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 /**
 851  * Return the integer part of a float (vector) value.  The returned value is
 852  * a float (vector).
 853  * Ex: trunc(-1.5) = 1.0
 854  */
 855 LLVMValueRef
 856 lp_build_trunc(struct lp_build_context *bld,
 857                LLVMValueRef a)
 858 {
 859    const struct lp_type type = bld->type;
 860
 861    assert(type.floating);
 862    assert(lp_check_value(type, a));
 863
 864    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 865       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 866    else {
 867       LLVMTypeRef vec_type = lp_build_vec_type(type);
 868       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 869       LLVMValueRef res;
 870       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 871       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 872       return res;
 873    }
 874 }
 875
 876
 877 /**
 878  * Return float (vector) rounded to nearest integer (vector).  The returned
 879  * value is a float (vector).
 880  * Ex: round(0.9) = 1.0
 881  * Ex: round(-1.5) = -2.0
 882  */
 883 LLVMValueRef
 884 lp_build_round(struct lp_build_context *bld,
 885                LLVMValueRef a)
 886 {
 887    const struct lp_type type = bld->type;
 888
 889    assert(type.floating);
 890    assert(lp_check_value(type, a));
 891
 892    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 893       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 894    else {
 895       LLVMTypeRef vec_type = lp_build_vec_type(type);
 896       LLVMValueRef res;
 897       res = lp_build_iround(bld, a);
 898       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 899       return res;
 900    }
 901 }
 902
 903
 904 /**
 905  * Return floor of float (vector), result is a float (vector)
 906  * Ex: floor(1.1) = 1.0
 907  * Ex: floor(-1.1) = -2.0
 908  */
 909 LLVMValueRef
 910 lp_build_floor(struct lp_build_context *bld,
 911                LLVMValueRef a)
 912 {
 913    const struct lp_type type = bld->type;
 914
 915    assert(type.floating);
 916    assert(lp_check_value(type, a));
 917
 918    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 919       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 920    else {
 921       LLVMTypeRef vec_type = lp_build_vec_type(type);
 922       LLVMValueRef res;
 923       res = lp_build_ifloor(bld, a);
 924       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 925       return res;
 926    }
 927 }
 928
 929
 930 /**
 931  * Return ceiling of float (vector), returning float (vector).
 932  * Ex: ceil( 1.1) = 2.0
 933  * Ex: ceil(-1.1) = -1.0
 934  */
 935 LLVMValueRef
 936 lp_build_ceil(struct lp_build_context *bld,
 937               LLVMValueRef a)
 938 {
 939    const struct lp_type type = bld->type;
 940
 941    assert(type.floating);
 942    assert(lp_check_value(type, a));
 943
 944    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 945       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 946    else {
 947       LLVMTypeRef vec_type = lp_build_vec_type(type);
 948       LLVMValueRef res;
 949       res = lp_build_iceil(bld, a);
 950       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 951       return res;
 952    }
 953 }
 954
 955
 956 /**
 957  * Return fractional part of 'a' computed as a - floor(a)
 958  * Typically used in texture coord arithmetic.
 959  */
 960 LLVMValueRef
 961 lp_build_fract(struct lp_build_context *bld,
 962                LLVMValueRef a)
 963 {
 964    assert(bld->type.floating);
 965    return lp_build_sub(bld, a, lp_build_floor(bld, a));
 966 }
 967
 968
 969 /**
 970  * Return the integer part of a float (vector) value.  The returned value is
 971  * an integer (vector).
 972  * Ex: itrunc(-1.5) = 1
 973  */
 974 LLVMValueRef
 975 lp_build_itrunc(struct lp_build_context *bld,
 976                 LLVMValueRef a)
 977 {
 978    const struct lp_type type = bld->type;
 979    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 980
 981    assert(type.floating);
 982    assert(lp_check_value(type, a));
 983
 984    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 985 }
 986
 987
 988 /**
 989  * Return float (vector) rounded to nearest integer (vector).  The returned
 990  * value is an integer (vector).
