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 #define EXP_POLY_DEGREE 3
  64
  65 #define LOG_POLY_DEGREE 5
  66
  67
  68 /**
  69  * Generate min(a, b)
  70  * No checks for special case values of a or b = 1 or 0 are done.
  71  */
  72 static LLVMValueRef
  73 lp_build_min_simple(struct lp_build_context *bld,
  74                     LLVMValueRef a,
  75                     LLVMValueRef b)
  76 {
  77    const struct lp_type type = bld->type;
  78    const char *intrinsic = NULL;
  79    LLVMValueRef cond;
  80
  81    assert(lp_check_value(type, a));
  82    assert(lp_check_value(type, b));
  83
  84    /* TODO: optimize the constant case */
  85
  86    if(type.width * type.length == 128) {
  87       if(type.floating) {
  88          if(type.width == 32 && util_cpu_caps.has_sse)
  89             intrinsic = "llvm.x86.sse.min.ps";
  90          if(type.width == 64 && util_cpu_caps.has_sse2)
  91             intrinsic = "llvm.x86.sse2.min.pd";
  92       }
  93       else {
  94          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  95             intrinsic = "llvm.x86.sse2.pminu.b";
  96          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  97             intrinsic = "llvm.x86.sse41.pminsb";
  98          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  99             intrinsic = "llvm.x86.sse41.pminuw";
 100          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 101             intrinsic = "llvm.x86.sse2.pmins.w";
 102          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 103             intrinsic = "llvm.x86.sse41.pminud";
 104          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 105             intrinsic = "llvm.x86.sse41.pminsd";
 106       }
 107    }
 108
 109    if(intrinsic)
 110       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 111
 112    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 113    return lp_build_select(bld, cond, a, b);
 114 }
 115
 116
 117 /**
 118  * Generate max(a, b)
 119  * No checks for special case values of a or b = 1 or 0 are done.
 120  */
 121 static LLVMValueRef
 122 lp_build_max_simple(struct lp_build_context *bld,
 123                     LLVMValueRef a,
 124                     LLVMValueRef b)
 125 {
 126    const struct lp_type type = bld->type;
 127    const char *intrinsic = NULL;
 128    LLVMValueRef cond;
 129
 130    assert(lp_check_value(type, a));
 131    assert(lp_check_value(type, b));
 132
 133    /* TODO: optimize the constant case */
 134
 135    if(type.width * type.length == 128) {
 136       if(type.floating) {
 137          if(type.width == 32 && util_cpu_caps.has_sse)
 138             intrinsic = "llvm.x86.sse.max.ps";
 139          if(type.width == 64 && util_cpu_caps.has_sse2)
 140             intrinsic = "llvm.x86.sse2.max.pd";
 141       }
 142       else {
 143          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 144             intrinsic = "llvm.x86.sse2.pmaxu.b";
 145          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 146             intrinsic = "llvm.x86.sse41.pmaxsb";
 147          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 148             intrinsic = "llvm.x86.sse41.pmaxuw";
 149          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 150             intrinsic = "llvm.x86.sse2.pmaxs.w";
 151          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 152             intrinsic = "llvm.x86.sse41.pmaxud";
 153          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 154             intrinsic = "llvm.x86.sse41.pmaxsd";
 155       }
 156    }
 157
 158    if(intrinsic)
 159       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 160
 161    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 162    return lp_build_select(bld, cond, a, b);
 163 }
 164
 165
 166 /**
 167  * Generate 1 - a, or ~a depending on bld->type.
 168  */
 169 LLVMValueRef
 170 lp_build_comp(struct lp_build_context *bld,
 171               LLVMValueRef a)
 172 {
 173    const struct lp_type type = bld->type;
 174
 175    assert(lp_check_value(type, a));
 176
 177    if(a == bld->one)
 178       return bld->zero;
 179    if(a == bld->zero)
 180       return bld->one;
 181
 182    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 183       if(LLVMIsConstant(a))
 184          return LLVMConstNot(a);
 185       else
 186          return LLVMBuildNot(bld->builder, a, "");
 187    }
 188
 189    if(LLVMIsConstant(a))
 190       if (type.floating)
 191           return LLVMConstFSub(bld->one, a);
 192       else
 193           return LLVMConstSub(bld->one, a);
 194    else
 195       if (type.floating)
 196          return LLVMBuildFSub(bld->builder, bld->one, a, "");
 197       else
 198          return LLVMBuildSub(bld->builder, bld->one, a, "");
 199 }
 200
 201
 202 /**
 203  * Generate a + b
 204  */
 205 LLVMValueRef
 206 lp_build_add(struct lp_build_context *bld,
 207              LLVMValueRef a,
 208              LLVMValueRef b)
 209 {
 210    const struct lp_type type = bld->type;
 211    LLVMValueRef res;
 212
 213    assert(lp_check_value(type, a));
 214    assert(lp_check_value(type, b));
 215
 216    if(a == bld->zero)
 217       return b;
 218    if(b == bld->zero)
 219       return a;
 220    if(a == bld->undef || b == bld->undef)
 221       return bld->undef;
 222
 223    if(bld->type.norm) {
 224       const char *intrinsic = NULL;
 225
 226       if(a == bld->one || b == bld->one)
 227         return bld->one;
 228
 229       if(util_cpu_caps.has_sse2 &&
 230          type.width * type.length == 128 &&
 231          !type.floating && !type.fixed) {
 232          if(type.width == 8)
 233             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 234          if(type.width == 16)
 235             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 236       }
 237
 238       if(intrinsic)
 239          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 240    }
 241
 242    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 243       if (type.floating)
 244          res = LLVMConstFAdd(a, b);
 245       else
 246          res = LLVMConstAdd(a, b);
 247    else
 248       if (type.floating)
 249          res = LLVMBuildFAdd(bld->builder, a, b, "");
 250       else
 251          res = LLVMBuildAdd(bld->builder, a, b, "");
 252
 253    /* clamp to ceiling of 1.0 */
 254    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 255       res = lp_build_min_simple(bld, res, bld->one);
 256
 257    /* XXX clamp to floor of -1 or 0??? */
 258
 259    return res;
 260 }
 261
 262
 263 /** Return the scalar sum of the elements of a */
 264 LLVMValueRef
 265 lp_build_sum_vector(struct lp_build_context *bld,
 266                     LLVMValueRef a)
 267 {
 268    const struct lp_type type = bld->type;
 269    LLVMValueRef index, res;
 270    unsigned i;
 271
 272    assert(lp_check_value(type, a));
 273
 274    if (type.length == 1) {
 275       return a;
 276    }
 277
 278    assert(!bld->type.norm);
 279
 280    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 281    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 282
 283    for (i = 1; i < type.length; i++) {
 284       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 285       if (type.floating)
 286          res = LLVMBuildFAdd(bld->builder, res,
 287                             LLVMBuildExtractElement(bld->builder,
 288                                                     a, index, ""),
 289                             "");
 290       else
 291          res = LLVMBuildAdd(bld->builder, res,
 292                             LLVMBuildExtractElement(bld->builder,
 293                                                     a, index, ""),
 294                             "");
 295    }
 296
 297    return res;
 298 }
 299
 300
 301 /**
 302  * Generate a - b
 303  */
 304 LLVMValueRef
 305 lp_build_sub(struct lp_build_context *bld,
 306              LLVMValueRef a,
 307              LLVMValueRef b)
 308 {
 309    const struct lp_type type = bld->type;
 310    LLVMValueRef res;
 311
 312    assert(lp_check_value(type, a));
 313    assert(lp_check_value(type, b));
 314
 315    if(b == bld->zero)
 316       return a;
 317    if(a == bld->undef || b == bld->undef)
 318       return bld->undef;
 319    if(a == b)
 320       return bld->zero;
 321
 322    if(bld->type.norm) {
 323       const char *intrinsic = NULL;
 324
 325       if(b == bld->one)
 326         return bld->zero;
 327
 328       if(util_cpu_caps.has_sse2 &&
 329          type.width * type.length == 128 &&
 330          !type.floating && !type.fixed) {
 331          if(type.width == 8)
 332             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 333          if(type.width == 16)
 334             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 335       }
 336
 337       if(intrinsic)
 338          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 339    }
 340
 341    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 342       if (type.floating)
 343          res = LLVMConstFSub(a, b);
 344       else
 345          res = LLVMConstSub(a, b);
 346    else
 347       if (type.floating)
 348          res = LLVMBuildFSub(bld->builder, a, b, "");
 349       else
 350          res = LLVMBuildSub(bld->builder, a, b, "");
 351
 352    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 353       res = lp_build_max_simple(bld, res, bld->zero);
 354
 355    return res;
 356 }
 357
 358
 359 /**
 360  * Normalized 8bit multiplication.
