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_logic.h"
  58 #include "lp_bld_pack.h"
  59 #include "lp_bld_arit.h"
  60
  61
  62 /**
  63  * Generate min(a, b)
  64  * No checks for special case values of a or b = 1 or 0 are done.
  65  */
  66 static LLVMValueRef
  67 lp_build_min_simple(struct lp_build_context *bld,
  68                     LLVMValueRef a,
  69                     LLVMValueRef b)
  70 {
  71    const struct lp_type type = bld->type;
  72    const char *intrinsic = NULL;
  73    LLVMValueRef cond;
  74
  75    /* TODO: optimize the constant case */
  76
  77    if(type.width * type.length == 128) {
  78       if(type.floating) {
  79          if(type.width == 32 && util_cpu_caps.has_sse)
  80             intrinsic = "llvm.x86.sse.min.ps";
  81          if(type.width == 64 && util_cpu_caps.has_sse2)
  82             intrinsic = "llvm.x86.sse2.min.pd";
  83       }
  84       else {
  85          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  86             intrinsic = "llvm.x86.sse2.pminu.b";
  87          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  88             intrinsic = "llvm.x86.sse41.pminsb";
  89          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  90             intrinsic = "llvm.x86.sse41.pminuw";
  91          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  92             intrinsic = "llvm.x86.sse2.pmins.w";
  93          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  94             intrinsic = "llvm.x86.sse41.pminud";
  95          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  96             intrinsic = "llvm.x86.sse41.pminsd";
  97       }
  98    }
  99
 100    if(intrinsic)
 101       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 102
 103    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 104    return lp_build_select(bld, cond, a, b);
 105 }
 106
 107
 108 /**
 109  * Generate max(a, b)
 110  * No checks for special case values of a or b = 1 or 0 are done.
 111  */
 112 static LLVMValueRef
 113 lp_build_max_simple(struct lp_build_context *bld,
 114                     LLVMValueRef a,
 115                     LLVMValueRef b)
 116 {
 117    const struct lp_type type = bld->type;
 118    const char *intrinsic = NULL;
 119    LLVMValueRef cond;
 120
 121    /* TODO: optimize the constant case */
 122
 123    if(type.width * type.length == 128) {
 124       if(type.floating) {
 125          if(type.width == 32 && util_cpu_caps.has_sse)
 126             intrinsic = "llvm.x86.sse.max.ps";
 127          if(type.width == 64 && util_cpu_caps.has_sse2)
 128             intrinsic = "llvm.x86.sse2.max.pd";
 129       }
 130       else {
 131          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 132             intrinsic = "llvm.x86.sse2.pmaxu.b";
 133          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 134             intrinsic = "llvm.x86.sse41.pmaxsb";
 135          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 136             intrinsic = "llvm.x86.sse41.pmaxuw";
 137          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 138             intrinsic = "llvm.x86.sse2.pmaxs.w";
 139          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 140             intrinsic = "llvm.x86.sse41.pmaxud";
 141          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 142             intrinsic = "llvm.x86.sse41.pmaxsd";
 143       }
 144    }
 145
 146    if(intrinsic)
 147       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 148
 149    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 150    return lp_build_select(bld, cond, a, b);
 151 }
 152
 153
 154 /**
 155  * Generate 1 - a, or ~a depending on bld->type.
 156  */
 157 LLVMValueRef
 158 lp_build_comp(struct lp_build_context *bld,
 159               LLVMValueRef a)
 160 {
 161    const struct lp_type type = bld->type;
 162
 163    if(a == bld->one)
 164       return bld->zero;
 165    if(a == bld->zero)
 166       return bld->one;
 167
 168    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 169       if(LLVMIsConstant(a))
 170          return LLVMConstNot(a);
 171       else
 172          return LLVMBuildNot(bld->builder, a, "");
 173    }
 174
 175    if(LLVMIsConstant(a))
 176       return LLVMConstSub(bld->one, a);
 177    else
 178       return LLVMBuildSub(bld->builder, bld->one, a, "");
 179 }
 180
 181
 182 /**
 183  * Generate a + b
 184  */
 185 LLVMValueRef
 186 lp_build_add(struct lp_build_context *bld,
 187              LLVMValueRef a,
 188              LLVMValueRef b)
 189 {
 190    const struct lp_type type = bld->type;
 191    LLVMValueRef res;
 192
 193    if(a == bld->zero)
 194       return b;
 195    if(b == bld->zero)
 196       return a;
 197    if(a == bld->undef || b == bld->undef)
 198       return bld->undef;
 199
 200    if(bld->type.norm) {
 201       const char *intrinsic = NULL;
 202
 203       if(a == bld->one || b == bld->one)
 204         return bld->one;
 205
 206       if(util_cpu_caps.has_sse2 &&
 207          type.width * type.length == 128 &&
 208          !type.floating && !type.fixed) {
 209          if(type.width == 8)
 210             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 211          if(type.width == 16)
 212             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 213       }
 214
 215       if(intrinsic)
 216          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 217    }
 218
 219    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 220       res = LLVMConstAdd(a, b);
 221    else
 222       res = LLVMBuildAdd(bld->builder, a, b, "");
 223
 224    /* clamp to ceiling of 1.0 */
 225    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 226       res = lp_build_min_simple(bld, res, bld->one);
 227
 228    /* XXX clamp to floor of -1 or 0??? */
 229
 230    return res;
 231 }
 232
 233
 234 /** Return the sum of the elements of a */
 235 LLVMValueRef
 236 lp_build_sum_vector(struct lp_build_context *bld,
 237                     LLVMValueRef a)
 238 {
 239    const struct lp_type type = bld->type;
 240    LLVMValueRef index, res;
 241    unsigned i;
 242
 243    if (a == bld->zero)
 244       return bld->zero;
 245    if (a == bld->undef)
 246       return bld->undef;
 247    assert(type.length > 1);
 248
 249    assert(!bld->type.norm);
 250
 251    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 252    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 253
 254    for (i = 1; i < type.length; i++) {
 255       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 256       res = LLVMBuildAdd(bld->builder, res,
 257                          LLVMBuildExtractElement(bld->builder, a, index, ""),
 258                          "");
 259    }
 260
 261    return res;
 262 }
 263
 264
 265 /**
 266  * Generate a - b
 267  */
 268 LLVMValueRef
 269 lp_build_sub(struct lp_build_context *bld,
 270              LLVMValueRef a,
 271              LLVMValueRef b)
 272 {
 273    const struct lp_type type = bld->type;
 274    LLVMValueRef res;
 275
 276    if(b == bld->zero)
 277       return a;
 278    if(a == bld->undef || b == bld->undef)
 279       return bld->undef;
 280    if(a == b)
 281       return bld->zero;
 282
 283    if(bld->type.norm) {
 284       const char *intrinsic = NULL;
 285
 286       if(b == bld->one)
 287         return bld->zero;
 288
 289       if(util_cpu_caps.has_sse2 &&
 290          type.width * type.length == 128 &&
 291          !type.floating && !type.fixed) {
 292          if(type.width == 8)
 293             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 294          if(type.width == 16)
 295             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 296       }
 297
 298       if(intrinsic)
 299          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 300    }
 301
 302    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 303       res = LLVMConstSub(a, b);
 304    else
 305       res = LLVMBuildSub(bld->builder, a, b, "");
 306
 307    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 308       res = lp_build_max_simple(bld, res, bld->zero);
 309
 310    return res;
 311 }
 312
 313
 314 /**
 315  * Normalized 8bit multiplication.