 991  * Ex: iround(0.9) = 1
 992  * Ex: iround(-1.5) = -2
 993  */
 994 LLVMValueRef
 995 lp_build_iround(struct lp_build_context *bld,
 996                 LLVMValueRef a)
 997 {
 998    const struct lp_type type = bld->type;
 999    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1000    LLVMValueRef res;
1001
1002    assert(type.floating);
1003
1004    assert(lp_check_value(type, a));
1005
1006    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1007       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1008    }
1009    else {
1010       LLVMTypeRef vec_type = lp_build_vec_type(type);
1011       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1012       LLVMValueRef sign;
1013       LLVMValueRef half;
1014
1015       /* get sign bit */
1016       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1017       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1018
1019       /* sign * 0.5 */
1020       half = lp_build_const_vec(type, 0.5);
1021       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1022       half = LLVMBuildOr(bld->builder, sign, half, "");
1023       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1024
1025       res = LLVMBuildAdd(bld->builder, a, half, "");
1026    }
1027
1028    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1029
1030    return res;
1031 }
1032
1033
1034 /**
1035  * Return floor of float (vector), result is an int (vector)
1036  * Ex: ifloor(1.1) = 1.0
1037  * Ex: ifloor(-1.1) = -2.0
1038  */
1039 LLVMValueRef
1040 lp_build_ifloor(struct lp_build_context *bld,
1041                 LLVMValueRef a)
1042 {
1043    const struct lp_type type = bld->type;
1044    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1045    LLVMValueRef res;
1046
1047    assert(type.floating);
1048    assert(lp_check_value(type, a));
1049
1050    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1051       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1052    }
1053    else {
1054       /* Take the sign bit and add it to 1 constant */
1055       LLVMTypeRef vec_type = lp_build_vec_type(type);
1056       unsigned mantissa = lp_mantissa(type);
1057       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1058       LLVMValueRef sign;
1059       LLVMValueRef offset;
1060
1061       /* sign = a < 0 ? ~0 : 0 */
1062       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1063       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1064       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1065
1066       /* offset = -0.99999(9)f */
1067       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1068       offset = LLVMConstBitCast(offset, int_vec_type);
1069
1070       /* offset = a < 0 ? offset : 0.0f */
1071       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1072       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1073
1074       res = LLVMBuildAdd(bld->builder, a, offset, "ifloor.res");
1075    }
1076
1077    /* round to nearest (toward zero) */
1078    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1079
1080    return res;
1081 }
1082
1083
1084 /**
1085  * Return ceiling of float (vector), returning int (vector).
1086  * Ex: iceil( 1.1) = 2
1087  * Ex: iceil(-1.1) = -1
1088  */
1089 LLVMValueRef
1090 lp_build_iceil(struct lp_build_context *bld,
1091                LLVMValueRef a)
1092 {
1093    const struct lp_type type = bld->type;
1094    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1095    LLVMValueRef res;
1096
1097    assert(type.floating);
1098    assert(lp_check_value(type, a));
1099
1100    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1101       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1102    }
1103    else {
1104       LLVMTypeRef vec_type = lp_build_vec_type(type);
1105       unsigned mantissa = lp_mantissa(type);
1106       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1107       LLVMValueRef sign;
1108       LLVMValueRef offset;
1109
1110       /* sign = a < 0 ? 0 : ~0 */
1111       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1112       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1113       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1114       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1115
1116       /* offset = 0.99999(9)f */
1117       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1118       offset = LLVMConstBitCast(offset, int_vec_type);
1119
1120       /* offset = a < 0 ? 0.0 : offset */
1121       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1122       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1123
1124       res = LLVMBuildAdd(bld->builder, a, offset, "iceil.res");
1125    }
1126
1127    /* round to nearest (toward zero) */
1128    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1129
1130    return res;
1131 }
1132
1133
1134 LLVMValueRef
1135 lp_build_sqrt(struct lp_build_context *bld,
1136               LLVMValueRef a)
1137 {
1138    const struct lp_type type = bld->type;
1139    LLVMTypeRef vec_type = lp_build_vec_type(type);
1140    char intrinsic[32];
1141
1142    /* TODO: optimize the constant case */
1143    /* TODO: optimize the constant case */
1144
1145    assert(type.floating);
1146    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1147
1148    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1149 }
1150
1151
1152 LLVMValueRef
1153 lp_build_rcp(struct lp_build_context *bld,
1154              LLVMValueRef a)
1155 {
1156    const struct lp_type type = bld->type;
1157
1158    if(a == bld->zero)
1159       return bld->undef;
1160    if(a == bld->one)
1161       return bld->one;
1162    if(a == bld->undef)
1163       return bld->undef;
1164
1165    assert(type.floating);
1166
1167    if(LLVMIsConstant(a))
1168       return LLVMConstFDiv(bld->one, a);
1169
1170    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1171       /*
1172        * XXX: Added precision is not always necessary, so only enable this
1173        * when we have a better system in place to track minimum precision.