 361  *
 362  * - alpha plus one
 363  *
 364  *     makes the following approximation to the division (Sree)
 365  *
 366  *       a*b/255 ~= (a*(b + 1)) >> 256
 367  *
 368  *     which is the fastest method that satisfies the following OpenGL criteria
 369  *
 370  *       0*0 = 0 and 255*255 = 255
 371  *
 372  * - geometric series
 373  *
 374  *     takes the geometric series approximation to the division
 375  *
 376  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 377  *
 378  *     in this case just the first two terms to fit in 16bit arithmetic
 379  *
 380  *       t/255 ~= (t + (t >> 8)) >> 8
 381  *
 382  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 383  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 384  *     must be used
 385  *
 386  * - geometric series plus rounding
 387  *
 388  *     when using a geometric series division instead of truncating the result
 389  *     use roundoff in the approximation (Jim Blinn)
 390  *
 391  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 392  *
 393  *     achieving the exact results
 394  *
 395  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 396  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 397  * @sa Michael Herf, The "double blend trick", May 2000,
 398  *     http://www.stereopsis.com/doubleblend.html
 399  */
 400 static LLVMValueRef
 401 lp_build_mul_u8n(LLVMBuilderRef builder,
 402                  struct lp_type i16_type,
 403                  LLVMValueRef a, LLVMValueRef b)
 404 {
 405    LLVMValueRef c8;
 406    LLVMValueRef ab;
 407
 408    assert(!i16_type.floating);
 409    assert(lp_check_value(i16_type, a));
 410    assert(lp_check_value(i16_type, b));
 411
 412    c8 = lp_build_const_int_vec(i16_type, 8);
 413
 414 #if 0
 415
 416    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 417    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 418    ab = LLVMBuildMul(builder, a, b, "");
 419
 420 #else
 421
 422    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 423    ab = LLVMBuildMul(builder, a, b, "");
 424    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 425    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 426
 427 #endif
 428
 429    ab = LLVMBuildLShr(builder, ab, c8, "");
 430
 431    return ab;
 432 }
 433
 434
 435 /**
 436  * Generate a * b
 437  */
 438 LLVMValueRef
 439 lp_build_mul(struct lp_build_context *bld,
 440              LLVMValueRef a,
 441              LLVMValueRef b)
 442 {
 443    const struct lp_type type = bld->type;
 444    LLVMValueRef shift;
 445    LLVMValueRef res;
 446
 447    assert(lp_check_value(type, a));
 448    assert(lp_check_value(type, b));
 449
 450    if(a == bld->zero)
 451       return bld->zero;
 452    if(a == bld->one)
 453       return b;
 454    if(b == bld->zero)
 455       return bld->zero;
 456    if(b == bld->one)
 457       return a;
 458    if(a == bld->undef || b == bld->undef)
 459       return bld->undef;
 460
 461    if(!type.floating && !type.fixed && type.norm) {
 462       if(type.width == 8) {
 463          struct lp_type i16_type = lp_wider_type(type);
 464          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 465
 466          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 467          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 468
 469          /* PMULLW, PSRLW, PADDW */
 470          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 471          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 472
 473          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 474
 475          return ab;
 476       }
 477
 478       /* FIXME */
 479       assert(0);
 480    }
 481
 482    if(type.fixed)
 483       shift = lp_build_const_int_vec(type, type.width/2);
 484    else
 485       shift = NULL;
 486
 487    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 488       if (type.floating)
 489          res = LLVMConstFMul(a, b);
 490       else
 491          res = LLVMConstMul(a, b);
 492       if(shift) {
 493          if(type.sign)
 494             res = LLVMConstAShr(res, shift);
 495          else
 496             res = LLVMConstLShr(res, shift);
 497       }
 498    }
 499    else {
 500       if (type.floating)
 501          res = LLVMBuildFMul(bld->builder, a, b, "");
 502       else
 503          res = LLVMBuildMul(bld->builder, a, b, "");
 504       if(shift) {
 505          if(type.sign)
 506             res = LLVMBuildAShr(bld->builder, res, shift, "");
 507          else
 508             res = LLVMBuildLShr(bld->builder, res, shift, "");
 509       }
 510    }
 511
 512    return res;
 513 }
 514
 515
 516 /**
 517  * Small vector x scale multiplication optimization.
 518  */
 519 LLVMValueRef
 520 lp_build_mul_imm(struct lp_build_context *bld,
 521                  LLVMValueRef a,
 522                  int b)
 523 {
 524    LLVMValueRef factor;
 525
 526    assert(lp_check_value(bld->type, a));
 527
 528    if(b == 0)
 529       return bld->zero;
 530
 531    if(b == 1)
 532       return a;
 533
 534    if(b == -1)
 535       return lp_build_negate(bld, a);
 536
 537    if(b == 2 && bld->type.floating)
 538       return lp_build_add(bld, a, a);
 539
 540    if(util_is_power_of_two(b)) {
 541       unsigned shift = ffs(b) - 1;
 542
 543       if(bld->type.floating) {
 544 #if 0
 545          /*
 546           * Power of two multiplication by directly manipulating the mantissa.
 547           *
 548           * XXX: This might not be always faster, it will introduce a small error
 549           * for multiplication by zero, and it will produce wrong results
 550           * for Inf and NaN.
 551           */
 552          unsigned mantissa = lp_mantissa(bld->type);
 553          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 554          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 555          a = LLVMBuildAdd(bld->builder, a, factor, "");
 556          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 557          return a;
 558 #endif
 559       }
 560       else {
 561          factor = lp_build_const_vec(bld->type, shift);
 562          return LLVMBuildShl(bld->builder, a, factor, "");
 563       }
 564    }
 565
 566    factor = lp_build_const_vec(bld->type, (double)b);
 567    return lp_build_mul(bld, a, factor);
 568 }
 569
 570
 571 /**
 572  * Generate a / b
 573  */
 574 LLVMValueRef
 575 lp_build_div(struct lp_build_context *bld,
 576              LLVMValueRef a,
 577              LLVMValueRef b)
 578 {
 579    const struct lp_type type = bld->type;
 580
 581    assert(lp_check_value(type, a));
 582    assert(lp_check_value(type, b));
 583
 584    if(a == bld->zero)
 585       return bld->zero;
 586    if(a == bld->one)
 587       return lp_build_rcp(bld, b);
 588    if(b == bld->zero)
 589       return bld->undef;
 590    if(b == bld->one)
 591       return a;
 592    if(a == bld->undef || b == bld->undef)
 593       return bld->undef;
 594
 595    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 596       if (type.floating)
 597          return LLVMConstFDiv(a, b);
 598       else if (type.sign)
 599          return LLVMConstSDiv(a, b);
 600       else
 601          return LLVMConstUDiv(a, b);
 602    }
 603
 604    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 605       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 606
 607    if (type.floating)
 608       return LLVMBuildFDiv(bld->builder, a, b, "");
 609    else if (type.sign)
 610       return LLVMBuildSDiv(bld->builder, a, b, "");
 611    else
 612       return LLVMBuildUDiv(bld->builder, a, b, "");
 613 }
 614
 615
 616 /**
 617  * Linear interpolation -- without any checks.
