src/gallium/auxiliary/gallivm/lp_bld_arit.c

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  27
  28
  29 /**
  30  * @file
  31  * Helper
  32  *
  33  * LLVM IR doesn't support all basic arithmetic operations we care about (most
  34  * notably min/max and saturated operations), and it is often necessary to
  35  * resort machine-specific intrinsics directly. The functions here hide all
  36  * these implementation details from the other modules.
  37  *
  38  * We also do simple expressions simplification here. Reasons are:
  39  * - it is very easy given we have all necessary information readily available
  40  * - LLVM optimization passes fail to simplify several vector expressions
  41  * - We often know value constraints which the optimization passes have no way
  42  *   of knowing, such as when source arguments are known to be in [0, 1] range.
  43  *
  44  * @author Jose Fonseca <jfonseca@vmware.com>
  45  */
  46
  47
  48 #include "util/u_memory.h"
  49 #include "util/u_debug.h"
  50 #include "util/u_math.h"
  51 #include "util/u_string.h"
  52 #include "util/u_cpu_detect.h"
  53
  54 #include "lp_bld_type.h"
  55 #include "lp_bld_const.h"
  56 #include "lp_bld_intr.h"
  57 #include "lp_bld_logic.h"
  58 #include "lp_bld_pack.h"
  59 #include "lp_bld_arit.h"
  60
  61
  62 /**
  63  * Generate min(a, b)
  64  * No checks for special case values of a or b = 1 or 0 are done.
  65  */
  66 static LLVMValueRef
  67 lp_build_min_simple(struct lp_build_context *bld,
  68                     LLVMValueRef a,
  69                     LLVMValueRef b)
  70 {
  71    const struct lp_type type = bld->type;
  72    const char *intrinsic = NULL;
  73    LLVMValueRef cond;
  74
  75    assert(lp_check_value(type, a));
  76    assert(lp_check_value(type, b));
  77
  78    /* TODO: optimize the constant case */
  79
  80    if(type.width * type.length == 128) {
  81       if(type.floating) {
  82          if(type.width == 32 && util_cpu_caps.has_sse)
  83             intrinsic = "llvm.x86.sse.min.ps";
  84          if(type.width == 64 && util_cpu_caps.has_sse2)
  85             intrinsic = "llvm.x86.sse2.min.pd";
  86       }
  87       else {
  88          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  89             intrinsic = "llvm.x86.sse2.pminu.b";
  90          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  91             intrinsic = "llvm.x86.sse41.pminsb";
  92          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  93             intrinsic = "llvm.x86.sse41.pminuw";
  94          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  95             intrinsic = "llvm.x86.sse2.pmins.w";
  96          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  97             intrinsic = "llvm.x86.sse41.pminud";
  98          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  99             intrinsic = "llvm.x86.sse41.pminsd";
 100       }
 101    }
 102
 103    if(intrinsic)
 104       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 105
 106    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 107    return lp_build_select(bld, cond, a, b);
 108 }
 109
 110
 111 /**
 112  * Generate max(a, b)
 113  * No checks for special case values of a or b = 1 or 0 are done.
 114  */
 115 static LLVMValueRef
 116 lp_build_max_simple(struct lp_build_context *bld,
 117                     LLVMValueRef a,
 118                     LLVMValueRef b)
 119 {
 120    const struct lp_type type = bld->type;
 121    const char *intrinsic = NULL;
 122    LLVMValueRef cond;
 123
 124    assert(lp_check_value(type, a));
 125    assert(lp_check_value(type, b));
 126
 127    /* TODO: optimize the constant case */
 128
 129    if(type.width * type.length == 128) {
 130       if(type.floating) {
 131          if(type.width == 32 && util_cpu_caps.has_sse)
 132             intrinsic = "llvm.x86.sse.max.ps";
 133          if(type.width == 64 && util_cpu_caps.has_sse2)
 134             intrinsic = "llvm.x86.sse2.max.pd";
 135       }
 136       else {
 137          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 138             intrinsic = "llvm.x86.sse2.pmaxu.b";
 139          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 140             intrinsic = "llvm.x86.sse41.pmaxsb";
 141          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 142             intrinsic = "llvm.x86.sse41.pmaxuw";
 143          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 144             intrinsic = "llvm.x86.sse2.pmaxs.w";
 145          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 146             intrinsic = "llvm.x86.sse41.pmaxud";
 147          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 148             intrinsic = "llvm.x86.sse41.pmaxsd";
 149       }
 150    }
 151
 152    if(intrinsic)
 153       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 154
 155    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 156    return lp_build_select(bld, cond, a, b);
 157 }
 158
 159
 160 /**
 161  * Generate 1 - a, or ~a depending on bld->type.
 162  */
 163 LLVMValueRef
 164 lp_build_comp(struct lp_build_context *bld,
 165               LLVMValueRef a)
 166 {
 167    const struct lp_type type = bld->type;
 168
 169    assert(lp_check_value(type, a));
 170
 171    if(a == bld->one)
 172       return bld->zero;
 173    if(a == bld->zero)
 174       return bld->one;
 175
 176    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 177       if(LLVMIsConstant(a))
 178          return LLVMConstNot(a);
 179       else
 180          return LLVMBuildNot(bld->builder, a, "");
 181    }
 182
 183    if(LLVMIsConstant(a))
 184       if (type.floating)
 185           return LLVMConstFSub(bld->one, a);
 186       else
 187           return LLVMConstSub(bld->one, a);
 188    else
 189       if (type.floating)
 190          return LLVMBuildFSub(bld->builder, bld->one, a, "");
 191       else
 192          return LLVMBuildSub(bld->builder, bld->one, a, "");
 193 }
 194
 195
 196 /**
 197  * Generate a + b
 198  */
 199 LLVMValueRef
 200 lp_build_add(struct lp_build_context *bld,
 201              LLVMValueRef a,
 202              LLVMValueRef b)
 203 {
 204    const struct lp_type type = bld->type;
 205    LLVMValueRef res;
 206
 207    assert(lp_check_value(type, a));
 208    assert(lp_check_value(type, b));
 209
 210    if(a == bld->zero)
 211       return b;
 212    if(b == bld->zero)
 213       return a;
 214    if(a == bld->undef || b == bld->undef)
 215       return bld->undef;
 216
 217    if(bld->type.norm) {
 218       const char *intrinsic = NULL;
 219
 220       if(a == bld->one || b == bld->one)
 221         return bld->one;
 222
 223       if(util_cpu_caps.has_sse2 &&
 224          type.width * type.length == 128 &&
 225          !type.floating && !type.fixed) {
 226          if(type.width == 8)
 227             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 228          if(type.width == 16)
 229             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 230       }
 231
 232       if(intrinsic)
 233          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 234    }
 235
 236    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 237       if (type.floating)
 238          res = LLVMConstFAdd(a, b);
 239       else
 240          res = LLVMConstAdd(a, b);
 241    else
 242       if (type.floating)
 243          res = LLVMBuildFAdd(bld->builder, a, b, "");
 244       else
 245          res = LLVMBuildAdd(bld->builder, a, b, "");
 246
 247    /* clamp to ceiling of 1.0 */
 248    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 249       res = lp_build_min_simple(bld, res, bld->one);
 250
 251    /* XXX clamp to floor of -1 or 0??? */
 252
 253    return res;
