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       return LLVMConstFDiv(a, b);
 593
 594    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 595       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 596
 597    return LLVMBuildFDiv(bld->builder, a, b, "");
 598 }
 599
 600
 601 /**
 602  * Linear interpolation.
 603  *
 604  * This also works for integer values with a few caveats.
 605  *
 606  * @sa http://www.stereopsis.com/doubleblend.html
 607  */
 608 LLVMValueRef
 609 lp_build_lerp(struct lp_build_context *bld,
 610               LLVMValueRef x,
 611               LLVMValueRef v0,
 612               LLVMValueRef v1)
 613 {
 614    LLVMValueRef delta;
 615    LLVMValueRef res;
 616
 617    assert(lp_check_value(bld->type, x));
 618    assert(lp_check_value(bld->type, v0));
 619    assert(lp_check_value(bld->type, v1));
 620
 621    delta = lp_build_sub(bld, v1, v0);
 622
 623    res = lp_build_mul(bld, x, delta);
 624
 625    res = lp_build_add(bld, v0, res);
 626
 627    if(bld->type.fixed)
 628       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 629        * but it will be wrong for other uses. Basically we need a more
 630        * powerful lp_type, capable of further distinguishing the values
 631        * interpretation from the value storage. */
 632       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 633
 634    return res;
 635 }
 636
 637
 638 LLVMValueRef
 639 lp_build_lerp_2d(struct lp_build_context *bld,
 640                  LLVMValueRef x,
 641                  LLVMValueRef y,
 642                  LLVMValueRef v00,
 643                  LLVMValueRef v01,
 644                  LLVMValueRef v10,
 645                  LLVMValueRef v11)
 646 {
 647    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 648    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 649    return lp_build_lerp(bld, y, v0, v1);
 650 }
 651
 652
 653 /**
 654  * Generate min(a, b)
 655  * Do checks for special cases.
 656  */
 657 LLVMValueRef
 658 lp_build_min(struct lp_build_context *bld,
 659              LLVMValueRef a,
 660              LLVMValueRef b)
 661 {
 662    assert(lp_check_value(bld->type, a));
 663    assert(lp_check_value(bld->type, b));
 664
 665    if(a == bld->undef || b == bld->undef)
 666       return bld->undef;
 667
 668    if(a == b)
 669       return a;
 670
 671    if(bld->type.norm) {
 672       if(a == bld->zero || b == bld->zero)
 673          return bld->zero;
 674       if(a == bld->one)
 675          return b;
 676       if(b == bld->one)
 677          return a;
 678    }
 679
 680    return lp_build_min_simple(bld, a, b);
 681 }
 682
 683
 684 /**
 685  * Generate max(a, b)
 686  * Do checks for special cases.
 687  */
 688 LLVMValueRef
 689 lp_build_max(struct lp_build_context *bld,
 690              LLVMValueRef a,
 691              LLVMValueRef b)
 692 {
 693    assert(lp_check_value(bld->type, a));
 694    assert(lp_check_value(bld->type, b));
 695
 696    if(a == bld->undef || b == bld->undef)
 697       return bld->undef;
 698
 699    if(a == b)
 700       return a;
 701
 702    if(bld->type.norm) {
 703       if(a == bld->one || b == bld->one)
 704          return bld->one;
 705       if(a == bld->zero)
 706          return b;
 707       if(b == bld->zero)
 708          return a;
 709    }
 710
 711    return lp_build_max_simple(bld, a, b);
 712 }
 713
 714
 715 /**
 716  * Generate clamp(a, min, max)
 717  * Do checks for special cases.
 718  */
 719 LLVMValueRef
 720 lp_build_clamp(struct lp_build_context *bld,
 721                LLVMValueRef a,
 722                LLVMValueRef min,
 723                LLVMValueRef max)
 724 {
 725    assert(lp_check_value(bld->type, a));
 726    assert(lp_check_value(bld->type, min));
 727    assert(lp_check_value(bld->type, max));
 728
 729    a = lp_build_min(bld, a, max);
 730    a = lp_build_max(bld, a, min);
 731    return a;
 732 }
 733
 734
 735 /**
 736  * Generate abs(a)
 737  */
 738 LLVMValueRef
 739 lp_build_abs(struct lp_build_context *bld,
 740              LLVMValueRef a)
 741 {
 742    const struct lp_type type = bld->type;
 743    LLVMTypeRef vec_type = lp_build_vec_type(type);
 744
 745    assert(lp_check_value(type, a));
 746
 747    if(!type.sign)
 748       return a;
 749
 750    if(type.floating) {
 751       /* Mask out the sign bit */
 752       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 753       unsigned long long absMask = ~(1ULL << (type.width - 1));
 754       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 755       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 756       a = LLVMBuildAnd(bld->builder, a, mask, "");
 757       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 758       return a;
 759    }
 760
 761    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 762       switch(type.width) {
 763       case 8:
 764          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 765       case 16:
 766          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 767       case 32:
 768          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 769       }
 770    }
 771
 772    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 773 }
 774
 775
 776 LLVMValueRef
 777 lp_build_negate(struct lp_build_context *bld,
 778                 LLVMValueRef a)
 779 {
 780    assert(lp_check_value(bld->type, a));
 781
 782 #if HAVE_LLVM >= 0x0207
 783    if (bld->type.floating)
 784       a = LLVMBuildFNeg(bld->builder, a, "");
 785    else
 786 #endif