 618  *
 619  * @sa http://www.stereopsis.com/doubleblend.html
 620  */
 621 static INLINE LLVMValueRef
 622 lp_build_lerp_simple(struct lp_build_context *bld,
 623                      LLVMValueRef x,
 624                      LLVMValueRef v0,
 625                      LLVMValueRef v1)
 626 {
 627    LLVMValueRef delta;
 628    LLVMValueRef res;
 629
 630    assert(lp_check_value(bld->type, x));
 631    assert(lp_check_value(bld->type, v0));
 632    assert(lp_check_value(bld->type, v1));
 633
 634    delta = lp_build_sub(bld, v1, v0);
 635
 636    res = lp_build_mul(bld, x, delta);
 637
 638    res = lp_build_add(bld, v0, res);
 639
 640    if (bld->type.fixed) {
 641       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 642        * but it will be wrong for other uses. Basically we need a more
 643        * powerful lp_type, capable of further distinguishing the values
 644        * interpretation from the value storage. */
 645       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 646    }
 647
 648    return res;
 649 }
 650
 651
 652 /**
 653  * Linear interpolation.
 654  */
 655 LLVMValueRef
 656 lp_build_lerp(struct lp_build_context *bld,
 657               LLVMValueRef x,
 658               LLVMValueRef v0,
 659               LLVMValueRef v1)
 660 {
 661    const struct lp_type type = bld->type;
 662    LLVMValueRef res;
 663
 664    assert(lp_check_value(type, x));
 665    assert(lp_check_value(type, v0));
 666    assert(lp_check_value(type, v1));
 667
 668    if (type.norm) {
 669       struct lp_type wide_type;
 670       struct lp_build_context wide_bld;
 671       LLVMValueRef xl, xh, v0l, v0h, v1l, v1h, resl, resh;
 672       LLVMValueRef shift;
 673
 674       assert(type.length >= 2);
 675       assert(!type.sign);
 676
 677       /*
 678        * Create a wider type, enough to hold the intermediate result of the
 679        * multiplication.
 680        */
 681       memset(&wide_type, 0, sizeof wide_type);
 682       wide_type.fixed  = TRUE;
 683       wide_type.width  = type.width*2;
 684       wide_type.length = type.length/2;
 685
 686       lp_build_context_init(&wide_bld, bld->builder, wide_type);
 687
 688       lp_build_unpack2(bld->builder, type, wide_type, x,  &xl,  &xh);
 689       lp_build_unpack2(bld->builder, type, wide_type, v0, &v0l, &v0h);
 690       lp_build_unpack2(bld->builder, type, wide_type, v1, &v1l, &v1h);
 691
 692       /*
 693        * Scale x from [0, 255] to [0, 256]
 694        */
 695
 696       shift = lp_build_const_int_vec(wide_type, type.width - 1);
 697
 698       xl = lp_build_add(&wide_bld, xl,
 699                         LLVMBuildAShr(bld->builder, xl, shift, ""));
 700       xh = lp_build_add(&wide_bld, xh,
 701                         LLVMBuildAShr(bld->builder, xh, shift, ""));
 702
 703       /*
 704        * Lerp both halves.
 705        */
 706
 707       resl = lp_build_lerp_simple(&wide_bld, xl, v0l, v1l);
 708       resh = lp_build_lerp_simple(&wide_bld, xh, v0h, v1h);
 709
 710       res = lp_build_pack2(bld->builder, wide_type, type, resl, resh);
 711    } else {
 712       res = lp_build_lerp_simple(bld, x, v0, v1);
 713    }
 714
 715    return res;
 716 }
 717
 718
 719 LLVMValueRef
 720 lp_build_lerp_2d(struct lp_build_context *bld,
 721                  LLVMValueRef x,
 722                  LLVMValueRef y,
 723                  LLVMValueRef v00,
 724                  LLVMValueRef v01,
 725                  LLVMValueRef v10,
 726                  LLVMValueRef v11)
 727 {
 728    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 729    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 730    return lp_build_lerp(bld, y, v0, v1);
 731 }
 732
 733
 734 /**
 735  * Generate min(a, b)
 736  * Do checks for special cases.
 737  */
 738 LLVMValueRef
 739 lp_build_min(struct lp_build_context *bld,
 740              LLVMValueRef a,
 741              LLVMValueRef b)
 742 {
 743    assert(lp_check_value(bld->type, a));
 744    assert(lp_check_value(bld->type, b));
 745
 746    if(a == bld->undef || b == bld->undef)
 747       return bld->undef;
 748
 749    if(a == b)
 750       return a;
 751
 752    if(bld->type.norm) {
 753       if(a == bld->zero || b == bld->zero)
 754          return bld->zero;
 755       if(a == bld->one)
 756          return b;
 757       if(b == bld->one)
 758          return a;
 759    }
 760
 761    return lp_build_min_simple(bld, a, b);
 762 }
 763
 764
 765 /**
 766  * Generate max(a, b)
 767  * Do checks for special cases.
 768  */
 769 LLVMValueRef
 770 lp_build_max(struct lp_build_context *bld,
 771              LLVMValueRef a,
 772              LLVMValueRef b)
 773 {
 774    assert(lp_check_value(bld->type, a));
 775    assert(lp_check_value(bld->type, b));
 776
 777    if(a == bld->undef || b == bld->undef)
 778       return bld->undef;
 779
 780    if(a == b)
 781       return a;
 782
 783    if(bld->type.norm) {
 784       if(a == bld->one || b == bld->one)
 785          return bld->one;
 786       if(a == bld->zero)
 787          return b;
 788       if(b == bld->zero)
 789          return a;
 790    }
 791
 792    return lp_build_max_simple(bld, a, b);
 793 }
 794
 795
 796 /**
 797  * Generate clamp(a, min, max)
 798  * Do checks for special cases.
 799  */
 800 LLVMValueRef
 801 lp_build_clamp(struct lp_build_context *bld,
 802                LLVMValueRef a,
 803                LLVMValueRef min,
 804                LLVMValueRef max)
 805 {
 806    assert(lp_check_value(bld->type, a));
 807    assert(lp_check_value(bld->type, min));
 808    assert(lp_check_value(bld->type, max));
 809
 810    a = lp_build_min(bld, a, max);
 811    a = lp_build_max(bld, a, min);
 812    return a;
 813 }
 814
 815
 816 /**
 817  * Generate abs(a)
 818  */
 819 LLVMValueRef
 820 lp_build_abs(struct lp_build_context *bld,
 821              LLVMValueRef a)
 822 {
 823    const struct lp_type type = bld->type;
 824    LLVMTypeRef vec_type = lp_build_vec_type(type);
 825
 826    assert(lp_check_value(type, a));
 827
 828    if(!type.sign)
 829       return a;
 830
 831    if(type.floating) {
 832       /* Mask out the sign bit */
 833       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 834       unsigned long long absMask = ~(1ULL << (type.width - 1));
 835       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 836       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 837       a = LLVMBuildAnd(bld->builder, a, mask, "");
 838       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 839       return a;
 840    }
 841
 842    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 843       switch(type.width) {
 844       case 8:
 845          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 846       case 16:
 847          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 848       case 32:
 849          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 850       }
 851    }
 852
 853    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 854 }
 855
 856
 857 LLVMValueRef
 858 lp_build_negate(struct lp_build_context *bld,
 859                 LLVMValueRef a)
 860 {
 861    assert(lp_check_value(bld->type, a));
 862
 863 #if HAVE_LLVM >= 0x0207
 864    if (bld->type.floating)
 865       a = LLVMBuildFNeg(bld->builder, a, "");
 866    else
 867 #endif
 868       a = LLVMBuildNeg(bld->builder, a, "");
 869
 870    return a;
 871 }
 872
 873
 874 /** Return -1, 0 or +1 depending on the sign of a */
 875 LLVMValueRef
 876 lp_build_sgn(struct lp_build_context *bld,
 877              LLVMValueRef a)
 878 {
 879    const struct lp_type type = bld->type;
 880    LLVMValueRef cond;
 881    LLVMValueRef res;
 882
 883    assert(lp_check_value(type, a));
 884
 885    /* Handle non-zero case */
 886    if(!type.sign) {
 887       /* if not zero then sign must be positive */
 888       res = bld->one;
 889    }
 890    else if(type.floating) {
 891       LLVMTypeRef vec_type;
 892       LLVMTypeRef int_type;
 893       LLVMValueRef mask;
 894       LLVMValueRef sign;
 895       LLVMValueRef one;
 896       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 897
 898       int_type = lp_build_int_vec_type(type);
 899       vec_type = lp_build_vec_type(type);
 900       mask = lp_build_const_int_vec(type, maskBit);
 901
 902       /* Take the sign bit and add it to 1 constant */
 903       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 904       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 905       one = LLVMConstBitCast(bld->one, int_type);
 906       res = LLVMBuildOr(bld->builder, sign, one, "");
 907       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 908    }
 909    else
 910    {
 911       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 912       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 913       res = lp_build_select(bld, cond, bld->one, minus_one);
 914    }
 915
 916    /* Handle zero */
 917    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 918    res = lp_build_select(bld, cond, bld->zero, res);
 919
 920    return res;
 921 }
 922
 923
 924 /**
 925  * Set the sign of float vector 'a' according to 'sign'.