 316  *
 317  * - alpha plus one
 318  *
 319  *     makes the following approximation to the division (Sree)
 320  *
 321  *       a*b/255 ~= (a*(b + 1)) >> 256
 322  *
 323  *     which is the fastest method that satisfies the following OpenGL criteria
 324  *
 325  *       0*0 = 0 and 255*255 = 255
 326  *
 327  * - geometric series
 328  *
 329  *     takes the geometric series approximation to the division
 330  *
 331  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 332  *
 333  *     in this case just the first two terms to fit in 16bit arithmetic
 334  *
 335  *       t/255 ~= (t + (t >> 8)) >> 8
 336  *
 337  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 338  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 339  *     must be used
 340  *
 341  * - geometric series plus rounding
 342  *
 343  *     when using a geometric series division instead of truncating the result
 344  *     use roundoff in the approximation (Jim Blinn)
 345  *
 346  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 347  *
 348  *     achieving the exact results
 349  *
 350  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 351  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 352  * @sa Michael Herf, The "double blend trick", May 2000,
 353  *     http://www.stereopsis.com/doubleblend.html
 354  */
 355 static LLVMValueRef
 356 lp_build_mul_u8n(LLVMBuilderRef builder,
 357                  struct lp_type i16_type,
 358                  LLVMValueRef a, LLVMValueRef b)
 359 {
 360    LLVMValueRef c8;
 361    LLVMValueRef ab;
 362
 363    c8 = lp_build_const_int_vec(i16_type, 8);
 364
 365 #if 0
 366
 367    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 368    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 369    ab = LLVMBuildMul(builder, a, b, "");
 370
 371 #else
 372
 373    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 374    ab = LLVMBuildMul(builder, a, b, "");
 375    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 376    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 377
 378 #endif
 379
 380    ab = LLVMBuildLShr(builder, ab, c8, "");
 381
 382    return ab;
 383 }
 384
 385
 386 /**
 387  * Generate a * b
 388  */
 389 LLVMValueRef
 390 lp_build_mul(struct lp_build_context *bld,
 391              LLVMValueRef a,
 392              LLVMValueRef b)
 393 {
 394    const struct lp_type type = bld->type;
 395    LLVMValueRef shift;
 396    LLVMValueRef res;
 397
 398    if(a == bld->zero)
 399       return bld->zero;
 400    if(a == bld->one)
 401       return b;
 402    if(b == bld->zero)
 403       return bld->zero;
 404    if(b == bld->one)
 405       return a;
 406    if(a == bld->undef || b == bld->undef)
 407       return bld->undef;
 408
 409    if(!type.floating && !type.fixed && type.norm) {
 410       if(type.width == 8) {
 411          struct lp_type i16_type = lp_wider_type(type);
 412          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 413
 414          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 415          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 416
 417          /* PMULLW, PSRLW, PADDW */
 418          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 419          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 420
 421          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 422
 423          return ab;
 424       }
 425
 426       /* FIXME */
 427       assert(0);
 428    }
 429
 430    if(type.fixed)
 431       shift = lp_build_const_int_vec(type, type.width/2);
 432    else
 433       shift = NULL;
 434
 435    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 436       res =  LLVMConstMul(a, b);
 437       if(shift) {
 438          if(type.sign)
 439             res = LLVMConstAShr(res, shift);
 440          else
 441             res = LLVMConstLShr(res, shift);
 442       }
 443    }
 444    else {
 445       res = LLVMBuildMul(bld->builder, a, b, "");
 446       if(shift) {
 447          if(type.sign)
 448             res = LLVMBuildAShr(bld->builder, res, shift, "");
 449          else
 450             res = LLVMBuildLShr(bld->builder, res, shift, "");
 451       }
 452    }
 453
 454    return res;
 455 }
 456
 457
 458 /**
 459  * Small vector x scale multiplication optimization.
 460  */
 461 LLVMValueRef
 462 lp_build_mul_imm(struct lp_build_context *bld,
 463                  LLVMValueRef a,
 464                  int b)
 465 {
 466    LLVMValueRef factor;
 467
 468    if(b == 0)
 469       return bld->zero;
 470
 471    if(b == 1)
 472       return a;
 473
 474    if(b == -1)
 475       return LLVMBuildNeg(bld->builder, a, "");
 476
 477    if(b == 2 && bld->type.floating)
 478       return lp_build_add(bld, a, a);
 479
 480    if(util_is_pot(b)) {
 481       unsigned shift = ffs(b) - 1;
 482
 483       if(bld->type.floating) {
 484 #if 0
 485          /*
 486           * Power of two multiplication by directly manipulating the mantissa.
 487           *
 488           * XXX: This might not be always faster, it will introduce a small error
 489           * for multiplication by zero, and it will produce wrong results
 490           * for Inf and NaN.
 491           */
 492          unsigned mantissa = lp_mantissa(bld->type);
 493          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 494          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 495          a = LLVMBuildAdd(bld->builder, a, factor, "");
 496          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 497          return a;
 498 #endif
 499       }
 500       else {
 501          factor = lp_build_const_vec(bld->type, shift);
 502          return LLVMBuildShl(bld->builder, a, factor, "");
 503       }
 504    }
 505
 506    factor = lp_build_const_vec(bld->type, (double)b);
 507    return lp_build_mul(bld, a, factor);
 508 }
 509
 510
 511 /**
 512  * Generate a / b
 513  */
 514 LLVMValueRef
 515 lp_build_div(struct lp_build_context *bld,
 516              LLVMValueRef a,
 517              LLVMValueRef b)
 518 {
 519    const struct lp_type type = bld->type;
 520
 521    if(a == bld->zero)
 522       return bld->zero;
 523    if(a == bld->one)
 524       return lp_build_rcp(bld, b);
 525    if(b == bld->zero)
 526       return bld->undef;
 527    if(b == bld->one)
 528       return a;
 529    if(a == bld->undef || b == bld->undef)
 530       return bld->undef;
 531
 532    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 533       return LLVMConstFDiv(a, b);
 534
 535    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 536       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 537
 538    return LLVMBuildFDiv(bld->builder, a, b, "");
 539 }
 540
 541
 542 /**
 543  * Linear interpolation.
