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 LLVMValueRef
1363 lp_build_sqrt(struct lp_build_context *bld,
1364               LLVMValueRef a)
1365 {
1366    const struct lp_type type = bld->type;
1367    LLVMTypeRef vec_type = lp_build_vec_type(type);
1368    char intrinsic[32];
1369
1370    assert(lp_check_value(type, a));
1371
1372    /* TODO: optimize the constant case */
1373    /* TODO: optimize the constant case */
1374
1375    assert(type.floating);
1376    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1377
1378    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1379 }
1380
1381
1382 /**
1383  * Do one Newton-Raphson step to improve reciprocate precision:
1384  *
1385  *   x_{i+1} = x_i * (2 - a * x_i)
1386  *
1387  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
1388  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
1389  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
1390  * halo. It would be necessary to clamp the argument to prevent this.
1391  *
1392  * See also:
1393  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
1394  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1395  */
1396 static INLINE LLVMValueRef
1397 lp_build_rcp_refine(struct lp_build_context *bld,
1398                     LLVMValueRef a,
1399                     LLVMValueRef rcp_a)
1400 {
1401    LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1402    LLVMValueRef res;
1403
1404    res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1405    res = LLVMBuildFSub(bld->builder, two, res, "");
1406    res = LLVMBuildFMul(bld->builder, rcp_a, res, "");
1407
1408    return res;
1409 }
1410
1411
1412 LLVMValueRef
1413 lp_build_rcp(struct lp_build_context *bld,
1414              LLVMValueRef a)
1415 {
1416    const struct lp_type type = bld->type;
1417
1418    assert(lp_check_value(type, a));
1419
1420    if(a == bld->zero)
1421       return bld->undef;
1422    if(a == bld->one)
1423       return bld->one;
1424    if(a == bld->undef)
1425       return bld->undef;
1426
1427    assert(type.floating);
1428
1429    if(LLVMIsConstant(a))
1430       return LLVMConstFDiv(bld->one, a);
1431
1432    /*
1433     * We don't use RCPPS because:
1434     * - it only has 10bits of precision
1435     * - it doesn't even get the reciprocate of 1.0 exactly
1436     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
1437     * - for recent processors the benefit over DIVPS is marginal, a case
1438     *   depedent
1439     *
1440     * We could still use it on certain processors if benchmarks show that the
1441     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
1442     * particular uses that require less workarounds.
1443     */
1444
1445    if (FALSE && util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1446       const unsigned num_iterations = 0;
1447       LLVMValueRef res;
1448       unsigned i;
1449
1450       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", bld->vec_type, a);
1451
1452       for (i = 0; i < num_iterations; ++i) {
1453          res = lp_build_rcp_refine(bld, a, res);
1454       }
1455
1456       return res;
1457    }
1458
1459    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1460 }
1461
1462
1463 /**
1464  * Do one Newton-Raphson step to improve rsqrt precision:
1465  *
1466  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
1467  *
1468  * See also:
1469  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1470  */
1471 static INLINE LLVMValueRef
1472 lp_build_rsqrt_refine(struct lp_build_context *bld,
1473                       LLVMValueRef a,
1474                       LLVMValueRef rsqrt_a)
1475 {
1476    LLVMValueRef half = lp_build_const_vec(bld->type, 0.5);
1477    LLVMValueRef three = lp_build_const_vec(bld->type, 3.0);
1478    LLVMValueRef res;
1479
1480    res = LLVMBuildFMul(bld->builder, rsqrt_a, rsqrt_a, "");
1481    res = LLVMBuildFMul(bld->builder, a, res, "");
1482    res = LLVMBuildFSub(bld->builder, three, res, "");
1483    res = LLVMBuildFMul(bld->builder, rsqrt_a, res, "");
1484    res = LLVMBuildFMul(bld->builder, half, res, "");
1485
1486    return res;
1487 }
1488
1489
1490 /**
1491  * Generate 1/sqrt(a)
1492  */
1493 LLVMValueRef
1494 lp_build_rsqrt(struct lp_build_context *bld,
1495                LLVMValueRef a)
1496 {
1497    const struct lp_type type = bld->type;
1498
1499    assert(lp_check_value(type, a));
1500
1501    assert(type.floating);
1502
1503    if (util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1504       const unsigned num_iterations = 0;
1505       LLVMValueRef res;
1506       unsigned i;
1507
1508       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", bld->vec_type, a);
1509
1510       for (i = 0; i < num_iterations; ++i) {
1511          res = lp_build_rsqrt_refine(bld, a, res);
1512       }
1513
1514       return res;
1515    }
1516
1517    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1518 }
1519
1520
1521 static inline LLVMValueRef
1522 lp_build_const_v4si(unsigned long value)
1523 {
1524    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1525    LLVMValueRef elements[4] = { element, element, element, element };
1526    return LLVMConstVector(elements, 4);
1527 }
1528
1529 static inline LLVMValueRef
1530 lp_build_const_v4sf(float value)
1531 {
1532    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1533    LLVMValueRef elements[4] = { element, element, element, element };
1534    return LLVMConstVector(elements, 4);