 926  * If sign==0, return abs(a).
 927  * If sign==1, return -abs(a);
 928  * Other values for sign produce undefined results.
 929  */
 930 LLVMValueRef
 931 lp_build_set_sign(struct lp_build_context *bld,
 932                   LLVMValueRef a, LLVMValueRef sign)
 933 {
 934    const struct lp_type type = bld->type;
 935    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 936    LLVMTypeRef vec_type = lp_build_vec_type(type);
 937    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 938    LLVMValueRef mask = lp_build_const_int_vec(type,
 939                              ~((unsigned long long) 1 << (type.width - 1)));
 940    LLVMValueRef val, res;
 941
 942    assert(type.floating);
 943    assert(lp_check_value(type, a));
 944
 945    /* val = reinterpret_cast<int>(a) */
 946    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 947    /* val = val & mask */
 948    val = LLVMBuildAnd(bld->builder, val, mask, "");
 949    /* sign = sign << shift */
 950    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 951    /* res = val | sign */
 952    res = LLVMBuildOr(bld->builder, val, sign, "");
 953    /* res = reinterpret_cast<float>(res) */
 954    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 955
 956    return res;
 957 }
 958
 959
 960 /**
 961  * Convert vector of (or scalar) int to vector of (or scalar) float.
 962  */
 963 LLVMValueRef
 964 lp_build_int_to_float(struct lp_build_context *bld,
 965                       LLVMValueRef a)
 966 {
 967    const struct lp_type type = bld->type;
 968    LLVMTypeRef vec_type = lp_build_vec_type(type);
 969
 970    assert(type.floating);
 971
 972    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 973 }
 974
 975
 976
 977 enum lp_build_round_sse41_mode
 978 {
 979    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 980    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 981    LP_BUILD_ROUND_SSE41_CEIL = 2,
 982    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 983 };
 984
 985
 986 static INLINE LLVMValueRef
 987 lp_build_round_sse41(struct lp_build_context *bld,
 988                      LLVMValueRef a,
 989                      enum lp_build_round_sse41_mode mode)
 990 {
 991    const struct lp_type type = bld->type;
 992    LLVMTypeRef i32t = LLVMInt32Type();
 993    const char *intrinsic;
 994    LLVMValueRef res;
 995
 996    assert(type.floating);
 997
 998    assert(lp_check_value(type, a));
 999    assert(util_cpu_caps.has_sse4_1);
1000
1001    if (type.length == 1) {
1002       LLVMTypeRef vec_type;
1003       LLVMValueRef undef;
1004       LLVMValueRef args[3];
1005       LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);
1006
1007       switch(type.width) {
1008       case 32:
1009          intrinsic = "llvm.x86.sse41.round.ss";
1010          break;
1011       case 64:
1012          intrinsic = "llvm.x86.sse41.round.sd";
1013          break;
1014       default:
1015          assert(0);
1016          return bld->undef;
1017       }
1018
1019       vec_type = LLVMVectorType(bld->elem_type, 4);
1020
1021       undef = LLVMGetUndef(vec_type);
1022
1023       args[0] = undef;
1024       args[1] = LLVMBuildInsertElement(bld->builder, undef, a, index0, "");
1025       args[2] = LLVMConstInt(i32t, mode, 0);
1026
1027       res = lp_build_intrinsic(bld->builder, intrinsic,
1028                                vec_type, args, Elements(args));
1029
1030       res = LLVMBuildExtractElement(bld->builder, res, index0, "");
1031    }
1032    else {
1033       assert(type.width*type.length == 128);
1034
1035       switch(type.width) {
1036       case 32:
1037          intrinsic = "llvm.x86.sse41.round.ps";
1038          break;
1039       case 64:
1040          intrinsic = "llvm.x86.sse41.round.pd";
1041          break;
1042       default:
1043          assert(0);
1044          return bld->undef;
1045       }
1046
1047       res = lp_build_intrinsic_binary(bld->builder, intrinsic,
1048                                       bld->vec_type, a,
1049                                       LLVMConstInt(i32t, mode, 0));
1050    }
1051
1052    return res;
1053 }
1054
1055
1056 /**
1057  * Return the integer part of a float (vector) value.  The returned value is
1058  * a float (vector).
1059  * Ex: trunc(-1.5) = 1.0
1060  */
1061 LLVMValueRef
1062 lp_build_trunc(struct lp_build_context *bld,
1063                LLVMValueRef a)
1064 {
1065    const struct lp_type type = bld->type;
1066
1067    assert(type.floating);
1068    assert(lp_check_value(type, a));
1069
1070    if (util_cpu_caps.has_sse4_1 &&
1071        (type.length == 1 || type.width*type.length == 128)) {
1072       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
1073    }
1074    else {
1075       LLVMTypeRef vec_type = lp_build_vec_type(type);
1076       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1077       LLVMValueRef res;
1078       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1079       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1080       return res;
1081    }
1082 }
1083
1084
1085 /**
1086  * Return float (vector) rounded to nearest integer (vector).  The returned
1087  * value is a float (vector).
1088  * Ex: round(0.9) = 1.0
1089  * Ex: round(-1.5) = -2.0
1090  */
1091 LLVMValueRef
1092 lp_build_round(struct lp_build_context *bld,
1093                LLVMValueRef a)
1094 {
1095    const struct lp_type type = bld->type;
1096
1097    assert(type.floating);
1098    assert(lp_check_value(type, a));
1099
1100    if (util_cpu_caps.has_sse4_1 &&
1101        (type.length == 1 || type.width*type.length == 128)) {
1102       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1103    }
1104    else {
1105       LLVMTypeRef vec_type = lp_build_vec_type(type);
1106       LLVMValueRef res;
1107       res = lp_build_iround(bld, a);
1108       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1109       return res;
1110    }
1111 }
1112
1113
1114 /**
1115  * Return floor of float (vector), result is a float (vector)
1116  * Ex: floor(1.1) = 1.0
1117  * Ex: floor(-1.1) = -2.0
1118  */
1119 LLVMValueRef
1120 lp_build_floor(struct lp_build_context *bld,
1121                LLVMValueRef a)
1122 {
1123    const struct lp_type type = bld->type;
1124
1125    assert(type.floating);
1126    assert(lp_check_value(type, a));
1127
1128    if (util_cpu_caps.has_sse4_1 &&
1129        (type.length == 1 || type.width*type.length == 128)) {
1130       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1131    }
1132    else {
1133       LLVMTypeRef vec_type = lp_build_vec_type(type);
1134       LLVMValueRef res;
1135       res = lp_build_ifloor(bld, a);
1136       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1137       return res;
1138    }
1139 }
1140
1141
1142 /**
1143  * Return ceiling of float (vector), returning float (vector).
1144  * Ex: ceil( 1.1) = 2.0
1145  * Ex: ceil(-1.1) = -1.0
1146  */
1147 LLVMValueRef
1148 lp_build_ceil(struct lp_build_context *bld,
1149               LLVMValueRef a)
1150 {
1151    const struct lp_type type = bld->type;
1152
1153    assert(type.floating);
1154    assert(lp_check_value(type, a));
1155
1156    if (util_cpu_caps.has_sse4_1 &&
1157        (type.length == 1 || type.width*type.length == 128)) {
1158       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1159    }
1160    else {
1161       LLVMTypeRef vec_type = lp_build_vec_type(type);
1162       LLVMValueRef res;
1163       res = lp_build_iceil(bld, a);
1164       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1165       return res;
1166    }
1167 }
1168
1169
1170 /**
1171  * Return fractional part of 'a' computed as a - floor(a)
1172  * Typically used in texture coord arithmetic.
