src/gallium/auxiliary/gallivm/lp_bld_arit.c

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  27
  28
  29 /**
  30  * @file
  31  * Helper
  32  *
  33  * LLVM IR doesn't support all basic arithmetic operations we care about (most
  34  * notably min/max and saturated operations), and it is often necessary to
  35  * resort machine-specific intrinsics directly. The functions here hide all
  36  * these implementation details from the other modules.
  37  *
  38  * We also do simple expressions simplification here. Reasons are:
  39  * - it is very easy given we have all necessary information readily available
  40  * - LLVM optimization passes fail to simplify several vector expressions
  41  * - We often know value constraints which the optimization passes have no way
  42  *   of knowing, such as when source arguments are known to be in [0, 1] range.
  43  *
  44  * @author Jose Fonseca <jfonseca@vmware.com>
  45  */
  46
  47
  48 #include "util/u_memory.h"
  49 #include "util/u_debug.h"
  50 #include "util/u_math.h"
  51 #include "util/u_string.h"
  52 #include "util/u_cpu_detect.h"
  53
  54 #include "lp_bld_type.h"
  55 #include "lp_bld_const.h"
  56 #include "lp_bld_intr.h"
  57 #include "lp_bld_logic.h"
  58 #include "lp_bld_pack.h"
  59 #include "lp_bld_arit.h"
  60
  61
  62 /**
  63  * Generate min(a, b)
  64  * No checks for special case values of a or b = 1 or 0 are done.
  65  */
  66 static LLVMValueRef
  67 lp_build_min_simple(struct lp_build_context *bld,
  68                     LLVMValueRef a,
  69                     LLVMValueRef b)
  70 {
  71    const struct lp_type type = bld->type;
  72    const char *intrinsic = NULL;
  73    LLVMValueRef cond;
  74
  75    /* TODO: optimize the constant case */
  76
  77    if(type.width * type.length == 128) {
  78       if(type.floating) {
  79          if(type.width == 32 && util_cpu_caps.has_sse)
  80             intrinsic = "llvm.x86.sse.min.ps";
  81          if(type.width == 64 && util_cpu_caps.has_sse2)
  82             intrinsic = "llvm.x86.sse2.min.pd";
  83       }
  84       else {
  85          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  86             intrinsic = "llvm.x86.sse2.pminu.b";
  87          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  88             intrinsic = "llvm.x86.sse41.pminsb";
  89          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  90             intrinsic = "llvm.x86.sse41.pminuw";
  91          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  92             intrinsic = "llvm.x86.sse2.pmins.w";
  93          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  94             intrinsic = "llvm.x86.sse41.pminud";
  95          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  96             intrinsic = "llvm.x86.sse41.pminsd";
  97       }
  98    }
  99
 100    if(intrinsic)
 101       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 102
 103    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 104    return lp_build_select(bld, cond, a, b);
 105 }
 106
 107
 108 /**
 109  * Generate max(a, b)
 110  * No checks for special case values of a or b = 1 or 0 are done.
 111  */
 112 static LLVMValueRef
 113 lp_build_max_simple(struct lp_build_context *bld,
 114                     LLVMValueRef a,
 115                     LLVMValueRef b)
 116 {
 117    const struct lp_type type = bld->type;
 118    const char *intrinsic = NULL;
 119    LLVMValueRef cond;
 120
 121    /* TODO: optimize the constant case */
 122
 123    if(type.width * type.length == 128) {
 124       if(type.floating) {
 125          if(type.width == 32 && util_cpu_caps.has_sse)
 126             intrinsic = "llvm.x86.sse.max.ps";
 127          if(type.width == 64 && util_cpu_caps.has_sse2)
 128             intrinsic = "llvm.x86.sse2.max.pd";
 129       }
 130       else {
 131          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 132             intrinsic = "llvm.x86.sse2.pmaxu.b";
 133          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 134             intrinsic = "llvm.x86.sse41.pmaxsb";
 135          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 136             intrinsic = "llvm.x86.sse41.pmaxuw";
 137          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 138             intrinsic = "llvm.x86.sse2.pmaxs.w";
 139          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 140             intrinsic = "llvm.x86.sse41.pmaxud";
 141          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 142             intrinsic = "llvm.x86.sse41.pmaxsd";
 143       }
 144    }
 145
 146    if(intrinsic)
 147       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 148
 149    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 150    return lp_build_select(bld, cond, a, b);
 151 }
 152
 153
 154 /**
 155  * Generate 1 - a, or ~a depending on bld->type.
 156  */
 157 LLVMValueRef
 158 lp_build_comp(struct lp_build_context *bld,
 159               LLVMValueRef a)
 160 {
 161    const struct lp_type type = bld->type;
 162
 163    if(a == bld->one)
 164       return bld->zero;
 165    if(a == bld->zero)
 166       return bld->one;
 167
 168    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 169       if(LLVMIsConstant(a))
 170          return LLVMConstNot(a);
 171       else
 172          return LLVMBuildNot(bld->builder, a, "");
 173    }
 174
 175    if(LLVMIsConstant(a))
 176       if (type.floating)
 177           return LLVMConstFSub(bld->one, a);
 178       else
 179           return LLVMConstSub(bld->one, a);
 180    else
 181       if (type.floating)
 182          return LLVMBuildFSub(bld->builder, bld->one, a, "");
 183       else
 184          return LLVMBuildSub(bld->builder, bld->one, a, "");
 185 }
 186
 187
 188 /**
 189  * Generate a + b
 190  */
 191 LLVMValueRef
 192 lp_build_add(struct lp_build_context *bld,
 193              LLVMValueRef a,
 194              LLVMValueRef b)
 195 {
 196    const struct lp_type type = bld->type;
 197    LLVMValueRef res;
 198
 199    assert(lp_check_value(type, a));
 200    assert(lp_check_value(type, b));
 201
 202    if(a == bld->zero)
 203       return b;
 204    if(b == bld->zero)
 205       return a;
 206    if(a == bld->undef || b == bld->undef)
 207       return bld->undef;
 208
 209    if(bld->type.norm) {
 210       const char *intrinsic = NULL;
 211
 212       if(a == bld->one || b == bld->one)
 213         return bld->one;
 214
 215       if(util_cpu_caps.has_sse2 &&
 216          type.width * type.length == 128 &&
 217          !type.floating && !type.fixed) {
 218          if(type.width == 8)
 219             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 220          if(type.width == 16)
 221             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 222       }
 223
 224       if(intrinsic)
 225          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 226    }
 227
 228    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 229       if (type.floating)
 230          res = LLVMConstFAdd(a, b);
 231       else
 232          res = LLVMConstAdd(a, b);
 233    else
 234       if (type.floating)
 235          res = LLVMBuildFAdd(bld->builder, a, b, "");
 236       else
 237          res = LLVMBuildAdd(bld->builder, a, b, "");
 238
 239    /* clamp to ceiling of 1.0 */
 240    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 241       res = lp_build_min_simple(bld, res, bld->one);
 242
 243    /* XXX clamp to floor of -1 or 0??? */
 244
 245    return res;
 246 }
 247
 248