 544  *
 545  * This also works for integer values with a few caveats.
 546  *
 547  * @sa http://www.stereopsis.com/doubleblend.html
 548  */
 549 LLVMValueRef
 550 lp_build_lerp(struct lp_build_context *bld,
 551               LLVMValueRef x,
 552               LLVMValueRef v0,
 553               LLVMValueRef v1)
 554 {
 555    LLVMValueRef delta;
 556    LLVMValueRef res;
 557
 558    delta = lp_build_sub(bld, v1, v0);
 559
 560    res = lp_build_mul(bld, x, delta);
 561
 562    res = lp_build_add(bld, v0, res);
 563
 564    if(bld->type.fixed)
 565       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 566        * but it will be wrong for other uses. Basically we need a more
 567        * powerful lp_type, capable of further distinguishing the values
 568        * interpretation from the value storage. */
 569       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 570
 571    return res;
 572 }
 573
 574
 575 LLVMValueRef
 576 lp_build_lerp_2d(struct lp_build_context *bld,
 577                  LLVMValueRef x,
 578                  LLVMValueRef y,
 579                  LLVMValueRef v00,
 580                  LLVMValueRef v01,
 581                  LLVMValueRef v10,
 582                  LLVMValueRef v11)
 583 {
 584    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 585    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 586    return lp_build_lerp(bld, y, v0, v1);
 587 }
 588
 589
 590 /**
 591  * Generate min(a, b)
 592  * Do checks for special cases.
 593  */
 594 LLVMValueRef
 595 lp_build_min(struct lp_build_context *bld,
 596              LLVMValueRef a,
 597              LLVMValueRef b)
 598 {
 599    if(a == bld->undef || b == bld->undef)
 600       return bld->undef;
 601
 602    if(a == b)
 603       return a;
 604
 605    if(bld->type.norm) {
 606       if(a == bld->zero || b == bld->zero)
 607          return bld->zero;
 608       if(a == bld->one)
 609          return b;
 610       if(b == bld->one)
 611          return a;
 612    }
 613
 614    return lp_build_min_simple(bld, a, b);
 615 }
 616
 617
 618 /**
 619  * Generate max(a, b)
 620  * Do checks for special cases.
 621  */
 622 LLVMValueRef
 623 lp_build_max(struct lp_build_context *bld,
 624              LLVMValueRef a,
 625              LLVMValueRef b)
 626 {
 627    if(a == bld->undef || b == bld->undef)
 628       return bld->undef;
 629
 630    if(a == b)
 631       return a;
 632
 633    if(bld->type.norm) {
 634       if(a == bld->one || b == bld->one)
 635          return bld->one;
 636       if(a == bld->zero)
 637          return b;
 638       if(b == bld->zero)
 639          return a;
 640    }
 641
 642    return lp_build_max_simple(bld, a, b);
 643 }
 644
 645
 646 /**
 647  * Generate clamp(a, min, max)
 648  * Do checks for special cases.
 649  */
 650 LLVMValueRef
 651 lp_build_clamp(struct lp_build_context *bld,
 652                LLVMValueRef a,
 653                LLVMValueRef min,
 654                LLVMValueRef max)
 655 {
 656    a = lp_build_min(bld, a, max);
 657    a = lp_build_max(bld, a, min);
 658    return a;
 659 }
 660
 661
 662 /**
 663  * Generate abs(a)
 664  */
 665 LLVMValueRef
 666 lp_build_abs(struct lp_build_context *bld,
 667              LLVMValueRef a)
 668 {
 669    const struct lp_type type = bld->type;
 670    LLVMTypeRef vec_type = lp_build_vec_type(type);
 671
 672    if(!type.sign)
 673       return a;
 674
 675    if(type.floating) {
 676       /* Mask out the sign bit */
 677       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 678       unsigned long long absMask = ~(1ULL << (type.width - 1));
 679       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 680       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 681       a = LLVMBuildAnd(bld->builder, a, mask, "");
 682       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 683       return a;
 684    }
 685
 686    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 687       switch(type.width) {
 688       case 8:
 689          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 690       case 16:
 691          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 692       case 32:
 693          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 694       }
 695    }
 696
 697    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 698 }
 699
 700
 701 LLVMValueRef
 702 lp_build_negate(struct lp_build_context *bld,
 703                 LLVMValueRef a)
 704 {
 705    return LLVMBuildNeg(bld->builder, a, "");
 706 }
 707
 708
 709 /** Return -1, 0 or +1 depending on the sign of a */
 710 LLVMValueRef
 711 lp_build_sgn(struct lp_build_context *bld,
 712              LLVMValueRef a)
 713 {
 714    const struct lp_type type = bld->type;
 715    LLVMValueRef cond;
 716    LLVMValueRef res;
 717
 718    /* Handle non-zero case */
 719    if(!type.sign) {
 720       /* if not zero then sign must be positive */
 721       res = bld->one;
 722    }
 723    else if(type.floating) {
 724       LLVMTypeRef vec_type;
 725       LLVMTypeRef int_type;
 726       LLVMValueRef mask;
 727       LLVMValueRef sign;
 728       LLVMValueRef one;
 729       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 730
 731       int_type = lp_build_int_vec_type(type);
 732       vec_type = lp_build_vec_type(type);
 733       mask = lp_build_const_int_vec(type, maskBit);
 734
 735       /* Take the sign bit and add it to 1 constant */
 736       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 737       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 738       one = LLVMConstBitCast(bld->one, int_type);
 739       res = LLVMBuildOr(bld->builder, sign, one, "");
 740       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 741    }
 742    else
 743    {
 744       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 745       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 746       res = lp_build_select(bld, cond, bld->one, minus_one);
 747    }
 748
 749    /* Handle zero */
 750    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 751    res = lp_build_select(bld, cond, bld->zero, res);
 752
 753    return res;
 754 }
 755
 756
 757 /**
 758  * Set the sign of float vector 'a' according to 'sign'.
 759  * If sign==0, return abs(a).
 760  * If sign==1, return -abs(a);
 761  * Other values for sign produce undefined results.
 762  */
 763 LLVMValueRef
 764 lp_build_set_sign(struct lp_build_context *bld,
 765                   LLVMValueRef a, LLVMValueRef sign)
 766 {
 767    const struct lp_type type = bld->type;
 768    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 769    LLVMTypeRef vec_type = lp_build_vec_type(type);
 770    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 771    LLVMValueRef mask = lp_build_const_int_vec(type,
 772                              ~((unsigned long long) 1 << (type.width - 1)));
 773    LLVMValueRef val, res;
 774
 775    assert(type.floating);
 776
 777    /* val = reinterpret_cast<int>(a) */
 778    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 779    /* val = val & mask */
 780    val = LLVMBuildAnd(bld->builder, val, mask, "");
 781    /* sign = sign << shift */
 782    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 783    /* res = val | sign */
 784    res = LLVMBuildOr(bld->builder, val, sign, "");
 785    /* res = reinterpret_cast<float>(res) */
 786    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 787
 788    return res;
 789 }
 790
 791
 792 /**
 793  * Convert vector of (or scalar) int to vector of (or scalar) float.