1174        */
1175
1176 #if 0
1177       /*
1178        * Do one Newton-Raphson step to improve precision:
1179        *
1180        *   x1 = (2 - a * rcp(a)) * rcp(a)
1181        */
1182
1183       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1184       LLVMValueRef rcp_a;
1185       LLVMValueRef res;
1186
1187       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1188
1189       res = LLVMBuildMul(bld->builder, a, rcp_a, "");
1190       res = LLVMBuildSub(bld->builder, two, res, "");
1191       res = LLVMBuildMul(bld->builder, res, rcp_a, "");
1192
1193       return rcp_a;
1194 #else
1195       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1196 #endif
1197    }
1198
1199    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1200 }
1201
1202
1203 /**
1204  * Generate 1/sqrt(a)
1205  */
1206 LLVMValueRef
1207 lp_build_rsqrt(struct lp_build_context *bld,
1208                LLVMValueRef a)
1209 {
1210    const struct lp_type type = bld->type;
1211
1212    assert(type.floating);
1213
1214    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1215       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1216
1217    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1218 }
1219
1220
1221 static inline LLVMValueRef
1222 lp_build_const_v4si(unsigned long value)
1223 {
1224    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1225    LLVMValueRef elements[4] = { element, element, element, element };
1226    return LLVMConstVector(elements, 4);
1227 }
1228
1229 static inline LLVMValueRef
1230 lp_build_const_v4sf(float value)
1231 {
1232    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1233    LLVMValueRef elements[4] = { element, element, element, element };
1234    return LLVMConstVector(elements, 4);
1235 }
1236
1237
1238 /**
1239  * Generate sin(a) using SSE2
1240  */
1241 LLVMValueRef
1242 lp_build_sin(struct lp_build_context *bld,
1243              LLVMValueRef a)
1244 {
1245    struct lp_type int_type = lp_int_type(bld->type);
1246    LLVMBuilderRef b = bld->builder;
1247    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1248    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1249
1250    /*
1251     *  take the absolute value,
1252     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1253     */
1254
1255    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1256    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1257
1258    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1259    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1260
1261    /*
1262     * extract the sign bit (upper one)
1263     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1264     */
1265    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1266    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1267
1268    /*
1269     * scale by 4/Pi
1270     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1271     */
1272
1273    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1274    LLVMValueRef scale_y = LLVMBuildMul(b, x_abs, FOPi, "scale_y");
1275
1276    /*
1277     * store the integer part of y in mm0
1278     * emm2 = _mm_cvttps_epi32(y);
1279     */
1280
1281    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1282
1283    /*
1284     * j=(j+1) & (~1) (see the cephes sources)
1285     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1286     */
1287
1288    LLVMValueRef all_one = lp_build_const_v4si(1);
1289    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1290    /*
1291     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1292     */
1293    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1294    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1295
1296    /*
1297     * y = _mm_cvtepi32_ps(emm2);
1298     */
1299    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1300
1301    /* get the swap sign flag
1302     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1303     */
1304    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1305    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1306
1307    /*
1308     * emm2 = _mm_slli_epi32(emm0, 29);
1309     */
1310    LLVMValueRef const_29 = lp_build_const_v4si(29);
1311    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1312
1313    /*
1314     * get the polynom selection mask
1315     * there is one polynom for 0 <= x <= Pi/4
1316     * and another one for Pi/4<x<=Pi/2
1317     * Both branches will be computed.
