src/gallium/auxiliary/gallivm/lp_bld_arit.c

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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 "util/u_memory.h"
  49 #include "util/u_debug.h"
  50 #include "util/u_math.h"
  51 #include "util/u_string.h"
  52 #include "util/u_cpu_detect.h"
  53
  54 #include "lp_bld_type.h"
  55 #include "lp_bld_const.h"
  56 #include "lp_bld_intr.h"
  57 #include "lp_bld_init.h" /* for lp_build_engine */
  58 #include "lp_bld_logic.h"
  59 #include "lp_bld_pack.h"
  60 #include "lp_bld_debug.h"
  61 #include "lp_bld_arit.h"
  62
  63
  64 /**
  65  * Generate min(a, b)
  66  * No checks for special case values of a or b = 1 or 0 are done.
  67  */
  68 static LLVMValueRef
  69 lp_build_min_simple(struct lp_build_context *bld,
  70                     LLVMValueRef a,
  71                     LLVMValueRef b)
  72 {
  73    const struct lp_type type = bld->type;
  74    const char *intrinsic = NULL;
  75    LLVMValueRef cond;
  76
  77    /* TODO: optimize the constant case */
  78
  79    if(type.width * type.length == 128) {
  80       if(type.floating) {
  81          if(type.width == 32 && util_cpu_caps.has_sse)
  82             intrinsic = "llvm.x86.sse.min.ps";
  83          if(type.width == 64 && util_cpu_caps.has_sse2)
  84             intrinsic = "llvm.x86.sse2.min.pd";
  85       }
  86       else {
  87          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  88             intrinsic = "llvm.x86.sse2.pminu.b";
  89          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  90             intrinsic = "llvm.x86.sse41.pminsb";
  91          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  92             intrinsic = "llvm.x86.sse41.pminuw";
  93          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  94             intrinsic = "llvm.x86.sse2.pmins.w";
  95          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  96             intrinsic = "llvm.x86.sse41.pminud";
  97          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  98             intrinsic = "llvm.x86.sse41.pminsd";
  99       }
 100    }
 101
 102    if(intrinsic)
 103       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 104
 105    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 106    return lp_build_select(bld, cond, a, b);
 107 }
 108
 109
 110 /**
 111  * Generate max(a, b)
 112  * No checks for special case values of a or b = 1 or 0 are done.
 113  */
 114 static LLVMValueRef
 115 lp_build_max_simple(struct lp_build_context *bld,
 116                     LLVMValueRef a,
 117                     LLVMValueRef b)
 118 {
 119    const struct lp_type type = bld->type;
 120    const char *intrinsic = NULL;
 121    LLVMValueRef cond;
 122
 123    /* TODO: optimize the constant case */
 124
 125    if(type.width * type.length == 128) {
 126       if(type.floating) {
 127          if(type.width == 32 && util_cpu_caps.has_sse)
 128             intrinsic = "llvm.x86.sse.max.ps";
 129          if(type.width == 64 && util_cpu_caps.has_sse2)
 130             intrinsic = "llvm.x86.sse2.max.pd";
 131       }
 132       else {
 133          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 134             intrinsic = "llvm.x86.sse2.pmaxu.b";
 135          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 136             intrinsic = "llvm.x86.sse41.pmaxsb";
 137          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 138             intrinsic = "llvm.x86.sse41.pmaxuw";
 139          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 140             intrinsic = "llvm.x86.sse2.pmaxs.w";
 141          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 142             intrinsic = "llvm.x86.sse41.pmaxud";
 143          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 144             intrinsic = "llvm.x86.sse41.pmaxsd";
 145       }
 146    }
 147
 148    if(intrinsic)
 149       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 150
 151    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 152    return lp_build_select(bld, cond, a, b);
 153 }
 154
 155
 156 /**
 157  * Generate 1 - a, or ~a depending on bld->type.
 158  */
 159 LLVMValueRef
 160 lp_build_comp(struct lp_build_context *bld,
 161               LLVMValueRef a)
 162 {
 163    const struct lp_type type = bld->type;
 164
 165    if(a == bld->one)
 166       return bld->zero;
 167    if(a == bld->zero)
 168       return bld->one;
 169
 170    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 171       if(LLVMIsConstant(a))
 172          return LLVMConstNot(a);
 173       else
 174          return LLVMBuildNot(bld->builder, a, "");
 175    }
 176
 177    if(LLVMIsConstant(a))
 178       return LLVMConstSub(bld->one, a);
 179    else
 180       return LLVMBuildSub(bld->builder, bld->one, a, "");
 181 }
 182
 183
 184 /**
 185  * Generate a + b
 186  */
 187 LLVMValueRef
 188 lp_build_add(struct lp_build_context *bld,
 189              LLVMValueRef a,
 190              LLVMValueRef b)
 191 {
 192    const struct lp_type type = bld->type;
 193    LLVMValueRef res;
 194
 195    if(a == bld->zero)
 196       return b;
 197    if(b == bld->zero)
 198       return a;
 199    if(a == bld->undef || b == bld->undef)
 200       return bld->undef;
 201
 202    if(bld->type.norm) {
 203       const char *intrinsic = NULL;
 204
 205       if(a == bld->one || b == bld->one)
 206         return bld->one;
 207
 208       if(util_cpu_caps.has_sse2 &&
 209          type.width * type.length == 128 &&
 210          !type.floating && !type.fixed) {
 211          if(type.width == 8)
 212             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 213          if(type.width == 16)
 214             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 215       }
 216
 217       if(intrinsic)
 218          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 219    }
 220
 221    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 222       res = LLVMConstAdd(a, b);
 223    else
 224       res = LLVMBuildAdd(bld->builder, a, b, "");
 225
 226    /* clamp to ceiling of 1.0 */
 227    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 228       res = lp_build_min_simple(bld, res, bld->one);
 229
 230    /* XXX clamp to floor of -1 or 0??? */
 231
 232    return res;
 233 }
 234
 235
 236 /** Return the sum of the elements of a */
 237 LLVMValueRef
 238 lp_build_sum_vector(struct lp_build_context *bld,
 239                     LLVMValueRef a)