 794  */
 795 LLVMValueRef
 796 lp_build_int_to_float(struct lp_build_context *bld,
 797                       LLVMValueRef a)
 798 {
 799    const struct lp_type type = bld->type;
 800    LLVMTypeRef vec_type = lp_build_vec_type(type);
 801
 802    assert(type.floating);
 803
 804    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 805 }
 806
 807
 808
 809 enum lp_build_round_sse41_mode
 810 {
 811    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 812    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 813    LP_BUILD_ROUND_SSE41_CEIL = 2,
 814    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 815 };
 816
 817
 818 static INLINE LLVMValueRef
 819 lp_build_round_sse41(struct lp_build_context *bld,
 820                      LLVMValueRef a,
 821                      enum lp_build_round_sse41_mode mode)
 822 {
 823    const struct lp_type type = bld->type;
 824    LLVMTypeRef vec_type = lp_build_vec_type(type);
 825    const char *intrinsic;
 826
 827    assert(type.floating);
 828    assert(type.width*type.length == 128);
 829    assert(lp_check_value(type, a));
 830    assert(util_cpu_caps.has_sse4_1);
 831
 832    switch(type.width) {
 833    case 32:
 834       intrinsic = "llvm.x86.sse41.round.ps";
 835       break;
 836    case 64:
 837       intrinsic = "llvm.x86.sse41.round.pd";
 838       break;
 839    default:
 840       assert(0);
 841       return bld->undef;
 842    }
 843
 844    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 845                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 846 }
 847
 848
 849 /**
 850  * Return the integer part of a float (vector) value.  The returned value is
 851  * a float (vector).
 852  * Ex: trunc(-1.5) = 1.0
 853  */
 854 LLVMValueRef
 855 lp_build_trunc(struct lp_build_context *bld,
 856                LLVMValueRef a)
 857 {
 858    const struct lp_type type = bld->type;
 859
 860    assert(type.floating);
 861    assert(lp_check_value(type, a));
 862
 863    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 864       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 865    else {
 866       LLVMTypeRef vec_type = lp_build_vec_type(type);
 867       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 868       LLVMValueRef res;
 869       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 870       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 871       return res;
 872    }
 873 }
 874
 875
 876 /**
 877  * Return float (vector) rounded to nearest integer (vector).  The returned
 878  * value is a float (vector).
 879  * Ex: round(0.9) = 1.0
 880  * Ex: round(-1.5) = -2.0
 881  */
 882 LLVMValueRef
 883 lp_build_round(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 && type.width*type.length == 128)
 892       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 893    else {
 894       LLVMTypeRef vec_type = lp_build_vec_type(type);
 895       LLVMValueRef res;
 896       res = lp_build_iround(bld, a);
 897       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 898       return res;
 899    }
 900 }
 901
 902
 903 /**
 904  * Return floor of float (vector), result is a float (vector)
 905  * Ex: floor(1.1) = 1.0
 906  * Ex: floor(-1.1) = -2.0
 907  */
 908 LLVMValueRef
 909 lp_build_floor(struct lp_build_context *bld,
 910                LLVMValueRef a)
 911 {
 912    const struct lp_type type = bld->type;
 913
 914    assert(type.floating);
 915    assert(lp_check_value(type, a));
 916
 917    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 918       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 919    else {
 920       LLVMTypeRef vec_type = lp_build_vec_type(type);
 921       LLVMValueRef res;
 922       res = lp_build_ifloor(bld, a);
 923       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 924       return res;
 925    }
 926 }
 927
 928
 929 /**
 930  * Return ceiling of float (vector), returning float (vector).
 931  * Ex: ceil( 1.1) = 2.0
 932  * Ex: ceil(-1.1) = -1.0
 933  */
 934 LLVMValueRef
 935 lp_build_ceil(struct lp_build_context *bld,
 936               LLVMValueRef a)
 937 {
 938    const struct lp_type type = bld->type;
 939
 940    assert(type.floating);
 941    assert(lp_check_value(type, a));
 942
 943    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 944       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 945    else {
 946       LLVMTypeRef vec_type = lp_build_vec_type(type);
 947       LLVMValueRef res;
 948       res = lp_build_iceil(bld, a);
 949       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 950       return res;
 951    }
 952 }
 953
 954
 955 /**
 956  * Return fractional part of 'a' computed as a - floor(a)
 957  * Typically used in texture coord arithmetic.
 958  */
 959 LLVMValueRef
 960 lp_build_fract(struct lp_build_context *bld,
 961                LLVMValueRef a)
 962 {
 963    assert(bld->type.floating);
 964    return lp_build_sub(bld, a, lp_build_floor(bld, a));
 965 }
 966
 967
 968 /**
 969  * Return the integer part of a float (vector) value.  The returned value is
 970  * an integer (vector).
 971  * Ex: itrunc(-1.5) = 1
 972  */
 973 LLVMValueRef
 974 lp_build_itrunc(struct lp_build_context *bld,
 975                 LLVMValueRef a)
 976 {
 977    const struct lp_type type = bld->type;
 978    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 979
 980    assert(type.floating);
 981    assert(lp_check_value(type, a));
 982
 983    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 984 }
 985
 986
 987 /**
 988  * Return float (vector) rounded to nearest integer (vector).  The returned
 989  * value is an integer (vector).
 990  * Ex: iround(0.9) = 1
 991  * Ex: iround(-1.5) = -2
 992  */
 993 LLVMValueRef
 994 lp_build_iround(struct lp_build_context *bld,
 995                 LLVMValueRef a)
 996 {
 997    const struct lp_type type = bld->type;
 998    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 999    LLVMValueRef res;
1000
1001    assert(type.floating);
1002
1003    assert(lp_check_value(type, a));
1004
1005    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1006       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1007    }
1008    else {
1009       LLVMTypeRef vec_type = lp_build_vec_type(type);
1010       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1011       LLVMValueRef sign;
1012       LLVMValueRef half;
1013
1014       /* get sign bit */
1015       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1016       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1017
1018       /* sign * 0.5 */
1019       half = lp_build_const_vec(type, 0.5);
1020       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1021       half = LLVMBuildOr(bld->builder, sign, half, "");
1022       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1023
1024       res = LLVMBuildAdd(bld->builder, a, half, "");
1025    }
1026
1027    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1028
1029    return res;
1030 }
1031
1032
1033 /**
1034  * Return floor of float (vector), result is an int (vector)
1035  * Ex: ifloor(1.1) = 1.0
1036  * Ex: ifloor(-1.1) = -2.0
1037  */
1038 LLVMValueRef
1039 lp_build_ifloor(struct lp_build_context *bld,
1040                 LLVMValueRef a)
1041 {
1042    const struct lp_type type = bld->type;
1043    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1044    LLVMValueRef res;
1045
1046    assert(type.floating);
1047    assert(lp_check_value(type, a));
1048
1049    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1050       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1051    }
1052    else {
1053       /* Take the sign bit and add it to 1 constant */
1054       LLVMTypeRef vec_type = lp_build_vec_type(type);
1055       unsigned mantissa = lp_mantissa(type);
1056       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1057       LLVMValueRef sign;
1058       LLVMValueRef offset;
1059
1060       /* sign = a < 0 ? ~0 : 0 */
1061       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1062       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1063       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1064
1065       /* offset = -0.99999(9)f */
1066       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1067       offset = LLVMConstBitCast(offset, int_vec_type);
1068
1069       /* offset = a < 0 ? offset : 0.0f */
1070       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1071       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1072
1073       res = LLVMBuildAdd(bld->builder, a, offset, "ifloor.res");
1074    }
1075
1076    /* round to nearest (toward zero) */
1077    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1078
1079    return res;
1080 }
1081
1082
1083 /**
1084  * Return ceiling of float (vector), returning int (vector).