 249 /** Return the sum of the elements of a */
 250 LLVMValueRef
 251 lp_build_sum_vector(struct lp_build_context *bld,
 252                     LLVMValueRef a)
 253 {
 254    const struct lp_type type = bld->type;
 255    LLVMValueRef index, res;
 256    unsigned i;
 257
 258    if (a == bld->zero)
 259       return bld->zero;
 260    if (a == bld->undef)
 261       return bld->undef;
 262    assert(type.length > 1);
 263
 264    assert(!bld->type.norm);
 265
 266    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 267    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 268
 269    for (i = 1; i < type.length; i++) {
 270       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 271       if (type.floating)
 272          res = LLVMBuildFAdd(bld->builder, res,
 273                             LLVMBuildExtractElement(bld->builder,
 274                                                     a, index, ""),
 275                             "");
 276       else
 277          res = LLVMBuildAdd(bld->builder, res,
 278                             LLVMBuildExtractElement(bld->builder,
 279                                                     a, index, ""),
 280                             "");
 281    }
 282
 283    return res;
 284 }
 285
 286
 287 /**
 288  * Generate a - b
 289  */
 290 LLVMValueRef
 291 lp_build_sub(struct lp_build_context *bld,
 292              LLVMValueRef a,
 293              LLVMValueRef b)
 294 {
 295    const struct lp_type type = bld->type;
 296    LLVMValueRef res;
 297
 298    assert(lp_check_value(type, a));
 299    assert(lp_check_value(type, b));
 300
 301    if(b == bld->zero)
 302       return a;
 303    if(a == bld->undef || b == bld->undef)
 304       return bld->undef;
 305    if(a == b)
 306       return bld->zero;
 307
 308    if(bld->type.norm) {
 309       const char *intrinsic = NULL;
 310
 311       if(b == bld->one)
 312         return bld->zero;
 313
 314       if(util_cpu_caps.has_sse2 &&
 315          type.width * type.length == 128 &&
 316          !type.floating && !type.fixed) {
 317          if(type.width == 8)
 318             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 319          if(type.width == 16)
 320             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 321       }
 322
 323       if(intrinsic)
 324          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 325    }
 326
 327    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 328       if (type.floating)
 329          res = LLVMConstFSub(a, b);
 330       else
 331          res = LLVMConstSub(a, b);
 332    else
 333       if (type.floating)
 334          res = LLVMBuildFSub(bld->builder, a, b, "");
 335       else
 336          res = LLVMBuildSub(bld->builder, a, b, "");
 337
 338    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 339       res = lp_build_max_simple(bld, res, bld->zero);
 340
 341    return res;
 342 }
 343
 344
 345 /**
 346  * Normalized 8bit multiplication.
 347  *
 348  * - alpha plus one
 349  *
 350  *     makes the following approximation to the division (Sree)
 351  *
 352  *       a*b/255 ~= (a*(b + 1)) >> 256
 353  *
 354  *     which is the fastest method that satisfies the following OpenGL criteria
 355  *
 356  *       0*0 = 0 and 255*255 = 255
 357  *
 358  * - geometric series
 359  *
 360  *     takes the geometric series approximation to the division
 361  *
 362  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 363  *
 364  *     in this case just the first two terms to fit in 16bit arithmetic
 365  *
 366  *       t/255 ~= (t + (t >> 8)) >> 8
 367  *
 368  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 369  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 370  *     must be used
 371  *
 372  * - geometric series plus rounding
 373  *
 374  *     when using a geometric series division instead of truncating the result
 375  *     use roundoff in the approximation (Jim Blinn)
 376  *
 377  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 378  *
 379  *     achieving the exact results
 380  *
 381  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 382  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 383  * @sa Michael Herf, The "double blend trick", May 2000,
 384  *     http://www.stereopsis.com/doubleblend.html
 385  */
 386 static LLVMValueRef
 387 lp_build_mul_u8n(LLVMBuilderRef builder,
 388                  struct lp_type i16_type,
 389                  LLVMValueRef a, LLVMValueRef b)
 390 {
 391    LLVMValueRef c8;
 392    LLVMValueRef ab;
 393
 394    c8 = lp_build_const_int_vec(i16_type, 8);
 395
 396 #if 0
 397
 398    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 399    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 400    ab = LLVMBuildMul(builder, a, b, "");
 401
 402 #else
 403
 404    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 405    ab = LLVMBuildMul(builder, a, b, "");
 406    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 407    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 408
 409 #endif
 410
 411    ab = LLVMBuildLShr(builder, ab, c8, "");
 412
 413    return ab;
 414 }
 415
 416
 417 /**
 418  * Generate a * b
 419  */
 420 LLVMValueRef
 421 lp_build_mul(struct lp_build_context *bld,
 422              LLVMValueRef a,
 423              LLVMValueRef b)
 424 {
 425    const struct lp_type type = bld->type;
 426    LLVMValueRef shift;
 427    LLVMValueRef res;
 428
 429    assert(lp_check_value(type, a));
 430    assert(lp_check_value(type, b));
 431
 432    if(a == bld->zero)
 433       return bld->zero;
 434    if(a == bld->one)
 435       return b;
 436    if(b == bld->zero)
 437       return bld->zero;
 438    if(b == bld->one)
 439       return a;
 440    if(a == bld->undef || b == bld->undef)
 441       return bld->undef;
 442
 443    if(!type.floating && !type.fixed && type.norm) {
 444       if(type.width == 8) {
 445          struct lp_type i16_type = lp_wider_type(type);
 446          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 447
 448          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 449          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 450
 451          /* PMULLW, PSRLW, PADDW */
 452          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 453          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 454
 455          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 456
 457          return ab;
 458       }
 459
 460       /* FIXME */
 461       assert(0);
 462    }
 463
 464    if(type.fixed)
 465       shift = lp_build_const_int_vec(type, type.width/2);
 466    else
 467       shift = NULL;
 468
 469    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 470       if (type.floating)
 471          res = LLVMConstFMul(a, b);
 472       else
 473          res = LLVMConstMul(a, b);
 474       if(shift) {
 475          if(type.sign)
 476             res = LLVMConstAShr(res, shift);
 477          else
 478             res = LLVMConstLShr(res, shift);
 479       }
 480    }
 481    else {
 482       if (type.floating)
 483          res = LLVMBuildFMul(bld->builder, a, b, "");
 484       else
 485          res = LLVMBuildMul(bld->builder, a, b, "");
 486       if(shift) {
 487          if(type.sign)
 488             res = LLVMBuildAShr(bld->builder, res, shift, "");
 489          else
 490             res = LLVMBuildLShr(bld->builder, res, shift, "");
 491       }
 492    }
 493
 494    return res;
 495 }
 496
 497
 498 /**
 499  * Small vector x scale multiplication optimization.