 254 }
 255
 256
 257 /** Return the sum of the elements of a */
 258 LLVMValueRef
 259 lp_build_sum_vector(struct lp_build_context *bld,
 260                     LLVMValueRef a)
 261 {
 262    const struct lp_type type = bld->type;
 263    LLVMValueRef index, res;
 264    unsigned i;
 265
 266    assert(lp_check_value(type, a));
 267
 268    if (a == bld->zero)
 269       return bld->zero;
 270    if (a == bld->undef)
 271       return bld->undef;
 272    assert(type.length > 1);
 273
 274    assert(!bld->type.norm);
 275
 276    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 277    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 278
 279    for (i = 1; i < type.length; i++) {
 280       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 281       if (type.floating)
 282          res = LLVMBuildFAdd(bld->builder, res,
 283                             LLVMBuildExtractElement(bld->builder,
 284                                                     a, index, ""),
 285                             "");
 286       else
 287          res = LLVMBuildAdd(bld->builder, res,
 288                             LLVMBuildExtractElement(bld->builder,
 289                                                     a, index, ""),
 290                             "");
 291    }
 292
 293    return res;
 294 }
 295
 296
 297 /**
 298  * Generate a - b
 299  */
 300 LLVMValueRef
 301 lp_build_sub(struct lp_build_context *bld,
 302              LLVMValueRef a,
 303              LLVMValueRef b)
 304 {
 305    const struct lp_type type = bld->type;
 306    LLVMValueRef res;
 307
 308    assert(lp_check_value(type, a));
 309    assert(lp_check_value(type, b));
 310
 311    if(b == bld->zero)
 312       return a;
 313    if(a == bld->undef || b == bld->undef)
 314       return bld->undef;
 315    if(a == b)
 316       return bld->zero;
 317
 318    if(bld->type.norm) {
 319       const char *intrinsic = NULL;
 320
 321       if(b == bld->one)
 322         return bld->zero;
 323
 324       if(util_cpu_caps.has_sse2 &&
 325          type.width * type.length == 128 &&
 326          !type.floating && !type.fixed) {
 327          if(type.width == 8)
 328             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 329          if(type.width == 16)
 330             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 331       }
 332
 333       if(intrinsic)
 334          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 335    }
 336
 337    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 338       if (type.floating)
 339          res = LLVMConstFSub(a, b);
 340       else
 341          res = LLVMConstSub(a, b);
 342    else
 343       if (type.floating)
 344          res = LLVMBuildFSub(bld->builder, a, b, "");
 345       else
 346          res = LLVMBuildSub(bld->builder, a, b, "");
 347
 348    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 349       res = lp_build_max_simple(bld, res, bld->zero);
 350
 351    return res;
 352 }
 353
 354
 355 /**
 356  * Normalized 8bit multiplication.
 357  *
 358  * - alpha plus one
 359  *
 360  *     makes the following approximation to the division (Sree)
 361  *
 362  *       a*b/255 ~= (a*(b + 1)) >> 256
 363  *
 364  *     which is the fastest method that satisfies the following OpenGL criteria
 365  *
 366  *       0*0 = 0 and 255*255 = 255
 367  *
 368  * - geometric series
 369  *
 370  *     takes the geometric series approximation to the division
 371  *
 372  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 373  *
 374  *     in this case just the first two terms to fit in 16bit arithmetic
 375  *
 376  *       t/255 ~= (t + (t >> 8)) >> 8
 377  *
 378  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 379  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 380  *     must be used
 381  *
 382  * - geometric series plus rounding
 383  *
 384  *     when using a geometric series division instead of truncating the result
 385  *     use roundoff in the approximation (Jim Blinn)
 386  *
 387  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 388  *
 389  *     achieving the exact results
 390  *
 391  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 392  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 393  * @sa Michael Herf, The "double blend trick", May 2000,
 394  *     http://www.stereopsis.com/doubleblend.html
 395  */
 396 static LLVMValueRef
 397 lp_build_mul_u8n(LLVMBuilderRef builder,
 398                  struct lp_type i16_type,
 399                  LLVMValueRef a, LLVMValueRef b)
 400 {
 401    LLVMValueRef c8;
 402    LLVMValueRef ab;
 403
 404    assert(!i16_type.floating);
 405    assert(lp_check_value(i16_type, a));
 406    assert(lp_check_value(i16_type, b));
 407
 408    c8 = lp_build_const_int_vec(i16_type, 8);
 409
 410 #if 0
 411
 412    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 413    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 414    ab = LLVMBuildMul(builder, a, b, "");
 415
 416 #else
 417
 418    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 419    ab = LLVMBuildMul(builder, a, b, "");
 420    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 421    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 422
 423 #endif
 424
 425    ab = LLVMBuildLShr(builder, ab, c8, "");
 426
 427    return ab;
 428 }
 429
 430
 431 /**
 432  * Generate a * b
 433  */
 434 LLVMValueRef
 435 lp_build_mul(struct lp_build_context *bld,
 436              LLVMValueRef a,
 437              LLVMValueRef b)
 438 {
 439    const struct lp_type type = bld->type;
 440    LLVMValueRef shift;
 441    LLVMValueRef res;
 442
 443    assert(lp_check_value(type, a));
 444    assert(lp_check_value(type, b));
 445
 446    if(a == bld->zero)
 447       return bld->zero;
 448    if(a == bld->one)
 449       return b;
 450    if(b == bld->zero)
 451       return bld->zero;
 452    if(b == bld->one)
 453       return a;
 454    if(a == bld->undef || b == bld->undef)
 455       return bld->undef;
 456
 457    if(!type.floating && !type.fixed && type.norm) {
 458       if(type.width == 8) {
 459          struct lp_type i16_type = lp_wider_type(type);
 460          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 461
 462          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 463          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 464
 465          /* PMULLW, PSRLW, PADDW */
 466          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 467          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 468
 469          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 470
 471          return ab;
 472       }
 473
 474       /* FIXME */
 475       assert(0);
 476    }
 477
 478    if(type.fixed)
 479       shift = lp_build_const_int_vec(type, type.width/2);
 480    else
 481       shift = NULL;
 482
 483    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 484       if (type.floating)
 485          res = LLVMConstFMul(a, b);
 486       else
 487          res = LLVMConstMul(a, b);
 488       if(shift) {
 489          if(type.sign)
 490             res = LLVMConstAShr(res, shift);
 491          else
 492             res = LLVMConstLShr(res, shift);
 493       }
 494    }
 495    else {
 496       if (type.floating)
 497          res = LLVMBuildFMul(bld->builder, a, b, "");
 498       else
 499          res = LLVMBuildMul(bld->builder, a, b, "");
 500       if(shift) {
 501          if(type.sign)
 502             res = LLVMBuildAShr(bld->builder, res, shift, "");
 503          else
 504             res = LLVMBuildLShr(bld->builder, res, shift, "");
 505       }
 506    }
 507
 508    return res;
 509 }
 510
 511
 512 /**
 513  * Small vector x scale multiplication optimization.
