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_debug.h"
  60 #include "lp_bld_arit.h"
  61
  62
  63 /**
  64  * Generate min(a, b)
  65  * No checks for special case values of a or b = 1 or 0 are done.
  66  */
  67 static LLVMValueRef
  68 lp_build_min_simple(struct lp_build_context *bld,
  69                     LLVMValueRef a,
  70                     LLVMValueRef b)
  71 {
  72    const struct lp_type type = bld->type;
  73    const char *intrinsic = NULL;
  74    LLVMValueRef cond;
  75
  76    /* TODO: optimize the constant case */
  77
  78    if(type.width * type.length == 128) {
  79       if(type.floating) {
  80          if(type.width == 32 && util_cpu_caps.has_sse)
  81             intrinsic = "llvm.x86.sse.min.ps";
  82          if(type.width == 64 && util_cpu_caps.has_sse2)
  83             intrinsic = "llvm.x86.sse2.min.pd";
  84       }
  85       else {
  86          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  87             intrinsic = "llvm.x86.sse2.pminu.b";
  88          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  89             intrinsic = "llvm.x86.sse41.pminsb";
  90          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  91             intrinsic = "llvm.x86.sse41.pminuw";
  92          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  93             intrinsic = "llvm.x86.sse2.pmins.w";
  94          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  95             intrinsic = "llvm.x86.sse41.pminud";
  96          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  97             intrinsic = "llvm.x86.sse41.pminsd";
  98       }
  99    }
 100
 101    if(intrinsic)
 102       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 103
 104    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 105    return lp_build_select(bld, cond, a, b);
 106 }
 107
 108
 109 /**
 110  * Generate max(a, b)
 111  * No checks for special case values of a or b = 1 or 0 are done.
 112  */
 113 static LLVMValueRef
 114 lp_build_max_simple(struct lp_build_context *bld,
 115                     LLVMValueRef a,
 116                     LLVMValueRef b)
 117 {
 118    const struct lp_type type = bld->type;
 119    const char *intrinsic = NULL;
 120    LLVMValueRef cond;
 121
 122    /* TODO: optimize the constant case */
 123
 124    if(type.width * type.length == 128) {
 125       if(type.floating) {
 126          if(type.width == 32 && util_cpu_caps.has_sse)
 127             intrinsic = "llvm.x86.sse.max.ps";
 128          if(type.width == 64 && util_cpu_caps.has_sse2)
 129             intrinsic = "llvm.x86.sse2.max.pd";
 130       }
 131       else {
 132          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 133             intrinsic = "llvm.x86.sse2.pmaxu.b";
 134          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 135             intrinsic = "llvm.x86.sse41.pmaxsb";
 136          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 137             intrinsic = "llvm.x86.sse41.pmaxuw";
 138          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 139             intrinsic = "llvm.x86.sse2.pmaxs.w";
 140          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 141             intrinsic = "llvm.x86.sse41.pmaxud";
 142          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 143             intrinsic = "llvm.x86.sse41.pmaxsd";
 144       }
 145    }
 146
 147    if(intrinsic)
 148       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 149
 150    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 151    return lp_build_select(bld, cond, a, b);
 152 }
 153
 154
 155 /**
 156  * Generate 1 - a, or ~a depending on bld->type.
 157  */
 158 LLVMValueRef
 159 lp_build_comp(struct lp_build_context *bld,
 160               LLVMValueRef a)
 161 {
 162    const struct lp_type type = bld->type;
 163
 164    if(a == bld->one)
 165       return bld->zero;
 166    if(a == bld->zero)
 167       return bld->one;
 168
 169    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 170       if(LLVMIsConstant(a))
 171          return LLVMConstNot(a);
 172       else
 173          return LLVMBuildNot(bld->builder, a, "");
 174    }
 175
 176    if(LLVMIsConstant(a))
 177       return LLVMConstSub(bld->one, a);
 178    else
 179       return LLVMBuildSub(bld->builder, bld->one, a, "");
 180 }
 181
 182
 183 /**
 184  * Generate a + b
 185  */
 186 LLVMValueRef
 187 lp_build_add(struct lp_build_context *bld,
 188              LLVMValueRef a,
 189              LLVMValueRef b)
 190 {
 191    const struct lp_type type = bld->type;
 192    LLVMValueRef res;
 193
 194    if(a == bld->zero)
 195       return b;
 196    if(b == bld->zero)
 197       return a;
 198    if(a == bld->undef || b == bld->undef)
 199       return bld->undef;
 200
 201    if(bld->type.norm) {
 202       const char *intrinsic = NULL;
 203
 204       if(a == bld->one || b == bld->one)
 205         return bld->one;
 206
 207       if(util_cpu_caps.has_sse2 &&
 208          type.width * type.length == 128 &&
 209          !type.floating && !type.fixed) {
 210          if(type.width == 8)
 211             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 212          if(type.width == 16)
 213             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 214       }
 215
 216       if(intrinsic)
 217          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 218    }
 219
 220    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 221       res = LLVMConstAdd(a, b);
 222    else
 223       res = LLVMBuildAdd(bld->builder, a, b, "");
 224
 225    /* clamp to ceiling of 1.0 */
 226    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 227       res = lp_build_min_simple(bld, res, bld->one);
 228
 229    /* XXX clamp to floor of -1 or 0??? */
 230
 231    return res;
 232 }
 233
 234
 235 /** Return the sum of the elements of a */
 236 LLVMValueRef
 237 lp_build_sum_vector(struct lp_build_context *bld,
 238                     LLVMValueRef a)
 239 {
 240    const struct lp_type type = bld->type;
 241    LLVMValueRef index, res;
 242    unsigned i;
 243
 244    if (a == bld->zero)
 245       return bld->zero;
 246    if (a == bld->undef)
 247       return bld->undef;
 248    assert(type.length > 1);
 249
 250    assert(!bld->type.norm);
 251
 252    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 253    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 254
 255    for (i = 1; i < type.length; i++) {
 256       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 257       res = LLVMBuildAdd(bld->builder, res,
 258                          LLVMBuildExtractElement(bld->builder, a, index, ""),
 259                          "");
 260    }
 261
 262    return res;
 263 }
 264
 265
 266 /**
 267  * Generate a - b
 268  */
 269 LLVMValueRef
 270 lp_build_sub(struct lp_build_context *bld,
 271              LLVMValueRef a,
 272              LLVMValueRef b)
 273 {
 274    const struct lp_type type = bld->type;
 275    LLVMValueRef res;
 276
 277    if(b == bld->zero)
 278       return a;
 279    if(a == bld->undef || b == bld->undef)
 280       return bld->undef;
 281    if(a == b)
 282       return bld->zero;
 283
 284    if(bld->type.norm) {
 285       const char *intrinsic = NULL;
 286
 287       if(b == bld->one)
 288         return bld->zero;
 289
 290       if(util_cpu_caps.has_sse2 &&
 291          type.width * type.length == 128 &&
 292          !type.floating && !type.fixed) {
 293          if(type.width == 8)
 294             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 295          if(type.width == 16)
 296             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 297       }
 298
 299       if(intrinsic)
 300          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 301    }
 302
 303    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 304       res = LLVMConstSub(a, b);
 305    else
 306       res = LLVMBuildSub(bld->builder, a, b, "");
 307
 308    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 309       res = lp_build_max_simple(bld, res, bld->zero);
 310
 311    return res;
 312 }
 313
 314
 315 /**
 316  * Normalized 8bit multiplication.