 240 {
 241    const struct lp_type type = bld->type;
 242    LLVMValueRef index, res;
 243    unsigned i;
 244
 245    if (a == bld->zero)
 246       return bld->zero;
 247    if (a == bld->undef)
 248       return bld->undef;
 249    assert(type.length > 1);
 250
 251    assert(!bld->type.norm);
 252
 253    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 254    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 255
 256    for (i = 1; i < type.length; i++) {
 257       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 258       res = LLVMBuildAdd(bld->builder, res,
 259                          LLVMBuildExtractElement(bld->builder, a, index, ""),
 260                          "");
 261    }
 262
 263    return res;
 264 }
 265
 266
 267 /**
 268  * Generate a - b
 269  */
 270 LLVMValueRef
 271 lp_build_sub(struct lp_build_context *bld,
 272              LLVMValueRef a,
 273              LLVMValueRef b)
 274 {
 275    const struct lp_type type = bld->type;
 276    LLVMValueRef res;
 277
 278    if(b == bld->zero)
 279       return a;
 280    if(a == bld->undef || b == bld->undef)
 281       return bld->undef;
 282    if(a == b)
 283       return bld->zero;
 284
 285    if(bld->type.norm) {
 286       const char *intrinsic = NULL;
 287
 288       if(b == bld->one)
 289         return bld->zero;
 290
 291       if(util_cpu_caps.has_sse2 &&
 292          type.width * type.length == 128 &&
 293          !type.floating && !type.fixed) {
 294          if(type.width == 8)
 295             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 296          if(type.width == 16)
 297             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 298       }
 299
 300       if(intrinsic)
 301          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 302    }
 303
 304    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 305       res = LLVMConstSub(a, b);
 306    else
 307       res = LLVMBuildSub(bld->builder, a, b, "");
 308
 309    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 310       res = lp_build_max_simple(bld, res, bld->zero);
 311
 312    return res;
 313 }
 314
 315
 316 /**
 317  * Normalized 8bit multiplication.
 318  *
 319  * - alpha plus one
 320  *
 321  *     makes the following approximation to the division (Sree)
 322  *
 323  *       a*b/255 ~= (a*(b + 1)) >> 256
 324  *
 325  *     which is the fastest method that satisfies the following OpenGL criteria
 326  *
 327  *       0*0 = 0 and 255*255 = 255
 328  *
 329  * - geometric series
 330  *
 331  *     takes the geometric series approximation to the division
 332  *
 333  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 334  *
 335  *     in this case just the first two terms to fit in 16bit arithmetic
 336  *
 337  *       t/255 ~= (t + (t >> 8)) >> 8
 338  *
 339  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 340  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 341  *     must be used
 342  *
 343  * - geometric series plus rounding
 344  *
 345  *     when using a geometric series division instead of truncating the result
 346  *     use roundoff in the approximation (Jim Blinn)
 347  *
 348  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 349  *
 350  *     achieving the exact results
 351  *
 352  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 353  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 354  * @sa Michael Herf, The "double blend trick", May 2000,
 355  *     http://www.stereopsis.com/doubleblend.html
 356  */
 357 static LLVMValueRef
 358 lp_build_mul_u8n(LLVMBuilderRef builder,
 359                  struct lp_type i16_type,
 360                  LLVMValueRef a, LLVMValueRef b)
 361 {
 362    LLVMValueRef c8;
 363    LLVMValueRef ab;
 364
 365    c8 = lp_build_const_int_vec(i16_type, 8);
 366
 367 #if 0
 368
 369    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 370    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 371    ab = LLVMBuildMul(builder, a, b, "");
 372
 373 #else
 374
 375    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 376    ab = LLVMBuildMul(builder, a, b, "");
 377    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 378    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 379
 380 #endif
 381
 382    ab = LLVMBuildLShr(builder, ab, c8, "");
 383
 384    return ab;
 385 }
 386
 387
 388 /**
 389  * Generate a * b
 390  */
 391 LLVMValueRef
 392 lp_build_mul(struct lp_build_context *bld,
 393              LLVMValueRef a,
 394              LLVMValueRef b)
 395 {
 396    const struct lp_type type = bld->type;
 397    LLVMValueRef shift;
 398    LLVMValueRef res;
 399
 400    if(a == bld->zero)
 401       return bld->zero;
 402    if(a == bld->one)
 403       return b;
 404    if(b == bld->zero)
 405       return bld->zero;
 406    if(b == bld->one)
 407       return a;
 408    if(a == bld->undef || b == bld->undef)
 409       return bld->undef;
 410
 411    if(!type.floating && !type.fixed && type.norm) {
 412       if(type.width == 8) {
 413          struct lp_type i16_type = lp_wider_type(type);
 414          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 415
 416          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 417          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 418
 419          /* PMULLW, PSRLW, PADDW */
 420          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 421          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 422
 423          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 424
 425          return ab;
 426       }
 427
 428       /* FIXME */
 429       assert(0);
 430    }
 431
 432    if(type.fixed)
 433       shift = lp_build_const_int_vec(type, type.width/2);
 434    else
 435       shift = NULL;
 436
 437    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 438       res =  LLVMConstMul(a, b);
 439       if(shift) {
 440          if(type.sign)
 441             res = LLVMConstAShr(res, shift);
 442          else
 443             res = LLVMConstLShr(res, shift);
 444       }
 445    }
 446    else {
 447       res = LLVMBuildMul(bld->builder, a, b, "");
 448       if(shift) {
 449          if(type.sign)
 450             res = LLVMBuildAShr(bld->builder, res, shift, "");
 451          else
 452             res = LLVMBuildLShr(bld->builder, res, shift, "");
 453       }
 454    }
 455
 456    return res;
 457 }
 458
 459
 460 /**
 461  * Small vector x scale multiplication optimization.