1318     *
1319     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1320     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1321     */
1322
1323    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1324    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1325    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1326                                              emm2_3, lp_build_const_v4si(0));
1327    /*
1328     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1329     */
1330    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1331
1332    /*
1333     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1334     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1335     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1336     */
1337    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1338    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1339    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1340
1341    /*
1342     * The magic pass: "Extended precision modular arithmetic"
1343     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1344     * xmm1 = _mm_mul_ps(y, xmm1);
1345     * xmm2 = _mm_mul_ps(y, xmm2);
1346     * xmm3 = _mm_mul_ps(y, xmm3);
1347     */
1348    LLVMValueRef xmm1 = LLVMBuildMul(b, y_2, DP1, "xmm1");
1349    LLVMValueRef xmm2 = LLVMBuildMul(b, y_2, DP2, "xmm2");
1350    LLVMValueRef xmm3 = LLVMBuildMul(b, y_2, DP3, "xmm3");
1351
1352    /*
1353     * x = _mm_add_ps(x, xmm1);
1354     * x = _mm_add_ps(x, xmm2);
1355     * x = _mm_add_ps(x, xmm3);
1356     */
1357
1358    LLVMValueRef x_1 = LLVMBuildAdd(b, x_abs, xmm1, "x_1");
1359    LLVMValueRef x_2 = LLVMBuildAdd(b, x_1, xmm2, "x_2");
1360    LLVMValueRef x_3 = LLVMBuildAdd(b, x_2, xmm3, "x_3");
1361
1362    /*
1363     * Evaluate the first polynom  (0 <= x <= Pi/4)
1364     *
1365     * z = _mm_mul_ps(x,x);
1366     */
1367    LLVMValueRef z = LLVMBuildMul(b, x_3, x_3, "z");
1368
1369    /*
1370     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1371     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1372     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1373     */
1374    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1375    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1376    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1377
1378    /*
1379     * y = *(v4sf*)_ps_coscof_p0;
1380     * y = _mm_mul_ps(y, z);
1381     */
1382    LLVMValueRef y_3 = LLVMBuildMul(b, z, coscof_p0, "y_3");
1383    LLVMValueRef y_4 = LLVMBuildAdd(b, y_3, coscof_p1, "y_4");
1384    LLVMValueRef y_5 = LLVMBuildMul(b, y_4, z, "y_5");
1385    LLVMValueRef y_6 = LLVMBuildAdd(b, y_5, coscof_p2, "y_6");
1386    LLVMValueRef y_7 = LLVMBuildMul(b, y_6, z, "y_7");
1387    LLVMValueRef y_8 = LLVMBuildMul(b, y_7, z, "y_8");
1388
1389
1390    /*
1391     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1392     * y = _mm_sub_ps(y, tmp);
1393     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1394     */
1395    LLVMValueRef half = lp_build_const_v4sf(0.5);
1396    LLVMValueRef tmp = LLVMBuildMul(b, z, half, "tmp");
1397    LLVMValueRef y_9 = LLVMBuildSub(b, y_8, tmp, "y_8");
1398    LLVMValueRef one = lp_build_const_v4sf(1.0);
1399    LLVMValueRef y_10 = LLVMBuildAdd(b, y_9, one, "y_9");
1400
1401    /*
1402     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1403     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1404     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1405     */
1406    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1407    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1408    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1409
1410    /*
1411     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1412     *
1413     * y2 = *(v4sf*)_ps_sincof_p0;
1414     * y2 = _mm_mul_ps(y2, z);
1415     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1416     * y2 = _mm_mul_ps(y2, z);
1417     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1418     * y2 = _mm_mul_ps(y2, z);
1419     * y2 = _mm_mul_ps(y2, x);
1420     * y2 = _mm_add_ps(y2, x);
1421     */