1535 }
1536
1537
1538 /**
1539  * Generate sin(a) using SSE2
1540  */
1541 LLVMValueRef
1542 lp_build_sin(struct lp_build_context *bld,
1543              LLVMValueRef a)
1544 {
1545    struct lp_type int_type = lp_int_type(bld->type);
1546    LLVMBuilderRef b = bld->builder;
1547    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1548    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1549
1550    /*
1551     *  take the absolute value,
1552     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1553     */
1554
1555    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1556    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1557
1558    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1559    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1560
1561    /*
1562     * extract the sign bit (upper one)
1563     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1564     */
1565    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1566    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1567
1568    /*
1569     * scale by 4/Pi
1570     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1571     */
1572
1573    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1574    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1575
1576    /*
1577     * store the integer part of y in mm0
1578     * emm2 = _mm_cvttps_epi32(y);
1579     */
1580
1581    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1582
1583    /*
1584     * j=(j+1) & (~1) (see the cephes sources)
1585     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1586     */
1587
1588    LLVMValueRef all_one = lp_build_const_v4si(1);
1589    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1590    /*
1591     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1592     */
1593    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1594    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1595
1596    /*
1597     * y = _mm_cvtepi32_ps(emm2);
1598     */
1599    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1600
1601    /* get the swap sign flag
1602     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1603     */
1604    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1605    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1606
1607    /*
1608     * emm2 = _mm_slli_epi32(emm0, 29);
1609     */
1610    LLVMValueRef const_29 = lp_build_const_v4si(29);
1611    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1612
1613    /*
1614     * get the polynom selection mask
1615     * there is one polynom for 0 <= x <= Pi/4
1616     * and another one for Pi/4<x<=Pi/2
1617     * Both branches will be computed.
1618     *
1619     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1620     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1621     */
1622
1623    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1624    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1625    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1626                                              emm2_3, lp_build_const_v4si(0));
1627    /*
1628     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1629     */
1630    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1631
1632    /*
1633     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1634     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1635     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1636     */
1637    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1638    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1639    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1640
1641    /*
1642     * The magic pass: "Extended precision modular arithmetic"
1643     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1644     * xmm1 = _mm_mul_ps(y, xmm1);
1645     * xmm2 = _mm_mul_ps(y, xmm2);
1646     * xmm3 = _mm_mul_ps(y, xmm3);
1647     */
1648    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1649    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1650    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1651
1652    /*
1653     * x = _mm_add_ps(x, xmm1);
1654     * x = _mm_add_ps(x, xmm2);
1655     * x = _mm_add_ps(x, xmm3);
1656     */
1657
1658    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1659    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1660    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1661
1662    /*
1663     * Evaluate the first polynom  (0 <= x <= Pi/4)
1664     *
1665     * z = _mm_mul_ps(x,x);
1666     */
1667    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1668
1669    /*
1670     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1671     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1672     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1673     */
1674    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1675    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1676    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1677
1678    /*
1679     * y = *(v4sf*)_ps_coscof_p0;
1680     * y = _mm_mul_ps(y, z);
1681     */
1682    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1683    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1684    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1685    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1686    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1687    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1688