 462  */
 463 LLVMValueRef
 464 lp_build_mul_imm(struct lp_build_context *bld,
 465                  LLVMValueRef a,
 466                  int b)
 467 {
 468    LLVMValueRef factor;
 469
 470    if(b == 0)
 471       return bld->zero;
 472
 473    if(b == 1)
 474       return a;
 475
 476    if(b == -1)
 477       return LLVMBuildNeg(bld->builder, a, "");
 478
 479    if(b == 2 && bld->type.floating)
 480       return lp_build_add(bld, a, a);
 481
 482    if(util_is_pot(b)) {
 483       unsigned shift = ffs(b) - 1;
 484
 485       if(bld->type.floating) {
 486 #if 0
 487          /*
 488           * Power of two multiplication by directly manipulating the mantissa.
 489           *
 490           * XXX: This might not be always faster, it will introduce a small error
 491           * for multiplication by zero, and it will produce wrong results
 492           * for Inf and NaN.
 493           */
 494          unsigned mantissa = lp_mantissa(bld->type);
 495          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 496          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 497          a = LLVMBuildAdd(bld->builder, a, factor, "");
 498          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 499          return a;
 500 #endif
 501       }
 502       else {
 503          factor = lp_build_const_vec(bld->type, shift);
 504          return LLVMBuildShl(bld->builder, a, factor, "");
 505       }
 506    }
 507
 508    factor = lp_build_const_vec(bld->type, (double)b);
 509    return lp_build_mul(bld, a, factor);
 510 }
 511
 512
 513 /**
 514  * Generate a / b
 515  */
 516 LLVMValueRef
 517 lp_build_div(struct lp_build_context *bld,
 518              LLVMValueRef a,
 519              LLVMValueRef b)
 520 {
 521    const struct lp_type type = bld->type;
 522
 523    if(a == bld->zero)
 524       return bld->zero;
 525    if(a == bld->one)
 526       return lp_build_rcp(bld, b);
 527    if(b == bld->zero)
 528       return bld->undef;
 529    if(b == bld->one)
 530       return a;
 531    if(a == bld->undef || b == bld->undef)
 532       return bld->undef;
 533
 534    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 535       return LLVMConstFDiv(a, b);
 536
 537    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 538       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 539
 540    return LLVMBuildFDiv(bld->builder, a, b, "");
 541 }
 542
 543
 544 /**
 545  * Linear interpolation.
 546  *
 547  * This also works for integer values with a few caveats.
 548  *
 549  * @sa http://www.stereopsis.com/doubleblend.html
 550  */
 551 LLVMValueRef
 552 lp_build_lerp(struct lp_build_context *bld,
 553               LLVMValueRef x,
 554               LLVMValueRef v0,
 555               LLVMValueRef v1)
 556 {
 557    LLVMValueRef delta;
 558    LLVMValueRef res;
 559
 560    delta = lp_build_sub(bld, v1, v0);
 561
 562    res = lp_build_mul(bld, x, delta);
 563
 564    res = lp_build_add(bld, v0, res);
 565
 566    if(bld->type.fixed)
 567       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 568        * but it will be wrong for other uses. Basically we need a more
 569        * powerful lp_type, capable of further distinguishing the values
 570        * interpretation from the value storage. */
 571       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 572
 573    return res;
 574 }
 575
 576
 577 LLVMValueRef
 578 lp_build_lerp_2d(struct lp_build_context *bld,
 579                  LLVMValueRef x,
 580                  LLVMValueRef y,
 581                  LLVMValueRef v00,
 582                  LLVMValueRef v01,
 583                  LLVMValueRef v10,
 584                  LLVMValueRef v11)
 585 {
 586    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 587    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 588    return lp_build_lerp(bld, y, v0, v1);
 589 }
 590
 591
 592 /**
 593  * Generate min(a, b)
 594  * Do checks for special cases.
 595  */
 596 LLVMValueRef
 597 lp_build_min(struct lp_build_context *bld,
 598              LLVMValueRef a,
 599              LLVMValueRef b)
 600 {
 601    if(a == bld->undef || b == bld->undef)
 602       return bld->undef;
 603
 604    if(a == b)
 605       return a;
 606
 607    if(bld->type.norm) {
 608       if(a == bld->zero || b == bld->zero)
 609          return bld->zero;
 610       if(a == bld->one)
 611          return b;
 612       if(b == bld->one)
 613          return a;
 614    }
 615
 616    return lp_build_min_simple(bld, a, b);
 617 }
 618
 619
 620 /**
 621  * Generate max(a, b)
 622  * Do checks for special cases.