1422
1423    LLVMValueRef y2_3 = LLVMBuildMul(b, z, sincof_p0, "y2_3");
1424    LLVMValueRef y2_4 = LLVMBuildAdd(b, y2_3, sincof_p1, "y2_4");
1425    LLVMValueRef y2_5 = LLVMBuildMul(b, y2_4, z, "y2_5");
1426    LLVMValueRef y2_6 = LLVMBuildAdd(b, y2_5, sincof_p2, "y2_6");
1427    LLVMValueRef y2_7 = LLVMBuildMul(b, y2_6, z, "y2_7");
1428    LLVMValueRef y2_8 = LLVMBuildMul(b, y2_7, x_3, "y2_8");
1429    LLVMValueRef y2_9 = LLVMBuildAdd(b, y2_8, x_3, "y2_9");
1430
1431    /*
1432     * select the correct result from the two polynoms
1433     * xmm3 = poly_mask;
1434     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1435     * y = _mm_andnot_ps(xmm3, y);
1436     * y = _mm_add_ps(y,y2);
1437     */
1438    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1439    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1440    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1441    LLVMValueRef inv = lp_build_const_v4si(~0);
1442    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1443    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1444    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1445
1446    /*
1447     * update the sign
1448     * y = _mm_xor_ps(y, sign_bit);
1449     */
1450    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1451    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1452    return y_result;
1453 }
1454
1455
1456 /**
1457  * Generate cos(a) using SSE2
1458  */
1459 LLVMValueRef
1460 lp_build_cos(struct lp_build_context *bld,
1461              LLVMValueRef a)
1462 {
1463    struct lp_type int_type = lp_int_type(bld->type);
1464    LLVMBuilderRef b = bld->builder;
1465    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1466    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1467
1468    /*
1469     *  take the absolute value,
1470     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1471     */
1472
1473    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1474    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1475
1476    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1477    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1478
1479    /*
1480     * scale by 4/Pi
1481     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1482     */
1483
1484    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1485    LLVMValueRef scale_y = LLVMBuildMul(b, x_abs, FOPi, "scale_y");
1486
1487    /*
1488     * store the integer part of y in mm0
1489     * emm2 = _mm_cvttps_epi32(y);
1490     */
1491
1492    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1493
1494    /*
1495     * j=(j+1) & (~1) (see the cephes sources)
1496     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1497     */
1498
1499    LLVMValueRef all_one = lp_build_const_v4si(1);
1500    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1501    /*
1502     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1503     */
1504    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1505    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1506
1507    /*
1508     * y = _mm_cvtepi32_ps(emm2);
1509     */
1510    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1511
1512
1513    /*
1514     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1515     */
1516    LLVMValueRef const_2 = lp_build_const_v4si(2);
1517    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1518
1519
1520    /* get the swap sign flag
1521     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1522     */
1523    LLVMValueRef inv = lp_build_const_v4si(~0);
1524    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1525    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1526    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1527
1528    /*
1529     * emm2 = _mm_slli_epi32(emm0, 29);
1530     */
1531    LLVMValueRef const_29 = lp_build_const_v4si(29);
1532    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1533
1534    /*
1535     * get the polynom selection mask
1536     * there is one polynom for 0 <= x <= Pi/4
1537     * and another one for Pi/4<x<=Pi/2
1538     * Both branches will be computed.