1689
1690    /*
1691     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1692     * y = _mm_sub_ps(y, tmp);
1693     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1694     */
1695    LLVMValueRef half = lp_build_const_v4sf(0.5);
1696    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1697    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1698    LLVMValueRef one = lp_build_const_v4sf(1.0);
1699    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1700
1701    /*
1702     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1703     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1704     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1705     */
1706    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1707    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1708    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1709
1710    /*
1711     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1712     *
1713     * y2 = *(v4sf*)_ps_sincof_p0;
1714     * y2 = _mm_mul_ps(y2, z);
1715     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1716     * y2 = _mm_mul_ps(y2, z);
1717     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1718     * y2 = _mm_mul_ps(y2, z);
1719     * y2 = _mm_mul_ps(y2, x);
1720     * y2 = _mm_add_ps(y2, x);
1721     */
1722
1723    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1724    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1725    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1726    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1727    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1728    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1729    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1730
1731    /*
1732     * select the correct result from the two polynoms
1733     * xmm3 = poly_mask;
1734     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1735     * y = _mm_andnot_ps(xmm3, y);
1736     * y = _mm_add_ps(y,y2);
1737     */
1738    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1739    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1740    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1741    LLVMValueRef inv = lp_build_const_v4si(~0);
1742    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1743    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1744    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1745
1746    /*
1747     * update the sign
1748     * y = _mm_xor_ps(y, sign_bit);
1749     */
1750    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1751    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1752    return y_result;
1753 }
1754
1755
1756 /**
1757  * Generate cos(a) using SSE2
1758  */
1759 LLVMValueRef
1760 lp_build_cos(struct lp_build_context *bld,
1761              LLVMValueRef a)
1762 {
1763    struct lp_type int_type = lp_int_type(bld->type);
1764    LLVMBuilderRef b = bld->builder;
1765    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1766    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1767
1768    /*
1769     *  take the absolute value,
1770     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1771     */
1772
1773    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1774    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1775
1776    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1777    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1778
1779    /*
1780     * scale by 4/Pi
1781     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1782     */
1783
1784    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1785    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1786
1787    /*
1788     * store the integer part of y in mm0
1789     * emm2 = _mm_cvttps_epi32(y);
1790     */
1791
1792    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1793
1794    /*
1795     * j=(j+1) & (~1) (see the cephes sources)
1796     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1797     */
1798
1799    LLVMValueRef all_one = lp_build_const_v4si(1);
1800    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1801    /*
1802     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1803     */
1804    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1805    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1806
1807    /*
1808     * y = _mm_cvtepi32_ps(emm2);
1809     */
1810    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1811
1812
1813    /*
1814     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1815     */
1816    LLVMValueRef const_2 = lp_build_const_v4si(2);
1817    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1818
1819
1820    /* get the swap sign flag
1821     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1822     */
1823    LLVMValueRef inv = lp_build_const_v4si(~0);
1824    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1825    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1826    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1827
1828    /*
1829     * emm2 = _mm_slli_epi32(emm0, 29);
1830     */
1831    LLVMValueRef const_29 = lp_build_const_v4si(29);
1832    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1833
1834    /*
1835     * get the polynom selection mask
1836     * there is one polynom for 0 <= x <= Pi/4
1837     * and another one for Pi/4<x<=Pi/2
1838     * Both branches will be computed.