 514  */
 515 LLVMValueRef
 516 lp_build_mul_imm(struct lp_build_context *bld,
 517                  LLVMValueRef a,
 518                  int b)
 519 {
 520    LLVMValueRef factor;
 521
 522    assert(lp_check_value(bld->type, a));
 523
 524    if(b == 0)
 525       return bld->zero;
 526
 527    if(b == 1)
 528       return a;
 529
 530    if(b == -1)
 531       return lp_build_negate(bld, a);
 532
 533    if(b == 2 && bld->type.floating)
 534       return lp_build_add(bld, a, a);
 535
 536    if(util_is_pot(b)) {
 537       unsigned shift = ffs(b) - 1;
 538
 539       if(bld->type.floating) {
 540 #if 0
 541          /*
 542           * Power of two multiplication by directly manipulating the mantissa.
 543           *
 544           * XXX: This might not be always faster, it will introduce a small error
 545           * for multiplication by zero, and it will produce wrong results
 546           * for Inf and NaN.
 547           */
 548          unsigned mantissa = lp_mantissa(bld->type);
 549          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 550          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 551          a = LLVMBuildAdd(bld->builder, a, factor, "");
 552          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 553          return a;
 554 #endif
 555       }
 556       else {
 557          factor = lp_build_const_vec(bld->type, shift);
 558          return LLVMBuildShl(bld->builder, a, factor, "");
 559       }
 560    }
 561
 562    factor = lp_build_const_vec(bld->type, (double)b);
 563    return lp_build_mul(bld, a, factor);
 564 }
 565
 566
 567 /**
 568  * Generate a / b
 569  */
 570 LLVMValueRef
 571 lp_build_div(struct lp_build_context *bld,
 572              LLVMValueRef a,
 573              LLVMValueRef b)
 574 {
 575    const struct lp_type type = bld->type;
 576
 577    assert(lp_check_value(type, a));
 578    assert(lp_check_value(type, b));
 579
 580    if(a == bld->zero)
 581       return bld->zero;
 582    if(a == bld->one)
 583       return lp_build_rcp(bld, b);
 584    if(b == bld->zero)
 585       return bld->undef;
 586    if(b == bld->one)
 587       return a;
 588    if(a == bld->undef || b == bld->undef)
 589       return bld->undef;
 590
 591    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 592       if (type.floating)
 593          return LLVMConstFDiv(a, b);
 594       else if (type.sign)
 595          return LLVMConstSDiv(a, b);
 596       else
 597          return LLVMConstUDiv(a, b);
 598    }
 599
 600    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 601       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 602
 603    if (type.floating)
 604       return LLVMBuildFDiv(bld->builder, a, b, "");
 605    else if (type.sign)
 606       return LLVMBuildSDiv(bld->builder, a, b, "");
 607    else
 608       return LLVMBuildUDiv(bld->builder, a, b, "");
 609 }
 610
 611
 612 /**
 613  * Linear interpolation.
 614  *
 615  * This also works for integer values with a few caveats.
 616  *
 617  * @sa http://www.stereopsis.com/doubleblend.html
 618  */
 619 LLVMValueRef
 620 lp_build_lerp(struct lp_build_context *bld,
 621               LLVMValueRef x,
 622               LLVMValueRef v0,
 623               LLVMValueRef v1)
 624 {
 625    LLVMValueRef delta;
 626    LLVMValueRef res;
 627
 628    assert(lp_check_value(bld->type, x));
 629    assert(lp_check_value(bld->type, v0));
 630    assert(lp_check_value(bld->type, v1));
 631
 632    delta = lp_build_sub(bld, v1, v0);
 633
 634    res = lp_build_mul(bld, x, delta);
 635
 636    res = lp_build_add(bld, v0, res);
 637
 638    if(bld->type.fixed)
 639       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 640        * but it will be wrong for other uses. Basically we need a more
 641        * powerful lp_type, capable of further distinguishing the values
 642        * interpretation from the value storage. */
 643       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 644
 645    return res;
 646 }
 647
 648
 649 LLVMValueRef
 650 lp_build_lerp_2d(struct lp_build_context *bld,
 651                  LLVMValueRef x,
 652                  LLVMValueRef y,
 653                  LLVMValueRef v00,
 654                  LLVMValueRef v01,
 655                  LLVMValueRef v10,
 656                  LLVMValueRef v11)
 657 {
 658    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 659    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 660    return lp_build_lerp(bld, y, v0, v1);
 661 }
 662
 663
 664 /**
 665  * Generate min(a, b)
 666  * Do checks for special cases.
 667  */
 668 LLVMValueRef
 669 lp_build_min(struct lp_build_context *bld,
 670              LLVMValueRef a,
 671              LLVMValueRef b)
 672 {
 673    assert(lp_check_value(bld->type, a));
 674    assert(lp_check_value(bld->type, b));
 675
 676    if(a == bld->undef || b == bld->undef)
 677       return bld->undef;
 678
 679    if(a == b)
 680       return a;
 681
 682    if(bld->type.norm) {
 683       if(a == bld->zero || b == bld->zero)
 684          return bld->zero;
 685       if(a == bld->one)
 686          return b;
 687       if(b == bld->one)
 688          return a;
 689    }
 690
 691    return lp_build_min_simple(bld, a, b);
 692 }
 693
 694
 695 /**
 696  * Generate max(a, b)
 697  * Do checks for special cases.
 698  */
 699 LLVMValueRef
 700 lp_build_max(struct lp_build_context *bld,
 701              LLVMValueRef a,
 702              LLVMValueRef b)
 703 {
 704    assert(lp_check_value(bld->type, a));
 705    assert(lp_check_value(bld->type, b));
 706
 707    if(a == bld->undef || b == bld->undef)
 708       return bld->undef;
 709
 710    if(a == b)
 711       return a;
 712
 713    if(bld->type.norm) {
 714       if(a == bld->one || b == bld->one)
 715          return bld->one;
 716       if(a == bld->zero)
 717          return b;
 718       if(b == bld->zero)
 719          return a;
 720    }
 721
 722    return lp_build_max_simple(bld, a, b);
 723 }
 724
 725
 726 /**
 727  * Generate clamp(a, min, max)
 728  * Do checks for special cases.