1539     *
1540     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1541     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1542     */
1543
1544    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1545    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1546    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1547                                              emm2_3, lp_build_const_v4si(0));
1548
1549    /*
1550     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1551     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1552     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1553     */
1554    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1555    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1556    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1557
1558    /*
1559     * The magic pass: "Extended precision modular arithmetic"
1560     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1561     * xmm1 = _mm_mul_ps(y, xmm1);
1562     * xmm2 = _mm_mul_ps(y, xmm2);
1563     * xmm3 = _mm_mul_ps(y, xmm3);
1564     */
1565    LLVMValueRef xmm1 = LLVMBuildMul(b, y_2, DP1, "xmm1");
1566    LLVMValueRef xmm2 = LLVMBuildMul(b, y_2, DP2, "xmm2");
1567    LLVMValueRef xmm3 = LLVMBuildMul(b, y_2, DP3, "xmm3");
1568
1569    /*
1570     * x = _mm_add_ps(x, xmm1);
1571     * x = _mm_add_ps(x, xmm2);
1572     * x = _mm_add_ps(x, xmm3);
1573     */
1574
1575    LLVMValueRef x_1 = LLVMBuildAdd(b, x_abs, xmm1, "x_1");
1576    LLVMValueRef x_2 = LLVMBuildAdd(b, x_1, xmm2, "x_2");
1577    LLVMValueRef x_3 = LLVMBuildAdd(b, x_2, xmm3, "x_3");
1578
1579    /*
1580     * Evaluate the first polynom  (0 <= x <= Pi/4)
1581     *
1582     * z = _mm_mul_ps(x,x);
1583     */
1584    LLVMValueRef z = LLVMBuildMul(b, x_3, x_3, "z");
1585
1586    /*
1587     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1588     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1589     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1590     */
1591    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1592    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1593    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1594
1595    /*
1596     * y = *(v4sf*)_ps_coscof_p0;
1597     * y = _mm_mul_ps(y, z);
1598     */
1599    LLVMValueRef y_3 = LLVMBuildMul(b, z, coscof_p0, "y_3");
1600    LLVMValueRef y_4 = LLVMBuildAdd(b, y_3, coscof_p1, "y_4");
1601    LLVMValueRef y_5 = LLVMBuildMul(b, y_4, z, "y_5");
1602    LLVMValueRef y_6 = LLVMBuildAdd(b, y_5, coscof_p2, "y_6");
1603    LLVMValueRef y_7 = LLVMBuildMul(b, y_6, z, "y_7");
1604    LLVMValueRef y_8 = LLVMBuildMul(b, y_7, z, "y_8");
1605
1606
1607    /*
1608     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1609     * y = _mm_sub_ps(y, tmp);
1610     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1611     */
1612    LLVMValueRef half = lp_build_const_v4sf(0.5);
1613    LLVMValueRef tmp = LLVMBuildMul(b, z, half, "tmp");
1614    LLVMValueRef y_9 = LLVMBuildSub(b, y_8, tmp, "y_8");
1615    LLVMValueRef one = lp_build_const_v4sf(1.0);
1616    LLVMValueRef y_10 = LLVMBuildAdd(b, y_9, one, "y_9");
1617
1618    /*
1619     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1620     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1621     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1622     */
1623    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1624    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1625    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1626
1627    /*
1628     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1629     *
1630     * y2 = *(v4sf*)_ps_sincof_p0;
1631     * y2 = _mm_mul_ps(y2, z);
1632     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1633     * y2 = _mm_mul_ps(y2, z);
1634     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1635     * y2 = _mm_mul_ps(y2, z);
1636     * y2 = _mm_mul_ps(y2, x);
1637     * y2 = _mm_add_ps(y2, x);
1638     */
1639
1640    LLVMValueRef y2_3 = LLVMBuildMul(b, z, sincof_p0, "y2_3");
1641    LLVMValueRef y2_4 = LLVMBuildAdd(b, y2_3, sincof_p1, "y2_4");
1642    LLVMValueRef y2_5 = LLVMBuildMul(b, y2_4, z, "y2_5");
1643    LLVMValueRef y2_6 = LLVMBuildAdd(b, y2_5, sincof_p2, "y2_6");
1644    LLVMValueRef y2_7 = LLVMBuildMul(b, y2_6, z, "y2_7");
1645    LLVMValueRef y2_8 = LLVMBuildMul(b, y2_7, x_3, "y2_8");
1646    LLVMValueRef y2_9 = LLVMBuildAdd(b, y2_8, x_3, "y2_9");
1647
1648    /*
1649     * select the correct result from the two polynoms
1650     * xmm3 = poly_mask;
1651     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1652     * y = _mm_andnot_ps(xmm3, y);
1653     * y = _mm_add_ps(y,y2);
1654     */
1655    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1656    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1657    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1658    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1659    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1660    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1661
1662    /*
1663     * update the sign
1664     * y = _mm_xor_ps(y, sign_bit);
1665     */
1666    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1667    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1668    return y_result;
1669 }
1670
1671
1672 /**
1673  * Generate pow(x, y)
1674  */
1675 LLVMValueRef
1676 lp_build_pow(struct lp_build_context *bld,
1677              LLVMValueRef x,
1678              LLVMValueRef y)
1679 {
1680    /* TODO: optimize the constant case */
1681    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1682       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1683                    __FUNCTION__);
1684
1685    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1686 }
1687
1688
1689 /**
1690  * Generate exp(x)
1691  */
1692 LLVMValueRef
1693 lp_build_exp(struct lp_build_context *bld,
1694              LLVMValueRef x)
1695 {
1696    /* log2(e) = 1/log(2) */
1697    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1698
1699    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1700 }
1701
1702
1703 /**
1704  * Generate log(x)
1705  */
1706 LLVMValueRef
1707 lp_build_log(struct lp_build_context *bld,
1708              LLVMValueRef x)
1709 {
1710    /* log(2) */
1711    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1712
1713    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1714 }
1715
1716
1717 #define EXP_POLY_DEGREE 3
1718 #define LOG_POLY_DEGREE 5
1719
1720
1721 /**
1722  * Generate polynomial.