1173  */
1174 LLVMValueRef
1175 lp_build_fract(struct lp_build_context *bld,
1176                LLVMValueRef a)
1177 {
1178    assert(bld->type.floating);
1179    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1180 }
1181
1182
1183 /**
1184  * Return the integer part of a float (vector) value.  The returned value is
1185  * an integer (vector).
1186  * Ex: itrunc(-1.5) = 1
1187  */
1188 LLVMValueRef
1189 lp_build_itrunc(struct lp_build_context *bld,
1190                 LLVMValueRef a)
1191 {
1192    const struct lp_type type = bld->type;
1193    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1194
1195    assert(type.floating);
1196    assert(lp_check_value(type, a));
1197
1198    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1199 }
1200
1201
1202 /**
1203  * Return float (vector) rounded to nearest integer (vector).  The returned
1204  * value is an integer (vector).
1205  * Ex: iround(0.9) = 1
1206  * Ex: iround(-1.5) = -2
1207  */
1208 LLVMValueRef
1209 lp_build_iround(struct lp_build_context *bld,
1210                 LLVMValueRef a)
1211 {
1212    const struct lp_type type = bld->type;
1213    LLVMTypeRef int_vec_type = bld->int_vec_type;
1214    LLVMValueRef res;
1215
1216    assert(type.floating);
1217
1218    assert(lp_check_value(type, a));
1219
1220    if (util_cpu_caps.has_sse4_1 &&
1221        (type.length == 1 || type.width*type.length == 128)) {
1222       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1223    }
1224    else {
1225       LLVMValueRef half;
1226
1227       half = lp_build_const_vec(type, 0.5);
1228
1229       if (type.sign) {
1230          LLVMTypeRef vec_type = bld->vec_type;
1231          LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1232          LLVMValueRef sign;
1233
1234          /* get sign bit */
1235          sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1236          sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1237
1238          /* sign * 0.5 */
1239          half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1240          half = LLVMBuildOr(bld->builder, sign, half, "");
1241          half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1242       }
1243
1244       res = LLVMBuildFAdd(bld->builder, a, half, "");
1245    }
1246
1247    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1248
1249    return res;
1250 }
1251
1252
1253 /**
1254  * Return floor of float (vector), result is an int (vector)
1255  * Ex: ifloor(1.1) = 1.0
1256  * Ex: ifloor(-1.1) = -2.0
1257  */
1258 LLVMValueRef
1259 lp_build_ifloor(struct lp_build_context *bld,
1260                 LLVMValueRef a)
1261 {
1262    const struct lp_type type = bld->type;
1263    LLVMTypeRef int_vec_type = bld->int_vec_type;
1264    LLVMValueRef res;
1265
1266    assert(type.floating);
1267    assert(lp_check_value(type, a));
1268
1269    if (util_cpu_caps.has_sse4_1 &&
1270        (type.length == 1 || type.width*type.length == 128)) {
1271       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1272    }
1273    else {
1274       res = a;
1275
1276       if (type.sign) {
1277          /* Take the sign bit and add it to 1 constant */
1278          LLVMTypeRef vec_type = bld->vec_type;
1279          unsigned mantissa = lp_mantissa(type);
1280          LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1281          LLVMValueRef sign;
1282          LLVMValueRef offset;
1283
1284          /* sign = a < 0 ? ~0 : 0 */
1285          sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1286          sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1287          sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1288
1289          /* offset = -0.99999(9)f */
1290          offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1291          offset = LLVMConstBitCast(offset, int_vec_type);
1292
1293          /* offset = a < 0 ? offset : 0.0f */
1294          offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1295          offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1296
1297          res = LLVMBuildFAdd(bld->builder, res, offset, "ifloor.res");
1298       }
1299    }
1300
1301    /* round to nearest (toward zero) */
1302    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1303
1304    return res;
1305 }
1306
1307
1308 /**
1309  * Return ceiling of float (vector), returning int (vector).
1310  * Ex: iceil( 1.1) = 2
1311  * Ex: iceil(-1.1) = -1
1312  */
1313 LLVMValueRef
1314 lp_build_iceil(struct lp_build_context *bld,
1315                LLVMValueRef a)
1316 {
1317    const struct lp_type type = bld->type;
1318    LLVMTypeRef int_vec_type = bld->int_vec_type;
1319    LLVMValueRef res;
1320
1321    assert(type.floating);
1322    assert(lp_check_value(type, a));
1323
1324    if (util_cpu_caps.has_sse4_1 &&
1325        (type.length == 1 || type.width*type.length == 128)) {
1326       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1327    }
1328    else {
1329       LLVMTypeRef vec_type = bld->vec_type;
1330       unsigned mantissa = lp_mantissa(type);
1331       LLVMValueRef offset;
1332
1333       /* offset = 0.99999(9)f */
1334       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1335
1336       if (type.sign) {
1337          LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1338          LLVMValueRef sign;
1339
1340          /* sign = a < 0 ? 0 : ~0 */
1341          sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1342          sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1343          sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1344          sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1345
1346          /* offset = a < 0 ? 0.0 : offset */
1347          offset = LLVMConstBitCast(offset, int_vec_type);
1348          offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1349          offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1350       }
1351
1352       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1353    }
1354
1355    /* round to nearest (toward zero) */
1356    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1357
1358    return res;
1359 }
1360
1361
1362 /**
1363  * Combined ifloor() & fract().
1364  *
1365  * Preferred to calling the functions separately, as it will ensure that the
1366  * stratergy (floor() vs ifloor()) that results in less redundant work is used.
1367  */
1368 void
1369 lp_build_ifloor_fract(struct lp_build_context *bld,
1370                       LLVMValueRef a,
1371                       LLVMValueRef *out_ipart,
1372                       LLVMValueRef *out_fpart)
1373 {
1374
1375
1376    const struct lp_type type = bld->type;
1377    LLVMValueRef ipart;
1378
1379    assert(type.floating);
1380    assert(lp_check_value(type, a));
1381
1382    if (util_cpu_caps.has_sse4_1 &&
1383        (type.length == 1 || type.width*type.length == 128)) {
1384       /*
1385        * floor() is easier.
1386        */
1387
1388       ipart = lp_build_floor(bld, a);
1389       *out_fpart = LLVMBuildFSub(bld->builder, a, ipart, "fpart");
1390       *out_ipart = LLVMBuildFPToSI(bld->builder, ipart, bld->int_vec_type, "ipart");
1391    }
1392    else {
1393       /*
1394        * ifloor() is easier.
1395        */
1396
1397       *out_ipart = lp_build_ifloor(bld, a);
1398       ipart = LLVMBuildSIToFP(bld->builder, *out_ipart, bld->vec_type, "ipart");
1399       *out_fpart = LLVMBuildFSub(bld->builder, a, ipart, "fpart");
1400    }
1401 }
1402
1403
1404 LLVMValueRef
1405 lp_build_sqrt(struct lp_build_context *bld,
1406               LLVMValueRef a)
1407 {
1408    const struct lp_type type = bld->type;
1409    LLVMTypeRef vec_type = lp_build_vec_type(type);
1410    char intrinsic[32];
1411
1412    assert(lp_check_value(type, a));
1413
1414    /* TODO: optimize the constant case */
1415    /* TODO: optimize the constant case */
1416
1417    assert(type.floating);
1418    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1419
1420    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1421 }
1422
1423
1424 /**
1425  * Do one Newton-Raphson step to improve reciprocate precision:
1426  *
1427  *   x_{i+1} = x_i * (2 - a * x_i)
1428  *
1429  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
1430  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
1431  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
1432  * halo. It would be necessary to clamp the argument to prevent this.