 623  */
 624 LLVMValueRef
 625 lp_build_max(struct lp_build_context *bld,
 626              LLVMValueRef a,
 627              LLVMValueRef b)
 628 {
 629    if(a == bld->undef || b == bld->undef)
 630       return bld->undef;
 631
 632    if(a == b)
 633       return a;
 634
 635    if(bld->type.norm) {
 636       if(a == bld->one || b == bld->one)
 637          return bld->one;
 638       if(a == bld->zero)
 639          return b;
 640       if(b == bld->zero)
 641          return a;
 642    }
 643
 644    return lp_build_max_simple(bld, a, b);
 645 }
 646
 647
 648 /**
 649  * Generate clamp(a, min, max)
 650  * Do checks for special cases.
 651  */
 652 LLVMValueRef
 653 lp_build_clamp(struct lp_build_context *bld,
 654                LLVMValueRef a,
 655                LLVMValueRef min,
 656                LLVMValueRef max)
 657 {
 658    a = lp_build_min(bld, a, max);
 659    a = lp_build_max(bld, a, min);
 660    return a;
 661 }
 662
 663
 664 /**
 665  * Generate abs(a)
 666  */
 667 LLVMValueRef
 668 lp_build_abs(struct lp_build_context *bld,
 669              LLVMValueRef a)
 670 {
 671    const struct lp_type type = bld->type;
 672    LLVMTypeRef vec_type = lp_build_vec_type(type);
 673
 674    if(!type.sign)
 675       return a;
 676
 677    if(type.floating) {
 678       /* Mask out the sign bit */
 679       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 680       unsigned long long absMask = ~(1ULL << (type.width - 1));
 681       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 682       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 683       a = LLVMBuildAnd(bld->builder, a, mask, "");
 684       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 685       return a;
 686    }
 687
 688    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 689       switch(type.width) {
 690       case 8:
 691          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 692       case 16:
 693          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 694       case 32:
 695          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 696       }
 697    }
 698
 699    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 700 }
 701
 702
 703 LLVMValueRef
 704 lp_build_negate(struct lp_build_context *bld,
 705                 LLVMValueRef a)
 706 {
 707    return LLVMBuildNeg(bld->builder, a, "");
 708 }
 709
 710
 711 /** Return -1, 0 or +1 depending on the sign of a */
 712 LLVMValueRef
 713 lp_build_sgn(struct lp_build_context *bld,
 714              LLVMValueRef a)
 715 {
 716    const struct lp_type type = bld->type;
 717    LLVMValueRef cond;
 718    LLVMValueRef res;
 719
 720    /* Handle non-zero case */
 721    if(!type.sign) {
 722       /* if not zero then sign must be positive */
 723       res = bld->one;
 724    }
 725    else if(type.floating) {
 726       LLVMTypeRef vec_type;
 727       LLVMTypeRef int_type;
 728       LLVMValueRef mask;
 729       LLVMValueRef sign;
 730       LLVMValueRef one;
 731       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 732
 733       int_type = lp_build_int_vec_type(type);
 734       vec_type = lp_build_vec_type(type);
 735       mask = lp_build_const_int_vec(type, maskBit);
 736
 737       /* Take the sign bit and add it to 1 constant */
 738       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 739       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 740       one = LLVMConstBitCast(bld->one, int_type);
 741       res = LLVMBuildOr(bld->builder, sign, one, "");
 742       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 743    }
 744    else
 745    {
 746       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 747       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 748       res = lp_build_select(bld, cond, bld->one, minus_one);
 749    }
 750
 751    /* Handle zero */
 752    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 753    res = lp_build_select(bld, cond, bld->zero, res);
 754
 755    return res;
 756 }
 757
 758
 759 /**
 760  * Set the sign of float vector 'a' according to 'sign'.
 761  * If sign==0, return abs(a).
 762  * If sign==1, return -abs(a);
 763  * Other values for sign produce undefined results.
 764  */
 765 LLVMValueRef
 766 lp_build_set_sign(struct lp_build_context *bld,
 767                   LLVMValueRef a, LLVMValueRef sign)
 768 {
 769    const struct lp_type type = bld->type;
 770    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 771    LLVMTypeRef vec_type = lp_build_vec_type(type);
 772    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 773    LLVMValueRef mask = lp_build_const_int_vec(type,
 774                              ~((unsigned long long) 1 << (type.width - 1)));
 775    LLVMValueRef val, res;
 776
 777    assert(type.floating);
 778
 779    /* val = reinterpret_cast<int>(a) */
 780    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 781    /* val = val & mask */
 782    val = LLVMBuildAnd(bld->builder, val, mask, "");
 783    /* sign = sign << shift */
 784    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 785    /* res = val | sign */
 786    res = LLVMBuildOr(bld->builder, val, sign, "");
 787    /* res = reinterpret_cast<float>(res) */
 788    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 789
 790    return res;
 791 }
 792
 793
 794 /**
 795  * Convert vector of (or scalar) int to vector of (or scalar) float.