1839     *
1840     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1841     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1842     */
1843
1844    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1845    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1846    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1847                                              emm2_3, lp_build_const_v4si(0));
1848
1849    /*
1850     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1851     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1852     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1853     */
1854    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1855    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1856    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1857
1858    /*
1859     * The magic pass: "Extended precision modular arithmetic"
1860     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1861     * xmm1 = _mm_mul_ps(y, xmm1);
1862     * xmm2 = _mm_mul_ps(y, xmm2);
1863     * xmm3 = _mm_mul_ps(y, xmm3);
1864     */
1865    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1866    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1867    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1868
1869    /*
1870     * x = _mm_add_ps(x, xmm1);
1871     * x = _mm_add_ps(x, xmm2);
1872     * x = _mm_add_ps(x, xmm3);
1873     */
1874
1875    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1876    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1877    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1878
1879    /*
1880     * Evaluate the first polynom  (0 <= x <= Pi/4)
1881     *
1882     * z = _mm_mul_ps(x,x);
1883     */
1884    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1885
1886    /*
1887     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1888     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1889     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1890     */
1891    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1892    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1893    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1894
1895    /*
1896     * y = *(v4sf*)_ps_coscof_p0;
1897     * y = _mm_mul_ps(y, z);
1898     */
1899    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1900    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1901    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1902    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1903    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1904    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1905
1906
1907    /*
1908     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1909     * y = _mm_sub_ps(y, tmp);
1910     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1911     */
1912    LLVMValueRef half = lp_build_const_v4sf(0.5);
1913    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1914    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1915    LLVMValueRef one = lp_build_const_v4sf(1.0);
1916    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1917
1918    /*
1919     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1920     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1921     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1922     */
1923    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1924    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1925    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1926
1927    /*
1928     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1929     *
1930     * y2 = *(v4sf*)_ps_sincof_p0;
1931     * y2 = _mm_mul_ps(y2, z);
1932     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1933     * y2 = _mm_mul_ps(y2, z);
1934     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1935     * y2 = _mm_mul_ps(y2, z);
1936     * y2 = _mm_mul_ps(y2, x);
1937     * y2 = _mm_add_ps(y2, x);
1938     */
1939
1940    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1941    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1942    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1943    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1944    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1945    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1946    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1947
1948    /*
1949     * select the correct result from the two polynoms
1950     * xmm3 = poly_mask;
1951     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1952     * y = _mm_andnot_ps(xmm3, y);
1953     * y = _mm_add_ps(y,y2);
1954     */
1955    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1956    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1957    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1958    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1959    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1960    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1961
1962    /*
1963     * update the sign
1964     * y = _mm_xor_ps(y, sign_bit);
1965     */
1966    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1967    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1968    return y_result;
1969 }
1970
1971
1972 /**
1973  * Generate pow(x, y)
1974  */
1975 LLVMValueRef
1976 lp_build_pow(struct lp_build_context *bld,
1977              LLVMValueRef x,
1978              LLVMValueRef y)
1979 {
1980    /* TODO: optimize the constant case */
1981    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
1982        LLVMIsConstant(x) && LLVMIsConstant(y)) {
1983       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1984                    __FUNCTION__);
1985    }
1986
1987    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1988 }
1989
1990
1991 /**
1992  * Generate exp(x)
1993  */
1994 LLVMValueRef
1995 lp_build_exp(struct lp_build_context *bld,
1996              LLVMValueRef x)
1997 {
1998    /* log2(e) = 1/log(2) */
1999    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
2000
2001    assert(lp_check_value(bld->type, x));
2002
2003    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
2004 }
2005
2006
2007 /**
2008  * Generate log(x)
2009  */
2010 LLVMValueRef
2011 lp_build_log(struct lp_build_context *bld,
2012              LLVMValueRef x)
2013 {
2014    /* log(2) */
2015    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
2016
2017    assert(lp_check_value(bld->type, x));
2018
2019    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
2020 }
2021
2022
2023 /**
2024  * Generate polynomial.