 500  */
 501 LLVMValueRef
 502 lp_build_mul_imm(struct lp_build_context *bld,
 503                  LLVMValueRef a,
 504                  int b)
 505 {
 506    LLVMValueRef factor;
 507
 508    if(b == 0)
 509       return bld->zero;
 510
 511    if(b == 1)
 512       return a;
 513
 514    if(b == -1)
 515       if (bld->type.floating)
 516          return LLVMBuildFNeg(bld->builder, a, "");
 517       else
 518          return LLVMBuildNeg(bld->builder, a, "");
 519
 520    if(b == 2 && bld->type.floating)
 521       return lp_build_add(bld, a, a);
 522
 523    if(util_is_pot(b)) {
 524       unsigned shift = ffs(b) - 1;
 525
 526       if(bld->type.floating) {
 527 #if 0
 528          /*
 529           * Power of two multiplication by directly manipulating the mantissa.
 530           *
 531           * XXX: This might not be always faster, it will introduce a small error
 532           * for multiplication by zero, and it will produce wrong results
 533           * for Inf and NaN.
 534           */
 535          unsigned mantissa = lp_mantissa(bld->type);
 536          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 537          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 538          a = LLVMBuildAdd(bld->builder, a, factor, "");
 539          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 540          return a;
 541 #endif
 542       }
 543       else {
 544          factor = lp_build_const_vec(bld->type, shift);
 545          return LLVMBuildShl(bld->builder, a, factor, "");
 546       }
 547    }
 548
 549    factor = lp_build_const_vec(bld->type, (double)b);
 550    return lp_build_mul(bld, a, factor);
 551 }
 552
 553
 554 /**
 555  * Generate a / b
 556  */
 557 LLVMValueRef
 558 lp_build_div(struct lp_build_context *bld,
 559              LLVMValueRef a,
 560              LLVMValueRef b)
 561 {
 562    const struct lp_type type = bld->type;
 563
 564    assert(lp_check_value(type, a));
 565    assert(lp_check_value(type, b));
 566
 567    if(a == bld->zero)
 568       return bld->zero;
 569    if(a == bld->one)
 570       return lp_build_rcp(bld, b);
 571    if(b == bld->zero)
 572       return bld->undef;
 573    if(b == bld->one)
 574       return a;
 575    if(a == bld->undef || b == bld->undef)
 576       return bld->undef;
 577
 578    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 579       return LLVMConstFDiv(a, b);
 580
 581    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 582       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 583
 584    return LLVMBuildFDiv(bld->builder, a, b, "");
 585 }
 586
 587
 588 /**
 589  * Linear interpolation.
 590  *
 591  * This also works for integer values with a few caveats.
 592  *
 593  * @sa http://www.stereopsis.com/doubleblend.html
 594  */
 595 LLVMValueRef
 596 lp_build_lerp(struct lp_build_context *bld,
 597               LLVMValueRef x,
 598               LLVMValueRef v0,
 599               LLVMValueRef v1)
 600 {
 601    LLVMValueRef delta;
 602    LLVMValueRef res;
 603
 604    delta = lp_build_sub(bld, v1, v0);
 605
 606    res = lp_build_mul(bld, x, delta);
 607
 608    res = lp_build_add(bld, v0, res);
 609
 610    if(bld->type.fixed)
 611       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 612        * but it will be wrong for other uses. Basically we need a more
 613        * powerful lp_type, capable of further distinguishing the values
 614        * interpretation from the value storage. */
 615       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 616
 617    return res;
 618 }
 619
 620
 621 LLVMValueRef
 622 lp_build_lerp_2d(struct lp_build_context *bld,
 623                  LLVMValueRef x,
 624                  LLVMValueRef y,
 625                  LLVMValueRef v00,
 626                  LLVMValueRef v01,
 627                  LLVMValueRef v10,
 628                  LLVMValueRef v11)
 629 {
 630    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 631    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 632    return lp_build_lerp(bld, y, v0, v1);
 633 }
 634
 635
 636 /**
 637  * Generate min(a, b)
 638  * Do checks for special cases.
 639  */
 640 LLVMValueRef
 641 lp_build_min(struct lp_build_context *bld,
 642              LLVMValueRef a,
 643              LLVMValueRef b)
 644 {
 645    if(a == bld->undef || b == bld->undef)
 646       return bld->undef;
 647
 648    if(a == b)
 649       return a;
 650
 651    if(bld->type.norm) {
 652       if(a == bld->zero || b == bld->zero)
 653          return bld->zero;
 654       if(a == bld->one)
 655          return b;
 656       if(b == bld->one)
 657          return a;
 658    }
 659
 660    return lp_build_min_simple(bld, a, b);
 661 }
 662
 663
 664 /**
 665  * Generate max(a, b)
 666  * Do checks for special cases.
 667  */
 668 LLVMValueRef
 669 lp_build_max(struct lp_build_context *bld,
 670              LLVMValueRef a,
 671              LLVMValueRef b)
 672 {
 673    if(a == bld->undef || b == bld->undef)
 674       return bld->undef;
 675
 676    if(a == b)
 677       return a;
 678
 679    if(bld->type.norm) {
 680       if(a == bld->one || b == bld->one)
 681          return bld->one;
 682       if(a == bld->zero)
 683          return b;
 684       if(b == bld->zero)
 685          return a;
 686    }
 687
 688    return lp_build_max_simple(bld, a, b);
 689 }
 690
 691
 692 /**
 693  * Generate clamp(a, min, max)
 694  * Do checks for special cases.