 796  */
 797 LLVMValueRef
 798 lp_build_int_to_float(struct lp_build_context *bld,
 799                       LLVMValueRef a)
 800 {
 801    const struct lp_type type = bld->type;
 802    LLVMTypeRef vec_type = lp_build_vec_type(type);
 803
 804    assert(type.floating);
 805
 806    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 807 }
 808
 809
 810
 811 enum lp_build_round_sse41_mode
 812 {
 813    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 814    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 815    LP_BUILD_ROUND_SSE41_CEIL = 2,
 816    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 817 };
 818
 819
 820 static INLINE LLVMValueRef
 821 lp_build_round_sse41(struct lp_build_context *bld,
 822                      LLVMValueRef a,
 823                      enum lp_build_round_sse41_mode mode)
 824 {
 825    const struct lp_type type = bld->type;
 826    LLVMTypeRef vec_type = lp_build_vec_type(type);
 827    const char *intrinsic;
 828
 829    assert(type.floating);
 830    assert(type.width*type.length == 128);
 831    assert(lp_check_value(type, a));
 832    assert(util_cpu_caps.has_sse4_1);
 833
 834    switch(type.width) {
 835    case 32:
 836       intrinsic = "llvm.x86.sse41.round.ps";
 837       break;
 838    case 64:
 839       intrinsic = "llvm.x86.sse41.round.pd";
 840       break;
 841    default:
 842       assert(0);
 843       return bld->undef;
 844    }
 845
 846    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 847                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 848 }
 849
 850
 851 LLVMValueRef
 852 lp_build_trunc(struct lp_build_context *bld,
 853                LLVMValueRef a)
 854 {
 855    const struct lp_type type = bld->type;
 856
 857    assert(type.floating);
 858    assert(lp_check_value(type, a));
 859
 860    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 861       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 862    else {
 863       LLVMTypeRef vec_type = lp_build_vec_type(type);
 864       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 865       LLVMValueRef res;
 866       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 867       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 868       return res;
 869    }
 870 }
 871
 872
 873 LLVMValueRef
 874 lp_build_round(struct lp_build_context *bld,
 875                LLVMValueRef a)
 876 {
 877    const struct lp_type type = bld->type;
 878
 879    assert(type.floating);
 880    assert(lp_check_value(type, a));
 881
 882    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 883       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 884    else {
 885       LLVMTypeRef vec_type = lp_build_vec_type(type);
 886       LLVMValueRef res;
 887       res = lp_build_iround(bld, a);
 888       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 889       return res;
 890    }
 891 }
 892
 893
 894 LLVMValueRef
 895 lp_build_floor(struct lp_build_context *bld,
 896                LLVMValueRef a)
 897 {
 898    const struct lp_type type = bld->type;
 899
 900    assert(type.floating);
 901    assert(lp_check_value(type, a));
 902
 903    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 904       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 905    else {
 906       LLVMTypeRef vec_type = lp_build_vec_type(type);
 907       LLVMValueRef res;
 908       res = lp_build_ifloor(bld, a);
 909       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 910       return res;
 911    }
 912 }
 913
 914
 915 LLVMValueRef
 916 lp_build_ceil(struct lp_build_context *bld,
 917               LLVMValueRef a)
 918 {
 919    const struct lp_type type = bld->type;
 920
 921    assert(type.floating);
 922    assert(lp_check_value(type, a));
 923
 924    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 925       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 926    else {
 927       LLVMTypeRef vec_type = lp_build_vec_type(type);
 928       LLVMValueRef res;
 929       res = lp_build_iceil(bld, a);
 930       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 931       return res;
 932    }
 933 }
 934
 935
 936 /**
 937  * Return fractional part of 'a' computed as a - floor(f)
 938  * Typically used in texture coord arithmetic.
 939  */
 940 LLVMValueRef
 941 lp_build_fract(struct lp_build_context *bld,
 942                LLVMValueRef a)
 943 {
 944    assert(bld->type.floating);
 945    return lp_build_sub(bld, a, lp_build_floor(bld, a));
 946 }
 947
 948
 949 /**
 950  * Convert to integer, through whichever rounding method that's fastest,
 951  * typically truncating toward zero.
 952  */
 953 LLVMValueRef
 954 lp_build_itrunc(struct lp_build_context *bld,
 955                 LLVMValueRef a)
 956 {
 957    const struct lp_type type = bld->type;
 958    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 959
 960    assert(type.floating);
 961    assert(lp_check_value(type, a));
 962
 963    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 964 }
 965
 966
 967 /**
 968  * Convert float[] to int[] with round().
 969  */
 970 LLVMValueRef
 971 lp_build_iround(struct lp_build_context *bld,
 972                 LLVMValueRef a)
 973 {
 974    const struct lp_type type = bld->type;
 975    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 976    LLVMValueRef res;
 977
 978    assert(type.floating);
 979
 980    assert(lp_check_value(type, a));
 981
 982    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
 983       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 984    }
 985    else {
 986       LLVMTypeRef vec_type = lp_build_vec_type(type);
 987       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
 988       LLVMValueRef sign;
 989       LLVMValueRef half;
 990
 991       /* get sign bit */
 992       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 993       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 994
 995       /* sign * 0.5 */
 996       half = lp_build_const_vec(type, 0.5);
 997       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
 998       half = LLVMBuildOr(bld->builder, sign, half, "");
 999       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1000
1001       res = LLVMBuildAdd(bld->builder, a, half, "");
1002    }
1003
1004    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1005
1006    return res;
1007 }
1008
1009
1010 /**
1011  * Convert float[] to int[] with floor().