 729  */
 730 LLVMValueRef
 731 lp_build_clamp(struct lp_build_context *bld,
 732                LLVMValueRef a,
 733                LLVMValueRef min,
 734                LLVMValueRef max)
 735 {
 736    assert(lp_check_value(bld->type, a));
 737    assert(lp_check_value(bld->type, min));
 738    assert(lp_check_value(bld->type, max));
 739
 740    a = lp_build_min(bld, a, max);
 741    a = lp_build_max(bld, a, min);
 742    return a;
 743 }
 744
 745
 746 /**
 747  * Generate abs(a)
 748  */
 749 LLVMValueRef
 750 lp_build_abs(struct lp_build_context *bld,
 751              LLVMValueRef a)
 752 {
 753    const struct lp_type type = bld->type;
 754    LLVMTypeRef vec_type = lp_build_vec_type(type);
 755
 756    assert(lp_check_value(type, a));
 757
 758    if(!type.sign)
 759       return a;
 760
 761    if(type.floating) {
 762       /* Mask out the sign bit */
 763       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 764       unsigned long long absMask = ~(1ULL << (type.width - 1));
 765       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 766       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 767       a = LLVMBuildAnd(bld->builder, a, mask, "");
 768       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 769       return a;
 770    }
 771
 772    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 773       switch(type.width) {
 774       case 8:
 775          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 776       case 16:
 777          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 778       case 32:
 779          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 780       }
 781    }
 782
 783    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 784 }
 785
 786
 787 LLVMValueRef
 788 lp_build_negate(struct lp_build_context *bld,
 789                 LLVMValueRef a)
 790 {
 791    assert(lp_check_value(bld->type, a));
 792
 793 #if HAVE_LLVM >= 0x0207
 794    if (bld->type.floating)
 795       a = LLVMBuildFNeg(bld->builder, a, "");
 796    else
 797 #endif
 798       a = LLVMBuildNeg(bld->builder, a, "");
 799
 800    return a;
 801 }
 802
 803
 804 /** Return -1, 0 or +1 depending on the sign of a */
 805 LLVMValueRef
 806 lp_build_sgn(struct lp_build_context *bld,
 807              LLVMValueRef a)
 808 {
 809    const struct lp_type type = bld->type;
 810    LLVMValueRef cond;
 811    LLVMValueRef res;
 812
 813    assert(lp_check_value(type, a));
 814
 815    /* Handle non-zero case */
 816    if(!type.sign) {
 817       /* if not zero then sign must be positive */
 818       res = bld->one;
 819    }
 820    else if(type.floating) {
 821       LLVMTypeRef vec_type;
 822       LLVMTypeRef int_type;
 823       LLVMValueRef mask;
 824       LLVMValueRef sign;
 825       LLVMValueRef one;
 826       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 827
 828       int_type = lp_build_int_vec_type(type);
 829       vec_type = lp_build_vec_type(type);
 830       mask = lp_build_const_int_vec(type, maskBit);
 831
 832       /* Take the sign bit and add it to 1 constant */
 833       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 834       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 835       one = LLVMConstBitCast(bld->one, int_type);
 836       res = LLVMBuildOr(bld->builder, sign, one, "");
 837       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 838    }
 839    else
 840    {
 841       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 842       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 843       res = lp_build_select(bld, cond, bld->one, minus_one);
 844    }
 845
 846    /* Handle zero */
 847    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 848    res = lp_build_select(bld, cond, bld->zero, res);
 849
 850    return res;
 851 }
 852
 853
 854 /**
 855  * Set the sign of float vector 'a' according to 'sign'.
 856  * If sign==0, return abs(a).
 857  * If sign==1, return -abs(a);
 858  * Other values for sign produce undefined results.
 859  */
 860 LLVMValueRef
 861 lp_build_set_sign(struct lp_build_context *bld,
 862                   LLVMValueRef a, LLVMValueRef sign)
 863 {
 864    const struct lp_type type = bld->type;
 865    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 866    LLVMTypeRef vec_type = lp_build_vec_type(type);
 867    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 868    LLVMValueRef mask = lp_build_const_int_vec(type,
 869                              ~((unsigned long long) 1 << (type.width - 1)));
 870    LLVMValueRef val, res;
 871
 872    assert(type.floating);
 873    assert(lp_check_value(type, a));
 874
 875    /* val = reinterpret_cast<int>(a) */
 876    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 877    /* val = val & mask */
 878    val = LLVMBuildAnd(bld->builder, val, mask, "");
 879    /* sign = sign << shift */
 880    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 881    /* res = val | sign */
 882    res = LLVMBuildOr(bld->builder, val, sign, "");
 883    /* res = reinterpret_cast<float>(res) */
 884    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 885
 886    return res;
 887 }
 888
 889
 890 /**
 891  * Convert vector of (or scalar) int to vector of (or scalar) float.
 892  */
 893 LLVMValueRef
 894 lp_build_int_to_float(struct lp_build_context *bld,
 895                       LLVMValueRef a)
 896 {
 897    const struct lp_type type = bld->type;
 898    LLVMTypeRef vec_type = lp_build_vec_type(type);
 899
 900    assert(type.floating);
 901
 902    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 903 }
 904
 905
 906
 907 enum lp_build_round_sse41_mode
 908 {
 909    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 910    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 911    LP_BUILD_ROUND_SSE41_CEIL = 2,
 912    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 913 };
 914
 915
 916 static INLINE LLVMValueRef
 917 lp_build_round_sse41(struct lp_build_context *bld,
 918                      LLVMValueRef a,
 919                      enum lp_build_round_sse41_mode mode)
 920 {
 921    const struct lp_type type = bld->type;
 922    LLVMTypeRef vec_type = lp_build_vec_type(type);
 923    const char *intrinsic;
 924
 925    assert(type.floating);
 926    assert(type.width*type.length == 128);
 927    assert(lp_check_value(type, a));
 928    assert(util_cpu_caps.has_sse4_1);
 929
 930    switch(type.width) {
 931    case 32:
 932       intrinsic = "llvm.x86.sse41.round.ps";
 933       break;
 934    case 64:
 935       intrinsic = "llvm.x86.sse41.round.pd";
 936       break;
 937    default:
 938       assert(0);
 939       return bld->undef;
 940    }
 941
 942    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 943                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 944 }
 945
 946
 947 /**
 948  * Return the integer part of a float (vector) value.  The returned value is
 949  * a float (vector).
 950  * Ex: trunc(-1.5) = 1.0
 951  */
 952 LLVMValueRef
 953 lp_build_trunc(struct lp_build_context *bld,
 954                LLVMValueRef a)
 955 {
 956    const struct lp_type type = bld->type;
 957
 958    assert(type.floating);
 959    assert(lp_check_value(type, a));
 960
 961    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 962       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 963    else {
 964       LLVMTypeRef vec_type = lp_build_vec_type(type);
 965       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 966       LLVMValueRef res;
 967       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 968       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 969       return res;
 970    }
 971 }
 972
 973
 974 /**
 975  * Return float (vector) rounded to nearest integer (vector).  The returned
 976  * value is a float (vector).