 695  */
 696 LLVMValueRef
 697 lp_build_clamp(struct lp_build_context *bld,
 698                LLVMValueRef a,
 699                LLVMValueRef min,
 700                LLVMValueRef max)
 701 {
 702    a = lp_build_min(bld, a, max);
 703    a = lp_build_max(bld, a, min);
 704    return a;
 705 }
 706
 707
 708 /**
 709  * Generate abs(a)
 710  */
 711 LLVMValueRef
 712 lp_build_abs(struct lp_build_context *bld,
 713              LLVMValueRef a)
 714 {
 715    const struct lp_type type = bld->type;
 716    LLVMTypeRef vec_type = lp_build_vec_type(type);
 717
 718    if(!type.sign)
 719       return a;
 720
 721    if(type.floating) {
 722       /* Mask out the sign bit */
 723       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 724       unsigned long long absMask = ~(1ULL << (type.width - 1));
 725       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 726       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 727       a = LLVMBuildAnd(bld->builder, a, mask, "");
 728       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 729       return a;
 730    }
 731
 732    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 733       switch(type.width) {
 734       case 8:
 735          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 736       case 16:
 737          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 738       case 32:
 739          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 740       }
 741    }
 742
 743    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 744 }
 745
 746
 747 LLVMValueRef
 748 lp_build_negate(struct lp_build_context *bld,
 749                 LLVMValueRef a)
 750 {
 751    if (bld->type.floating)
 752       a = LLVMBuildFNeg(bld->builder, a, "");
 753    else
 754       a = LLVMBuildNeg(bld->builder, a, "");
 755
 756    return a;
 757 }
 758
 759
 760 /** Return -1, 0 or +1 depending on the sign of a */
 761 LLVMValueRef
 762 lp_build_sgn(struct lp_build_context *bld,
 763              LLVMValueRef a)
 764 {
 765    const struct lp_type type = bld->type;
 766    LLVMValueRef cond;
 767    LLVMValueRef res;
 768
 769    /* Handle non-zero case */
 770    if(!type.sign) {
 771       /* if not zero then sign must be positive */
 772       res = bld->one;
 773    }
 774    else if(type.floating) {
 775       LLVMTypeRef vec_type;
 776       LLVMTypeRef int_type;
 777       LLVMValueRef mask;
 778       LLVMValueRef sign;
 779       LLVMValueRef one;
 780       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 781
 782       int_type = lp_build_int_vec_type(type);
 783       vec_type = lp_build_vec_type(type);
 784       mask = lp_build_const_int_vec(type, maskBit);
 785
 786       /* Take the sign bit and add it to 1 constant */
 787       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 788       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 789       one = LLVMConstBitCast(bld->one, int_type);
 790       res = LLVMBuildOr(bld->builder, sign, one, "");
 791       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 792    }
 793    else
 794    {
 795       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 796       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 797       res = lp_build_select(bld, cond, bld->one, minus_one);
 798    }
 799
 800    /* Handle zero */
 801    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 802    res = lp_build_select(bld, cond, bld->zero, res);
 803
 804    return res;
 805 }
 806
 807
 808 /**
 809  * Set the sign of float vector 'a' according to 'sign'.
 810  * If sign==0, return abs(a).
 811  * If sign==1, return -abs(a);
 812  * Other values for sign produce undefined results.
 813  */
 814 LLVMValueRef
 815 lp_build_set_sign(struct lp_build_context *bld,
 816                   LLVMValueRef a, LLVMValueRef sign)
 817 {
 818    const struct lp_type type = bld->type;
 819    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 820    LLVMTypeRef vec_type = lp_build_vec_type(type);
 821    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 822    LLVMValueRef mask = lp_build_const_int_vec(type,
 823                              ~((unsigned long long) 1 << (type.width - 1)));
 824    LLVMValueRef val, res;
 825
 826    assert(type.floating);
 827
 828    /* val = reinterpret_cast<int>(a) */
 829    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 830    /* val = val & mask */
 831    val = LLVMBuildAnd(bld->builder, val, mask, "");
 832    /* sign = sign << shift */
 833    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 834    /* res = val | sign */
 835    res = LLVMBuildOr(bld->builder, val, sign, "");
 836    /* res = reinterpret_cast<float>(res) */
 837    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 838
 839    return res;
 840 }
 841
 842
 843 /**
 844  * Convert vector of (or scalar) int to vector of (or scalar) float.
 845  */
 846 LLVMValueRef
 847 lp_build_int_to_float(struct lp_build_context *bld,
 848                       LLVMValueRef a)
 849 {
 850    const struct lp_type type = bld->type;
 851    LLVMTypeRef vec_type = lp_build_vec_type(type);
 852
 853    assert(type.floating);
 854
 855    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 856 }
 857
 858
 859
 860 enum lp_build_round_sse41_mode
 861 {
 862    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 863    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 864    LP_BUILD_ROUND_SSE41_CEIL = 2,
 865    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 866 };
 867
 868
 869 static INLINE LLVMValueRef
 870 lp_build_round_sse41(struct lp_build_context *bld,
 871                      LLVMValueRef a,
 872                      enum lp_build_round_sse41_mode mode)
 873 {
 874    const struct lp_type type = bld->type;
 875    LLVMTypeRef vec_type = lp_build_vec_type(type);
 876    const char *intrinsic;
 877
 878    assert(type.floating);
 879    assert(type.width*type.length == 128);
 880    assert(lp_check_value(type, a));
 881    assert(util_cpu_caps.has_sse4_1);
 882
 883    switch(type.width) {
 884    case 32:
 885       intrinsic = "llvm.x86.sse41.round.ps";
 886       break;
 887    case 64:
 888       intrinsic = "llvm.x86.sse41.round.pd";
 889       break;
 890    default:
 891       assert(0);
 892       return bld->undef;
 893    }
 894
 895    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 896                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 897 }
 898
 899
 900 /**
 901  * Return the integer part of a float (vector) value.  The returned value is
 902  * a float (vector).
 903  * Ex: trunc(-1.5) = 1.0
 904  */
 905 LLVMValueRef
 906 lp_build_trunc(struct lp_build_context *bld,
 907                LLVMValueRef a)
 908 {
 909    const struct lp_type type = bld->type;
 910
 911    assert(type.floating);
 912    assert(lp_check_value(type, a));
 913
 914    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 915       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 916    else {
 917       LLVMTypeRef vec_type = lp_build_vec_type(type);
 918       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 919       LLVMValueRef res;
 920       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 921       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 922       return res;
 923    }
 924 }
 925
 926
 927 /**
 928  * Return float (vector) rounded to nearest integer (vector).  The returned
 929  * value is a float (vector).