1012  */
1013 LLVMValueRef
1014 lp_build_ifloor(struct lp_build_context *bld,
1015                 LLVMValueRef a)
1016 {
1017    const struct lp_type type = bld->type;
1018    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1019    LLVMValueRef res;
1020
1021    assert(type.floating);
1022    assert(lp_check_value(type, a));
1023
1024    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1025       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1026    }
1027    else {
1028       /* Take the sign bit and add it to 1 constant */
1029       LLVMTypeRef vec_type = lp_build_vec_type(type);
1030       unsigned mantissa = lp_mantissa(type);
1031       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1032       LLVMValueRef sign;
1033       LLVMValueRef offset;
1034
1035       /* sign = a < 0 ? ~0 : 0 */
1036       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1037       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1038       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "");
1039       lp_build_name(sign, "floor.sign");
1040
1041       /* offset = -0.99999(9)f */
1042       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 1)/((unsigned long long)1 << mantissa));
1043       offset = LLVMConstBitCast(offset, int_vec_type);
1044
1045       /* offset = a < 0 ? -0.99999(9)f : 0.0f */
1046       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1047       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "");
1048       lp_build_name(offset, "floor.offset");
1049
1050       res = LLVMBuildAdd(bld->builder, a, offset, "");
1051       lp_build_name(res, "floor.res");
1052    }
1053
1054    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1055    lp_build_name(res, "floor");
1056
1057    return res;
1058 }
1059
1060
1061 LLVMValueRef
1062 lp_build_iceil(struct lp_build_context *bld,
1063                LLVMValueRef a)
1064 {
1065    const struct lp_type type = bld->type;
1066    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1067    LLVMValueRef res;
1068
1069    assert(type.floating);
1070    assert(lp_check_value(type, a));
1071
1072    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1073       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1074    }
1075    else {
1076       /* TODO: mimic lp_build_ifloor() here */
1077       assert(0);
1078       res = bld->undef;
1079    }
1080
1081    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1082
1083    return res;
1084 }
1085
1086
1087 LLVMValueRef
1088 lp_build_sqrt(struct lp_build_context *bld,
1089               LLVMValueRef a)
1090 {
1091    const struct lp_type type = bld->type;
1092    LLVMTypeRef vec_type = lp_build_vec_type(type);
1093    char intrinsic[32];
1094
1095    /* TODO: optimize the constant case */
1096    /* TODO: optimize the constant case */
1097
1098    assert(type.floating);
1099    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1100
1101    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1102 }
1103
1104
1105 LLVMValueRef
1106 lp_build_rcp(struct lp_build_context *bld,
1107              LLVMValueRef a)
1108 {
1109    const struct lp_type type = bld->type;
1110
1111    if(a == bld->zero)
1112       return bld->undef;
1113    if(a == bld->one)
1114       return bld->one;
1115    if(a == bld->undef)
1116       return bld->undef;
1117
1118    assert(type.floating);
1119
1120    if(LLVMIsConstant(a))
1121       return LLVMConstFDiv(bld->one, a);
1122
1123    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1124       /*
1125        * XXX: Added precision is not always necessary, so only enable this
1126        * when we have a better system in place to track minimum precision.
1127        */
1128
1129 #if 0
1130       /*
1131        * Do one Newton-Raphson step to improve precision:
1132        *
1133        *   x1 = (2 - a * rcp(a)) * rcp(a)
1134        */
1135
1136       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1137       LLVMValueRef rcp_a;
1138       LLVMValueRef res;
1139
1140       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1141
1142       res = LLVMBuildMul(bld->builder, a, rcp_a, "");
1143       res = LLVMBuildSub(bld->builder, two, res, "");
1144       res = LLVMBuildMul(bld->builder, res, rcp_a, "");
1145
1146       return rcp_a;
1147 #else
1148       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1149 #endif
1150    }
1151
1152    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1153 }
1154
1155
1156 /**
1157  * Generate 1/sqrt(a)
1158  */
1159 LLVMValueRef
1160 lp_build_rsqrt(struct lp_build_context *bld,
1161                LLVMValueRef a)
1162 {
1163    const struct lp_type type = bld->type;
1164
1165    assert(type.floating);
1166
1167    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1168       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1169
1170    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1171 }
1172
1173
1174 #ifdef PIPE_OS_WINDOWS
1175
1176 /*
1177  * XXX: X86 backend translates llvm.cos.v4f32 to 4 calls to CRT's cosf()
1178  * which is neither efficient nor does the CRT linkage work on Windows
1179  * causing segmentation fault.
1180  *
1181  * XXX: With LLVM 2.7 both schemes cause an assertion failure.