 317  *
 318  * - alpha plus one
 319  *
 320  *     makes the following approximation to the division (Sree)
 321  *
 322  *       a*b/255 ~= (a*(b + 1)) >> 256
 323  *
 324  *     which is the fastest method that satisfies the following OpenGL criteria
 325  *
 326  *       0*0 = 0 and 255*255 = 255
 327  *
 328  * - geometric series
 329  *
 330  *     takes the geometric series approximation to the division
 331  *
 332  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 333  *
 334  *     in this case just the first two terms to fit in 16bit arithmetic
 335  *
 336  *       t/255 ~= (t + (t >> 8)) >> 8
 337  *
 338  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 339  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 340  *     must be used
 341  *
 342  * - geometric series plus rounding
 343  *
 344  *     when using a geometric series division instead of truncating the result
 345  *     use roundoff in the approximation (Jim Blinn)
 346  *
 347  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 348  *
 349  *     achieving the exact results
 350  *
 351  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 352  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 353  * @sa Michael Herf, The "double blend trick", May 2000,
 354  *     http://www.stereopsis.com/doubleblend.html
 355  */
 356 static LLVMValueRef
 357 lp_build_mul_u8n(LLVMBuilderRef builder,
 358                  struct lp_type i16_type,
 359                  LLVMValueRef a, LLVMValueRef b)
 360 {
 361    LLVMValueRef c8;
 362    LLVMValueRef ab;
 363
 364    c8 = lp_build_const_int_vec(i16_type, 8);
 365
 366 #if 0
 367
 368    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 369    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 370    ab = LLVMBuildMul(builder, a, b, "");
 371
 372 #else
 373
 374    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 375    ab = LLVMBuildMul(builder, a, b, "");
 376    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 377    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 378
 379 #endif
 380
 381    ab = LLVMBuildLShr(builder, ab, c8, "");
 382
 383    return ab;
 384 }
 385
 386
 387 /**
 388  * Generate a * b
 389  */
 390 LLVMValueRef
 391 lp_build_mul(struct lp_build_context *bld,
 392              LLVMValueRef a,
 393              LLVMValueRef b)
 394 {
 395    const struct lp_type type = bld->type;
 396    LLVMValueRef shift;
 397    LLVMValueRef res;
 398
 399    if(a == bld->zero)
 400       return bld->zero;
 401    if(a == bld->one)
 402       return b;
 403    if(b == bld->zero)
 404       return bld->zero;
 405    if(b == bld->one)
 406       return a;
 407    if(a == bld->undef || b == bld->undef)
 408       return bld->undef;
 409
 410    if(!type.floating && !type.fixed && type.norm) {
 411       if(type.width == 8) {
 412          struct lp_type i16_type = lp_wider_type(type);
 413          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 414
 415          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 416          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 417
 418          /* PMULLW, PSRLW, PADDW */
 419          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 420          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 421
 422          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 423
 424          return ab;
 425       }
 426
 427       /* FIXME */
 428       assert(0);
 429    }
 430
 431    if(type.fixed)
 432       shift = lp_build_const_int_vec(type, type.width/2);
 433    else
 434       shift = NULL;
 435
 436    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 437       res =  LLVMConstMul(a, b);
 438       if(shift) {
 439          if(type.sign)
 440             res = LLVMConstAShr(res, shift);
 441          else
 442             res = LLVMConstLShr(res, shift);
 443       }
 444    }
 445    else {
 446       res = LLVMBuildMul(bld->builder, a, b, "");
 447       if(shift) {
 448          if(type.sign)
 449             res = LLVMBuildAShr(bld->builder, res, shift, "");
 450          else
 451             res = LLVMBuildLShr(bld->builder, res, shift, "");
 452       }
 453    }
 454
 455    return res;
 456 }
 457
 458
 459 /**
 460  * Small vector x scale multiplication optimization.
 461  */
 462 LLVMValueRef
 463 lp_build_mul_imm(struct lp_build_context *bld,
 464                  LLVMValueRef a,
 465                  int b)
 466 {
 467    LLVMValueRef factor;
 468
 469    if(b == 0)
 470       return bld->zero;
 471
 472    if(b == 1)
 473       return a;
 474
 475    if(b == -1)
 476       return LLVMBuildNeg(bld->builder, a, "");
 477
 478    if(b == 2 && bld->type.floating)
 479       return lp_build_add(bld, a, a);
 480
 481    if(util_is_pot(b)) {
 482       unsigned shift = ffs(b) - 1;
 483
 484       if(bld->type.floating) {
 485 #if 0
 486          /*
 487           * Power of two multiplication by directly manipulating the mantissa.
 488           *
 489           * XXX: This might not be always faster, it will introduce a small error
 490           * for multiplication by zero, and it will produce wrong results
 491           * for Inf and NaN.
 492           */
 493          unsigned mantissa = lp_mantissa(bld->type);
 494          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 495          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 496          a = LLVMBuildAdd(bld->builder, a, factor, "");
 497          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 498          return a;
 499 #endif
 500       }
 501       else {
 502          factor = lp_build_const_vec(bld->type, shift);
 503          return LLVMBuildShl(bld->builder, a, factor, "");
 504       }
 505    }
 506
 507    factor = lp_build_const_vec(bld->type, (double)b);
 508    return lp_build_mul(bld, a, factor);
 509 }
 510
 511
 512 /**
 513  * Generate a / b
 514  */
 515 LLVMValueRef
 516 lp_build_div(struct lp_build_context *bld,
 517              LLVMValueRef a,
 518              LLVMValueRef b)
 519 {
 520    const struct lp_type type = bld->type;
 521
 522    if(a == bld->zero)
 523       return bld->zero;
 524    if(a == bld->one)
 525       return lp_build_rcp(bld, b);
 526    if(b == bld->zero)
 527       return bld->undef;
 528    if(b == bld->one)
 529       return a;
 530    if(a == bld->undef || b == bld->undef)
 531       return bld->undef;
 532
 533    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 534       return LLVMConstFDiv(a, b);
 535
 536    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 537       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 538
 539    return LLVMBuildFDiv(bld->builder, a, b, "");
 540 }
 541
 542
 543 /**
 544  * Linear interpolation.