1085  * Ex: iceil( 1.1) = 2
1086  * Ex: iceil(-1.1) = -1
1087  */
1088 LLVMValueRef
1089 lp_build_iceil(struct lp_build_context *bld,
1090                LLVMValueRef a)
1091 {
1092    const struct lp_type type = bld->type;
1093    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1094    LLVMValueRef res;
1095
1096    assert(type.floating);
1097    assert(lp_check_value(type, a));
1098
1099    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1100       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1101    }
1102    else {
1103       LLVMTypeRef vec_type = lp_build_vec_type(type);
1104       unsigned mantissa = lp_mantissa(type);
1105       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1106       LLVMValueRef sign;
1107       LLVMValueRef offset;
1108
1109       /* sign = a < 0 ? 0 : ~0 */
1110       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1111       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1112       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1113       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1114
1115       /* offset = 0.99999(9)f */
1116       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1117       offset = LLVMConstBitCast(offset, int_vec_type);
1118
1119       /* offset = a < 0 ? 0.0 : offset */
1120       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1121       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1122
1123       res = LLVMBuildAdd(bld->builder, a, offset, "iceil.res");
1124    }
1125
1126    /* round to nearest (toward zero) */
1127    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1128
1129    return res;
1130 }
1131
1132
1133 LLVMValueRef
1134 lp_build_sqrt(struct lp_build_context *bld,
1135               LLVMValueRef a)
1136 {
1137    const struct lp_type type = bld->type;
1138    LLVMTypeRef vec_type = lp_build_vec_type(type);
1139    char intrinsic[32];
1140
1141    /* TODO: optimize the constant case */
1142    /* TODO: optimize the constant case */
1143
1144    assert(type.floating);
1145    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1146
1147    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1148 }
1149
1150
1151 LLVMValueRef
1152 lp_build_rcp(struct lp_build_context *bld,
1153              LLVMValueRef a)
1154 {
1155    const struct lp_type type = bld->type;
1156
1157    if(a == bld->zero)
1158       return bld->undef;
1159    if(a == bld->one)
1160       return bld->one;
1161    if(a == bld->undef)
1162       return bld->undef;
1163
1164    assert(type.floating);
1165
1166    if(LLVMIsConstant(a))
1167       return LLVMConstFDiv(bld->one, a);
1168
1169    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1170       /*
1171        * XXX: Added precision is not always necessary, so only enable this
1172        * when we have a better system in place to track minimum precision.
1173        */
1174
1175 #if 0
1176       /*
1177        * Do one Newton-Raphson step to improve precision:
1178        *
1179        *   x1 = (2 - a * rcp(a)) * rcp(a)
1180        */
1181
1182       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1183       LLVMValueRef rcp_a;
1184       LLVMValueRef res;
1185
1186       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1187
1188       res = LLVMBuildMul(bld->builder, a, rcp_a, "");
1189       res = LLVMBuildSub(bld->builder, two, res, "");
1190       res = LLVMBuildMul(bld->builder, res, rcp_a, "");
1191
1192       return rcp_a;
1193 #else
1194       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1195 #endif
1196    }
1197
1198    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1199 }
1200
1201
1202 /**
1203  * Generate 1/sqrt(a)
1204  */
1205 LLVMValueRef
1206 lp_build_rsqrt(struct lp_build_context *bld,
1207                LLVMValueRef a)
1208 {
1209    const struct lp_type type = bld->type;
1210
1211    assert(type.floating);
1212
1213    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1214       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1215
1216    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1217 }
1218
1219
1220 static inline LLVMValueRef
1221 lp_build_const_v4si(unsigned long value)
1222 {
1223    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1224    LLVMValueRef elements[4] = { element, element, element, element };
1225    return LLVMConstVector(elements, 4);
1226 }
1227
1228 static inline LLVMValueRef
1229 lp_build_const_v4sf(float value)
1230 {
1231    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1232    LLVMValueRef elements[4] = { element, element, element, element };
1233    return LLVMConstVector(elements, 4);
1234 }
1235
1236
1237 /**
1238  * Generate sin(a) using SSE2
1239  */
1240 LLVMValueRef
1241 lp_build_sin(struct lp_build_context *bld,
1242              LLVMValueRef a)
1243 {
1244    struct lp_type int_type = lp_int_type(bld->type);
1245    LLVMBuilderRef b = bld->builder;
1246    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1247    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1248
1249    /*
1250     *  take the absolute value,
1251     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1252     */
1253
1254    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1255    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1256
1257    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1258    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1259
1260    /*
1261     * extract the sign bit (upper one)
1262     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1263     */
1264    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1265    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1266
1267    /*
1268     * scale by 4/Pi
1269     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1270     */
1271
1272    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1273    LLVMValueRef scale_y = LLVMBuildMul(b, x_abs, FOPi, "scale_y");
1274
1275    /*
1276     * store the integer part of y in mm0
1277     * emm2 = _mm_cvttps_epi32(y);
1278     */
1279
1280    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1281
1282    /*
1283     * j=(j+1) & (~1) (see the cephes sources)
1284     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1285     */
1286
1287    LLVMValueRef all_one = lp_build_const_v4si(1);
1288    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1289    /*
1290     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1291     */
1292    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1293    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1294
1295    /*
1296     * y = _mm_cvtepi32_ps(emm2);
1297     */
1298    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1299
1300    /* get the swap sign flag
1301     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1302     */
1303    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1304    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1305
1306    /*
1307     * emm2 = _mm_slli_epi32(emm0, 29);
1308     */
1309    LLVMValueRef const_29 = lp_build_const_v4si(29);
1310    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1311
1312    /*
1313     * get the polynom selection mask
1314     * there is one polynom for 0 <= x <= Pi/4
1315     * and another one for Pi/4<x<=Pi/2
1316     * Both branches will be computed.