 977  * Ex: round(0.9) = 1.0
 978  * Ex: round(-1.5) = -2.0
 979  */
 980 LLVMValueRef
 981 lp_build_round(struct lp_build_context *bld,
 982                LLVMValueRef a)
 983 {
 984    const struct lp_type type = bld->type;
 985
 986    assert(type.floating);
 987    assert(lp_check_value(type, a));
 988
 989    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 990       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 991    else {
 992       LLVMTypeRef vec_type = lp_build_vec_type(type);
 993       LLVMValueRef res;
 994       res = lp_build_iround(bld, a);
 995       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 996       return res;
 997    }
 998 }
 999
1000
1001 /**
1002  * Return floor of float (vector), result is a float (vector)
1003  * Ex: floor(1.1) = 1.0
1004  * Ex: floor(-1.1) = -2.0
1005  */
1006 LLVMValueRef
1007 lp_build_floor(struct lp_build_context *bld,
1008                LLVMValueRef a)
1009 {
1010    const struct lp_type type = bld->type;
1011
1012    assert(type.floating);
1013    assert(lp_check_value(type, a));
1014
1015    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1016       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1017    else {
1018       LLVMTypeRef vec_type = lp_build_vec_type(type);
1019       LLVMValueRef res;
1020       res = lp_build_ifloor(bld, a);
1021       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1022       return res;
1023    }
1024 }
1025
1026
1027 /**
1028  * Return ceiling of float (vector), returning float (vector).
1029  * Ex: ceil( 1.1) = 2.0
1030  * Ex: ceil(-1.1) = -1.0
1031  */
1032 LLVMValueRef
1033 lp_build_ceil(struct lp_build_context *bld,
1034               LLVMValueRef a)
1035 {
1036    const struct lp_type type = bld->type;
1037
1038    assert(type.floating);
1039    assert(lp_check_value(type, a));
1040
1041    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1042       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1043    else {
1044       LLVMTypeRef vec_type = lp_build_vec_type(type);
1045       LLVMValueRef res;
1046       res = lp_build_iceil(bld, a);
1047       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1048       return res;
1049    }
1050 }
1051
1052
1053 /**
1054  * Return fractional part of 'a' computed as a - floor(a)
1055  * Typically used in texture coord arithmetic.
1056  */
1057 LLVMValueRef
1058 lp_build_fract(struct lp_build_context *bld,
1059                LLVMValueRef a)
1060 {
1061    assert(bld->type.floating);
1062    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1063 }
1064
1065
1066 /**
1067  * Return the integer part of a float (vector) value.  The returned value is
1068  * an integer (vector).
1069  * Ex: itrunc(-1.5) = 1
1070  */
1071 LLVMValueRef
1072 lp_build_itrunc(struct lp_build_context *bld,
1073                 LLVMValueRef a)
1074 {
1075    const struct lp_type type = bld->type;
1076    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1077
1078    assert(type.floating);
1079    assert(lp_check_value(type, a));
1080
1081    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1082 }
1083
1084
1085 /**
1086  * Return float (vector) rounded to nearest integer (vector).  The returned
1087  * value is an integer (vector).
1088  * Ex: iround(0.9) = 1
1089  * Ex: iround(-1.5) = -2
1090  */
1091 LLVMValueRef
1092 lp_build_iround(struct lp_build_context *bld,
1093                 LLVMValueRef a)
1094 {
1095    const struct lp_type type = bld->type;
1096    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1097    LLVMValueRef res;
1098
1099    assert(type.floating);
1100
1101    assert(lp_check_value(type, a));
1102
1103    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1104       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1105    }
1106    else {
1107       LLVMTypeRef vec_type = lp_build_vec_type(type);
1108       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1109       LLVMValueRef sign;
1110       LLVMValueRef half;
1111
1112       /* get sign bit */
1113       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1114       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1115
1116       /* sign * 0.5 */
1117       half = lp_build_const_vec(type, 0.5);
1118       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1119       half = LLVMBuildOr(bld->builder, sign, half, "");
1120       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1121
1122       res = LLVMBuildFAdd(bld->builder, a, half, "");
1123    }
1124
1125    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1126
1127    return res;
1128 }
1129
1130
1131 /**
1132  * Return floor of float (vector), result is an int (vector)
1133  * Ex: ifloor(1.1) = 1.0
1134  * Ex: ifloor(-1.1) = -2.0
1135  */
1136 LLVMValueRef
1137 lp_build_ifloor(struct lp_build_context *bld,
1138                 LLVMValueRef a)
1139 {
1140    const struct lp_type type = bld->type;
1141    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1142    LLVMValueRef res;
1143
1144    assert(type.floating);
1145    assert(lp_check_value(type, a));
1146
1147    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1148       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1149    }
1150    else {
1151       /* Take the sign bit and add it to 1 constant */
1152       LLVMTypeRef vec_type = lp_build_vec_type(type);
1153       unsigned mantissa = lp_mantissa(type);
1154       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1155       LLVMValueRef sign;
1156       LLVMValueRef offset;
1157
1158       /* sign = a < 0 ? ~0 : 0 */
1159       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1160       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1161       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1162
1163       /* offset = -0.99999(9)f */
1164       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1165       offset = LLVMConstBitCast(offset, int_vec_type);
1166
1167       /* offset = a < 0 ? offset : 0.0f */
1168       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1169       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1170
1171       res = LLVMBuildFAdd(bld->builder, a, offset, "ifloor.res");
1172    }
1173
1174    /* round to nearest (toward zero) */
1175    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1176
1177    return res;
1178 }
1179
1180
1181 /**
1182  * Return ceiling of float (vector), returning int (vector).
