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    int 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       if (type.length == 1) {
 680          LLVMTypeRef int_type = LLVMIntType(type.width);
 681          LLVMTypeRef float_type = LLVMFloatType();
 682          unsigned long long absMask = ~(1ULL << (type.width - 1));
 683          LLVMValueRef mask = LLVMConstInt(int_type, absMask, 0);
 684          a = LLVMBuildBitCast(bld->builder, a, int_type, "");
 685          a = LLVMBuildAnd(bld->builder, a, mask, "");
 686          a = LLVMBuildBitCast(bld->builder, a, float_type, "");
 687          return a;
 688       }
 689       else {
 690          /* vector of floats */
 691          LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 692          unsigned long long absMask = ~(1ULL << (type.width - 1));
 693          LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 694          a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 695          a = LLVMBuildAnd(bld->builder, a, mask, "");
 696          a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 697          return a;
 698       }
 699    }
 700
 701    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 702       switch(type.width) {
 703       case 8:
 704          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 705       case 16:
 706          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 707       case 32:
 708          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 709       }
 710    }
 711
 712    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 713 }
 714
 715
 716 LLVMValueRef
 717 lp_build_negate(struct lp_build_context *bld,
 718                 LLVMValueRef a)
 719 {
 720    return LLVMBuildNeg(bld->builder, a, "");
 721 }
 722
 723
 724 /** Return -1, 0 or +1 depending on the sign of a */
 725 LLVMValueRef
 726 lp_build_sgn(struct lp_build_context *bld,
 727              LLVMValueRef a)
 728 {
 729    const struct lp_type type = bld->type;
 730    LLVMValueRef cond;
 731    LLVMValueRef res;
 732
 733    /* Handle non-zero case */
 734    if(!type.sign) {
 735       /* if not zero then sign must be positive */
 736       res = bld->one;
 737    }
 738    else if(type.floating) {
 739       LLVMTypeRef vec_type;
 740       LLVMTypeRef int_type;
 741       LLVMValueRef mask;
 742       LLVMValueRef sign;
 743       LLVMValueRef one;
 744       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 745
 746       if (type.length == 1) {
 747          int_type = lp_build_int_elem_type(type);
 748          vec_type = lp_build_elem_type(type);
 749          mask = LLVMConstInt(int_type, maskBit, 0);
 750       }
 751       else {
 752          /* vector */
 753          int_type = lp_build_int_vec_type(type);
 754          vec_type = lp_build_vec_type(type);
 755          mask = lp_build_const_int_vec(type, maskBit);
 756       }
 757
 758       /* Take the sign bit and add it to 1 constant */
 759       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 760       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 761       one = LLVMConstBitCast(bld->one, int_type);
 762       res = LLVMBuildOr(bld->builder, sign, one, "");
 763       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 764    }
 765    else
 766    {
 767       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 768       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 769       res = lp_build_select(bld, cond, bld->one, minus_one);
 770    }
 771
 772    /* Handle zero */
 773    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 774    res = lp_build_select(bld, cond, bld->zero, res);
 775
 776    return res;
 777 }
 778
 779
 780 /**
 781  * Set the sign of float vector 'a' according to 'sign'.
 782  * If sign==0, return abs(a).
 783  * If sign==1, return -abs(a);
 784  * Other values for sign produce undefined results.
 785  */
 786 LLVMValueRef
 787 lp_build_set_sign(struct lp_build_context *bld,
 788                   LLVMValueRef a, LLVMValueRef sign)
 789 {
 790    const struct lp_type type = bld->type;
 791    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 792    LLVMTypeRef vec_type = lp_build_vec_type(type);
 793    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 794    LLVMValueRef mask = lp_build_const_int_vec(type,
 795                              ~((unsigned long long) 1 << (type.width - 1)));
 796    LLVMValueRef val, res;
 797
 798    assert(type.floating);
 799
 800    /* val = reinterpret_cast<int>(a) */
 801    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 802    /* val = val & mask */
 803    val = LLVMBuildAnd(bld->builder, val, mask, "");
 804    /* sign = sign << shift */
 805    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 806    /* res = val | sign */
 807    res = LLVMBuildOr(bld->builder, val, sign, "");
 808    /* res = reinterpret_cast<float>(res) */
 809    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 810
 811    return res;
 812 }
 813
 814
 815 /**
 816  * Convert vector of (or scalar) int to vector of (or scalar) float.