 545  *
 546  * This also works for integer values with a few caveats.
 547  *
 548  * @sa http://www.stereopsis.com/doubleblend.html
 549  */
 550 LLVMValueRef
 551 lp_build_lerp(struct lp_build_context *bld,
 552               LLVMValueRef x,
 553               LLVMValueRef v0,
 554               LLVMValueRef v1)
 555 {
 556    LLVMValueRef delta;
 557    LLVMValueRef res;
 558
 559    delta = lp_build_sub(bld, v1, v0);
 560
 561    res = lp_build_mul(bld, x, delta);
 562
 563    res = lp_build_add(bld, v0, res);
 564
 565    if(bld->type.fixed)
 566       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 567        * but it will be wrong for other uses. Basically we need a more
 568        * powerful lp_type, capable of further distinguishing the values
 569        * interpretation from the value storage. */
 570       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 571
 572    return res;
 573 }
 574
 575
 576 LLVMValueRef
 577 lp_build_lerp_2d(struct lp_build_context *bld,
 578                  LLVMValueRef x,
 579                  LLVMValueRef y,
 580                  LLVMValueRef v00,
 581                  LLVMValueRef v01,
 582                  LLVMValueRef v10,
 583                  LLVMValueRef v11)
 584 {
 585    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 586    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 587    return lp_build_lerp(bld, y, v0, v1);
 588 }
 589
 590
 591 /**
 592  * Generate min(a, b)
 593  * Do checks for special cases.
 594  */
 595 LLVMValueRef
 596 lp_build_min(struct lp_build_context *bld,
 597              LLVMValueRef a,
 598              LLVMValueRef b)
 599 {
 600    if(a == bld->undef || b == bld->undef)
 601       return bld->undef;
 602
 603    if(a == b)
 604       return a;
 605
 606    if(bld->type.norm) {
 607       if(a == bld->zero || b == bld->zero)
 608          return bld->zero;
 609       if(a == bld->one)
 610          return b;
 611       if(b == bld->one)
 612          return a;
 613    }
 614
 615    return lp_build_min_simple(bld, a, b);
 616 }
 617
 618
 619 /**
 620  * Generate max(a, b)
 621  * Do checks for special cases.
 622  */
 623 LLVMValueRef
 624 lp_build_max(struct lp_build_context *bld,
 625              LLVMValueRef a,
 626              LLVMValueRef b)
 627 {
 628    if(a == bld->undef || b == bld->undef)
 629       return bld->undef;
 630
 631    if(a == b)
 632       return a;
 633
 634    if(bld->type.norm) {
 635       if(a == bld->one || b == bld->one)
 636          return bld->one;
 637       if(a == bld->zero)
 638          return b;
 639       if(b == bld->zero)
 640          return a;
 641    }
 642
 643    return lp_build_max_simple(bld, a, b);
 644 }
 645
 646
 647 /**
 648  * Generate clamp(a, min, max)
 649  * Do checks for special cases.
 650  */
 651 LLVMValueRef
 652 lp_build_clamp(struct lp_build_context *bld,
 653                LLVMValueRef a,
 654                LLVMValueRef min,
 655                LLVMValueRef max)
 656 {
 657    a = lp_build_min(bld, a, max);
 658    a = lp_build_max(bld, a, min);
 659    return a;
 660 }
 661
 662
 663 /**
 664  * Generate abs(a)
 665  */
 666 LLVMValueRef
 667 lp_build_abs(struct lp_build_context *bld,
 668              LLVMValueRef a)
 669 {
 670    const struct lp_type type = bld->type;
 671    LLVMTypeRef vec_type = lp_build_vec_type(type);
 672
 673    if(!type.sign)
 674       return a;
 675
 676    if(type.floating) {
 677       /* Mask out the sign bit */
 678       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 679       unsigned long long absMask = ~(1ULL << (type.width - 1));
 680       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 681       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 682       a = LLVMBuildAnd(bld->builder, a, mask, "");
 683       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 684       return a;
 685    }
 686
 687    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 688       switch(type.width) {
 689       case 8:
 690          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 691       case 16:
 692          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 693       case 32:
 694          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 695       }
 696    }
 697
 698    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 699 }
 700
 701
 702 LLVMValueRef
 703 lp_build_negate(struct lp_build_context *bld,
 704                 LLVMValueRef a)
 705 {
 706    return LLVMBuildNeg(bld->builder, a, "");
 707 }
 708
 709
 710 /** Return -1, 0 or +1 depending on the sign of a */
 711 LLVMValueRef
 712 lp_build_sgn(struct lp_build_context *bld,
 713              LLVMValueRef a)
 714 {
 715    const struct lp_type type = bld->type;
 716    LLVMValueRef cond;
 717    LLVMValueRef res;
 718
 719    /* Handle non-zero case */
 720    if(!type.sign) {
 721       /* if not zero then sign must be positive */
 722       res = bld->one;
 723    }
 724    else if(type.floating) {
 725       LLVMTypeRef vec_type;
 726       LLVMTypeRef int_type;
 727       LLVMValueRef mask;
 728       LLVMValueRef sign;
 729       LLVMValueRef one;
 730       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 731
 732       int_type = lp_build_int_vec_type(type);
 733       vec_type = lp_build_vec_type(type);
 734       mask = lp_build_const_int_vec(type, maskBit);
 735
 736       /* Take the sign bit and add it to 1 constant */
 737       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 738       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 739       one = LLVMConstBitCast(bld->one, int_type);
 740       res = LLVMBuildOr(bld->builder, sign, one, "");
 741       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 742    }
 743    else
 744    {
 745       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 746       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 747       res = lp_build_select(bld, cond, bld->one, minus_one);
 748    }
 749
 750    /* Handle zero */
 751    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 752    res = lp_build_select(bld, cond, bld->zero, res);
 753
 754    return res;
 755 }
 756
 757
 758 /**
 759  * Set the sign of float vector 'a' according to 'sign'.
 760  * If sign==0, return abs(a).
 761  * If sign==1, return -abs(a);
 762  * Other values for sign produce undefined results.