2025  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
2026  */
2027 static LLVMValueRef
2028 lp_build_polynomial(struct lp_build_context *bld,
2029                     LLVMValueRef x,
2030                     const double *coeffs,
2031                     unsigned num_coeffs)
2032 {
2033    const struct lp_type type = bld->type;
2034    LLVMValueRef res = NULL;
2035    unsigned i;
2036
2037    assert(lp_check_value(bld->type, x));
2038
2039    /* TODO: optimize the constant case */
2040    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2041        LLVMIsConstant(x)) {
2042       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2043                    __FUNCTION__);
2044    }
2045
2046    for (i = num_coeffs; i--; ) {
2047       LLVMValueRef coeff;
2048
2049       coeff = lp_build_const_vec(type, coeffs[i]);
2050
2051       if(res)
2052          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
2053       else
2054          res = coeff;
2055    }
2056
2057    if(res)
2058       return res;
2059    else
2060       return bld->undef;
2061 }
2062
2063
2064 /**
2065  * Minimax polynomial fit of 2**x, in range [0, 1[
2066  */
2067 const double lp_build_exp2_polynomial[] = {
2068 #if EXP_POLY_DEGREE == 5
2069    0.999999999690134838155,
2070    0.583974334321735217258,
2071    0.164553105719676828492,
2072    0.0292811063701710962255,
2073    0.00354944426657875141846,
2074    0.000296253726543423377365
2075 #elif EXP_POLY_DEGREE == 4
2076    1.00000001502262084505,
2077    0.563586057338685991394,
2078    0.150436017652442413623,
2079    0.0243220604213317927308,
2080    0.0025359088446580436489
2081 #elif EXP_POLY_DEGREE == 3
2082    0.999925218562710312959,
2083    0.695833540494823811697,
2084    0.226067155427249155588,
2085    0.0780245226406372992967
2086 #elif EXP_POLY_DEGREE == 2
2087    1.00172476321474503578,
2088    0.657636275736077639316,
2089    0.33718943461968720704
2090 #else
2091 #error
2092 #endif
2093 };
2094
2095
2096 void
2097 lp_build_exp2_approx(struct lp_build_context *bld,
2098                      LLVMValueRef x,
2099                      LLVMValueRef *p_exp2_int_part,
2100                      LLVMValueRef *p_frac_part,
2101                      LLVMValueRef *p_exp2)
2102 {
2103    const struct lp_type type = bld->type;
2104    LLVMTypeRef vec_type = lp_build_vec_type(type);
2105    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2106    LLVMValueRef ipart = NULL;
2107    LLVMValueRef fpart = NULL;
2108    LLVMValueRef expipart = NULL;
2109    LLVMValueRef expfpart = NULL;
2110    LLVMValueRef res = NULL;
2111
2112    assert(lp_check_value(bld->type, x));
2113
2114    if(p_exp2_int_part || p_frac_part || p_exp2) {
2115       /* TODO: optimize the constant case */
2116       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2117           LLVMIsConstant(x)) {
2118          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2119                       __FUNCTION__);
2120       }
2121
2122       assert(type.floating && type.width == 32);
2123
2124       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
2125       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
2126
2127       /* ipart = floor(x) */
2128       ipart = lp_build_floor(bld, x);
2129
2130       /* fpart = x - ipart */
2131       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
2132    }
2133
2134    if(p_exp2_int_part || p_exp2) {
2135       /* expipart = (float) (1 << ipart) */
2136       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
2137       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
2138       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
2139       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
2140    }
2141
2142    if(p_exp2) {
2143       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
2144                                      Elements(lp_build_exp2_polynomial));
2145
2146       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
2147    }
2148
2149    if(p_exp2_int_part)
2150       *p_exp2_int_part = expipart;
2151
2152    if(p_frac_part)
2153       *p_frac_part = fpart;
2154
2155    if(p_exp2)
2156       *p_exp2 = res;
2157 }
2158
2159
2160 LLVMValueRef
2161 lp_build_exp2(struct lp_build_context *bld,
2162               LLVMValueRef x)
2163 {
2164    LLVMValueRef res;
2165    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
2166    return res;
2167 }
2168
2169
2170 /**
2171  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
2172  * These coefficients can be generate with
2173  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2174  */
2175 const double lp_build_log2_polynomial[] = {
2176 #if LOG_POLY_DEGREE == 6
2177    3.11578814719469302614,
2178    -3.32419399085241980044,
2179    2.59883907202499966007,
2180    -1.23152682416275988241,
2181    0.318212422185251071475,
2182    -0.0344359067839062357313
2183 #elif LOG_POLY_DEGREE == 5
2184    2.8882704548164776201,