1182  */
1183 static LLVMValueRef
1184 lp_build_sincos(struct lp_build_context *bld,
1185                 const char *name,
1186                 float (*func)(float),
1187                 LLVMValueRef a)
1188 {
1189    LLVMModuleRef module =
1190          LLVMGetGlobalParent(LLVMGetBasicBlockParent(LLVMGetInsertBlock(bld->builder)));
1191    LLVMValueRef function;
1192    LLVMValueRef res;
1193    unsigned i;
1194
1195    assert(bld->type.floating);
1196    assert(bld->type.width == 32);
1197
1198    function = LLVMGetNamedFunction(module, name);
1199    if (!function) {
1200       LLVMTypeRef ret_type;
1201       LLVMTypeRef arg_types[1];
1202       LLVMTypeRef function_type;
1203
1204       ret_type = LLVMFloatType();
1205       arg_types[0] = LLVMFloatType();
1206       function_type = LLVMFunctionType(ret_type, arg_types, Elements(arg_types), 0);
1207       function = LLVMAddFunction(module, name, function_type);
1208
1209       LLVMSetFunctionCallConv(function, LLVMCCallConv);
1210       LLVMSetLinkage(function, LLVMPrivateLinkage);
1211
1212       assert(LLVMIsDeclaration(function));
1213
1214       LLVMAddGlobalMapping(lp_build_engine, function, func);
1215    }
1216
1217    res = bld->undef;
1218
1219    for (i = 0; i < bld->type.length; ++i) {
1220       LLVMValueRef index = LLVMConstInt(LLVMInt32Type(), i, 0);
1221       LLVMValueRef args[1];
1222       LLVMValueRef tmp;
1223
1224       args[0] = LLVMBuildExtractElement(bld->builder, a, index, "");
1225
1226       tmp = LLVMBuildCall(bld->builder, function, args, Elements(args), "");
1227
1228       res = LLVMBuildInsertElement(bld->builder, res, tmp, index, "");
1229    }
1230
1231    return res;
1232 }
1233
1234 static float c_cosf( float f )
1235 {
1236    return (float) cos( (double) f );
1237 }
1238
1239 static float c_sinf( float f )
1240 {
1241    return (float) sin( (double) f );
1242 }
1243
1244 LLVMValueRef
1245 lp_build_cos(struct lp_build_context *bld,
1246              LLVMValueRef a)
1247 {
1248    return lp_build_sincos(bld, "cosf", &c_cosf, a);
1249 }
1250
1251 LLVMValueRef
1252 lp_build_sin(struct lp_build_context *bld,
1253              LLVMValueRef a)
1254 {
1255    return lp_build_sincos(bld, "sinf", &c_sinf, a);
1256 }
1257
1258 #else /* !PIPE_OS_WINDOWS */
1259
1260 /**
1261  * Generate cos(a)
1262  */
1263 LLVMValueRef
1264 lp_build_cos(struct lp_build_context *bld,
1265               LLVMValueRef a)
1266 {
1267    const struct lp_type type = bld->type;
1268    LLVMTypeRef vec_type = lp_build_vec_type(type);
1269    char intrinsic[32];
1270
1271    /* TODO: optimize the constant case */
1272
1273    assert(type.floating);
1274    util_snprintf(intrinsic, sizeof intrinsic, "llvm.cos.v%uf%u", type.length, type.width);
1275
1276    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1277 }
1278
1279
1280 /**
1281  * Generate sin(a)
1282  */
1283 LLVMValueRef
1284 lp_build_sin(struct lp_build_context *bld,
1285               LLVMValueRef a)
1286 {
1287    const struct lp_type type = bld->type;
1288    LLVMTypeRef vec_type = lp_build_vec_type(type);
1289    char intrinsic[32];
1290
1291    /* TODO: optimize the constant case */
1292
1293    assert(type.floating);
1294    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sin.v%uf%u", type.length, type.width);
1295
1296    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1297 }
1298
1299 #endif /* !PIPE_OS_WINDOWS */
1300
1301
1302 /**
1303  * Generate pow(x, y)
1304  */
1305 LLVMValueRef
1306 lp_build_pow(struct lp_build_context *bld,
1307              LLVMValueRef x,
1308              LLVMValueRef y)
1309 {
1310    /* TODO: optimize the constant case */
1311    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1312       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1313                    __FUNCTION__);
1314
1315    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1316 }
1317
1318
1319 /**
1320  * Generate exp(x)
1321  */
1322 LLVMValueRef
1323 lp_build_exp(struct lp_build_context *bld,
1324              LLVMValueRef x)
1325 {
1326    /* log2(e) = 1/log(2) */
1327    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1328
1329    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1330 }
1331
1332
1333 /**
1334  * Generate log(x)
1335  */
1336 LLVMValueRef
1337 lp_build_log(struct lp_build_context *bld,
1338              LLVMValueRef x)
1339 {
1340    /* log(2) */
1341    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1342
1343    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1344 }
1345
1346
1347 #define EXP_POLY_DEGREE 3
1348 #define LOG_POLY_DEGREE 5
1349
1350
1351 /**
1352  * Generate polynomial.
1353  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1354  */
1355 static LLVMValueRef
1356 lp_build_polynomial(struct lp_build_context *bld,
1357                     LLVMValueRef x,
1358                     const double *coeffs,
1359                     unsigned num_coeffs)
1360 {
1361    const struct lp_type type = bld->type;
1362    LLVMValueRef res = NULL;
1363    unsigned i;
1364
1365    /* TODO: optimize the constant case */
1366    if(LLVMIsConstant(x))
1367       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1368                    __FUNCTION__);
1369
1370    for (i = num_coeffs; i--; ) {
1371       LLVMValueRef coeff;
1372
1373       coeff = lp_build_const_vec(type, coeffs[i]);
1374
1375       if(res)
1376          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1377       else
1378          res = coeff;
1379    }
1380
1381    if(res)
1382       return res;
1383    else
1384       return bld->undef;
1385 }
1386
1387
1388 /**
1389  * Minimax polynomial fit of 2**x, in range [0, 1[
1390  */
1391 const double lp_build_exp2_polynomial[] = {
1392 #if EXP_POLY_DEGREE == 5
1393    0.999999999690134838155,
1394    0.583974334321735217258,
1395    0.164553105719676828492,
1396    0.0292811063701710962255,
1397    0.00354944426657875141846,
1398    0.000296253726543423377365
1399 #elif EXP_POLY_DEGREE == 4
1400    1.00000001502262084505,
1401    0.563586057338685991394,
1402    0.150436017652442413623,
1403    0.0243220604213317927308,
1404    0.0025359088446580436489
1405 #elif EXP_POLY_DEGREE == 3
1406    0.999925218562710312959,
1407    0.695833540494823811697,