 817  */
 818 LLVMValueRef
 819 lp_build_int_to_float(struct lp_build_context *bld,
 820                       LLVMValueRef a)
 821 {
 822    const struct lp_type type = bld->type;
 823
 824    assert(type.floating);
 825    /*assert(lp_check_value(type, a));*/
 826
 827    if (type.length == 1) {
 828       LLVMTypeRef float_type = LLVMFloatType();
 829       return LLVMBuildSIToFP(bld->builder, a, float_type, "");
 830    }
 831    else {
 832       LLVMTypeRef vec_type = lp_build_vec_type(type);
 833       /*LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);*/
 834       LLVMValueRef res;
 835       res = LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 836       return res;
 837    }
 838 }
 839
 840
 841
 842 enum lp_build_round_sse41_mode
 843 {
 844    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 845    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 846    LP_BUILD_ROUND_SSE41_CEIL = 2,
 847    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 848 };
 849
 850
 851 static INLINE LLVMValueRef
 852 lp_build_round_sse41(struct lp_build_context *bld,
 853                      LLVMValueRef a,
 854                      enum lp_build_round_sse41_mode mode)
 855 {
 856    const struct lp_type type = bld->type;
 857    LLVMTypeRef vec_type = lp_build_vec_type(type);
 858    const char *intrinsic;
 859
 860    assert(type.floating);
 861    assert(type.width*type.length == 128);
 862    assert(lp_check_value(type, a));
 863    assert(util_cpu_caps.has_sse4_1);
 864
 865    switch(type.width) {
 866    case 32:
 867       intrinsic = "llvm.x86.sse41.round.ps";
 868       break;
 869    case 64:
 870       intrinsic = "llvm.x86.sse41.round.pd";
 871       break;
 872    default:
 873       assert(0);
 874       return bld->undef;
 875    }
 876
 877    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 878                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 879 }
 880
 881
 882 LLVMValueRef
 883 lp_build_trunc(struct lp_build_context *bld,
 884                LLVMValueRef a)
 885 {
 886    const struct lp_type type = bld->type;
 887
 888    assert(type.floating);
 889    assert(lp_check_value(type, a));
 890
 891    if(util_cpu_caps.has_sse4_1)
 892       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 893    else {
 894       LLVMTypeRef vec_type = lp_build_vec_type(type);
 895       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 896       LLVMValueRef res;
 897       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 898       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 899       return res;
 900    }
 901 }
 902
 903
 904 LLVMValueRef
 905 lp_build_round(struct lp_build_context *bld,
 906                LLVMValueRef a)
 907 {
 908    const struct lp_type type = bld->type;
 909
 910    assert(type.floating);
 911    assert(lp_check_value(type, a));
 912
 913    if(util_cpu_caps.has_sse4_1)
 914       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 915    else {
 916       LLVMTypeRef vec_type = lp_build_vec_type(type);
 917       LLVMValueRef res;
 918       res = lp_build_iround(bld, a);
 919       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 920       return res;
 921    }
 922 }
 923
 924
 925 LLVMValueRef
 926 lp_build_floor(struct lp_build_context *bld,
 927                LLVMValueRef a)
 928 {
 929    const struct lp_type type = bld->type;
 930
 931    assert(type.floating);
 932
 933    if (type.length == 1) {
 934       LLVMValueRef res;
 935       res = lp_build_ifloor(bld, a);
 936       res = LLVMBuildSIToFP(bld->builder, res, LLVMFloatType(), "");
 937       return res;
 938    }
 939
 940    if(util_cpu_caps.has_sse4_1)
 941       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 942    else {
 943       LLVMTypeRef vec_type = lp_build_vec_type(type);
 944       LLVMValueRef res;
 945       res = lp_build_ifloor(bld, a);
 946       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 947       return res;
 948    }
 949 }
 950
 951
 952 LLVMValueRef
 953 lp_build_ceil(struct lp_build_context *bld,
 954               LLVMValueRef a)
 955 {
 956    const struct lp_type type = bld->type;
 957
 958    assert(type.floating);
 959    assert(lp_check_value(type, a));
 960
 961    if(util_cpu_caps.has_sse4_1)
 962       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 963    else {
 964       LLVMTypeRef vec_type = lp_build_vec_type(type);
 965       LLVMValueRef res;
 966       res = lp_build_iceil(bld, a);
 967       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 968       return res;
 969    }
 970 }
 971
 972
 973 /**
 974  * Return fractional part of 'a' computed as a - floor(f)
 975  * Typically used in texture coord arithmetic.