1183  * Ex: iceil( 1.1) = 2
1184  * Ex: iceil(-1.1) = -1
1185  */
1186 LLVMValueRef
1187 lp_build_iceil(struct lp_build_context *bld,
1188                LLVMValueRef a)
1189 {
1190    const struct lp_type type = bld->type;
1191    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1192    LLVMValueRef res;
1193
1194    assert(type.floating);
1195    assert(lp_check_value(type, a));
1196
1197    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1198       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1199    }
1200    else {
1201       LLVMTypeRef vec_type = lp_build_vec_type(type);
1202       unsigned mantissa = lp_mantissa(type);
1203       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1204       LLVMValueRef sign;
1205       LLVMValueRef offset;
1206
1207       /* sign = a < 0 ? 0 : ~0 */
1208       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1209       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1210       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1211       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1212
1213       /* offset = 0.99999(9)f */
1214       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1215       offset = LLVMConstBitCast(offset, int_vec_type);
1216
1217       /* offset = a < 0 ? 0.0 : offset */
1218       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1219       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1220
1221       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1222    }
1223
1224    /* round to nearest (toward zero) */
1225    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1226
1227    return res;
1228 }
1229
1230
1231 LLVMValueRef
1232 lp_build_sqrt(struct lp_build_context *bld,
1233               LLVMValueRef a)
1234 {
1235    const struct lp_type type = bld->type;
1236    LLVMTypeRef vec_type = lp_build_vec_type(type);
1237    char intrinsic[32];
1238
1239    assert(lp_check_value(type, a));
1240
1241    /* TODO: optimize the constant case */
1242    /* TODO: optimize the constant case */
1243
1244    assert(type.floating);
1245    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1246
1247    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1248 }
1249
1250
1251 LLVMValueRef
1252 lp_build_rcp(struct lp_build_context *bld,
1253              LLVMValueRef a)
1254 {
1255    const struct lp_type type = bld->type;
1256
1257    assert(lp_check_value(type, a));
1258
1259    if(a == bld->zero)
1260       return bld->undef;
1261    if(a == bld->one)
1262       return bld->one;
1263    if(a == bld->undef)
1264       return bld->undef;
1265
1266    assert(type.floating);
1267
1268    if(LLVMIsConstant(a))
1269       return LLVMConstFDiv(bld->one, a);
1270
1271    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1272       /*
1273        * XXX: Added precision is not always necessary, so only enable this
1274        * when we have a better system in place to track minimum precision.
1275        */
1276
1277 #if 1
1278       /*
1279        * Do one Newton-Raphson step to improve precision:
1280        *
1281        *   x1 = (2 - a * rcp(a)) * rcp(a)
1282        */
1283
1284       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1285       LLVMValueRef rcp_a;
1286       LLVMValueRef res;
1287
1288       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1289
1290       res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1291       res = LLVMBuildFSub(bld->builder, two, res, "");
1292       res = LLVMBuildFMul(bld->builder, res, rcp_a, "");
1293
1294       return res;
1295 #else
1296       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1297 #endif
1298    }
1299
1300    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1301 }
1302
1303
1304 /**
1305  * Generate 1/sqrt(a)
1306  */
1307 LLVMValueRef
1308 lp_build_rsqrt(struct lp_build_context *bld,
1309                LLVMValueRef a)
1310 {
1311    const struct lp_type type = bld->type;
1312
1313    assert(lp_check_value(type, a));
1314
1315    assert(type.floating);
1316
1317    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1318       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1319
1320    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1321 }
1322
1323
1324 static inline LLVMValueRef
1325 lp_build_const_v4si(unsigned long value)
1326 {
1327    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1328    LLVMValueRef elements[4] = { element, element, element, element };
1329    return LLVMConstVector(elements, 4);
1330 }
1331
1332 static inline LLVMValueRef
1333 lp_build_const_v4sf(float value)
1334 {
1335    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1336    LLVMValueRef elements[4] = { element, element, element, element };
1337    return LLVMConstVector(elements, 4);
1338 }
1339
1340
1341 /**
1342  * Generate sin(a) using SSE2
1343  */
1344 LLVMValueRef
1345 lp_build_sin(struct lp_build_context *bld,
1346              LLVMValueRef a)
1347 {
1348    struct lp_type int_type = lp_int_type(bld->type);
1349    LLVMBuilderRef b = bld->builder;
1350    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1351    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1352
1353    /*
1354     *  take the absolute value,
1355     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1356     */
1357
1358    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1359    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1360
1361    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1362    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1363
1364    /*
1365     * extract the sign bit (upper one)
1366     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1367     */
1368    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1369    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1370
1371    /*
1372     * scale by 4/Pi
1373     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1374     */
1375
1376    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1377    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1378
1379    /*
1380     * store the integer part of y in mm0
1381     * emm2 = _mm_cvttps_epi32(y);
1382     */
1383
1384    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1385
1386    /*
1387     * j=(j+1) & (~1) (see the cephes sources)
1388     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1389     */
1390
1391    LLVMValueRef all_one = lp_build_const_v4si(1);
1392    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1393    /*
1394     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1395     */
1396    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1397    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1398
1399    /*
1400     * y = _mm_cvtepi32_ps(emm2);
1401     */
1402    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1403
1404    /* get the swap sign flag
1405     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1406     */
1407    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1408    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1409
1410    /*
1411     * emm2 = _mm_slli_epi32(emm0, 29);
1412     */
1413    LLVMValueRef const_29 = lp_build_const_v4si(29);
1414    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1415
1416    /*
1417     * get the polynom selection mask
1418     * there is one polynom for 0 <= x <= Pi/4
1419     * and another one for Pi/4<x<=Pi/2
1420     * Both branches will be computed.
1421     *
1422     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1423     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1424     */
1425
1426    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1427    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1428    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1429                                              emm2_3, lp_build_const_v4si(0));
1430    /*
1431     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1432     */
1433    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1434
1435    /*
1436     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1437     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1438     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1439     */
1440    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1441    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1442    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1443
1444    /*
1445     * The magic pass: "Extended precision modular arithmetic"
1446     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1447     * xmm1 = _mm_mul_ps(y, xmm1);
1448     * xmm2 = _mm_mul_ps(y, xmm2);
1449     * xmm3 = _mm_mul_ps(y, xmm3);
1450     */
1451    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1452    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1453    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1454
1455    /*
1456     * x = _mm_add_ps(x, xmm1);
1457     * x = _mm_add_ps(x, xmm2);
1458     * x = _mm_add_ps(x, xmm3);
1459     */
1460
1461    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1462    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1463    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1464
1465    /*
1466     * Evaluate the first polynom  (0 <= x <= Pi/4)
1467     *
1468     * z = _mm_mul_ps(x,x);
1469     */
1470    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1471
1472    /*
1473     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1474     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1475     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1476     */
1477    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1478    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1479    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1480
1481    /*
1482     * y = *(v4sf*)_ps_coscof_p0;
1483     * y = _mm_mul_ps(y, z);
1484     */
1485    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1486    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1487    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1488    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1489    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1490    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1491
1492
1493    /*
1494     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1495     * y = _mm_sub_ps(y, tmp);
1496     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1497     */
1498    LLVMValueRef half = lp_build_const_v4sf(0.5);
1499    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1500    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1501    LLVMValueRef one = lp_build_const_v4sf(1.0);
1502    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1503
1504    /*
1505     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1506     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1507     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1508     */
1509    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1510    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1511    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1512