 763  */
 764 LLVMValueRef
 765 lp_build_set_sign(struct lp_build_context *bld,
 766                   LLVMValueRef a, LLVMValueRef sign)
 767 {
 768    const struct lp_type type = bld->type;
 769    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 770    LLVMTypeRef vec_type = lp_build_vec_type(type);
 771    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 772    LLVMValueRef mask = lp_build_const_int_vec(type,
 773                              ~((unsigned long long) 1 << (type.width - 1)));
 774    LLVMValueRef val, res;
 775
 776    assert(type.floating);
 777
 778    /* val = reinterpret_cast<int>(a) */
 779    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 780    /* val = val & mask */
 781    val = LLVMBuildAnd(bld->builder, val, mask, "");
 782    /* sign = sign << shift */
 783    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 784    /* res = val | sign */
 785    res = LLVMBuildOr(bld->builder, val, sign, "");
 786    /* res = reinterpret_cast<float>(res) */
 787    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 788
 789    return res;
 790 }
 791
 792
 793 /**
 794  * Convert vector of (or scalar) int to vector of (or scalar) float.
 795  */
 796 LLVMValueRef
 797 lp_build_int_to_float(struct lp_build_context *bld,
 798                       LLVMValueRef a)
 799 {
 800    const struct lp_type type = bld->type;
 801    LLVMTypeRef vec_type = lp_build_vec_type(type);
 802
 803    assert(type.floating);
 804
 805    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 806 }
 807
 808
 809
 810 enum lp_build_round_sse41_mode
 811 {
 812    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 813    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 814    LP_BUILD_ROUND_SSE41_CEIL = 2,
 815    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 816 };
 817
 818
 819 static INLINE LLVMValueRef
 820 lp_build_round_sse41(struct lp_build_context *bld,
 821                      LLVMValueRef a,
 822                      enum lp_build_round_sse41_mode mode)
 823 {
 824    const struct lp_type type = bld->type;
 825    LLVMTypeRef vec_type = lp_build_vec_type(type);
 826    const char *intrinsic;
 827
 828    assert(type.floating);
 829    assert(type.width*type.length == 128);
 830    assert(lp_check_value(type, a));
 831    assert(util_cpu_caps.has_sse4_1);
 832
 833    switch(type.width) {
 834    case 32:
 835       intrinsic = "llvm.x86.sse41.round.ps";
 836       break;
 837    case 64:
 838       intrinsic = "llvm.x86.sse41.round.pd";
 839       break;
 840    default:
 841       assert(0);
 842       return bld->undef;
 843    }
 844
 845    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 846                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 847 }
 848
 849
 850 LLVMValueRef
 851 lp_build_trunc(struct lp_build_context *bld,
 852                LLVMValueRef a)
 853 {
 854    const struct lp_type type = bld->type;
 855
 856    assert(type.floating);
 857    assert(lp_check_value(type, a));
 858
 859    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 860       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 861    else {
 862       LLVMTypeRef vec_type = lp_build_vec_type(type);
 863       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 864       LLVMValueRef res;
 865       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 866       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 867       return res;
 868    }
 869 }
 870
 871
 872 LLVMValueRef
 873 lp_build_round(struct lp_build_context *bld,
 874                LLVMValueRef a)
 875 {
 876    const struct lp_type type = bld->type;
 877
 878    assert(type.floating);
 879    assert(lp_check_value(type, a));
 880
 881    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 882       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 883    else {
 884       LLVMTypeRef vec_type = lp_build_vec_type(type);
 885       LLVMValueRef res;
 886       res = lp_build_iround(bld, a);
 887       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 888       return res;
 889    }
 890 }
 891
 892
 893 LLVMValueRef
 894 lp_build_floor(struct lp_build_context *bld,
 895                LLVMValueRef a)
 896 {
 897    const struct lp_type type = bld->type;
 898
 899    assert(type.floating);
 900    assert(lp_check_value(type, a));
 901
 902    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 903       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 904    else {
 905       LLVMTypeRef vec_type = lp_build_vec_type(type);
 906       LLVMValueRef res;
 907       res = lp_build_ifloor(bld, a);
 908       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 909       return res;
 910    }
 911 }
 912
 913
 914 LLVMValueRef
 915 lp_build_ceil(struct lp_build_context *bld,
 916               LLVMValueRef a)
 917 {
 918    const struct lp_type type = bld->type;
 919
 920    assert(type.floating);
 921    assert(lp_check_value(type, a));
 922
 923    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 924       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 925    else {
 926       LLVMTypeRef vec_type = lp_build_vec_type(type);
 927       LLVMValueRef res;
 928       res = lp_build_iceil(bld, a);
 929       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 930       return res;
 931    }
 932 }
 933
 934
 935 /**
 936  * Return fractional part of 'a' computed as a - floor(f)
 937  * Typically used in texture coord arithmetic.
 938  */
 939 LLVMValueRef
 940 lp_build_fract(struct lp_build_context *bld,
 941                LLVMValueRef a)
 942 {
 943    assert(bld->type.floating);
 944    return lp_build_sub(bld, a, lp_build_floor(bld, a));
 945 }
 946
 947
 948 /**
 949  * Convert to integer, through whichever rounding method that's fastest,
 950  * typically truncating toward zero.
 951  */
 952 LLVMValueRef
 953 lp_build_itrunc(struct lp_build_context *bld,
 954                 LLVMValueRef a)
 955 {
 956    const struct lp_type type = bld->type;
 957    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 958
 959    assert(type.floating);
 960    assert(lp_check_value(type, a));
 961
 962    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 963 }
 964
 965
 966 /**
 967  * Convert float[] to int[] with round().
 968  */
 969 LLVMValueRef
 970 lp_build_iround(struct lp_build_context *bld,
 971                 LLVMValueRef a)
 972 {
 973    const struct lp_type type = bld->type;
 974    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 975    LLVMValueRef res;
 976
 977    assert(type.floating);
 978
 979    assert(lp_check_value(type, a));
 980
 981    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
 982       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 983    }
 984    else {
 985       LLVMTypeRef vec_type = lp_build_vec_type(type);
 986       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
 987       LLVMValueRef sign;
 988       LLVMValueRef half;
 989
 990       /* get sign bit */
 991       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 992       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 993
 994       /* sign * 0.5 */
 995       half = lp_build_const_vec(type, 0.5);
 996       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
 997       half = LLVMBuildOr(bld->builder, sign, half, "");
 998       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
 999
1000       res = LLVMBuildAdd(bld->builder, a, half, "");
1001    }
1002
1003    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1004
1005    return res;
1006 }
1007
1008
1009 /**
1010  * Convert float[] to int[] with floor().