1317     *
1318     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1319     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1320     */
1321
1322    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1323    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1324    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1325                                              emm2_3, lp_build_const_v4si(0));
1326    /*
1327     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1328     */
1329    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1330
1331    /*
1332     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1333     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1334     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1335     */
1336    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1337    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1338    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1339
1340    /*
1341     * The magic pass: "Extended precision modular arithmetic"
1342     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1343     * xmm1 = _mm_mul_ps(y, xmm1);
1344     * xmm2 = _mm_mul_ps(y, xmm2);
1345     * xmm3 = _mm_mul_ps(y, xmm3);
1346     */
1347    LLVMValueRef xmm1 = LLVMBuildMul(b, y_2, DP1, "xmm1");
1348    LLVMValueRef xmm2 = LLVMBuildMul(b, y_2, DP2, "xmm2");
1349    LLVMValueRef xmm3 = LLVMBuildMul(b, y_2, DP3, "xmm3");
1350
1351    /*
1352     * x = _mm_add_ps(x, xmm1);
1353     * x = _mm_add_ps(x, xmm2);
1354     * x = _mm_add_ps(x, xmm3);
1355     */
1356
1357    LLVMValueRef x_1 = LLVMBuildAdd(b, x_abs, xmm1, "x_1");
1358    LLVMValueRef x_2 = LLVMBuildAdd(b, x_1, xmm2, "x_2");
1359    LLVMValueRef x_3 = LLVMBuildAdd(b, x_2, xmm3, "x_3");
1360
1361    /*
1362     * Evaluate the first polynom  (0 <= x <= Pi/4)
1363     *
1364     * z = _mm_mul_ps(x,x);
1365     */
1366    LLVMValueRef z = LLVMBuildMul(b, x_3, x_3, "z");
1367
1368    /*
1369     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1370     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1371     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1372     */
1373    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1374    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1375    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1376
1377    /*
1378     * y = *(v4sf*)_ps_coscof_p0;
1379     * y = _mm_mul_ps(y, z);
1380     */
1381    LLVMValueRef y_3 = LLVMBuildMul(b, z, coscof_p0, "y_3");
1382    LLVMValueRef y_4 = LLVMBuildAdd(b, y_3, coscof_p1, "y_4");
1383    LLVMValueRef y_5 = LLVMBuildMul(b, y_4, z, "y_5");
1384    LLVMValueRef y_6 = LLVMBuildAdd(b, y_5, coscof_p2, "y_6");
1385    LLVMValueRef y_7 = LLVMBuildMul(b, y_6, z, "y_7");
1386    LLVMValueRef y_8 = LLVMBuildMul(b, y_7, z, "y_8");
1387
1388
1389    /*
1390     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1391     * y = _mm_sub_ps(y, tmp);
1392     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1393     */
1394    LLVMValueRef half = lp_build_const_v4sf(0.5);
1395    LLVMValueRef tmp = LLVMBuildMul(b, z, half, "tmp");
1396    LLVMValueRef y_9 = LLVMBuildSub(b, y_8, tmp, "y_8");
1397    LLVMValueRef one = lp_build_const_v4sf(1.0);
1398    LLVMValueRef y_10 = LLVMBuildAdd(b, y_9, one, "y_9");
1399
1400    /*
1401     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1402     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1403     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1404     */
1405    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1406    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1407    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1408
1409    /*
1410     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1411     *
1412     * y2 = *(v4sf*)_ps_sincof_p0;
1413     * y2 = _mm_mul_ps(y2, z);
1414     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1415     * y2 = _mm_mul_ps(y2, z);
1416     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1417     * y2 = _mm_mul_ps(y2, z);
1418     * y2 = _mm_mul_ps(y2, x);
1419     * y2 = _mm_add_ps(y2, x);
1420     */
1421
1422    LLVMValueRef y2_3 = LLVMBuildMul(b, z, sincof_p0, "y2_3");
1423    LLVMValueRef y2_4 = LLVMBuildAdd(b, y2_3, sincof_p1, "y2_4");
1424    LLVMValueRef y2_5 = LLVMBuildMul(b, y2_4, z, "y2_5");
1425    LLVMValueRef y2_6 = LLVMBuildAdd(b, y2_5, sincof_p2, "y2_6");
1426    LLVMValueRef y2_7 = LLVMBuildMul(b, y2_6, z, "y2_7");
1427    LLVMValueRef y2_8 = LLVMBuildMul(b, y2_7, x_3, "y2_8");
1428    LLVMValueRef y2_9 = LLVMBuildAdd(b, y2_8, x_3, "y2_9");
1429
1430    /*
1431     * select the correct result from the two polynoms
1432     * xmm3 = poly_mask;
1433     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1434     * y = _mm_andnot_ps(xmm3, y);
1435     * y = _mm_add_ps(y,y2);
1436     */
1437    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1438    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1439    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1440    LLVMValueRef inv = lp_build_const_v4si(~0);
1441    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1442    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1443    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1444
1445    /*
1446     * update the sign
1447     * y = _mm_xor_ps(y, sign_bit);
1448     */
1449    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1450    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1451    return y_result;
1452 }
1453
1454
1455 /**
1456  * Generate cos(a) using SSE2
1457  */
1458 LLVMValueRef
1459 lp_build_cos(struct lp_build_context *bld,
1460              LLVMValueRef a)
1461 {
1462    struct lp_type int_type = lp_int_type(bld->type);
1463    LLVMBuilderRef b = bld->builder;
1464    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1465    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1466
1467    /*
1468     *  take the absolute value,
1469     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1470     */
1471
1472    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1473    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1474
1475    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1476    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1477
1478    /*
1479     * scale by 4/Pi
1480     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1481     */
1482
1483    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1484    LLVMValueRef scale_y = LLVMBuildMul(b, x_abs, FOPi, "scale_y");
1485
1486    /*
1487     * store the integer part of y in mm0
1488     * emm2 = _mm_cvttps_epi32(y);
1489     */
1490
1491    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1492
1493    /*
1494     * j=(j+1) & (~1) (see the cephes sources)
1495     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1496     */
1497
1498    LLVMValueRef all_one = lp_build_const_v4si(1);
1499    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1500    /*
1501     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1502     */
1503    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1504    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1505
1506    /*
1507     * y = _mm_cvtepi32_ps(emm2);
1508     */
1509    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1510
1511
1512    /*
1513     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1514     */
1515    LLVMValueRef const_2 = lp_build_const_v4si(2);
1516    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1517
1518
1519    /* get the swap sign flag
1520     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1521     */
1522    LLVMValueRef inv = lp_build_const_v4si(~0);
1523    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1524    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1525    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1526
1527    /*
1528     * emm2 = _mm_slli_epi32(emm0, 29);
1529     */
1530    LLVMValueRef const_29 = lp_build_const_v4si(29);
1531    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1532
1533    /*
1534     * get the polynom selection mask
1535     * there is one polynom for 0 <= x <= Pi/4
1536     * and another one for Pi/4<x<=Pi/2
1537     * Both branches will be computed.