 930  * Ex: round(0.9) = 1.0
 931  * Ex: round(-1.5) = -2.0
 932  */
 933 LLVMValueRef
 934 lp_build_round(struct lp_build_context *bld,
 935                LLVMValueRef a)
 936 {
 937    const struct lp_type type = bld->type;
 938
 939    assert(type.floating);
 940    assert(lp_check_value(type, a));
 941
 942    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 943       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 944    else {
 945       LLVMTypeRef vec_type = lp_build_vec_type(type);
 946       LLVMValueRef res;
 947       res = lp_build_iround(bld, a);
 948       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 949       return res;
 950    }
 951 }
 952
 953
 954 /**
 955  * Return floor of float (vector), result is a float (vector)
 956  * Ex: floor(1.1) = 1.0
 957  * Ex: floor(-1.1) = -2.0
 958  */
 959 LLVMValueRef
 960 lp_build_floor(struct lp_build_context *bld,
 961                LLVMValueRef a)
 962 {
 963    const struct lp_type type = bld->type;
 964
 965    assert(type.floating);
 966    assert(lp_check_value(type, a));
 967
 968    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 969       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 970    else {
 971       LLVMTypeRef vec_type = lp_build_vec_type(type);
 972       LLVMValueRef res;
 973       res = lp_build_ifloor(bld, a);
 974       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 975       return res;
 976    }
 977 }
 978
 979
 980 /**
 981  * Return ceiling of float (vector), returning float (vector).
 982  * Ex: ceil( 1.1) = 2.0
 983  * Ex: ceil(-1.1) = -1.0
 984  */
 985 LLVMValueRef
 986 lp_build_ceil(struct lp_build_context *bld,
 987               LLVMValueRef a)
 988 {
 989    const struct lp_type type = bld->type;
 990
 991    assert(type.floating);
 992    assert(lp_check_value(type, a));
 993
 994    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 995       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 996    else {
 997       LLVMTypeRef vec_type = lp_build_vec_type(type);
 998       LLVMValueRef res;
 999       res = lp_build_iceil(bld, a);
1000       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1001       return res;
1002    }
1003 }
1004
1005
1006 /**
1007  * Return fractional part of 'a' computed as a - floor(a)
1008  * Typically used in texture coord arithmetic.
1009  */
1010 LLVMValueRef
1011 lp_build_fract(struct lp_build_context *bld,
1012                LLVMValueRef a)
1013 {
1014    assert(bld->type.floating);
1015    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1016 }
1017
1018
1019 /**
1020  * Return the integer part of a float (vector) value.  The returned value is
1021  * an integer (vector).
1022  * Ex: itrunc(-1.5) = 1
1023  */
1024 LLVMValueRef
1025 lp_build_itrunc(struct lp_build_context *bld,
1026                 LLVMValueRef a)
1027 {
1028    const struct lp_type type = bld->type;
1029    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1030
1031    assert(type.floating);
1032    assert(lp_check_value(type, a));
1033
1034    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1035 }
1036
1037
1038 /**
1039  * Return float (vector) rounded to nearest integer (vector).  The returned
1040  * value is an integer (vector).
1041  * Ex: iround(0.9) = 1
1042  * Ex: iround(-1.5) = -2
1043  */
1044 LLVMValueRef
1045 lp_build_iround(struct lp_build_context *bld,
1046                 LLVMValueRef a)
1047 {
1048    const struct lp_type type = bld->type;
1049    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1050    LLVMValueRef res;
1051
1052    assert(type.floating);
1053
1054    assert(lp_check_value(type, a));
1055
1056    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1057       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1058    }
1059    else {
1060       LLVMTypeRef vec_type = lp_build_vec_type(type);
1061       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1062       LLVMValueRef sign;
1063       LLVMValueRef half;
1064
1065       /* get sign bit */
1066       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1067       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1068
1069       /* sign * 0.5 */
1070       half = lp_build_const_vec(type, 0.5);
1071       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1072       half = LLVMBuildOr(bld->builder, sign, half, "");
1073       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1074
1075       res = LLVMBuildFAdd(bld->builder, a, half, "");
1076    }
1077
1078    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1079
1080    return res;
1081 }
1082
1083
1084 /**
1085  * Return floor of float (vector), result is an int (vector)
1086  * Ex: ifloor(1.1) = 1.0
1087  * Ex: ifloor(-1.1) = -2.0
1088  */
1089 LLVMValueRef
1090 lp_build_ifloor(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_FLOOR);
1102    }
1103    else {
1104       /* Take the sign bit and add it to 1 constant */
1105       LLVMTypeRef vec_type = lp_build_vec_type(type);
1106       unsigned mantissa = lp_mantissa(type);
1107       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1108       LLVMValueRef sign;
1109       LLVMValueRef offset;
1110
1111       /* sign = a < 0 ? ~0 : 0 */
1112       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1113       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1114       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
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 ? offset : 0.0f */
1121       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1122       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1123
1124       res = LLVMBuildFAdd(bld->builder, a, offset, "ifloor.res");
1125    }
1126
1127    /* round to nearest (toward zero) */
1128    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1129
1130    return res;
1131 }
1132
1133
1134 /**
1135  * Return ceiling of float (vector), returning int (vector).
1136  * Ex: iceil( 1.1) = 2
1137  * Ex: iceil(-1.1) = -1
1138  */
1139 LLVMValueRef
1140 lp_build_iceil(struct lp_build_context *bld,
1141                LLVMValueRef a)
1142 {
1143    const struct lp_type type = bld->type;
1144    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1145    LLVMValueRef res;
1146
1147    assert(type.floating);
1148    assert(lp_check_value(type, a));
1149
1150    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1151       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1152    }
1153    else {
1154       LLVMTypeRef vec_type = lp_build_vec_type(type);
1155       unsigned mantissa = lp_mantissa(type);
1156       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1157       LLVMValueRef sign;
1158       LLVMValueRef offset;
1159
1160       /* sign = a < 0 ? 0 : ~0 */
1161       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1162       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1163       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1164       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1165
1166       /* offset = 0.99999(9)f */
1167       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1168       offset = LLVMConstBitCast(offset, int_vec_type);
1169
1170       /* offset = a < 0 ? 0.0 : offset */
1171       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1172       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1173
1174       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1175    }
1176
1177    /* round to nearest (toward zero) */
1178    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1179
1180    return res;
1181 }
1182
1183
1184 LLVMValueRef
1185 lp_build_sqrt(struct lp_build_context *bld,
1186               LLVMValueRef a)
1187 {
1188    const struct lp_type type = bld->type;
1189    LLVMTypeRef vec_type = lp_build_vec_type(type);
1190    char intrinsic[32];
1191
1192    /* TODO: optimize the constant case */
1193    /* TODO: optimize the constant case */
1194
1195    assert(type.floating);
1196    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1197
1198    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1199 }
1200
1201
1202 LLVMValueRef
1203 lp_build_rcp(struct lp_build_context *bld,
1204              LLVMValueRef a)
1205 {
1206    const struct lp_type type = bld->type;
1207
1208    if(a == bld->zero)
1209       return bld->undef;
1210    if(a == bld->one)
1211       return bld->one;
1212    if(a == bld->undef)
1213       return bld->undef;
1214
1215    assert(type.floating);
1216
1217    if(LLVMIsConstant(a))
1218       return LLVMConstFDiv(bld->one, a);
1219
1220    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1221       /*
1222        * XXX: Added precision is not always necessary, so only enable this
1223        * when we have a better system in place to track minimum precision.