 976  */
 977 LLVMValueRef
 978 lp_build_fract(struct lp_build_context *bld,
 979                LLVMValueRef a)
 980 {
 981    assert(bld->type.floating);
 982    return lp_build_sub(bld, a, lp_build_floor(bld, a));
 983 }
 984
 985
 986 /**
 987  * Convert to integer, through whichever rounding method that's fastest,
 988  * typically truncating toward zero.
 989  */
 990 LLVMValueRef
 991 lp_build_itrunc(struct lp_build_context *bld,
 992                 LLVMValueRef a)
 993 {
 994    const struct lp_type type = bld->type;
 995
 996    assert(type.floating);
 997
 998    if (type.length == 1) {
 999       LLVMTypeRef int_type = LLVMIntType(type.width);
1000       return LLVMBuildFPToSI(bld->builder, a, int_type, "");
1001    }
1002    else {
1003       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1004       assert(lp_check_value(type, a));
1005       return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1006    }
1007 }
1008
1009
1010 /**
1011  * Convert float[] to int[] with round().
1012  */
1013 LLVMValueRef
1014 lp_build_iround(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
1023    if (type.length == 1) {
1024       /* scalar float to int */
1025       LLVMTypeRef int_type = LLVMIntType(type.width);
1026       /* XXX we want rounding here! */
1027       res = LLVMBuildFPToSI(bld->builder, a, int_type, "");
1028       return res;
1029    }
1030
1031    assert(lp_check_value(type, a));
1032
1033    if(util_cpu_caps.has_sse4_1) {
1034       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1035    }
1036    else {
1037       LLVMTypeRef vec_type = lp_build_vec_type(type);
1038       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1039       LLVMValueRef sign;
1040       LLVMValueRef half;
1041
1042       /* get sign bit */
1043       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1044       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1045
1046       /* sign * 0.5 */
1047       half = lp_build_const_vec(type, 0.5);
1048       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1049       half = LLVMBuildOr(bld->builder, sign, half, "");
1050       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1051
1052       res = LLVMBuildAdd(bld->builder, a, half, "");
1053    }
1054
1055    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1056
1057    return res;
1058 }
1059
1060
1061 /**
1062  * Convert float[] to int[] with floor().