1433  *
1434  * See also:
1435  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
1436  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1437  */
1438 static INLINE LLVMValueRef
1439 lp_build_rcp_refine(struct lp_build_context *bld,
1440                     LLVMValueRef a,
1441                     LLVMValueRef rcp_a)
1442 {
1443    LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1444    LLVMValueRef res;
1445
1446    res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1447    res = LLVMBuildFSub(bld->builder, two, res, "");
1448    res = LLVMBuildFMul(bld->builder, rcp_a, res, "");
1449
1450    return res;
1451 }
1452
1453
1454 LLVMValueRef
1455 lp_build_rcp(struct lp_build_context *bld,
1456              LLVMValueRef a)
1457 {
1458    const struct lp_type type = bld->type;
1459
1460    assert(lp_check_value(type, a));
1461
1462    if(a == bld->zero)
1463       return bld->undef;
1464    if(a == bld->one)
1465       return bld->one;
1466    if(a == bld->undef)
1467       return bld->undef;
1468
1469    assert(type.floating);
1470
1471    if(LLVMIsConstant(a))
1472       return LLVMConstFDiv(bld->one, a);
1473
1474    /*
1475     * We don't use RCPPS because:
1476     * - it only has 10bits of precision
1477     * - it doesn't even get the reciprocate of 1.0 exactly
1478     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
1479     * - for recent processors the benefit over DIVPS is marginal, a case
1480     *   depedent
1481     *
1482     * We could still use it on certain processors if benchmarks show that the
1483     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
1484     * particular uses that require less workarounds.
1485     */
1486
1487    if (FALSE && util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1488       const unsigned num_iterations = 0;
1489       LLVMValueRef res;
1490       unsigned i;
1491
1492       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", bld->vec_type, a);
1493
1494       for (i = 0; i < num_iterations; ++i) {
1495          res = lp_build_rcp_refine(bld, a, res);
1496       }
1497
1498       return res;
1499    }
1500
1501    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1502 }
1503
1504
1505 /**
1506  * Do one Newton-Raphson step to improve rsqrt precision:
1507  *
1508  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
1509  *
1510  * See also:
1511  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1512  */
1513 static INLINE LLVMValueRef
1514 lp_build_rsqrt_refine(struct lp_build_context *bld,
1515                       LLVMValueRef a,
1516                       LLVMValueRef rsqrt_a)
1517 {
1518    LLVMValueRef half = lp_build_const_vec(bld->type, 0.5);
1519    LLVMValueRef three = lp_build_const_vec(bld->type, 3.0);
1520    LLVMValueRef res;
1521
1522    res = LLVMBuildFMul(bld->builder, rsqrt_a, rsqrt_a, "");
1523    res = LLVMBuildFMul(bld->builder, a, res, "");
1524    res = LLVMBuildFSub(bld->builder, three, res, "");
1525    res = LLVMBuildFMul(bld->builder, rsqrt_a, res, "");
1526    res = LLVMBuildFMul(bld->builder, half, res, "");
1527
1528    return res;
1529 }
1530
1531
1532 /**
1533  * Generate 1/sqrt(a)
1534  */
1535 LLVMValueRef
1536 lp_build_rsqrt(struct lp_build_context *bld,
1537                LLVMValueRef a)
1538 {
1539    const struct lp_type type = bld->type;
1540
1541    assert(lp_check_value(type, a));
1542
1543    assert(type.floating);
1544
1545    if (util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1546       const unsigned num_iterations = 0;
1547       LLVMValueRef res;
1548       unsigned i;
1549
1550       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", bld->vec_type, a);
1551
1552       for (i = 0; i < num_iterations; ++i) {
1553          res = lp_build_rsqrt_refine(bld, a, res);
1554       }
1555
1556       return res;
1557    }
1558
1559    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1560 }
1561
1562
1563 static inline LLVMValueRef
1564 lp_build_const_v4si(unsigned long value)
1565 {
1566    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1567    LLVMValueRef elements[4] = { element, element, element, element };
1568    return LLVMConstVector(elements, 4);
1569 }
1570
1571 static inline LLVMValueRef
1572 lp_build_const_v4sf(float value)
1573 {
1574    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1575    LLVMValueRef elements[4] = { element, element, element, element };
1576    return LLVMConstVector(elements, 4);
1577 }
1578
1579
1580 /**
1581  * Generate sin(a) using SSE2
1582  */
1583 LLVMValueRef
1584 lp_build_sin(struct lp_build_context *bld,
1585              LLVMValueRef a)
1586 {
1587    struct lp_type int_type = lp_int_type(bld->type);
1588    LLVMBuilderRef b = bld->builder;
1589    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1590    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1591
1592    /*
1593     *  take the absolute value,
1594     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1595     */
1596
1597    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1598    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1599
1600    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1601    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1602
1603    /*
1604     * extract the sign bit (upper one)
1605     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1606     */
1607    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1608    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1609
1610    /*
1611     * scale by 4/Pi
1612     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1613     */
1614
1615    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1616    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1617
1618    /*
1619     * store the integer part of y in mm0
1620     * emm2 = _mm_cvttps_epi32(y);
1621     */
1622
1623    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1624
1625    /*
1626     * j=(j+1) & (~1) (see the cephes sources)
1627     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1628     */
1629
1630    LLVMValueRef all_one = lp_build_const_v4si(1);
1631    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1632    /*
1633     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1634     */
1635    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1636    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1637
1638    /*
1639     * y = _mm_cvtepi32_ps(emm2);
1640     */
1641    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1642
1643    /* get the swap sign flag
1644     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1645     */
1646    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1647    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1648
1649    /*
1650     * emm2 = _mm_slli_epi32(emm0, 29);
1651     */
1652    LLVMValueRef const_29 = lp_build_const_v4si(29);
1653    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1654
1655    /*
1656     * get the polynom selection mask
1657     * there is one polynom for 0 <= x <= Pi/4
1658     * and another one for Pi/4<x<=Pi/2
1659     * Both branches will be computed.
1660     *
1661     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1662     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1663     */
1664
1665    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1666    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1667    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1668                                              emm2_3, lp_build_const_v4si(0));
1669    /*
1670     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1671     */
1672    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1673
1674    /*
1675     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1676     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1677     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1678     */
1679    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1680    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1681    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1682
1683    /*
1684     * The magic pass: "Extended precision modular arithmetic"
1685     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1686     * xmm1 = _mm_mul_ps(y, xmm1);
1687     * xmm2 = _mm_mul_ps(y, xmm2);
1688     * xmm3 = _mm_mul_ps(y, xmm3);
1689     */
1690    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1691    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1692    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1693
1694    /*
1695     * x = _mm_add_ps(x, xmm1);
1696     * x = _mm_add_ps(x, xmm2);
1697     * x = _mm_add_ps(x, xmm3);
1698     */
1699
1700    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1701    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1702    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1703
1704    /*
1705     * Evaluate the first polynom  (0 <= x <= Pi/4)
1706     *
1707     * z = _mm_mul_ps(x,x);
1708     */
1709    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1710
1711    /*
1712     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1713     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1714     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1715     */
1716    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1717    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1718    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1719
1720    /*
1721     * y = *(v4sf*)_ps_coscof_p0;
1722     * y = _mm_mul_ps(y, z);
1723     */
1724    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1725    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1726    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1727    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1728    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1729    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1730
1731
1732    /*
1733     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1734     * y = _mm_sub_ps(y, tmp);
1735     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1736     */
1737    LLVMValueRef half = lp_build_const_v4sf(0.5);
1738    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1739    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1740    LLVMValueRef one = lp_build_const_v4sf(1.0);
1741    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1742
1743    /*
1744     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1745     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1746     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1747     */
1748    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1749    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1750    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1751
1752    /*
1753     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1754     *
1755     * y2 = *(v4sf*)_ps_sincof_p0;
1756     * y2 = _mm_mul_ps(y2, z);
1757     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1758     * y2 = _mm_mul_ps(y2, z);
1759     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1760     * y2 = _mm_mul_ps(y2, z);
1761     * y2 = _mm_mul_ps(y2, x);
1762     * y2 = _mm_add_ps(y2, x);
1763     */
1764
1765    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1766    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1767    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1768    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1769    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1770    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1771    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1772
1773    /*
1774     * select the correct result from the two polynoms
1775     * xmm3 = poly_mask;
1776     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1777     * y = _mm_andnot_ps(xmm3, y);
1778     * y = _mm_add_ps(y,y2);
1779     */
1780    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1781    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1782    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1783    LLVMValueRef inv = lp_build_const_v4si(~0);
1784    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1785    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1786    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1787
1788    /*
1789     * update the sign
1790     * y = _mm_xor_ps(y, sign_bit);
1791     */
1792    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1793    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1794    return y_result;
1795 }
1796
1797
1798 /**
1799  * Generate cos(a) using SSE2
1800  */
1801 LLVMValueRef
1802 lp_build_cos(struct lp_build_context *bld,
1803              LLVMValueRef a)
1804 {
1805    struct lp_type int_type = lp_int_type(bld->type);
1806    LLVMBuilderRef b = bld->builder;
1807    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1808    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1809
1810    /*
1811     *  take the absolute value,
1812     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1813     */
1814
1815    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1816    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1817
1818    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1819    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1820
1821    /*
1822     * scale by 4/Pi
1823     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1824     */
1825
1826    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1827    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1828
1829    /*
1830     * store the integer part of y in mm0
1831     * emm2 = _mm_cvttps_epi32(y);
1832     */
1833
1834    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1835
1836    /*
1837     * j=(j+1) & (~1) (see the cephes sources)
1838     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1839     */
1840
1841    LLVMValueRef all_one = lp_build_const_v4si(1);
1842    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1843    /*
1844     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1845     */
1846    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1847    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1848
1849    /*
1850     * y = _mm_cvtepi32_ps(emm2);
1851     */
1852    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1853
1854
1855    /*
1856     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1857     */
1858    LLVMValueRef const_2 = lp_build_const_v4si(2);
1859    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1860
1861
1862    /* get the swap sign flag
1863     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1864     */
1865    LLVMValueRef inv = lp_build_const_v4si(~0);
1866    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1867    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1868    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1869
1870    /*
1871     * emm2 = _mm_slli_epi32(emm0, 29);
1872     */
1873    LLVMValueRef const_29 = lp_build_const_v4si(29);
1874    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1875
1876    /*
1877     * get the polynom selection mask
1878     * there is one polynom for 0 <= x <= Pi/4
1879     * and another one for Pi/4<x<=Pi/2
1880     * Both branches will be computed.