2185    -2.52074962577807006663,
2186    1.48116647521213171641,
2187    -0.465725644288844778798,
2188    0.0596515482674574969533
2189 #elif LOG_POLY_DEGREE == 4
2190    2.61761038894603480148,
2191    -1.75647175389045657003,
2192    0.688243882994381274313,
2193    -0.107254423828329604454
2194 #elif LOG_POLY_DEGREE == 3
2195    2.28330284476918490682,
2196    -1.04913055217340124191,
2197    0.204446009836232697516
2198 #else
2199 #error
2200 #endif
2201 };
2202
2203
2204 /**
2205  * See http://www.devmaster.net/forums/showthread.php?p=43580
2206  */
2207 void
2208 lp_build_log2_approx(struct lp_build_context *bld,
2209                      LLVMValueRef x,
2210                      LLVMValueRef *p_exp,
2211                      LLVMValueRef *p_floor_log2,
2212                      LLVMValueRef *p_log2)
2213 {
2214    const struct lp_type type = bld->type;
2215    LLVMTypeRef vec_type = lp_build_vec_type(type);
2216    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2217
2218    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2219    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2220    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2221
2222    LLVMValueRef i = NULL;
2223    LLVMValueRef exp = NULL;
2224    LLVMValueRef mant = NULL;
2225    LLVMValueRef logexp = NULL;
2226    LLVMValueRef logmant = NULL;
2227    LLVMValueRef res = NULL;
2228
2229    assert(lp_check_value(bld->type, x));
2230
2231    if(p_exp || p_floor_log2 || p_log2) {
2232       /* TODO: optimize the constant case */
2233       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2234           LLVMIsConstant(x)) {
2235          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2236                       __FUNCTION__);
2237       }
2238
2239       assert(type.floating && type.width == 32);
2240
2241       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2242
2243       /* exp = (float) exponent(x) */
2244       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2245    }
2246
2247    if(p_floor_log2 || p_log2) {
2248       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2249       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2250       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2251    }
2252
2253    if(p_log2) {
2254       /* mant = (float) mantissa(x) */
2255       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2256       mant = LLVMBuildOr(bld->builder, mant, one, "");
2257       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2258
2259       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2260                                     Elements(lp_build_log2_polynomial));
2261
2262       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2263       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2264
2265       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2266    }
2267
2268    if(p_exp) {
2269       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2270       *p_exp = exp;
2271    }
2272
2273    if(p_floor_log2)
2274       *p_floor_log2 = logexp;
2275
2276    if(p_log2)
2277       *p_log2 = res;
2278 }
2279
2280
2281 LLVMValueRef
2282 lp_build_log2(struct lp_build_context *bld,
2283               LLVMValueRef x)
2284 {
2285    LLVMValueRef res;
2286    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2287    return res;
2288 }
2289
2290
2291 /**
2292  * Faster (and less accurate) log2.
2293  *
2294  *    log2(x) = floor(log2(x)) + frac(x)
2295  *
2296  * See http://www.flipcode.com/archives/Fast_log_Function.shtml
2297  */
2298 LLVMValueRef
2299 lp_build_fast_log2(struct lp_build_context *bld,
2300                    LLVMValueRef x)
2301 {
2302    const struct lp_type type = bld->type;
2303    LLVMTypeRef vec_type = bld->vec_type;
2304    LLVMTypeRef int_vec_type = bld->int_vec_type;
2305
2306    unsigned mantissa = lp_mantissa(type);
2307    LLVMValueRef mantmask = lp_build_const_int_vec(type, (1ULL << mantissa) - 1);
2308    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2309
2310    LLVMValueRef ipart;
2311    LLVMValueRef fpart;
2312
2313    assert(lp_check_value(bld->type, x));
2314
2315    assert(type.floating);
2316
2317    x = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2318
2319    /* ipart = floor(log2(x)) - 1 */
2320    ipart = LLVMBuildLShr(bld->builder, x, lp_build_const_int_vec(type, mantissa), "");
2321    ipart = LLVMBuildAnd(bld->builder, ipart, lp_build_const_int_vec(type, 255), "");
2322    ipart = LLVMBuildSub(bld->builder, ipart, lp_build_const_int_vec(type, 128), "");
2323    ipart = LLVMBuildSIToFP(bld->builder, ipart, vec_type, "");
2324
2325    /* fpart = 1.0 + frac(x) */
2326    fpart = LLVMBuildAnd(bld->builder, x, mantmask, "");
2327    fpart = LLVMBuildOr(bld->builder, fpart, one, "");
2328    fpart = LLVMBuildBitCast(bld->builder, fpart, vec_type, "");
2329
2330    /* floor(log2(x)) + frac(x) */
2331    return LLVMBuildFAdd(bld->builder, ipart, fpart, "");
2332 }