1063  */
1064 LLVMValueRef
1065 lp_build_ifloor(struct lp_build_context *bld,
1066                 LLVMValueRef a)
1067 {
1068    const struct lp_type type = bld->type;
1069    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1070    LLVMValueRef res;
1071
1072    assert(type.floating);
1073
1074    if (type.length == 1) {
1075       /* scalar float to int */
1076       LLVMTypeRef int_type = LLVMIntType(type.width);
1077       res = LLVMBuildFPToSI(bld->builder, a, int_type, "");
1078       return res;
1079    }
1080
1081    assert(lp_check_value(type, a));
1082
1083    if(util_cpu_caps.has_sse4_1) {
1084       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1085    }
1086    else {
1087       /* Take the sign bit and add it to 1 constant */
1088       LLVMTypeRef vec_type = lp_build_vec_type(type);
1089       unsigned mantissa = lp_mantissa(type);
1090       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1091       LLVMValueRef sign;
1092       LLVMValueRef offset;
1093
1094       /* sign = a < 0 ? ~0 : 0 */
1095       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1096       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1097       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "");
1098       lp_build_name(sign, "floor.sign");
1099
1100       /* offset = -0.99999(9)f */
1101       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 1)/((unsigned long long)1 << mantissa));
1102       offset = LLVMConstBitCast(offset, int_vec_type);
1103
1104       /* offset = a < 0 ? -0.99999(9)f : 0.0f */
1105       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1106       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "");
1107       lp_build_name(offset, "floor.offset");
1108
1109       res = LLVMBuildAdd(bld->builder, a, offset, "");
1110       lp_build_name(res, "floor.res");
1111    }
1112
1113    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1114    lp_build_name(res, "floor");
1115
1116    return res;
1117 }
1118
1119
1120 LLVMValueRef
1121 lp_build_iceil(struct lp_build_context *bld,
1122                LLVMValueRef a)
1123 {
1124    const struct lp_type type = bld->type;
1125    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1126    LLVMValueRef res;
1127
1128    assert(type.floating);
1129    assert(lp_check_value(type, a));
1130
1131    if(util_cpu_caps.has_sse4_1) {
1132       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1133    }
1134    else {
1135       assert(0);
1136       res = bld->undef;
1137    }
1138
1139    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1140
1141    return res;
1142 }
1143
1144
1145 LLVMValueRef
1146 lp_build_sqrt(struct lp_build_context *bld,
1147               LLVMValueRef a)
1148 {
1149    const struct lp_type type = bld->type;
1150    LLVMTypeRef vec_type = lp_build_vec_type(type);
1151    char intrinsic[32];
1152
1153    /* TODO: optimize the constant case */
1154    /* TODO: optimize the constant case */
1155
1156    assert(type.floating);
1157    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1158
1159    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1160 }
1161
1162
1163 LLVMValueRef
1164 lp_build_rcp(struct lp_build_context *bld,
1165              LLVMValueRef a)
1166 {
1167    const struct lp_type type = bld->type;
1168
1169    if(a == bld->zero)
1170       return bld->undef;
1171    if(a == bld->one)
1172       return bld->one;
1173    if(a == bld->undef)
1174       return bld->undef;
1175
1176    assert(type.floating);
1177
1178    if(LLVMIsConstant(a))
1179       return LLVMConstFDiv(bld->one, a);
1180
1181    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1182       /*
1183        * XXX: Added precision is not always necessary, so only enable this
1184        * when we have a better system in place to track minimum precision.
1185        */
1186
1187 #if 0
1188       /*
1189        * Do one Newton-Raphson step to improve precision:
1190        *
1191        *   x1 = (2 - a * rcp(a)) * rcp(a)
1192        */
1193
1194       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1195       LLVMValueRef rcp_a;
1196       LLVMValueRef res;
1197
1198       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1199
1200       res = LLVMBuildMul(bld->builder, a, rcp_a, "");
1201       res = LLVMBuildSub(bld->builder, two, res, "");
1202       res = LLVMBuildMul(bld->builder, res, rcp_a, "");
1203
1204       return rcp_a;
1205 #else
1206       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1207 #endif
1208    }
1209
1210    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1211 }
1212
1213
1214 /**
1215  * Generate 1/sqrt(a)
1216  */
1217 LLVMValueRef
1218 lp_build_rsqrt(struct lp_build_context *bld,
1219                LLVMValueRef a)
1220 {
1221    const struct lp_type type = bld->type;
1222
1223    assert(type.floating);
1224
1225    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1226       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1227
1228    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1229 }
1230
1231
1232 #ifdef PIPE_OS_WINDOWS
1233
1234 /*
1235  * XXX: X86 backend translates llvm.cos.v4f32 to 4 calls to CRT's cosf()
1236  * which is neither efficient nor does the CRT linkage work on Windows
1237  * causing segmentation fault.