1723  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1724  */
1725 static LLVMValueRef
1726 lp_build_polynomial(struct lp_build_context *bld,
1727                     LLVMValueRef x,
1728                     const double *coeffs,
1729                     unsigned num_coeffs)
1730 {
1731    const struct lp_type type = bld->type;
1732    LLVMValueRef res = NULL;
1733    unsigned i;
1734
1735    /* TODO: optimize the constant case */
1736    if(LLVMIsConstant(x))
1737       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1738                    __FUNCTION__);
1739
1740    for (i = num_coeffs; i--; ) {
1741       LLVMValueRef coeff;
1742
1743       coeff = lp_build_const_vec(type, coeffs[i]);
1744
1745       if(res)
1746          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1747       else
1748          res = coeff;
1749    }
1750
1751    if(res)
1752       return res;
1753    else
1754       return bld->undef;
1755 }
1756
1757
1758 /**
1759  * Minimax polynomial fit of 2**x, in range [0, 1[
1760  */
1761 const double lp_build_exp2_polynomial[] = {
1762 #if EXP_POLY_DEGREE == 5
1763    0.999999999690134838155,
1764    0.583974334321735217258,
1765    0.164553105719676828492,
1766    0.0292811063701710962255,
1767    0.00354944426657875141846,
1768    0.000296253726543423377365
1769 #elif EXP_POLY_DEGREE == 4
1770    1.00000001502262084505,
1771    0.563586057338685991394,
1772    0.150436017652442413623,
1773    0.0243220604213317927308,
1774    0.0025359088446580436489
1775 #elif EXP_POLY_DEGREE == 3
1776    0.999925218562710312959,
1777    0.695833540494823811697,
1778    0.226067155427249155588,
1779    0.0780245226406372992967
1780 #elif EXP_POLY_DEGREE == 2
1781    1.00172476321474503578,
1782    0.657636275736077639316,
1783    0.33718943461968720704
1784 #else
1785 #error
1786 #endif
1787 };
1788
1789
1790 void
1791 lp_build_exp2_approx(struct lp_build_context *bld,
1792                      LLVMValueRef x,
1793                      LLVMValueRef *p_exp2_int_part,
1794                      LLVMValueRef *p_frac_part,
1795                      LLVMValueRef *p_exp2)
1796 {
1797    const struct lp_type type = bld->type;
1798    LLVMTypeRef vec_type = lp_build_vec_type(type);
1799    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1800    LLVMValueRef ipart = NULL;
1801    LLVMValueRef fpart = NULL;
1802    LLVMValueRef expipart = NULL;
1803    LLVMValueRef expfpart = NULL;
1804    LLVMValueRef res = NULL;
1805
1806    if(p_exp2_int_part || p_frac_part || p_exp2) {
1807       /* TODO: optimize the constant case */
1808       if(LLVMIsConstant(x))
1809          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1810                       __FUNCTION__);
1811
1812       assert(type.floating && type.width == 32);
1813
1814       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1815       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1816
1817       /* ipart = floor(x) */
1818       ipart = lp_build_floor(bld, x);
1819
1820       /* fpart = x - ipart */
1821       fpart = LLVMBuildSub(bld->builder, x, ipart, "");
1822    }
1823
1824    if(p_exp2_int_part || p_exp2) {
1825       /* expipart = (float) (1 << ipart) */
1826       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1827       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1828       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1829       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1830    }
1831
1832    if(p_exp2) {
1833       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1834                                      Elements(lp_build_exp2_polynomial));
1835
1836       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1837    }
1838
1839    if(p_exp2_int_part)
1840       *p_exp2_int_part = expipart;
1841
1842    if(p_frac_part)
1843       *p_frac_part = fpart;
1844
1845    if(p_exp2)
1846       *p_exp2 = res;
1847 }
1848
1849
1850 LLVMValueRef