1881     *
1882     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1883     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1884     */
1885
1886    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1887    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1888    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1889                                              emm2_3, lp_build_const_v4si(0));
1890
1891    /*
1892     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1893     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1894     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1895     */
1896    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1897    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1898    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1899
1900    /*
1901     * The magic pass: "Extended precision modular arithmetic"
1902     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1903     * xmm1 = _mm_mul_ps(y, xmm1);
1904     * xmm2 = _mm_mul_ps(y, xmm2);
1905     * xmm3 = _mm_mul_ps(y, xmm3);
1906     */
1907    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1908    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1909    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1910
1911    /*
1912     * x = _mm_add_ps(x, xmm1);
1913     * x = _mm_add_ps(x, xmm2);
1914     * x = _mm_add_ps(x, xmm3);
1915     */
1916
1917    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1918    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1919    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1920
1921    /*
1922     * Evaluate the first polynom  (0 <= x <= Pi/4)
1923     *
1924     * z = _mm_mul_ps(x,x);
1925     */
1926    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1927
1928    /*
1929     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1930     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1931     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1932     */
1933    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1934    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1935    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1936
1937    /*
1938     * y = *(v4sf*)_ps_coscof_p0;
1939     * y = _mm_mul_ps(y, z);
1940     */
1941    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1942    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1943    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1944    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1945    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1946    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1947
1948
1949    /*
1950     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1951     * y = _mm_sub_ps(y, tmp);
1952     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1953     */
1954    LLVMValueRef half = lp_build_const_v4sf(0.5);
1955    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1956    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1957    LLVMValueRef one = lp_build_const_v4sf(1.0);
1958    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1959
1960    /*
1961     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1962     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1963     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1964     */
1965    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1966    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1967    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1968
1969    /*
1970     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1971     *
1972     * y2 = *(v4sf*)_ps_sincof_p0;
1973     * y2 = _mm_mul_ps(y2, z);
1974     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1975     * y2 = _mm_mul_ps(y2, z);
1976     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1977     * y2 = _mm_mul_ps(y2, z);
1978     * y2 = _mm_mul_ps(y2, x);
1979     * y2 = _mm_add_ps(y2, x);
1980     */
1981
1982    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1983    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1984    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1985    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1986    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1987    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1988    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1989
1990    /*
1991     * select the correct result from the two polynoms
1992     * xmm3 = poly_mask;
1993     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1994     * y = _mm_andnot_ps(xmm3, y);
1995     * y = _mm_add_ps(y,y2);
1996     */
1997    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1998    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1999    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
2000    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
2001    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
2002    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
2003
2004    /*
2005     * update the sign
2006     * y = _mm_xor_ps(y, sign_bit);
2007     */
2008    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
2009    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
2010    return y_result;
2011 }
2012
2013
2014 /**
2015  * Generate pow(x, y)
2016  */
2017 LLVMValueRef
2018 lp_build_pow(struct lp_build_context *bld,
2019              LLVMValueRef x,
2020              LLVMValueRef y)
2021 {
2022    /* TODO: optimize the constant case */
2023    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2024        LLVMIsConstant(x) && LLVMIsConstant(y)) {
2025       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2026                    __FUNCTION__);
2027    }
2028
2029    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
2030 }
2031
2032
2033 /**
2034  * Generate exp(x)
2035  */
2036 LLVMValueRef
2037 lp_build_exp(struct lp_build_context *bld,
2038              LLVMValueRef x)
2039 {
2040    /* log2(e) = 1/log(2) */
2041    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
2042
2043    assert(lp_check_value(bld->type, x));
2044
2045    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
2046 }
2047
2048
2049 /**
2050  * Generate log(x)
2051  */
2052 LLVMValueRef
2053 lp_build_log(struct lp_build_context *bld,
2054              LLVMValueRef x)
2055 {
2056    /* log(2) */
2057    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
2058
2059    assert(lp_check_value(bld->type, x));
2060
2061    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
2062 }
2063
2064
2065 /**
2066  * Generate polynomial.