1408    0.226067155427249155588,
1409    0.0780245226406372992967
1410 #elif EXP_POLY_DEGREE == 2
1411    1.00172476321474503578,
1412    0.657636275736077639316,
1413    0.33718943461968720704
1414 #else
1415 #error
1416 #endif
1417 };
1418
1419
1420 void
1421 lp_build_exp2_approx(struct lp_build_context *bld,
1422                      LLVMValueRef x,
1423                      LLVMValueRef *p_exp2_int_part,
1424                      LLVMValueRef *p_frac_part,
1425                      LLVMValueRef *p_exp2)
1426 {
1427    const struct lp_type type = bld->type;
1428    LLVMTypeRef vec_type = lp_build_vec_type(type);
1429    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1430    LLVMValueRef ipart = NULL;
1431    LLVMValueRef fpart = NULL;
1432    LLVMValueRef expipart = NULL;
1433    LLVMValueRef expfpart = NULL;
1434    LLVMValueRef res = NULL;
1435
1436    if(p_exp2_int_part || p_frac_part || p_exp2) {
1437       /* TODO: optimize the constant case */
1438       if(LLVMIsConstant(x))
1439          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1440                       __FUNCTION__);
1441
1442       assert(type.floating && type.width == 32);
1443
1444       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1445       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1446
1447       /* ipart = floor(x) */
1448       ipart = lp_build_floor(bld, x);
1449
1450       /* fpart = x - ipart */
1451       fpart = LLVMBuildSub(bld->builder, x, ipart, "");
1452    }
1453
1454    if(p_exp2_int_part || p_exp2) {
1455       /* expipart = (float) (1 << ipart) */
1456       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1457       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1458       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1459       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1460    }
1461
1462    if(p_exp2) {
1463       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1464                                      Elements(lp_build_exp2_polynomial));
1465
1466       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1467    }
1468
1469    if(p_exp2_int_part)
1470       *p_exp2_int_part = expipart;
1471
1472    if(p_frac_part)
1473       *p_frac_part = fpart;
1474
1475    if(p_exp2)
1476       *p_exp2 = res;
1477 }
1478
1479
1480 LLVMValueRef
1481 lp_build_exp2(struct lp_build_context *bld,
1482               LLVMValueRef x)
1483 {
1484    LLVMValueRef res;
1485    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1486    return res;
1487 }
1488
1489
1490 /**
1491  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1492  * These coefficients can be generate with
1493  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1494  */
1495 const double lp_build_log2_polynomial[] = {
1496 #if LOG_POLY_DEGREE == 6
1497    3.11578814719469302614,
1498    -3.32419399085241980044,
1499    2.59883907202499966007,
1500    -1.23152682416275988241,
1501    0.318212422185251071475,
1502    -0.0344359067839062357313
1503 #elif LOG_POLY_DEGREE == 5
1504    2.8882704548164776201,
1505    -2.52074962577807006663,
1506    1.48116647521213171641,
1507    -0.465725644288844778798,
1508    0.0596515482674574969533
1509 #elif LOG_POLY_DEGREE == 4
1510    2.61761038894603480148,
1511    -1.75647175389045657003,
1512    0.688243882994381274313,
1513    -0.107254423828329604454
1514 #elif LOG_POLY_DEGREE == 3
1515    2.28330284476918490682,
1516    -1.04913055217340124191,
1517    0.204446009836232697516
1518 #else
1519 #error
1520 #endif
1521 };
1522
1523
1524 /**
1525  * See http://www.devmaster.net/forums/showthread.php?p=43580
1526  */
1527 void
1528 lp_build_log2_approx(struct lp_build_context *bld,
1529                      LLVMValueRef x,
1530                      LLVMValueRef *p_exp,
1531                      LLVMValueRef *p_floor_log2,
1532                      LLVMValueRef *p_log2)
1533 {
1534    const struct lp_type type = bld->type;
1535    LLVMTypeRef vec_type = lp_build_vec_type(type);
1536    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1537
1538    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
1539    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
1540    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1541
1542    LLVMValueRef i = NULL;
1543    LLVMValueRef exp = NULL;
1544    LLVMValueRef mant = NULL;
1545    LLVMValueRef logexp = NULL;
1546    LLVMValueRef logmant = NULL;
1547    LLVMValueRef res = NULL;
1548
1549    if(p_exp || p_floor_log2 || p_log2) {
1550       /* TODO: optimize the constant case */
1551       if(LLVMIsConstant(x))
1552          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1553                       __FUNCTION__);
1554
1555       assert(type.floating && type.width == 32);
1556
1557       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1558
1559       /* exp = (float) exponent(x) */
1560       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1561    }
1562
1563    if(p_floor_log2 || p_log2) {
1564       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
1565       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
1566       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1567    }
1568
1569    if(p_log2) {
1570       /* mant = (float) mantissa(x) */
1571       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1572       mant = LLVMBuildOr(bld->builder, mant, one, "");
1573       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1574
1575       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1576                                     Elements(lp_build_log2_polynomial));
1577
1578       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1579       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1580
1581       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1582    }
1583
1584    if(p_exp) {
1585       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
1586       *p_exp = exp;
1587    }
1588
1589    if(p_floor_log2)
1590       *p_floor_log2 = logexp;
1591
1592    if(p_log2)
1593       *p_log2 = res;
1594 }
1595
1596
1597 LLVMValueRef
1598 lp_build_log2(struct lp_build_context *bld,
1599               LLVMValueRef x)
1600 {
1601    LLVMValueRef res;
1602    lp_build_log2_approx(bld, x, NULL, NULL, &res);
1603    return res;
1604 }