1011  */
1012 LLVMValueRef
1013 lp_build_ifloor(struct lp_build_context *bld,
1014                 LLVMValueRef a)
1015 {
1016    const struct lp_type type = bld->type;
1017    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1018    LLVMValueRef res;
1019
1020    assert(type.floating);
1021    assert(lp_check_value(type, a));
1022
1023    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1024       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1025    }
1026    else {
1027       /* Take the sign bit and add it to 1 constant */
1028       LLVMTypeRef vec_type = lp_build_vec_type(type);
1029       unsigned mantissa = lp_mantissa(type);
1030       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1031       LLVMValueRef sign;
1032       LLVMValueRef offset;
1033
1034       /* sign = a < 0 ? ~0 : 0 */
1035       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1036       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1037       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "");
1038       lp_build_name(sign, "floor.sign");
1039
1040       /* offset = -0.99999(9)f */
1041       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 1)/((unsigned long long)1 << mantissa));
1042       offset = LLVMConstBitCast(offset, int_vec_type);
1043
1044       /* offset = a < 0 ? -0.99999(9)f : 0.0f */
1045       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1046       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "");
1047       lp_build_name(offset, "floor.offset");
1048
1049       res = LLVMBuildAdd(bld->builder, a, offset, "");
1050       lp_build_name(res, "floor.res");
1051    }
1052
1053    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1054    lp_build_name(res, "floor");
1055
1056    return res;
1057 }
1058
1059
1060 LLVMValueRef
1061 lp_build_iceil(struct lp_build_context *bld,
1062                LLVMValueRef a)
1063 {
1064    const struct lp_type type = bld->type;
1065    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1066    LLVMValueRef res;
1067
1068    assert(type.floating);
1069    assert(lp_check_value(type, a));
1070
1071    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1072       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1073    }
1074    else {
1075       /* TODO: mimic lp_build_ifloor() here */
1076       assert(0);
1077       res = bld->undef;
1078    }
1079
1080    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1081
1082    return res;
1083 }
1084
1085
1086 LLVMValueRef
1087 lp_build_sqrt(struct lp_build_context *bld,
1088               LLVMValueRef a)
1089 {
1090    const struct lp_type type = bld->type;
1091    LLVMTypeRef vec_type = lp_build_vec_type(type);
1092    char intrinsic[32];
1093
1094    /* TODO: optimize the constant case */
1095    /* TODO: optimize the constant case */
1096
1097    assert(type.floating);
1098    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1099
1100    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1101 }
1102
1103
1104 LLVMValueRef
1105 lp_build_rcp(struct lp_build_context *bld,
1106              LLVMValueRef a)
1107 {
1108    const struct lp_type type = bld->type;
1109
1110    if(a == bld->zero)
1111       return bld->undef;
1112    if(a == bld->one)
1113       return bld->one;
1114    if(a == bld->undef)
1115       return bld->undef;
1116
1117    assert(type.floating);
1118
1119    if(LLVMIsConstant(a))
1120       return LLVMConstFDiv(bld->one, a);
1121
1122    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1123       /*
1124        * XXX: Added precision is not always necessary, so only enable this
1125        * when we have a better system in place to track minimum precision.
1126        */
1127
1128 #if 0
1129       /*
1130        * Do one Newton-Raphson step to improve precision:
1131        *
1132        *   x1 = (2 - a * rcp(a)) * rcp(a)
1133        */
1134
1135       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1136       LLVMValueRef rcp_a;
1137       LLVMValueRef res;
1138
1139       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1140
1141       res = LLVMBuildMul(bld->builder, a, rcp_a, "");
1142       res = LLVMBuildSub(bld->builder, two, res, "");
1143       res = LLVMBuildMul(bld->builder, res, rcp_a, "");
1144
1145       return rcp_a;
1146 #else
1147       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1148 #endif
1149    }
1150
1151    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1152 }
1153
1154
1155 /**
1156  * Generate 1/sqrt(a)
1157  */
1158 LLVMValueRef
1159 lp_build_rsqrt(struct lp_build_context *bld,
1160                LLVMValueRef a)
1161 {
1162    const struct lp_type type = bld->type;
1163
1164    assert(type.floating);
1165
1166    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1167       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1168
1169    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1170 }
1171
1172
1173 static inline LLVMValueRef
1174 lp_build_const_v4si(unsigned long value)
1175 {
1176    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1177    LLVMValueRef elements[4] = { element, element, element, element };
1178    return LLVMConstVector(elements, 4);
1179 }
1180
1181 static inline LLVMValueRef
1182 lp_build_const_v4sf(float value)
1183 {
1184    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1185    LLVMValueRef elements[4] = { element, element, element, element };
1186    return LLVMConstVector(elements, 4);
1187 }
1188
1189
1190 /**
1191  * Generate sin(a) using SSE2
1192  */
1193 LLVMValueRef
1194 lp_build_sin(struct lp_build_context *bld,
1195              LLVMValueRef a)
1196 {
1197    struct lp_type int_type = lp_int_type(bld->type);
1198    LLVMBuilderRef b = bld->builder;
1199    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1200    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1201
1202    /*
1203     *  take the absolute value,
1204     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1205     */
1206
1207    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1208    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1209
1210    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1211    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1212
1213    /*
1214     * extract the sign bit (upper one)
1215     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1216     */
1217    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1218    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1219
1220    /*
1221     * scale by 4/Pi
1222     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1223     */
1224
1225    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1226    LLVMValueRef scale_y = LLVMBuildMul(b, x_abs, FOPi, "scale_y");
1227
1228    /*
1229     * store the integer part of y in mm0
1230     * emm2 = _mm_cvttps_epi32(y);
1231     */
1232
1233    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1234
1235    /*
1236     * j=(j+1) & (~1) (see the cephes sources)
1237     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1238     */
1239
1240    LLVMValueRef all_one = lp_build_const_v4si(1);
1241    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1242    /*
1243     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1244     */
1245    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1246    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1247
1248    /*
1249     * y = _mm_cvtepi32_ps(emm2);
1250     */
1251    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1252
1253    /* get the swap sign flag
1254     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1255     */
1256    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1257    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1258
1259    /*
1260     * emm2 = _mm_slli_epi32(emm0, 29);
1261     */
1262    LLVMValueRef const_29 = lp_build_const_v4si(29);
1263    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1264
1265    /*
1266     * get the polynom selection mask
1267     * there is one polynom for 0 <= x <= Pi/4
1268     * and another one for Pi/4<x<=Pi/2
1269     * Both branches will be computed.