1238  *
1239  * XXX: With LLVM 2.7 both schemes cause an assertion failure.
1240  */
1241 static LLVMValueRef
1242 lp_build_sincos(struct lp_build_context *bld,
1243                 const char *name,
1244                 float (*func)(float),
1245                 LLVMValueRef a)
1246 {
1247    LLVMModuleRef module =
1248          LLVMGetGlobalParent(LLVMGetBasicBlockParent(LLVMGetInsertBlock(bld->builder)));
1249    LLVMValueRef function;
1250    LLVMValueRef res;
1251    unsigned i;
1252
1253    assert(bld->type.floating);
1254    assert(bld->type.width == 32);
1255
1256    function = LLVMGetNamedFunction(module, name);
1257    if (!function) {
1258       LLVMTypeRef ret_type;
1259       LLVMTypeRef arg_types[1];
1260       LLVMTypeRef function_type;
1261
1262       ret_type = LLVMFloatType();
1263       arg_types[0] = LLVMFloatType();
1264       function_type = LLVMFunctionType(ret_type, arg_types, Elements(arg_types), 0);
1265       function = LLVMAddFunction(module, name, function_type);
1266
1267       LLVMSetFunctionCallConv(function, LLVMCCallConv);
1268       LLVMSetLinkage(function, LLVMPrivateLinkage);
1269
1270       assert(LLVMIsDeclaration(function));
1271
1272       LLVMAddGlobalMapping(lp_build_engine, function, func);
1273    }
1274
1275    res = bld->undef;
1276
1277    for (i = 0; i < bld->type.length; ++i) {
1278       LLVMValueRef index = LLVMConstInt(LLVMInt32Type(), i, 0);
1279       LLVMValueRef args[1];
1280       LLVMValueRef tmp;
1281
1282       args[0] = LLVMBuildExtractElement(bld->builder, a, index, "");
1283
1284       tmp = LLVMBuildCall(bld->builder, function, args, Elements(args), "");
1285
1286       res = LLVMBuildInsertElement(bld->builder, res, tmp, index, "");
1287    }
1288
1289    return res;
1290 }
1291
1292 LLVMValueRef
1293 lp_build_cos(struct lp_build_context *bld,
1294              LLVMValueRef a)
1295 {
1296    return lp_build_sincos(bld, "cosf", &cosf, a);
1297 }
1298
1299 LLVMValueRef
1300 lp_build_sin(struct lp_build_context *bld,
1301              LLVMValueRef a)
1302 {
1303    return lp_build_sincos(bld, "sinf", &sinf, a);
1304 }
1305
1306 #else /* !PIPE_OS_WINDOWS */
1307
1308 /**
1309  * Generate cos(a)
1310  */
1311 LLVMValueRef
1312 lp_build_cos(struct lp_build_context *bld,
1313               LLVMValueRef a)
1314 {
1315    const struct lp_type type = bld->type;
1316    LLVMTypeRef vec_type = lp_build_vec_type(type);
1317    char intrinsic[32];
1318
1319    /* TODO: optimize the constant case */
1320
1321    assert(type.floating);
1322    util_snprintf(intrinsic, sizeof intrinsic, "llvm.cos.v%uf%u", type.length, type.width);
1323
1324    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1325 }
1326
1327
1328 /**
1329  * Generate sin(a)
1330  */
1331 LLVMValueRef
1332 lp_build_sin(struct lp_build_context *bld,
1333               LLVMValueRef a)
1334 {
1335    const struct lp_type type = bld->type;
1336    LLVMTypeRef vec_type = lp_build_vec_type(type);
1337    char intrinsic[32];
1338
1339    /* TODO: optimize the constant case */
1340
1341    assert(type.floating);
1342    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sin.v%uf%u", type.length, type.width);
1343
1344    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1345 }
1346
1347 #endif /* !PIPE_OS_WINDOWS */
1348
1349
1350 /**
1351  * Generate pow(x, y)
1352  */
1353 LLVMValueRef
1354 lp_build_pow(struct lp_build_context *bld,
1355              LLVMValueRef x,
1356              LLVMValueRef y)
1357 {
1358    /* TODO: optimize the constant case */
1359    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1360       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1361                    __FUNCTION__);
1362
1363    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1364 }