1851 lp_build_exp2(struct lp_build_context *bld,
1852               LLVMValueRef x)
1853 {
1854    LLVMValueRef res;
1855    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1856    return res;
1857 }
1858
1859
1860 /**
1861  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1862  * These coefficients can be generate with
1863  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1864  */
1865 const double lp_build_log2_polynomial[] = {
1866 #if LOG_POLY_DEGREE == 6
1867    3.11578814719469302614,
1868    -3.32419399085241980044,
1869    2.59883907202499966007,
1870    -1.23152682416275988241,
1871    0.318212422185251071475,
1872    -0.0344359067839062357313
1873 #elif LOG_POLY_DEGREE == 5
1874    2.8882704548164776201,
1875    -2.52074962577807006663,
1876    1.48116647521213171641,
1877    -0.465725644288844778798,
1878    0.0596515482674574969533
1879 #elif LOG_POLY_DEGREE == 4
1880    2.61761038894603480148,
1881    -1.75647175389045657003,
1882    0.688243882994381274313,
1883    -0.107254423828329604454
1884 #elif LOG_POLY_DEGREE == 3
1885    2.28330284476918490682,
1886    -1.04913055217340124191,
1887    0.204446009836232697516
1888 #else
1889 #error
1890 #endif
1891 };
1892
1893
1894 /**
1895  * See http://www.devmaster.net/forums/showthread.php?p=43580
1896  */
1897 void
1898 lp_build_log2_approx(struct lp_build_context *bld,
1899                      LLVMValueRef x,
1900                      LLVMValueRef *p_exp,
1901                      LLVMValueRef *p_floor_log2,
1902                      LLVMValueRef *p_log2)
1903 {
1904    const struct lp_type type = bld->type;
1905    LLVMTypeRef vec_type = lp_build_vec_type(type);
1906    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1907
1908    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
1909    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
1910    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1911
1912    LLVMValueRef i = NULL;
1913    LLVMValueRef exp = NULL;
1914    LLVMValueRef mant = NULL;
1915    LLVMValueRef logexp = NULL;
1916    LLVMValueRef logmant = NULL;
1917    LLVMValueRef res = NULL;
1918
1919    if(p_exp || p_floor_log2 || p_log2) {
1920       /* TODO: optimize the constant case */
1921       if(LLVMIsConstant(x))
1922          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1923                       __FUNCTION__);
1924
1925       assert(type.floating && type.width == 32);
1926
1927       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1928
1929       /* exp = (float) exponent(x) */
1930       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1931    }
1932
1933    if(p_floor_log2 || p_log2) {
1934       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
1935       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
1936       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1937    }
1938
1939    if(p_log2) {
1940       /* mant = (float) mantissa(x) */
1941       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1942       mant = LLVMBuildOr(bld->builder, mant, one, "");
1943       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1944
1945       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1946                                     Elements(lp_build_log2_polynomial));
1947
1948       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1949       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1950
1951       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1952    }
1953
1954    if(p_exp) {
1955       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
1956       *p_exp = exp;
1957    }
1958
1959    if(p_floor_log2)
1960       *p_floor_log2 = logexp;
1961
1962    if(p_log2)
1963       *p_log2 = res;
1964 }
1965
1966
1967 LLVMValueRef
1968 lp_build_log2(struct lp_build_context *bld,
1969               LLVMValueRef x)
1970 {
1971    LLVMValueRef res;
1972    lp_build_log2_approx(bld, x, NULL, NULL, &res);
1973    return res;
1974 }