1270     *
1271     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1272     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1273     */
1274
1275    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1276    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1277    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1278                                              emm2_3, lp_build_const_v4si(0));
1279    /*
1280     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1281     */
1282    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1283
1284    /*
1285     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1286     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1287     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1288     */
1289    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1290    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1291    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1292
1293    /*
1294     * The magic pass: "Extended precision modular arithmetic"
1295     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1296     * xmm1 = _mm_mul_ps(y, xmm1);
1297     * xmm2 = _mm_mul_ps(y, xmm2);
1298     * xmm3 = _mm_mul_ps(y, xmm3);
1299     */
1300    LLVMValueRef xmm1 = LLVMBuildMul(b, y_2, DP1, "xmm1");
1301    LLVMValueRef xmm2 = LLVMBuildMul(b, y_2, DP2, "xmm2");
1302    LLVMValueRef xmm3 = LLVMBuildMul(b, y_2, DP3, "xmm3");
1303
1304    /*
1305     * x = _mm_add_ps(x, xmm1);
1306     * x = _mm_add_ps(x, xmm2);
1307     * x = _mm_add_ps(x, xmm3);
1308     */
1309
1310    LLVMValueRef x_1 = LLVMBuildAdd(b, x_abs, xmm1, "x_1");
1311    LLVMValueRef x_2 = LLVMBuildAdd(b, x_1, xmm2, "x_2");
1312    LLVMValueRef x_3 = LLVMBuildAdd(b, x_2, xmm3, "x_3");
1313
1314    /*
1315     * Evaluate the first polynom  (0 <= x <= Pi/4)
1316     *
1317     * z = _mm_mul_ps(x,x);
1318     */
1319    LLVMValueRef z = LLVMBuildMul(b, x_3, x_3, "z");
1320
1321    /*
1322     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1323     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1324     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1325     */
1326    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1327    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1328    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1329
1330    /*
1331     * y = *(v4sf*)_ps_coscof_p0;
1332     * y = _mm_mul_ps(y, z);
1333     */
1334    LLVMValueRef y_3 = LLVMBuildMul(b, z, coscof_p0, "y_3");
1335    LLVMValueRef y_4 = LLVMBuildAdd(b, y_3, coscof_p1, "y_4");
1336    LLVMValueRef y_5 = LLVMBuildMul(b, y_4, z, "y_5");
1337    LLVMValueRef y_6 = LLVMBuildAdd(b, y_5, coscof_p2, "y_6");
1338    LLVMValueRef y_7 = LLVMBuildMul(b, y_6, z, "y_7");
1339    LLVMValueRef y_8 = LLVMBuildMul(b, y_7, z, "y_8");
1340
1341
1342    /*
1343     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1344     * y = _mm_sub_ps(y, tmp);
1345     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1346     */
1347    LLVMValueRef half = lp_build_const_v4sf(0.5);
1348    LLVMValueRef tmp = LLVMBuildMul(b, z, half, "tmp");
1349    LLVMValueRef y_9 = LLVMBuildSub(b, y_8, tmp, "y_8");
1350    LLVMValueRef one = lp_build_const_v4sf(1.0);
1351    LLVMValueRef y_10 = LLVMBuildAdd(b, y_9, one, "y_9");
1352
1353    /*
1354     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1355     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1356     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1357     */
1358    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1359    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1360    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1361
1362    /*
1363     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1364     *
1365     * y2 = *(v4sf*)_ps_sincof_p0;
1366     * y2 = _mm_mul_ps(y2, z);
1367     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1368     * y2 = _mm_mul_ps(y2, z);
1369     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1370     * y2 = _mm_mul_ps(y2, z);
1371     * y2 = _mm_mul_ps(y2, x);
1372     * y2 = _mm_add_ps(y2, x);
1373     */
1374
1375    LLVMValueRef y2_3 = LLVMBuildMul(b, z, sincof_p0, "y2_3");
1376    LLVMValueRef y2_4 = LLVMBuildAdd(b, y2_3, sincof_p1, "y2_4");
1377    LLVMValueRef y2_5 = LLVMBuildMul(b, y2_4, z, "y2_5");
1378    LLVMValueRef y2_6 = LLVMBuildAdd(b, y2_5, sincof_p2, "y2_6");
1379    LLVMValueRef y2_7 = LLVMBuildMul(b, y2_6, z, "y2_7");
1380    LLVMValueRef y2_8 = LLVMBuildMul(b, y2_7, x_3, "y2_8");
1381    LLVMValueRef y2_9 = LLVMBuildAdd(b, y2_8, x_3, "y2_9");
1382
1383    /*
1384     * select the correct result from the two polynoms
1385     * xmm3 = poly_mask;
1386     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1387     * y = _mm_andnot_ps(xmm3, y);
1388     * y = _mm_add_ps(y,y2);
1389     */
1390    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1391    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1392    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1393    LLVMValueRef inv = lp_build_const_v4si(~0);
1394    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1395    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1396    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1397
1398    /*
1399     * update the sign
1400     * y = _mm_xor_ps(y, sign_bit);
1401     */
1402    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1403    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1404    return y_result;
1405 }
1406
1407
1408 /**
1409  * Generate cos(a) using SSE2
1410  */
1411 LLVMValueRef
1412 lp_build_cos(struct lp_build_context *bld,
1413              LLVMValueRef a)
1414 {
1415    struct lp_type int_type = lp_int_type(bld->type);
1416    LLVMBuilderRef b = bld->builder;
1417    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1418    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1419
1420    /*
1421     *  take the absolute value,
1422     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1423     */
1424
1425    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1426    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1427
1428    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1429    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1430
1431    /*
1432     * scale by 4/Pi
1433     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1434     */
1435
1436    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1437    LLVMValueRef scale_y = LLVMBuildMul(b, x_abs, FOPi, "scale_y");
1438
1439    /*
1440     * store the integer part of y in mm0
1441     * emm2 = _mm_cvttps_epi32(y);
1442     */
1443
1444    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1445
1446    /*
1447     * j=(j+1) & (~1) (see the cephes sources)
1448     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1449     */
1450
1451    LLVMValueRef all_one = lp_build_const_v4si(1);
1452    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1453    /*
1454     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1455     */
1456    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1457    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1458
1459    /*
1460     * y = _mm_cvtepi32_ps(emm2);
1461     */
1462    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1463
1464
1465    /*
1466     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1467     */
1468    LLVMValueRef const_2 = lp_build_const_v4si(2);
1469    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1470
1471
1472    /* get the swap sign flag
1473     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1474     */
1475    LLVMValueRef inv = lp_build_const_v4si(~0);
1476    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1477    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1478    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1479
1480    /*
1481     * emm2 = _mm_slli_epi32(emm0, 29);
1482     */
1483    LLVMValueRef const_29 = lp_build_const_v4si(29);
1484    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1485
1486    /*
1487     * get the polynom selection mask
1488     * there is one polynom for 0 <= x <= Pi/4
1489     * and another one for Pi/4<x<=Pi/2
1490     * Both branches will be computed.