1224        */
1225
1226 #if 0
1227       /*
1228        * Do one Newton-Raphson step to improve precision:
1229        *
1230        *   x1 = (2 - a * rcp(a)) * rcp(a)
1231        */
1232
1233       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1234       LLVMValueRef rcp_a;
1235       LLVMValueRef res;
1236
1237       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1238
1239       res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1240       res = LLVMBuildFSub(bld->builder, two, res, "");
1241       res = LLVMBuildFMul(bld->builder, res, rcp_a, "");
1242
1243       return rcp_a;
1244 #else
1245       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1246 #endif
1247    }
1248
1249    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1250 }
1251
1252
1253 /**
1254  * Generate 1/sqrt(a)
1255  */
1256 LLVMValueRef
1257 lp_build_rsqrt(struct lp_build_context *bld,
1258                LLVMValueRef a)
1259 {
1260    const struct lp_type type = bld->type;
1261
1262    assert(type.floating);
1263
1264    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1265       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1266
1267    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1268 }
1269
1270
1271 static inline LLVMValueRef
1272 lp_build_const_v4si(unsigned long value)
1273 {
1274    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1275    LLVMValueRef elements[4] = { element, element, element, element };
1276    return LLVMConstVector(elements, 4);
1277 }
1278
1279 static inline LLVMValueRef
1280 lp_build_const_v4sf(float value)
1281 {
1282    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1283    LLVMValueRef elements[4] = { element, element, element, element };
1284    return LLVMConstVector(elements, 4);
1285 }
1286
1287
1288 /**
1289  * Generate sin(a) using SSE2
1290  */
1291 LLVMValueRef
1292 lp_build_sin(struct lp_build_context *bld,
1293              LLVMValueRef a)
1294 {
1295    struct lp_type int_type = lp_int_type(bld->type);
1296    LLVMBuilderRef b = bld->builder;
1297    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1298    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1299
1300    /*
1301     *  take the absolute value,
1302     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1303     */
1304
1305    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1306    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1307
1308    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1309    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1310
1311    /*
1312     * extract the sign bit (upper one)
1313     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1314     */
1315    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1316    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1317
1318    /*
1319     * scale by 4/Pi
1320     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1321     */
1322
1323    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1324    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1325
1326    /*
1327     * store the integer part of y in mm0
1328     * emm2 = _mm_cvttps_epi32(y);
1329     */
1330
1331    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1332
1333    /*
1334     * j=(j+1) & (~1) (see the cephes sources)
1335     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1336     */
1337
1338    LLVMValueRef all_one = lp_build_const_v4si(1);
1339    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1340    /*
1341     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1342     */
1343    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1344    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1345
1346    /*
1347     * y = _mm_cvtepi32_ps(emm2);
1348     */
1349    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1350
1351    /* get the swap sign flag
1352     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1353     */
1354    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1355    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1356
1357    /*
1358     * emm2 = _mm_slli_epi32(emm0, 29);
1359     */
1360    LLVMValueRef const_29 = lp_build_const_v4si(29);
1361    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1362
1363    /*
1364     * get the polynom selection mask
1365     * there is one polynom for 0 <= x <= Pi/4
1366     * and another one for Pi/4<x<=Pi/2
1367     * Both branches will be computed.
1368     *
1369     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1370     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1371     */
1372
1373    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1374    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1375    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1376                                              emm2_3, lp_build_const_v4si(0));
1377    /*
1378     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1379     */
1380    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1381
1382    /*
1383     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1384     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1385     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1386     */
1387    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1388    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1389    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1390
1391    /*
1392     * The magic pass: "Extended precision modular arithmetic"
1393     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1394     * xmm1 = _mm_mul_ps(y, xmm1);
1395     * xmm2 = _mm_mul_ps(y, xmm2);
1396     * xmm3 = _mm_mul_ps(y, xmm3);
1397     */
1398    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1399    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1400    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1401
1402    /*
1403     * x = _mm_add_ps(x, xmm1);
1404     * x = _mm_add_ps(x, xmm2);
1405     * x = _mm_add_ps(x, xmm3);
1406     */
1407
1408    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1409    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1410    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1411
1412    /*
1413     * Evaluate the first polynom  (0 <= x <= Pi/4)
1414     *
1415     * z = _mm_mul_ps(x,x);
1416     */
1417    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1418
1419    /*
1420     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1421     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1422     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1423     */
1424    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1425    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1426    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1427
1428    /*
1429     * y = *(v4sf*)_ps_coscof_p0;
1430     * y = _mm_mul_ps(y, z);
1431     */
1432    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1433    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1434    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1435    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1436    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1437    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1438
1439
1440    /*
1441     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1442     * y = _mm_sub_ps(y, tmp);
1443     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1444     */
1445    LLVMValueRef half = lp_build_const_v4sf(0.5);
1446    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1447    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1448    LLVMValueRef one = lp_build_const_v4sf(1.0);
1449    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1450
1451    /*
1452     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1453     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1454     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1455     */
1456    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1457    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1458    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1459
1460    /*
1461     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1462     *
1463     * y2 = *(v4sf*)_ps_sincof_p0;
1464     * y2 = _mm_mul_ps(y2, z);
1465     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1466     * y2 = _mm_mul_ps(y2, z);
1467     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1468     * y2 = _mm_mul_ps(y2, z);
1469     * y2 = _mm_mul_ps(y2, x);
1470     * y2 = _mm_add_ps(y2, x);
1471     */
1472
1473    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1474    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1475    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1476    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1477    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1478    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1479    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1480
1481    /*
1482     * select the correct result from the two polynoms
1483     * xmm3 = poly_mask;
1484     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1485     * y = _mm_andnot_ps(xmm3, y);
1486     * y = _mm_add_ps(y,y2);
1487     */
1488    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1489    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1490    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1491    LLVMValueRef inv = lp_build_const_v4si(~0);
1492    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1493    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1494    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1495
