK;
3484
3485       LLVMBuilderRef builder = gallivm->builder;
3486       LLVMValueRef mxcsr_ptr = lp_build_fpstate_get(gallivm);
3487       LLVMValueRef mxcsr =
3488          LLVMBuildLoad(builder, mxcsr_ptr, "mxcsr");
3489
3490       if (util_cpu_caps.has_daz) {
3491          /* Enable denormals are zero mode */
3492          daz_ftz |= _MM_DENORMALS_ZERO_MASK;
3493       }
3494       if (zero) {
3495          mxcsr = LLVMBuildOr(builder, mxcsr,
3496                              LLVMConstInt(LLVMTypeOf(mxcsr), daz_ftz, 0), "");
3497       } else {
3498          mxcsr = LLVMBuildAnd(builder, mxcsr,
3499                               LLVMConstInt(LLVMTypeOf(mxcsr), ~daz_ftz, 0), "");
3500       }
3501
3502       LLVMBuildStore(builder, mxcsr, mxcsr_ptr);
3503       lp_build_fpstate_set(gallivm, mxcsr_ptr);
3504    }
3505 }
3506
3507 void
3508 lp_build_fpstate_set(struct gallivm_state *gallivm,
3509                      LLVMValueRef mxcsr_ptr)
3510 {
3511    if (util_cpu_caps.has_sse) {
3512       LLVMBuilderRef builder = gallivm->builder;
3513       mxcsr_ptr = LLVMBuildPointerCast(builder, mxcsr_ptr,
3514                      LLVMPointerType(LLVMInt8TypeInContext(gallivm->context), 0), "");
3515       lp_build_intrinsic(builder,
3516                          "llvm.x86.sse.ldmxcsr",
3517                          LLVMVoidTypeInContext(gallivm->context),
3518                          &mxcsr_ptr, 1, 0);
3519    }
3520 }