1491     *
1492     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1493     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1494     */
1495
1496    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1497    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1498    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1499                                              emm2_3, lp_build_const_v4si(0));
1500
1501    /*
1502     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1503     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1504     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1505     */
1506    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1507    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1508    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1509
1510    /*
1511     * The magic pass: "Extended precision modular arithmetic"
1512     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1513     * xmm1 = _mm_mul_ps(y, xmm1);
1514     * xmm2 = _mm_mul_ps(y, xmm2);
1515     * xmm3 = _mm_mul_ps(y, xmm3);
1516     */
1517    LLVMValueRef xmm1 = LLVMBuildMul(b, y_2, DP1, "xmm1");
1518    LLVMValueRef xmm2 = LLVMBuildMul(b, y_2, DP2, "xmm2");
1519    LLVMValueRef xmm3 = LLVMBuildMul(b, y_2, DP3, "xmm3");
1520
1521    /*
1522     * x = _mm_add_ps(x, xmm1);
1523     * x = _mm_add_ps(x, xmm2);
1524     * x = _mm_add_ps(x, xmm3);
1525     */
1526
1527    LLVMValueRef x_1 = LLVMBuildAdd(b, x_abs, xmm1, "x_1");
1528    LLVMValueRef x_2 = LLVMBuildAdd(b, x_1, xmm2, "x_2");
1529    LLVMValueRef x_3 = LLVMBuildAdd(b, x_2, xmm3, "x_3");
1530
1531    /*
1532     * Evaluate the first polynom  (0 <= x <= Pi/4)
1533     *
1534     * z = _mm_mul_ps(x,x);
1535     */
1536    LLVMValueRef z = LLVMBuildMul(b, x_3, x_3, "z");
1537
1538    /*
1539     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1540     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1541     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1542     */
1543    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1544    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1545    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1546
1547    /*
1548     * y = *(v4sf*)_ps_coscof_p0;
1549     * y = _mm_mul_ps(y, z);
1550     */
1551    LLVMValueRef y_3 = LLVMBuildMul(b, z, coscof_p0, "y_3");
1552    LLVMValueRef y_4 = LLVMBuildAdd(b, y_3, coscof_p1, "y_4");
1553    LLVMValueRef y_5 = LLVMBuildMul(b, y_4, z, "y_5");
1554    LLVMValueRef y_6 = LLVMBuildAdd(b, y_5, coscof_p2, "y_6");
1555    LLVMValueRef y_7 = LLVMBuildMul(b, y_6, z, "y_7");
1556    LLVMValueRef y_8 = LLVMBuildMul(b, y_7, z, "y_8");
1557
1558
1559    /*
1560     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1561     * y = _mm_sub_ps(y, tmp);
1562     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1563     */
1564    LLVMValueRef half = lp_build_const_v4sf(0.5);
1565    LLVMValueRef tmp = LLVMBuildMul(b, z, half, "tmp");
1566    LLVMValueRef y_9 = LLVMBuildSub(b, y_8, tmp, "y_8");
1567    LLVMValueRef one = lp_build_const_v4sf(1.0);
1568    LLVMValueRef y_10 = LLVMBuildAdd(b, y_9, one, "y_9");
1569
1570    /*
1571     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1572     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1573     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1574     */
1575    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1576    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1577    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1578
1579    /*
1580     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1581     *
1582     * y2 = *(v4sf*)_ps_sincof_p0;
1583     * y2 = _mm_mul_ps(y2, z);
1584     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1585     * y2 = _mm_mul_ps(y2, z);
1586     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1587     * y2 = _mm_mul_ps(y2, z);
1588     * y2 = _mm_mul_ps(y2, x);
1589     * y2 = _mm_add_ps(y2, x);
1590     */
1591
1592    LLVMValueRef y2_3 = LLVMBuildMul(b, z, sincof_p0, "y2_3");
1593    LLVMValueRef y2_4 = LLVMBuildAdd(b, y2_3, sincof_p1, "y2_4");
1594    LLVMValueRef y2_5 = LLVMBuildMul(b, y2_4, z, "y2_5");
1595    LLVMValueRef y2_6 = LLVMBuildAdd(b, y2_5, sincof_p2, "y2_6");
1596    LLVMValueRef y2_7 = LLVMBuildMul(b, y2_6, z, "y2_7");
1597    LLVMValueRef y2_8 = LLVMBuildMul(b, y2_7, x_3, "y2_8");
1598    LLVMValueRef y2_9 = LLVMBuildAdd(b, y2_8, x_3, "y2_9");
1599
1600    /*
1601     * select the correct result from the two polynoms
1602     * xmm3 = poly_mask;
1603     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1604     * y = _mm_andnot_ps(xmm3, y);
1605     * y = _mm_add_ps(y,y2);
1606     */
1607    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1608    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1609    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1610    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1611    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1612    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1613
1614    /*
1615     * update the sign
1616     * y = _mm_xor_ps(y, sign_bit);
1617     */
1618    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1619    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1620    return y_result;
1621 }
1622
1623
1624 /**
1625  * Generate pow(x, y)
1626  */
1627 LLVMValueRef
1628 lp_build_pow(struct lp_build_context *bld,
1629              LLVMValueRef x,
1630              LLVMValueRef y)
1631 {
1632    /* TODO: optimize the constant case */
1633    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1634       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1635                    __FUNCTION__);
1636
1637    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1638 }
1639
1640
1641 /**
1642  * Generate exp(x)
1643  */
1644 LLVMValueRef
1645 lp_build_exp(struct lp_build_context *bld,
1646              LLVMValueRef x)
1647 {
1648    /* log2(e) = 1/log(2) */
1649    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1650
1651    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1652 }
1653
1654
1655 /**
1656  * Generate log(x)
1657  */
1658 LLVMValueRef
1659 lp_build_log(struct lp_build_context *bld,
1660              LLVMValueRef x)
1661 {
1662    /* log(2) */
1663    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1664
1665    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1666 }
1667
1668
1669 #define EXP_POLY_DEGREE 3
1670 #define LOG_POLY_DEGREE 5
1671
1672
1673 /**
1674  * Generate polynomial.