1496    /*
1497     * update the sign
1498     * y = _mm_xor_ps(y, sign_bit);
1499     */
1500    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1501    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1502    return y_result;
1503 }
1504
1505
1506 /**
1507  * Generate cos(a) using SSE2
1508  */
1509 LLVMValueRef
1510 lp_build_cos(struct lp_build_context *bld,
1511              LLVMValueRef a)
1512 {
1513    struct lp_type int_type = lp_int_type(bld->type);
1514    LLVMBuilderRef b = bld->builder;
1515    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1516    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1517
1518    /*
1519     *  take the absolute value,
1520     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1521     */
1522
1523    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1524    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1525
1526    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1527    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1528
1529    /*
1530     * scale by 4/Pi
1531     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1532     */
1533
1534    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1535    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1536
1537    /*
1538     * store the integer part of y in mm0
1539     * emm2 = _mm_cvttps_epi32(y);
1540     */
1541
1542    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1543
1544    /*
1545     * j=(j+1) & (~1) (see the cephes sources)
1546     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1547     */
1548
1549    LLVMValueRef all_one = lp_build_const_v4si(1);
1550    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1551    /*
1552     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1553     */
1554    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1555    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1556
1557    /*
1558     * y = _mm_cvtepi32_ps(emm2);
1559     */
1560    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1561
1562
1563    /*
1564     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1565     */
1566    LLVMValueRef const_2 = lp_build_const_v4si(2);
1567    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1568
1569
1570    /* get the swap sign flag
1571     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1572     */
1573    LLVMValueRef inv = lp_build_const_v4si(~0);
1574    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1575    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1576    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1577
1578    /*
1579     * emm2 = _mm_slli_epi32(emm0, 29);
1580     */
1581    LLVMValueRef const_29 = lp_build_const_v4si(29);
1582    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1583
1584    /*
1585     * get the polynom selection mask
1586     * there is one polynom for 0 <= x <= Pi/4
1587     * and another one for Pi/4<x<=Pi/2
1588     * Both branches will be computed.
1589     *
1590     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1591     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1592     */
1593
1594    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1595    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1596    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1597                                              emm2_3, lp_build_const_v4si(0));
1598
1599    /*
1600     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1601     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1602     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1603     */
1604    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1605    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1606    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1607
1608    /*
1609     * The magic pass: "Extended precision modular arithmetic"
1610     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1611     * xmm1 = _mm_mul_ps(y, xmm1);
1612     * xmm2 = _mm_mul_ps(y, xmm2);
1613     * xmm3 = _mm_mul_ps(y, xmm3);
1614     */
1615    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1616    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1617    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1618
1619    /*
1620     * x = _mm_add_ps(x, xmm1);
1621     * x = _mm_add_ps(x, xmm2);
1622     * x = _mm_add_ps(x, xmm3);
1623     */
1624
1625    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1626    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1627    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1628
1629    /*
1630     * Evaluate the first polynom  (0 <= x <= Pi/4)
1631     *
1632     * z = _mm_mul_ps(x,x);
1633     */
1634    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1635
1636    /*
1637     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1638     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1639     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1640     */
1641    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1642    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1643    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1644
1645    /*
1646     * y = *(v4sf*)_ps_coscof_p0;
1647     * y = _mm_mul_ps(y, z);
1648     */
1649    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1650    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1651    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1652    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1653    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1654    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1655
1656
1657    /*
1658     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1659     * y = _mm_sub_ps(y, tmp);
1660     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1661     */
1662    LLVMValueRef half = lp_build_const_v4sf(0.5);
1663    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1664    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1665    LLVMValueRef one = lp_build_const_v4sf(1.0);
1666    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1667
1668    /*
1669     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1670     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1671     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1672     */
1673    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1674    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1675    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1676
1677    /*
1678     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1679     *
1680     * y2 = *(v4sf*)_ps_sincof_p0;
1681     * y2 = _mm_mul_ps(y2, z);
1682     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1683     * y2 = _mm_mul_ps(y2, z);
1684     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1685     * y2 = _mm_mul_ps(y2, z);
1686     * y2 = _mm_mul_ps(y2, x);
1687     * y2 = _mm_add_ps(y2, x);
1688     */
1689
1690    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1691    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1692    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1693    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1694    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1695    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1696    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1697
1698    /*
1699     * select the correct result from the two polynoms
1700     * xmm3 = poly_mask;
1701     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1702     * y = _mm_andnot_ps(xmm3, y);
1703     * y = _mm_add_ps(y,y2);
1704     */
1705    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1706    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1707    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1708    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1709    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1710    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1711
1712    /*
1713     * update the sign
1714     * y = _mm_xor_ps(y, sign_bit);
1715     */
1716    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1717    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1718    return y_result;
1719 }
1720
1721
1722 /**
1723  * Generate pow(x, y)
1724  */
1725 LLVMValueRef
1726 lp_build_pow(struct lp_build_context *bld,
1727              LLVMValueRef x,
1728              LLVMValueRef y)
1729 {
1730    /* TODO: optimize the constant case */
1731    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1732       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1733                    __FUNCTION__);
1734
1735    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1736 }
1737
1738
1739 /**
1740  * Generate exp(x)
1741  */
1742 LLVMValueRef
1743 lp_build_exp(struct lp_build_context *bld,
1744              LLVMValueRef x)
1745 {
1746    /* log2(e) = 1/log(2) */
1747    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1748
1749    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1750 }
1751
1752
1753 /**
1754  * Generate log(x)
1755  */
1756 LLVMValueRef
1757 lp_build_log(struct lp_build_context *bld,
1758              LLVMValueRef x)
1759 {
1760    /* log(2) */
1761    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1762
1763    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1764 }
1765
1766
1767 #define EXP_POLY_DEGREE 3
1768 #define LOG_POLY_DEGREE 5
1769
1770
1771 /**
1772  * Generate polynomial.