1513    /*
1514     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1515     *
1516     * y2 = *(v4sf*)_ps_sincof_p0;
1517     * y2 = _mm_mul_ps(y2, z);
1518     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1519     * y2 = _mm_mul_ps(y2, z);
1520     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1521     * y2 = _mm_mul_ps(y2, z);
1522     * y2 = _mm_mul_ps(y2, x);
1523     * y2 = _mm_add_ps(y2, x);
1524     */
1525
1526    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1527    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1528    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1529    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1530    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1531    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1532    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1533
1534    /*
1535     * select the correct result from the two polynoms
1536     * xmm3 = poly_mask;
1537     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1538     * y = _mm_andnot_ps(xmm3, y);
1539     * y = _mm_add_ps(y,y2);
1540     */
1541    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1542    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1543    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1544    LLVMValueRef inv = lp_build_const_v4si(~0);
1545    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1546    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1547    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1548
1549    /*
1550     * update the sign
1551     * y = _mm_xor_ps(y, sign_bit);
1552     */
1553    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1554    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1555    return y_result;
1556 }
1557
1558
1559 /**
1560  * Generate cos(a) using SSE2
1561  */
1562 LLVMValueRef
1563 lp_build_cos(struct lp_build_context *bld,
1564              LLVMValueRef a)
1565 {
1566    struct lp_type int_type = lp_int_type(bld->type);
1567    LLVMBuilderRef b = bld->builder;
1568    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1569    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1570
1571    /*
1572     *  take the absolute value,
1573     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1574     */
1575
1576    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1577    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1578
1579    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1580    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1581
1582    /*
1583     * scale by 4/Pi
1584     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1585     */
1586
1587    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1588    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1589
1590    /*
1591     * store the integer part of y in mm0
1592     * emm2 = _mm_cvttps_epi32(y);
1593     */
1594
1595    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1596
1597    /*
1598     * j=(j+1) & (~1) (see the cephes sources)
1599     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1600     */
1601
1602    LLVMValueRef all_one = lp_build_const_v4si(1);
1603    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1604    /*
1605     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1606     */
1607    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1608    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1609
1610    /*
1611     * y = _mm_cvtepi32_ps(emm2);
1612     */
1613    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1614
1615
1616    /*
1617     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1618     */
1619    LLVMValueRef const_2 = lp_build_const_v4si(2);
1620    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1621
1622
1623    /* get the swap sign flag
1624     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1625     */
1626    LLVMValueRef inv = lp_build_const_v4si(~0);
1627    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1628    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1629    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1630
1631    /*
1632     * emm2 = _mm_slli_epi32(emm0, 29);
1633     */
1634    LLVMValueRef const_29 = lp_build_const_v4si(29);
1635    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1636
1637    /*
1638     * get the polynom selection mask
1639     * there is one polynom for 0 <= x <= Pi/4
1640     * and another one for Pi/4<x<=Pi/2
1641     * Both branches will be computed.
1642     *
1643     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1644     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1645     */
1646
1647    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1648    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1649    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1650                                              emm2_3, lp_build_const_v4si(0));
1651
1652    /*
1653     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1654     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1655     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1656     */
1657    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1658    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1659    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1660
1661    /*
1662     * The magic pass: "Extended precision modular arithmetic"
1663     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1664     * xmm1 = _mm_mul_ps(y, xmm1);
1665     * xmm2 = _mm_mul_ps(y, xmm2);
1666     * xmm3 = _mm_mul_ps(y, xmm3);
1667     */
1668    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1669    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1670    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1671
1672    /*
1673     * x = _mm_add_ps(x, xmm1);
1674     * x = _mm_add_ps(x, xmm2);
1675     * x = _mm_add_ps(x, xmm3);
1676     */
1677
1678    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1679    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1680    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1681
1682    /*
1683     * Evaluate the first polynom  (0 <= x <= Pi/4)
1684     *
1685     * z = _mm_mul_ps(x,x);
1686     */
1687    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1688
1689    /*
1690     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1691     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1692     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1693     */
1694    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1695    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1696    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1697
1698    /*
1699     * y = *(v4sf*)_ps_coscof_p0;
1700     * y = _mm_mul_ps(y, z);
1701     */
1702    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1703    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1704    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1705    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1706    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1707    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1708
1709
1710    /*
1711     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1712     * y = _mm_sub_ps(y, tmp);
1713     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1714     */
1715    LLVMValueRef half = lp_build_const_v4sf(0.5);
1716    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1717    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1718    LLVMValueRef one = lp_build_const_v4sf(1.0);
1719    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1720
1721    /*
1722     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1723     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1724     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1725     */
1726    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1727    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1728    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1729
1730    /*
1731     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1732     *
1733     * y2 = *(v4sf*)_ps_sincof_p0;
1734     * y2 = _mm_mul_ps(y2, z);
1735     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1736     * y2 = _mm_mul_ps(y2, z);
1737     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1738     * y2 = _mm_mul_ps(y2, z);
1739     * y2 = _mm_mul_ps(y2, x);
1740     * y2 = _mm_add_ps(y2, x);
1741     */
1742
1743    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1744    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1745    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1746    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1747    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1748    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1749    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1750
1751    /*
1752     * select the correct result from the two polynoms
1753     * xmm3 = poly_mask;
1754     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1755     * y = _mm_andnot_ps(xmm3, y);
1756     * y = _mm_add_ps(y,y2);
1757     */
1758    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1759    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1760    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1761    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1762    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1763    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1764
1765    /*
1766     * update the sign
1767     * y = _mm_xor_ps(y, sign_bit);
1768     */
1769    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1770    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1771    return y_result;
1772 }
1773
1774
1775 /**
1776  * Generate pow(x, y)
1777  */
1778 LLVMValueRef
1779 lp_build_pow(struct lp_build_context *bld,
1780              LLVMValueRef x,
1781              LLVMValueRef y)
1782 {
1783    /* TODO: optimize the constant case */
1784    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1785       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1786                    __FUNCTION__);
1787
1788    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1789 }
1790
1791
1792 /**
1793  * Generate exp(x)
1794  */
1795 LLVMValueRef
1796 lp_build_exp(struct lp_build_context *bld,
1797              LLVMValueRef x)
1798 {
1799    /* log2(e) = 1/log(2) */
1800    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1801
1802    assert(lp_check_value(bld->type, x));
1803
1804    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1805 }
1806
1807
1808 /**
1809  * Generate log(x)
1810  */
1811 LLVMValueRef
1812 lp_build_log(struct lp_build_context *bld,
1813              LLVMValueRef x)
1814 {
1815    /* log(2) */
1816    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1817
1818    assert(lp_check_value(bld->type, x));
1819
1820    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1821 }
1822
1823
1824 #define EXP_POLY_DEGREE 3
1825 #define LOG_POLY_DEGREE 5
1826
1827
1828 /**
1829  * Generate polynomial.