1365
1366
1367 /**
1368  * Generate exp(x)
1369  */
1370 LLVMValueRef
1371 lp_build_exp(struct lp_build_context *bld,
1372              LLVMValueRef x)
1373 {
1374    /* log2(e) = 1/log(2) */
1375    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1376
1377    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1378 }
1379
1380
1381 /**
1382  * Generate log(x)
1383  */
1384 LLVMValueRef
1385 lp_build_log(struct lp_build_context *bld,
1386              LLVMValueRef x)
1387 {
1388    /* log(2) */
1389    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1390
1391    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1392 }
1393
1394
1395 #define EXP_POLY_DEGREE 3
1396 #define LOG_POLY_DEGREE 5
1397
1398
1399 /**
1400  * Generate polynomial.
1401  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1402  */
1403 static LLVMValueRef
1404 lp_build_polynomial(struct lp_build_context *bld,
1405                     LLVMValueRef x,
1406                     const double *coeffs,
1407                     unsigned num_coeffs)
1408 {
1409    const struct lp_type type = bld->type;
1410    LLVMTypeRef float_type = LLVMFloatType();
1411    LLVMValueRef res = NULL;
1412    unsigned i;
1413
1414    /* TODO: optimize the constant case */
1415    if(LLVMIsConstant(x))
1416       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1417                    __FUNCTION__);
1418
1419    for (i = num_coeffs; i--; ) {
1420       LLVMValueRef coeff;
1421
1422       if (type.length == 1)
1423          coeff = LLVMConstReal(float_type, coeffs[i]);
1424       else
1425          coeff = lp_build_const_vec(type, coeffs[i]);
1426
1427       if(res)
1428          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1429       else
1430          res = coeff;
1431    }
1432
1433    if(res)
1434       return res;
1435    else
1436       return bld->undef;
1437 }
1438
1439
1440 /**
1441  * Minimax polynomial fit of 2**x, in range [-0.5, 0.5[
1442  */
1443 const double lp_build_exp2_polynomial[] = {
1444 #if EXP_POLY_DEGREE == 5
1445    9.9999994e-1, 6.9315308e-1, 2.4015361e-1, 5.5826318e-2, 8.9893397e-3, 1.8775767e-3
1446 #elif EXP_POLY_DEGREE == 4
1447    1.0000026, 6.9300383e-1, 2.4144275e-1, 5.2011464e-2, 1.3534167e-2
1448 #elif EXP_POLY_DEGREE == 3
1449    9.9992520e-1, 6.9583356e-1, 2.2606716e-1, 7.8024521e-2
1450 #elif EXP_POLY_DEGREE == 2
1451    1.0017247, 6.5763628e-1, 3.3718944e-1
1452 #else
1453 #error
1454 #endif
1455 };
1456
1457
1458 void
1459 lp_build_exp2_approx(struct lp_build_context *bld,
1460                      LLVMValueRef x,
1461                      LLVMValueRef *p_exp2_int_part,
1462                      LLVMValueRef *p_frac_part,
1463                      LLVMValueRef *p_exp2)
1464 {
1465    const struct lp_type type = bld->type;
1466    LLVMTypeRef vec_type = lp_build_vec_type(type);
1467    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1468    LLVMValueRef ipart = NULL;
1469    LLVMValueRef fpart = NULL;
1470    LLVMValueRef expipart = NULL;
1471    LLVMValueRef expfpart = NULL;
1472    LLVMValueRef res = NULL;
1473
1474    if(p_exp2_int_part || p_frac_part || p_exp2) {
1475       /* TODO: optimize the constant case */
1476       if(LLVMIsConstant(x))
1477          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1478                       __FUNCTION__);
1479
1480       assert(type.floating && type.width == 32);
1481
1482       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1483       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1484
1485       /* ipart = int(x - 0.5) */
1486       ipart = LLVMBuildSub(bld->builder, x, lp_build_const_vec(type, 0.5f), "");
1487       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1488
1489       /* fpart = x - ipart */