1538     *
1539     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1540     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1541     */
1542
1543    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1544    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1545    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1546                                              emm2_3, lp_build_const_v4si(0));
1547
1548    /*
1549     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1550     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1551     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1552     */
1553    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1554    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1555    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1556
1557    /*
1558     * The magic pass: "Extended precision modular arithmetic"
1559     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1560     * xmm1 = _mm_mul_ps(y, xmm1);
1561     * xmm2 = _mm_mul_ps(y, xmm2);
1562     * xmm3 = _mm_mul_ps(y, xmm3);
1563     */
1564    LLVMValueRef xmm1 = LLVMBuildMul(b, y_2, DP1, "xmm1");
1565    LLVMValueRef xmm2 = LLVMBuildMul(b, y_2, DP2, "xmm2");
1566    LLVMValueRef xmm3 = LLVMBuildMul(b, y_2, DP3, "xmm3");
1567
1568    /*
1569     * x = _mm_add_ps(x, xmm1);
1570     * x = _mm_add_ps(x, xmm2);
1571     * x = _mm_add_ps(x, xmm3);
1572     */
1573
1574    LLVMValueRef x_1 = LLVMBuildAdd(b, x_abs, xmm1, "x_1");
1575    LLVMValueRef x_2 = LLVMBuildAdd(b, x_1, xmm2, "x_2");
1576    LLVMValueRef x_3 = LLVMBuildAdd(b, x_2, xmm3, "x_3");
1577
1578    /*
1579     * Evaluate the first polynom  (0 <= x <= Pi/4)
1580     *
1581     * z = _mm_mul_ps(x,x);
1582     */
1583    LLVMValueRef z = LLVMBuildMul(b, x_3, x_3, "z");
1584
1585    /*
1586     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1587     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1588     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1589     */
1590    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1591    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1592    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1593
1594    /*
1595     * y = *(v4sf*)_ps_coscof_p0;
1596     * y = _mm_mul_ps(y, z);
1597     */
1598    LLVMValueRef y_3 = LLVMBuildMul(b, z, coscof_p0, "y_3");
1599    LLVMValueRef y_4 = LLVMBuildAdd(b, y_3, coscof_p1, "y_4");
1600    LLVMValueRef y_5 = LLVMBuildMul(b, y_4, z, "y_5");
1601    LLVMValueRef y_6 = LLVMBuildAdd(b, y_5, coscof_p2, "y_6");
1602    LLVMValueRef y_7 = LLVMBuildMul(b, y_6, z, "y_7");
1603    LLVMValueRef y_8 = LLVMBuildMul(b, y_7, z, "y_8");
1604
1605
1606    /*
1607     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1608     * y = _mm_sub_ps(y, tmp);
1609     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1610     */
1611    LLVMValueRef half = lp_build_const_v4sf(0.5);
1612    LLVMValueRef tmp = LLVMBuildMul(b, z, half, "tmp");
1613    LLVMValueRef y_9 = LLVMBuildSub(b, y_8, tmp, "y_8");
1614    LLVMValueRef one = lp_build_const_v4sf(1.0);
1615    LLVMValueRef y_10 = LLVMBuildAdd(b, y_9, one, "y_9");
1616
1617    /*
1618     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1619     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1620     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1621     */
1622    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1623    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1624    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1625
1626    /*
1627     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1628     *
1629     * y2 = *(v4sf*)_ps_sincof_p0;
1630     * y2 = _mm_mul_ps(y2, z);
1631     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1632     * y2 = _mm_mul_ps(y2, z);
1633     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1634     * y2 = _mm_mul_ps(y2, z);
1635     * y2 = _mm_mul_ps(y2, x);
1636     * y2 = _mm_add_ps(y2, x);
1637     */
1638
1639    LLVMValueRef y2_3 = LLVMBuildMul(b, z, sincof_p0, "y2_3");
1640    LLVMValueRef y2_4 = LLVMBuildAdd(b, y2_3, sincof_p1, "y2_4");
1641    LLVMValueRef y2_5 = LLVMBuildMul(b, y2_4, z, "y2_5");
1642    LLVMValueRef y2_6 = LLVMBuildAdd(b, y2_5, sincof_p2, "y2_6");
1643    LLVMValueRef y2_7 = LLVMBuildMul(b, y2_6, z, "y2_7");
1644    LLVMValueRef y2_8 = LLVMBuildMul(b, y2_7, x_3, "y2_8");
1645    LLVMValueRef y2_9 = LLVMBuildAdd(b, y2_8, x_3, "y2_9");
1646
1647    /*
1648     * select the correct result from the two polynoms
1649     * xmm3 = poly_mask;
1650     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1651     * y = _mm_andnot_ps(xmm3, y);
1652     * y = _mm_add_ps(y,y2);
1653     */
1654    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1655    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1656    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1657    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1658    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1659    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1660
1661    /*
1662     * update the sign
1663     * y = _mm_xor_ps(y, sign_bit);
1664     */
1665    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1666    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1667    return y_result;
1668 }
1669
1670
1671 /**
1672  * Generate pow(x, y)
1673  */
1674 LLVMValueRef
1675 lp_build_pow(struct lp_build_context *bld,
1676              LLVMValueRef x,
1677              LLVMValueRef y)
1678 {
1679    /* TODO: optimize the constant case */
1680    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1681       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1682                    __FUNCTION__);
1683
1684    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1685 }
1686
1687
1688 /**
1689  * Generate exp(x)
1690  */
1691 LLVMValueRef
1692 lp_build_exp(struct lp_build_context *bld,
1693              LLVMValueRef x)
1694 {
1695    /* log2(e) = 1/log(2) */
1696    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1697
1698    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1699 }
1700
1701
1702 /**
1703  * Generate log(x)
1704  */
1705 LLVMValueRef
1706 lp_build_log(struct lp_build_context *bld,
1707              LLVMValueRef x)
1708 {
1709    /* log(2) */
1710    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1711
1712    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1713 }
1714
1715
1716 #define EXP_POLY_DEGREE 3
1717 #define LOG_POLY_DEGREE 5
1718
1719
1720 /**
1721  * Generate polynomial.