1830  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1831  */
1832 static LLVMValueRef
1833 lp_build_polynomial(struct lp_build_context *bld,
1834                     LLVMValueRef x,
1835                     const double *coeffs,
1836                     unsigned num_coeffs)
1837 {
1838    const struct lp_type type = bld->type;
1839    LLVMValueRef res = NULL;
1840    unsigned i;
1841
1842    assert(lp_check_value(bld->type, x));
1843
1844    /* TODO: optimize the constant case */
1845    if(LLVMIsConstant(x))
1846       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1847                    __FUNCTION__);
1848
1849    for (i = num_coeffs; i--; ) {
1850       LLVMValueRef coeff;
1851
1852       coeff = lp_build_const_vec(type, coeffs[i]);
1853
1854       if(res)
1855          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1856       else
1857          res = coeff;
1858    }
1859
1860    if(res)
1861       return res;
1862    else
1863       return bld->undef;
1864 }
1865
1866
1867 /**
1868  * Minimax polynomial fit of 2**x, in range [0, 1[
1869  */
1870 const double lp_build_exp2_polynomial[] = {
1871 #if EXP_POLY_DEGREE == 5
1872    0.999999999690134838155,
1873    0.583974334321735217258,
1874    0.164553105719676828492,
1875    0.0292811063701710962255,
1876    0.00354944426657875141846,
1877    0.000296253726543423377365
1878 #elif EXP_POLY_DEGREE == 4
1879    1.00000001502262084505,
1880    0.563586057338685991394,
1881    0.150436017652442413623,
1882    0.0243220604213317927308,
1883    0.0025359088446580436489
1884 #elif EXP_POLY_DEGREE == 3
1885    0.999925218562710312959,
1886    0.695833540494823811697,
1887    0.226067155427249155588,
1888    0.0780245226406372992967
1889 #elif EXP_POLY_DEGREE == 2
1890    1.00172476321474503578,
1891    0.657636275736077639316,
1892    0.33718943461968720704
1893 #else
1894 #error
1895 #endif
1896 };
1897
1898
1899 void
1900 lp_build_exp2_approx(struct lp_build_context *bld,
1901                      LLVMValueRef x,
1902                      LLVMValueRef *p_exp2_int_part,
1903                      LLVMValueRef *p_frac_part,
1904                      LLVMValueRef *p_exp2)
1905 {
1906    const struct lp_type type = bld->type;
1907    LLVMTypeRef vec_type = lp_build_vec_type(type);
1908    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1909    LLVMValueRef ipart = NULL;
1910    LLVMValueRef fpart = NULL;
1911    LLVMValueRef expipart = NULL;
1912    LLVMValueRef expfpart = NULL;
1913    LLVMValueRef res = NULL;
1914
1915    assert(lp_check_value(bld->type, x));
1916
1917    if(p_exp2_int_part || p_frac_part || p_exp2) {
1918       /* TODO: optimize the constant case */
1919       if(LLVMIsConstant(x))
1920          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1921                       __FUNCTION__);
1922
1923       assert(type.floating && type.width == 32);
1924
1925       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1926       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1927
1928       /* ipart = floor(x) */
1929       ipart = lp_build_floor(bld, x);
1930
1931       /* fpart = x - ipart */
1932       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
1933    }
1934
1935    if(p_exp2_int_part || p_exp2) {
1936       /* expipart = (float) (1 << ipart) */
1937       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1938       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1939       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1940       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1941    }
1942
1943    if(p_exp2) {
1944       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1945                                      Elements(lp_build_exp2_polynomial));
1946
1947       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
1948    }
1949
1950    if(p_exp2_int_part)
1951       *p_exp2_int_part = expipart;
1952
1953    if(p_frac_part)
1954       *p_frac_part = fpart;
1955
1956    if(p_exp2)
1957       *p_exp2 = res;
1958 }
1959
1960
1961 LLVMValueRef
1962 lp_build_exp2(struct lp_build_context *bld,
1963               LLVMValueRef x)
1964 {
1965    LLVMValueRef res;
1966    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1967    return res;
1968 }
1969
1970
1971 /**
1972  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1973  * These coefficients can be generate with
1974  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1975  */
1976 const double lp_build_log2_polynomial[] = {
1977 #if LOG_POLY_DEGREE == 6
1978    3.11578814719469302614,
1979    -3.32419399085241980044,
1980    2.59883907202499966007,
1981    -1.23152682416275988241,
1982    0.318212422185251071475,
1983    -0.0344359067839062357313
1984 #elif LOG_POLY_DEGREE == 5
1985    2.8882704548164776201,
1986    -2.52074962577807006663,
1987    1.48116647521213171641,
1988    -0.465725644288844778798,
1989    0.0596515482674574969533
1990 #elif LOG_POLY_DEGREE == 4
1991    2.61761038894603480148,
1992    -1.75647175389045657003,
1993    0.688243882994381274313,
1994    -0.107254423828329604454
1995 #elif LOG_POLY_DEGREE == 3
1996    2.28330284476918490682,
1997    -1.04913055217340124191,
1998    0.204446009836232697516
1999 #else
2000 #error
2001 #endif
2002 };
2003
2004
2005 /**
2006  * See http://www.devmaster.net/forums/showthread.php?p=43580
2007  */
2008 void
2009 lp_build_log2_approx(struct lp_build_context *bld,
2010                      LLVMValueRef x,
2011                      LLVMValueRef *p_exp,
2012                      LLVMValueRef *p_floor_log2,
2013                      LLVMValueRef *p_log2)
2014 {
2015    const struct lp_type type = bld->type;
2016    LLVMTypeRef vec_type = lp_build_vec_type(type);
2017    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2018
2019    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2020    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2021    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2022
2023    LLVMValueRef i = NULL;
2024    LLVMValueRef exp = NULL;
2025    LLVMValueRef mant = NULL;
2026    LLVMValueRef logexp = NULL;
2027    LLVMValueRef logmant = NULL;
2028    LLVMValueRef res = NULL;
2029
2030    assert(lp_check_value(bld->type, x));
2031
2032    if(p_exp || p_floor_log2 || p_log2) {
2033       /* TODO: optimize the constant case */
2034       if(LLVMIsConstant(x))
2035          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2036                       __FUNCTION__);
2037
2038       assert(type.floating && type.width == 32);
2039
2040       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2041
2042       /* exp = (float) exponent(x) */
2043       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2044    }
2045
2046    if(p_floor_log2 || p_log2) {
2047       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2048       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2049       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2050    }
2051
2052    if(p_log2) {
2053       /* mant = (float) mantissa(x) */
2054       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2055       mant = LLVMBuildOr(bld->builder, mant, one, "");
2056       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2057
2058       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2059                                     Elements(lp_build_log2_polynomial));
2060
2061       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2062       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2063
2064       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2065    }
2066
2067    if(p_exp) {
2068       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2069       *p_exp = exp;
2070    }
2071
2072    if(p_floor_log2)
2073       *p_floor_log2 = logexp;
2074
2075    if(p_log2)
2076       *p_log2 = res;
2077 }
2078
2079
2080 LLVMValueRef
2081 lp_build_log2(struct lp_build_context *bld,
2082               LLVMValueRef x)
2083 {
2084    LLVMValueRef res;
2085    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2086    return res;
2087 }