2067  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
2068  */
2069 static LLVMValueRef
2070 lp_build_polynomial(struct lp_build_context *bld,
2071                     LLVMValueRef x,
2072                     const double *coeffs,
2073                     unsigned num_coeffs)
2074 {
2075    const struct lp_type type = bld->type;
2076    LLVMValueRef res = NULL;
2077    unsigned i;
2078
2079    assert(lp_check_value(bld->type, x));
2080
2081    /* TODO: optimize the constant case */
2082    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2083        LLVMIsConstant(x)) {
2084       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2085                    __FUNCTION__);
2086    }
2087
2088    for (i = num_coeffs; i--; ) {
2089       LLVMValueRef coeff;
2090
2091       coeff = lp_build_const_vec(type, coeffs[i]);
2092
2093       if(res)
2094          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
2095       else
2096          res = coeff;
2097    }
2098
2099    if(res)
2100       return res;
2101    else
2102       return bld->undef;
2103 }
2104
2105
2106 /**
2107  * Minimax polynomial fit of 2**x, in range [0, 1[
2108  */
2109 const double lp_build_exp2_polynomial[] = {
2110 #if EXP_POLY_DEGREE == 5
2111    0.999999999690134838155,
2112    0.583974334321735217258,
2113    0.164553105719676828492,
2114    0.0292811063701710962255,
2115    0.00354944426657875141846,
2116    0.000296253726543423377365
2117 #elif EXP_POLY_DEGREE == 4
2118    1.00000001502262084505,
2119    0.563586057338685991394,
2120    0.150436017652442413623,
2121    0.0243220604213317927308,
2122    0.0025359088446580436489
2123 #elif EXP_POLY_DEGREE == 3
2124    0.999925218562710312959,
2125    0.695833540494823811697,
2126    0.226067155427249155588,
2127    0.0780245226406372992967
2128 #elif EXP_POLY_DEGREE == 2
2129    1.00172476321474503578,
2130    0.657636275736077639316,
2131    0.33718943461968720704
2132 #else
2133 #error
2134 #endif
2135 };
2136
2137
2138 void
2139 lp_build_exp2_approx(struct lp_build_context *bld,
2140                      LLVMValueRef x,
2141                      LLVMValueRef *p_exp2_int_part,
2142                      LLVMValueRef *p_frac_part,
2143                      LLVMValueRef *p_exp2)
2144 {
2145    const struct lp_type type = bld->type;
2146    LLVMTypeRef vec_type = lp_build_vec_type(type);
2147    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2148    LLVMValueRef ipart = NULL;
2149    LLVMValueRef fpart = NULL;
2150    LLVMValueRef expipart = NULL;
2151    LLVMValueRef expfpart = NULL;
2152    LLVMValueRef res = NULL;
2153
2154    assert(lp_check_value(bld->type, x));
2155
2156    if(p_exp2_int_part || p_frac_part || p_exp2) {
2157       /* TODO: optimize the constant case */
2158       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2159           LLVMIsConstant(x)) {
2160          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2161                       __FUNCTION__);
2162       }
2163
2164       assert(type.floating && type.width == 32);
2165
2166       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
2167       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
2168
2169       /* ipart = floor(x) */
2170       ipart = lp_build_floor(bld, x);
2171
2172       /* fpart = x - ipart */
2173       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
2174    }
2175
2176    if(p_exp2_int_part || p_exp2) {
2177       /* expipart = (float) (1 << ipart) */
2178       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
2179       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
2180       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
2181       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
2182    }
2183
2184    if(p_exp2) {
2185       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
2186                                      Elements(lp_build_exp2_polynomial));
2187
2188       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
2189    }
2190
2191    if(p_exp2_int_part)
2192       *p_exp2_int_part = expipart;
2193
2194    if(p_frac_part)
2195       *p_frac_part = fpart;
2196
2197    if(p_exp2)
2198       *p_exp2 = res;
2199 }
2200
2201
2202 LLVMValueRef
2203 lp_build_exp2(struct lp_build_context *bld,
2204               LLVMValueRef x)
2205 {
2206    LLVMValueRef res;
2207    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
2208    return res;
2209 }
2210
2211
2212 /**
2213  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
2214  * These coefficients can be generate with
2215  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2216  */
2217 const double lp_build_log2_polynomial[] = {
2218 #if LOG_POLY_DEGREE == 6
2219    3.11578814719469302614,
2220    -3.32419399085241980044,
2221    2.59883907202499966007,
2222    -1.23152682416275988241,
2223    0.318212422185251071475,
2224    -0.0344359067839062357313
2225 #elif LOG_POLY_DEGREE == 5
2226    2.8882704548164776201,
2227    -2.52074962577807006663,
2228    1.48116647521213171641,
2229    -0.465725644288844778798,
2230    0.0596515482674574969533
2231 #elif LOG_POLY_DEGREE == 4
2232    2.61761038894603480148,
2233    -1.75647175389045657003,
2234    0.688243882994381274313,
2235    -0.107254423828329604454
2236 #elif LOG_POLY_DEGREE == 3
2237    2.28330284476918490682,
2238    -1.04913055217340124191,
2239    0.204446009836232697516
2240 #else
2241 #error
2242 #endif
2243 };
2244
2245
2246 /**
2247  * See http://www.devmaster.net/forums/showthread.php?p=43580
2248  */
2249 void
2250 lp_build_log2_approx(struct lp_build_context *bld,
2251                      LLVMValueRef x,
2252                      LLVMValueRef *p_exp,
2253                      LLVMValueRef *p_floor_log2,
2254                      LLVMValueRef *p_log2)
2255 {
2256    const struct lp_type type = bld->type;
2257    LLVMTypeRef vec_type = lp_build_vec_type(type);
2258    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2259
2260    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2261    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2262    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2263
2264    LLVMValueRef i = NULL;
2265    LLVMValueRef exp = NULL;
2266    LLVMValueRef mant = NULL;
2267    LLVMValueRef logexp = NULL;
2268    LLVMValueRef logmant = NULL;
2269    LLVMValueRef res = NULL;
2270
2271    assert(lp_check_value(bld->type, x));
2272
2273    if(p_exp || p_floor_log2 || p_log2) {
2274       /* TODO: optimize the constant case */
2275       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2276           LLVMIsConstant(x)) {
2277          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2278                       __FUNCTION__);
2279       }
2280
2281       assert(type.floating && type.width == 32);
2282
2283       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2284
2285       /* exp = (float) exponent(x) */
2286       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2287    }
2288
2289    if(p_floor_log2 || p_log2) {
2290       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2291       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2292       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2293    }
2294
2295    if(p_log2) {
2296       /* mant = (float) mantissa(x) */
2297       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2298       mant = LLVMBuildOr(bld->builder, mant, one, "");
2299       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2300
2301       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2302                                     Elements(lp_build_log2_polynomial));
2303
2304       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2305       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2306
2307       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2308    }
2309
2310    if(p_exp) {
2311       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2312       *p_exp = exp;
2313    }
2314
2315    if(p_floor_log2)
2316       *p_floor_log2 = logexp;
2317
2318    if(p_log2)
2319       *p_log2 = res;
2320 }
2321
2322
2323 LLVMValueRef
2324 lp_build_log2(struct lp_build_context *bld,
2325               LLVMValueRef x)
2326 {
2327    LLVMValueRef res;
2328    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2329    return res;
2330 }
2331
2332
2333 /**
2334  * Faster (and less accurate) log2.
2335  *
2336  *    log2(x) = floor(log2(x)) + frac(x)
2337  *
2338  * See http://www.flipcode.com/archives/Fast_log_Function.shtml
2339  */
2340 LLVMValueRef
2341 lp_build_fast_log2(struct lp_build_context *bld,
2342                    LLVMValueRef x)
2343 {
2344    const struct lp_type type = bld->type;
2345    LLVMTypeRef vec_type = bld->vec_type;
2346    LLVMTypeRef int_vec_type = bld->int_vec_type;
2347
2348    unsigned mantissa = lp_mantissa(type);
2349    LLVMValueRef mantmask = lp_build_const_int_vec(type, (1ULL << mantissa) - 1);
2350    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2351
2352    LLVMValueRef ipart;
2353    LLVMValueRef fpart;
2354
2355    assert(lp_check_value(bld->type, x));
2356
2357    assert(type.floating);
2358
2359    x = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2360
2361    /* ipart = floor(log2(x)) - 1 */
2362    ipart = LLVMBuildLShr(bld->builder, x, lp_build_const_int_vec(type, mantissa), "");
2363    ipart = LLVMBuildAnd(bld->builder, ipart, lp_build_const_int_vec(type, 255), "");
2364    ipart = LLVMBuildSub(bld->builder, ipart, lp_build_const_int_vec(type, 128), "");
2365    ipart = LLVMBuildSIToFP(bld->builder, ipart, vec_type, "");
2366
2367    /* fpart = 1.0 + frac(x) */
2368    fpart = LLVMBuildAnd(bld->builder, x, mantmask, "");
2369    fpart = LLVMBuildOr(bld->builder, fpart, one, "");
2370    fpart = LLVMBuildBitCast(bld->builder, fpart, vec_type, "");
2371
2372    /* floor(log2(x)) + frac(x) */
2373    return LLVMBuildFAdd(bld->builder, ipart, fpart, "");
2374 }
2375
2376
2377 /**
2378  * Fast implementation of iround(log2(x)).
2379  *
2380  * Not an approximation -- it should give accurate results all the time.
2381  */
2382 LLVMValueRef
2383 lp_build_ilog2(struct lp_build_context *bld,
2384                LLVMValueRef x)
2385 {
2386    const struct lp_type type = bld->type;
2387    LLVMTypeRef int_vec_type = bld->int_vec_type;
2388
2389    unsigned mantissa = lp_mantissa(type);
2390    LLVMValueRef sqrt2 = lp_build_const_vec(type, 1.4142135623730951);
2391
2392    LLVMValueRef ipart;
2393
2394    assert(lp_check_value(bld->type, x));
2395
2396    assert(type.floating);
2397
2398    /* x * 2^(0.5)   i.e., add 0.5 to the log2(x) */
2399    x = LLVMBuildFMul(bld->builder, x, sqrt2, "");
2400
2401    x = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2402
2403    /* ipart = floor(log2(x) + 0.5)  */
2404    ipart = LLVMBuildLShr(bld->builder, x, lp_build_const_int_vec(type, mantissa), "");
2405    ipart = LLVMBuildAnd(bld->builder, ipart, lp_build_const_int_vec(type, 255), "");
2406    ipart = LLVMBuildSub(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
2407
2408    return ipart;
2409 }