1722  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1723  */
1724 static LLVMValueRef
1725 lp_build_polynomial(struct lp_build_context *bld,
1726                     LLVMValueRef x,
1727                     const double *coeffs,
1728                     unsigned num_coeffs)
1729 {
1730    const struct lp_type type = bld->type;
1731    LLVMValueRef res = NULL;
1732    unsigned i;
1733
1734    /* TODO: optimize the constant case */
1735    if(LLVMIsConstant(x))
1736       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1737                    __FUNCTION__);
1738
1739    for (i = num_coeffs; i--; ) {
1740       LLVMValueRef coeff;
1741
1742       coeff = lp_build_const_vec(type, coeffs[i]);
1743
1744       if(res)
1745          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1746       else
1747          res = coeff;
1748    }
1749
1750    if(res)
1751       return res;
1752    else
1753       return bld->undef;
1754 }
1755
1756
1757 /**
1758  * Minimax polynomial fit of 2**x, in range [0, 1[
1759  */
1760 const double lp_build_exp2_polynomial[] = {
1761 #if EXP_POLY_DEGREE == 5
1762    0.999999999690134838155,
1763    0.583974334321735217258,
1764    0.164553105719676828492,
1765    0.0292811063701710962255,
1766    0.00354944426657875141846,
1767    0.000296253726543423377365
1768 #elif EXP_POLY_DEGREE == 4
1769    1.00000001502262084505,
1770    0.563586057338685991394,
1771    0.150436017652442413623,
1772    0.0243220604213317927308,
1773    0.0025359088446580436489
1774 #elif EXP_POLY_DEGREE == 3
1775    0.999925218562710312959,
1776    0.695833540494823811697,
1777    0.226067155427249155588,
1778    0.0780245226406372992967
1779 #elif EXP_POLY_DEGREE == 2
1780    1.00172476321474503578,
1781    0.657636275736077639316,
1782    0.33718943461968720704
1783 #else
1784 #error
1785 #endif
1786 };
1787
1788
1789 void
1790 lp_build_exp2_approx(struct lp_build_context *bld,
1791                      LLVMValueRef x,
1792                      LLVMValueRef *p_exp2_int_part,
1793                      LLVMValueRef *p_frac_part,
1794                      LLVMValueRef *p_exp2)
1795 {
1796    const struct lp_type type = bld->type;
1797    LLVMTypeRef vec_type = lp_build_vec_type(type);
1798    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1799    LLVMValueRef ipart = NULL;
1800    LLVMValueRef fpart = NULL;
1801    LLVMValueRef expipart = NULL;
1802    LLVMValueRef expfpart = NULL;
1803    LLVMValueRef res = NULL;
1804
1805    if(p_exp2_int_part || p_frac_part || p_exp2) {
1806       /* TODO: optimize the constant case */
1807       if(LLVMIsConstant(x))
1808          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1809                       __FUNCTION__);
1810
1811       assert(type.floating && type.width == 32);
1812
1813       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1814       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1815
1816       /* ipart = floor(x) */
1817       ipart = lp_build_floor(bld, x);
1818
1819       /* fpart = x - ipart */
1820       fpart = LLVMBuildSub(bld->builder, x, ipart, "");
1821    }
1822
1823    if(p_exp2_int_part || p_exp2) {
1824       /* expipart = (float) (1 << ipart) */
1825       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1826       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1827       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1828       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1829    }
1830
1831    if(p_exp2) {
1832       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1833                                      Elements(lp_build_exp2_polynomial));
1834
1835       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1836    }
1837
1838    if(p_exp2_int_part)
1839       *p_exp2_int_part = expipart;
1840
1841    if(p_frac_part)
1842       *p_frac_part = fpart;
1843
1844    if(p_exp2)
1845       *p_exp2 = res;
1846 }
1847
1848
1849 LLVMValueRef
1850 lp_build_exp2(struct lp_build_context *bld,
1851               LLVMValueRef x)
1852 {
1853    LLVMValueRef res;
1854    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1855    return res;
1856 }
1857
1858
1859 /**
1860  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1861  * These coefficients can be generate with
1862  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1863  */
1864 const double lp_build_log2_polynomial[] = {
1865 #if LOG_POLY_DEGREE == 6
1866    3.11578814719469302614,
1867    -3.32419399085241980044,
1868    2.59883907202499966007,
1869    -1.23152682416275988241,
1870    0.318212422185251071475,
1871    -0.0344359067839062357313
1872 #elif LOG_POLY_DEGREE == 5
1873    2.8882704548164776201,
1874    -2.52074962577807006663,
1875    1.48116647521213171641,
1876    -0.465725644288844778798,
1877    0.0596515482674574969533
1878 #elif LOG_POLY_DEGREE == 4
1879    2.61761038894603480148,
1880    -1.75647175389045657003,
1881    0.688243882994381274313,
1882    -0.107254423828329604454
1883 #elif LOG_POLY_DEGREE == 3
1884    2.28330284476918490682,
1885    -1.04913055217340124191,
1886    0.204446009836232697516
1887 #else
1888 #error
1889 #endif
1890 };
1891
1892
1893 /**
1894  * See http://www.devmaster.net/forums/showthread.php?p=43580
1895  */
1896 void
1897 lp_build_log2_approx(struct lp_build_context *bld,
1898                      LLVMValueRef x,
1899                      LLVMValueRef *p_exp,
1900                      LLVMValueRef *p_floor_log2,
1901                      LLVMValueRef *p_log2)
1902 {
1903    const struct lp_type type = bld->type;
1904    LLVMTypeRef vec_type = lp_build_vec_type(type);
1905    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1906
1907    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
1908    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
1909    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1910
1911    LLVMValueRef i = NULL;
1912    LLVMValueRef exp = NULL;
1913    LLVMValueRef mant = NULL;
1914    LLVMValueRef logexp = NULL;
1915    LLVMValueRef logmant = NULL;
1916    LLVMValueRef res = NULL;
1917
1918    if(p_exp || p_floor_log2 || p_log2) {
1919       /* TODO: optimize the constant case */
1920       if(LLVMIsConstant(x))
1921          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1922                       __FUNCTION__);
1923
1924       assert(type.floating && type.width == 32);
1925
1926       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1927
1928       /* exp = (float) exponent(x) */
1929       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1930    }
1931
1932    if(p_floor_log2 || p_log2) {
1933       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
1934       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
1935       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1936    }
1937
1938    if(p_log2) {
1939       /* mant = (float) mantissa(x) */
1940       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1941       mant = LLVMBuildOr(bld->builder, mant, one, "");
1942       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1943
1944       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1945                                     Elements(lp_build_log2_polynomial));
1946
1947       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1948       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1949
1950       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1951    }
1952
1953    if(p_exp) {
1954       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
1955       *p_exp = exp;
1956    }
1957
1958    if(p_floor_log2)
1959       *p_floor_log2 = logexp;
1960
1961    if(p_log2)
1962       *p_log2 = res;
1963 }
1964
1965
1966 LLVMValueRef
1967 lp_build_log2(struct lp_build_context *bld,
1968               LLVMValueRef x)
1969 {
1970    LLVMValueRef res;
1971    lp_build_log2_approx(bld, x, NULL, NULL, &res);
1972    return res;
1973 }