1490       fpart = LLVMBuildSIToFP(bld->builder, ipart, vec_type, "");
1491       fpart = LLVMBuildSub(bld->builder, x, fpart, "");
1492    }
1493
1494    if(p_exp2_int_part || p_exp2) {
1495       /* expipart = (float) (1 << ipart) */
1496       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1497       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1498       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1499    }
1500
1501    if(p_exp2) {
1502       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1503                                      Elements(lp_build_exp2_polynomial));
1504
1505       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1506    }
1507
1508    if(p_exp2_int_part)
1509       *p_exp2_int_part = expipart;
1510
1511    if(p_frac_part)
1512       *p_frac_part = fpart;
1513
1514    if(p_exp2)
1515       *p_exp2 = res;
1516 }
1517
1518
1519 LLVMValueRef
1520 lp_build_exp2(struct lp_build_context *bld,
1521               LLVMValueRef x)
1522 {
1523    LLVMValueRef res;
1524    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1525    return res;
1526 }
1527
1528
1529 /**
1530  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1531  * These coefficients can be generate with
1532  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1533  */
1534 const double lp_build_log2_polynomial[] = {
1535 #if LOG_POLY_DEGREE == 6
1536    3.11578814719469302614, -3.32419399085241980044, 2.59883907202499966007, -1.23152682416275988241, 0.318212422185251071475, -0.0344359067839062357313
1537 #elif LOG_POLY_DEGREE == 5
1538    2.8882704548164776201, -2.52074962577807006663, 1.48116647521213171641, -0.465725644288844778798, 0.0596515482674574969533
1539 #elif LOG_POLY_DEGREE == 4
1540    2.61761038894603480148, -1.75647175389045657003, 0.688243882994381274313, -0.107254423828329604454
1541 #elif LOG_POLY_DEGREE == 3
1542    2.28330284476918490682, -1.04913055217340124191, 0.204446009836232697516
1543 #else
1544 #error
1545 #endif
1546 };
1547
1548
1549 /**
1550  * See http://www.devmaster.net/forums/showthread.php?p=43580
1551  */
1552 void
1553 lp_build_log2_approx(struct lp_build_context *bld,
1554                      LLVMValueRef x,
1555                      LLVMValueRef *p_exp,
1556                      LLVMValueRef *p_floor_log2,
1557                      LLVMValueRef *p_log2)
1558 {
1559    const struct lp_type type = bld->type;
1560    LLVMTypeRef vec_type = lp_build_vec_type(type);
1561    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1562
1563    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
1564    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
1565    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1566
1567    LLVMValueRef i = NULL;
1568    LLVMValueRef exp = NULL;
1569    LLVMValueRef mant = NULL;
1570    LLVMValueRef logexp = NULL;
1571    LLVMValueRef logmant = NULL;
1572    LLVMValueRef res = NULL;
1573
1574    if(p_exp || p_floor_log2 || p_log2) {
1575       /* TODO: optimize the constant case */
1576       if(LLVMIsConstant(x))
1577          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1578                       __FUNCTION__);
1579
1580       assert(type.floating && type.width == 32);
1581
1582       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1583
1584       /* exp = (float) exponent(x) */
1585       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1586    }
1587
1588    if(p_floor_log2 || p_log2) {
1589       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
1590       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
1591       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1592    }
1593
1594    if(p_log2) {
1595       /* mant = (float) mantissa(x) */
1596       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1597       mant = LLVMBuildOr(bld->builder, mant, one, "");