1675  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1676  */
1677 static LLVMValueRef
1678 lp_build_polynomial(struct lp_build_context *bld,
1679                     LLVMValueRef x,
1680                     const double *coeffs,
1681                     unsigned num_coeffs)
1682 {
1683    const struct lp_type type = bld->type;
1684    LLVMValueRef res = NULL;
1685    unsigned i;
1686
1687    /* TODO: optimize the constant case */
1688    if(LLVMIsConstant(x))
1689       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1690                    __FUNCTION__);
1691
1692    for (i = num_coeffs; i--; ) {
1693       LLVMValueRef coeff;
1694
1695       coeff = lp_build_const_vec(type, coeffs[i]);
1696
1697       if(res)
1698          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1699       else
1700          res = coeff;
1701    }
1702
1703    if(res)
1704       return res;
1705    else
1706       return bld->undef;
1707 }
1708
1709
1710 /**
1711  * Minimax polynomial fit of 2**x, in range [0, 1[
1712  */
1713 const double lp_build_exp2_polynomial[] = {
1714 #if EXP_POLY_DEGREE == 5
1715    0.999999999690134838155,
1716    0.583974334321735217258,
1717    0.164553105719676828492,
1718    0.0292811063701710962255,
1719    0.00354944426657875141846,
1720    0.000296253726543423377365
1721 #elif EXP_POLY_DEGREE == 4
1722    1.00000001502262084505,
1723    0.563586057338685991394,
1724    0.150436017652442413623,
1725    0.0243220604213317927308,
1726    0.0025359088446580436489
1727 #elif EXP_POLY_DEGREE == 3
1728    0.999925218562710312959,
1729    0.695833540494823811697,
1730    0.226067155427249155588,
1731    0.0780245226406372992967
1732 #elif EXP_POLY_DEGREE == 2
1733    1.00172476321474503578,
1734    0.657636275736077639316,
1735    0.33718943461968720704
1736 #else
1737 #error
1738 #endif
1739 };
1740
1741
1742 void
1743 lp_build_exp2_approx(struct lp_build_context *bld,
1744                      LLVMValueRef x,
1745                      LLVMValueRef *p_exp2_int_part,
1746                      LLVMValueRef *p_frac_part,
1747                      LLVMValueRef *p_exp2)
1748 {
1749    const struct lp_type type = bld->type;
1750    LLVMTypeRef vec_type = lp_build_vec_type(type);
1751    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1752    LLVMValueRef ipart = NULL;
1753    LLVMValueRef fpart = NULL;
1754    LLVMValueRef expipart = NULL;
1755    LLVMValueRef expfpart = NULL;
1756    LLVMValueRef res = NULL;
1757
1758    if(p_exp2_int_part || p_frac_part || p_exp2) {
1759       /* TODO: optimize the constant case */
1760       if(LLVMIsConstant(x))
1761          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1762                       __FUNCTION__);
1763
1764       assert(type.floating && type.width == 32);
1765
1766       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1767       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1768
1769       /* ipart = floor(x) */
1770       ipart = lp_build_floor(bld, x);
1771
1772       /* fpart = x - ipart */
1773       fpart = LLVMBuildSub(bld->builder, x, ipart, "");
1774    }
1775
1776    if(p_exp2_int_part || p_exp2) {
1777       /* expipart = (float) (1 << ipart) */
1778       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1779       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1780       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1781       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1782    }
1783
1784    if(p_exp2) {
1785       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1786                                      Elements(lp_build_exp2_polynomial));
1787
1788       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1789    }
1790
1791    if(p_exp2_int_part)
1792       *p_exp2_int_part = expipart;
1793
1794    if(p_frac_part)
1795       *p_frac_part = fpart;
1796
1797    if(p_exp2)
1798       *p_exp2 = res;
1799 }
1800
1801
1802 LLVMValueRef
1803 lp_build_exp2(struct lp_build_context *bld,
1804               LLVMValueRef x)
1805 {
1806    LLVMValueRef res;
1807    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1808    return res;
1809 }
1810
1811
1812 /**
1813  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1814  * These coefficients can be generate with
1815  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1816  */
1817 const double lp_build_log2_polynomial[] = {
1818 #if LOG_POLY_DEGREE == 6
1819    3.11578814719469302614,
1820    -3.32419399085241980044,
1821    2.59883907202499966007,
1822    -1.23152682416275988241,
1823    0.318212422185251071475,
1824    -0.0344359067839062357313
1825 #elif LOG_POLY_DEGREE == 5
1826    2.8882704548164776201,
1827    -2.52074962577807006663,
1828    1.48116647521213171641,
1829    -0.465725644288844778798,
1830    0.0596515482674574969533
1831 #elif LOG_POLY_DEGREE == 4
1832    2.61761038894603480148,
1833    -1.75647175389045657003,
1834    0.688243882994381274313,
1835    -0.107254423828329604454
1836 #elif LOG_POLY_DEGREE == 3
1837    2.28330284476918490682,
1838    -1.04913055217340124191,
1839    0.204446009836232697516
1840 #else
1841 #error
1842 #endif
1843 };
1844
1845
1846 /**
1847  * See http://www.devmaster.net/forums/showthread.php?p=43580
1848  */
1849 void
1850 lp_build_log2_approx(struct lp_build_context *bld,
1851                      LLVMValueRef x,
1852                      LLVMValueRef *p_exp,
1853                      LLVMValueRef *p_floor_log2,
1854                      LLVMValueRef *p_log2)
1855 {
1856    const struct lp_type type = bld->type;
1857    LLVMTypeRef vec_type = lp_build_vec_type(type);
1858    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1859
1860    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
1861    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
1862    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1863
1864    LLVMValueRef i = NULL;
1865    LLVMValueRef exp = NULL;
1866    LLVMValueRef mant = NULL;
1867    LLVMValueRef logexp = NULL;
1868    LLVMValueRef logmant = NULL;
1869    LLVMValueRef res = NULL;
1870
1871    if(p_exp || p_floor_log2 || p_log2) {
1872       /* TODO: optimize the constant case */
1873       if(LLVMIsConstant(x))
1874          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1875                       __FUNCTION__);
1876
1877       assert(type.floating && type.width == 32);
1878
1879       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1880
1881       /* exp = (float) exponent(x) */
1882       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1883    }
1884
1885    if(p_floor_log2 || p_log2) {
1886       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
1887       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
1888       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1889    }
1890
1891    if(p_log2) {
1892       /* mant = (float) mantissa(x) */
1893       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1894       mant = LLVMBuildOr(bld->builder, mant, one, "");
1895       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1896
1897       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1898                                     Elements(lp_build_log2_polynomial));
1899
1900       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1901       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1902
1903       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1904    }
1905
1906    if(p_exp) {
1907       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
1908       *p_exp = exp;
1909    }
1910
1911    if(p_floor_log2)
1912       *p_floor_log2 = logexp;
1913
1914    if(p_log2)
1915       *p_log2 = res;
1916 }
1917
1918
1919 LLVMValueRef
1920 lp_build_log2(struct lp_build_context *bld,
1921               LLVMValueRef x)
1922 {
1923    LLVMValueRef res;
1924    lp_build_log2_approx(bld, x, NULL, NULL, &res);
1925    return res;
1926 }