1773  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1774  */
1775 static LLVMValueRef
1776 lp_build_polynomial(struct lp_build_context *bld,
1777                     LLVMValueRef x,
1778                     const double *coeffs,
1779                     unsigned num_coeffs)
1780 {
1781    const struct lp_type type = bld->type;
1782    LLVMValueRef res = NULL;
1783    unsigned i;
1784
1785    /* TODO: optimize the constant case */
1786    if(LLVMIsConstant(x))
1787       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1788                    __FUNCTION__);
1789
1790    for (i = num_coeffs; i--; ) {
1791       LLVMValueRef coeff;
1792
1793       coeff = lp_build_const_vec(type, coeffs[i]);
1794
1795       if(res)
1796          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1797       else
1798          res = coeff;
1799    }
1800
1801    if(res)
1802       return res;
1803    else
1804       return bld->undef;
1805 }
1806
1807
1808 /**
1809  * Minimax polynomial fit of 2**x, in range [0, 1[
1810  */
1811 const double lp_build_exp2_polynomial[] = {
1812 #if EXP_POLY_DEGREE == 5
1813    0.999999999690134838155,
1814    0.583974334321735217258,
1815    0.164553105719676828492,
1816    0.0292811063701710962255,
1817    0.00354944426657875141846,
1818    0.000296253726543423377365
1819 #elif EXP_POLY_DEGREE == 4
1820    1.00000001502262084505,
1821    0.563586057338685991394,
1822    0.150436017652442413623,
1823    0.0243220604213317927308,
1824    0.0025359088446580436489
1825 #elif EXP_POLY_DEGREE == 3
1826    0.999925218562710312959,
1827    0.695833540494823811697,
1828    0.226067155427249155588,
1829    0.0780245226406372992967
1830 #elif EXP_POLY_DEGREE == 2
1831    1.00172476321474503578,
1832    0.657636275736077639316,
1833    0.33718943461968720704
1834 #else
1835 #error
1836 #endif
1837 };
1838
1839
1840 void
1841 lp_build_exp2_approx(struct lp_build_context *bld,
1842                      LLVMValueRef x,
1843                      LLVMValueRef *p_exp2_int_part,
1844                      LLVMValueRef *p_frac_part,
1845                      LLVMValueRef *p_exp2)
1846 {
1847    const struct lp_type type = bld->type;
1848    LLVMTypeRef vec_type = lp_build_vec_type(type);
1849    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1850    LLVMValueRef ipart = NULL;
1851    LLVMValueRef fpart = NULL;
1852    LLVMValueRef expipart = NULL;
1853    LLVMValueRef expfpart = NULL;
1854    LLVMValueRef res = NULL;
1855
1856    if(p_exp2_int_part || p_frac_part || p_exp2) {
1857       /* TODO: optimize the constant case */
1858       if(LLVMIsConstant(x))
1859          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1860                       __FUNCTION__);
1861
1862       assert(type.floating && type.width == 32);
1863
1864       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1865       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1866
1867       /* ipart = floor(x) */
1868       ipart = lp_build_floor(bld, x);
1869
1870       /* fpart = x - ipart */
1871       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
1872    }
1873
1874    if(p_exp2_int_part || p_exp2) {
1875       /* expipart = (float) (1 << ipart) */
1876       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1877       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1878       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1879       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1880    }
1881
1882    if(p_exp2) {
1883       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1884                                      Elements(lp_build_exp2_polynomial));
1885
1886       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
1887    }
1888
1889    if(p_exp2_int_part)
1890       *p_exp2_int_part = expipart;
1891
1892    if(p_frac_part)
1893       *p_frac_part = fpart;
1894
1895    if(p_exp2)
1896       *p_exp2 = res;
1897 }
1898
1899
1900 LLVMValueRef
1901 lp_build_exp2(struct lp_build_context *bld,
1902               LLVMValueRef x)
1903 {
1904    LLVMValueRef res;
1905    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1906    return res;
1907 }
1908
1909
1910 /**
1911  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1912  * These coefficients can be generate with
1913  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1914  */
1915 const double lp_build_log2_polynomial[] = {
1916 #if LOG_POLY_DEGREE == 6
1917    3.11578814719469302614,
1918    -3.32419399085241980044,
1919    2.59883907202499966007,
1920    -1.23152682416275988241,
1921    0.318212422185251071475,
1922    -0.0344359067839062357313
1923 #elif LOG_POLY_DEGREE == 5
1924    2.8882704548164776201,
1925    -2.52074962577807006663,
1926    1.48116647521213171641,
1927    -0.465725644288844778798,
1928    0.0596515482674574969533
1929 #elif LOG_POLY_DEGREE == 4
1930    2.61761038894603480148,
1931    -1.75647175389045657003,
1932    0.688243882994381274313,
1933    -0.107254423828329604454
1934 #elif LOG_POLY_DEGREE == 3
1935    2.28330284476918490682,
1936    -1.04913055217340124191,
1937    0.204446009836232697516
1938 #else
1939 #error
1940 #endif
1941 };
1942
1943
1944 /**
1945  * See http://www.devmaster.net/forums/showthread.php?p=43580
1946  */
1947 void
1948 lp_build_log2_approx(struct lp_build_context *bld,
1949                      LLVMValueRef x,
1950                      LLVMValueRef *p_exp,
1951                      LLVMValueRef *p_floor_log2,
1952                      LLVMValueRef *p_log2)
1953 {
1954    const struct lp_type type = bld->type;
1955    LLVMTypeRef vec_type = lp_build_vec_type(type);
1956    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1957
1958    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
1959    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
1960    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1961
1962    LLVMValueRef i = NULL;
1963    LLVMValueRef exp = NULL;
1964    LLVMValueRef mant = NULL;
1965    LLVMValueRef logexp = NULL;
1966    LLVMValueRef logmant = NULL;
1967    LLVMValueRef res = NULL;
1968
1969    if(p_exp || p_floor_log2 || p_log2) {
1970       /* TODO: optimize the constant case */
1971       if(LLVMIsConstant(x))
1972          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1973                       __FUNCTION__);
1974
1975       assert(type.floating && type.width == 32);
1976
1977       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1978
1979       /* exp = (float) exponent(x) */
1980       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1981    }
1982
1983    if(p_floor_log2 || p_log2) {
1984       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
1985       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
1986       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1987    }
1988
1989    if(p_log2) {
1990       /* mant = (float) mantissa(x) */
1991       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1992       mant = LLVMBuildOr(bld->builder, mant, one, "");
1993       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1994
1995       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1996                                     Elements(lp_build_log2_polynomial));
1997
1998       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1999       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2000
2001       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2002    }
2003
2004    if(p_exp) {
2005       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2006       *p_exp = exp;
2007    }
2008
2009    if(p_floor_log2)
2010       *p_floor_log2 = logexp;
2011
2012    if(p_log2)
2013       *p_log2 = res;
2014 }
2015
2016
2017 LLVMValueRef
2018 lp_build_log2(struct lp_build_context *bld,
2019               LLVMValueRef x)
2020 {
2021    LLVMValueRef res;
2022    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2023    return res;
2024 }