1598       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1599
1600       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1601                                     Elements(lp_build_log2_polynomial));
1602
1603       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1604       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1605
1606       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1607    }
1608
1609    if(p_exp) {
1610       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
1611       *p_exp = exp;
1612    }
1613
1614    if(p_floor_log2)
1615       *p_floor_log2 = logexp;
1616
1617    if(p_log2)
1618       *p_log2 = res;
1619 }
1620
1621
1622 /** scalar version of above function */
1623 static void
1624 lp_build_float_log2_approx(struct lp_build_context *bld,
1625                            LLVMValueRef x,
1626                            LLVMValueRef *p_exp,
1627                            LLVMValueRef *p_floor_log2,
1628                            LLVMValueRef *p_log2)
1629 {
1630    const struct lp_type type = bld->type;
1631    LLVMTypeRef float_type = LLVMFloatType();
1632    LLVMTypeRef int_type = LLVMIntType(type.width);
1633
1634    LLVMValueRef expmask = LLVMConstInt(int_type, 0x7f800000, 0);
1635    LLVMValueRef mantmask = LLVMConstInt(int_type, 0x007fffff, 0);
1636    LLVMValueRef one = LLVMConstBitCast(bld->one, int_type);
1637
1638    LLVMValueRef i = NULL;
1639    LLVMValueRef exp = NULL;
1640    LLVMValueRef mant = NULL;
1641    LLVMValueRef logexp = NULL;
1642    LLVMValueRef logmant = NULL;
1643    LLVMValueRef res = NULL;
1644
1645    if(p_exp || p_floor_log2 || p_log2) {
1646       /* TODO: optimize the constant case */
1647       if(LLVMIsConstant(x))
1648          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1649                       __FUNCTION__);
1650
1651       assert(type.floating && type.width == 32);
1652
1653       i = LLVMBuildBitCast(bld->builder, x, int_type, "");
1654
1655       /* exp = (float) exponent(x) */
1656       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1657    }
1658
1659    if(p_floor_log2 || p_log2) {
1660       LLVMValueRef c23 = LLVMConstInt(int_type, 23, 0);
1661       LLVMValueRef c127 = LLVMConstInt(int_type, 127, 0);
1662       logexp = LLVMBuildLShr(bld->builder, exp, c23, "");
1663       logexp = LLVMBuildSub(bld->builder, logexp, c127, "");
1664       logexp = LLVMBuildSIToFP(bld->builder, logexp, float_type, "");
1665    }
1666
1667    if(p_log2) {
1668       /* mant = (float) mantissa(x) */
1669       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1670       mant = LLVMBuildOr(bld->builder, mant, one, "");
1671       mant = LLVMBuildBitCast(bld->builder, mant, float_type, "");
1672
1673       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1674                                     Elements(lp_build_log2_polynomial));
1675
1676       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1677       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1678
1679       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1680    }
1681
1682    if(p_exp) {
1683       exp = LLVMBuildBitCast(bld->builder, exp, float_type, "");
1684       *p_exp = exp;
1685    }
1686
1687    if(p_floor_log2)
1688       *p_floor_log2 = logexp;
1689
1690    if(p_log2)
1691       *p_log2 = res;
1692 }
1693
1694
1695 LLVMValueRef
1696 lp_build_log2(struct lp_build_context *bld,
1697               LLVMValueRef x)
1698 {
1699    LLVMValueRef res;
1700    if (bld->type.length == 1) {
1701       lp_build_float_log2_approx(bld, x, NULL, NULL, &res);
1702    }
1703    else {
1704       lp_build_log2_approx(bld, x, NULL, NULL, &res);
1705    }
1706    return res;
1707 }