 787       a = LLVMBuildNeg(bld->builder, a, "");
 788
 789    return a;
 790 }
 791
 792
 793 /** Return -1, 0 or +1 depending on the sign of a */
 794 LLVMValueRef
 795 lp_build_sgn(struct lp_build_context *bld,
 796              LLVMValueRef a)
 797 {
 798    const struct lp_type type = bld->type;
 799    LLVMValueRef cond;
 800    LLVMValueRef res;
 801
 802    assert(lp_check_value(type, a));
 803
 804    /* Handle non-zero case */
 805    if(!type.sign) {
 806       /* if not zero then sign must be positive */
 807       res = bld->one;
 808    }
 809    else if(type.floating) {
 810       LLVMTypeRef vec_type;
 811       LLVMTypeRef int_type;
 812       LLVMValueRef mask;
 813       LLVMValueRef sign;
 814       LLVMValueRef one;
 815       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 816
 817       int_type = lp_build_int_vec_type(type);
 818       vec_type = lp_build_vec_type(type);
 819       mask = lp_build_const_int_vec(type, maskBit);
 820
 821       /* Take the sign bit and add it to 1 constant */
 822       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 823       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 824       one = LLVMConstBitCast(bld->one, int_type);
 825       res = LLVMBuildOr(bld->builder, sign, one, "");
 826       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 827    }
 828    else
 829    {
 830       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 831       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 832       res = lp_build_select(bld, cond, bld->one, minus_one);
 833    }
 834
 835    /* Handle zero */
 836    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 837    res = lp_build_select(bld, cond, bld->zero, res);
 838
 839    return res;
 840 }
 841
 842
 843 /**
 844  * Set the sign of float vector 'a' according to 'sign'.
 845  * If sign==0, return abs(a).
 846  * If sign==1, return -abs(a);
 847  * Other values for sign produce undefined results.
 848  */
 849 LLVMValueRef
 850 lp_build_set_sign(struct lp_build_context *bld,
 851                   LLVMValueRef a, LLVMValueRef sign)
 852 {
 853    const struct lp_type type = bld->type;
 854    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 855    LLVMTypeRef vec_type = lp_build_vec_type(type);
 856    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 857    LLVMValueRef mask = lp_build_const_int_vec(type,
 858                              ~((unsigned long long) 1 << (type.width - 1)));
 859    LLVMValueRef val, res;
 860
 861    assert(type.floating);
 862    assert(lp_check_value(type, a));
 863
 864    /* val = reinterpret_cast<int>(a) */
 865    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 866    /* val = val & mask */
 867    val = LLVMBuildAnd(bld->builder, val, mask, "");
 868    /* sign = sign << shift */
 869    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 870    /* res = val | sign */
 871    res = LLVMBuildOr(bld->builder, val, sign, "");
 872    /* res = reinterpret_cast<float>(res) */
 873    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 874
 875    return res;
 876 }
 877
 878
 879 /**
 880  * Convert vector of (or scalar) int to vector of (or scalar) float.
 881  */
 882 LLVMValueRef
 883 lp_build_int_to_float(struct lp_build_context *bld,
 884                       LLVMValueRef a)
 885 {
 886    const struct lp_type type = bld->type;
 887    LLVMTypeRef vec_type = lp_build_vec_type(type);
 888
 889    assert(type.floating);
 890
 891    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 892 }
 893
 894
 895
 896 enum lp_build_round_sse41_mode
 897 {
 898    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 899    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 900    LP_BUILD_ROUND_SSE41_CEIL = 2,
 901    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 902 };
 903
 904
 905 static INLINE LLVMValueRef
 906 lp_build_round_sse41(struct lp_build_context *bld,
 907                      LLVMValueRef a,
 908                      enum lp_build_round_sse41_mode mode)
 909 {
 910    const struct lp_type type = bld->type;
 911    LLVMTypeRef vec_type = lp_build_vec_type(type);
 912    const char *intrinsic;
 913
 914    assert(type.floating);
 915    assert(type.width*type.length == 128);
 916    assert(lp_check_value(type, a));
 917    assert(util_cpu_caps.has_sse4_1);
 918
 919    switch(type.width) {
 920    case 32:
 921       intrinsic = "llvm.x86.sse41.round.ps";
 922       break;
 923    case 64:
 924       intrinsic = "llvm.x86.sse41.round.pd";
 925       break;
 926    default:
 927       assert(0);
 928       return bld->undef;
 929    }
 930
 931    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 932                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 933 }
 934
 935
 936 /**
 937  * Return the integer part of a float (vector) value.  The returned value is
 938  * a float (vector).
 939  * Ex: trunc(-1.5) = 1.0
 940  */
 941 LLVMValueRef
 942 lp_build_trunc(struct lp_build_context *bld,
 943                LLVMValueRef a)
 944 {
 945    const struct lp_type type = bld->type;
 946
 947    assert(type.floating);
 948    assert(lp_check_value(type, a));
 949
 950    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 951       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 952    else {
 953       LLVMTypeRef vec_type = lp_build_vec_type(type);
 954       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 955       LLVMValueRef res;
 956       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 957       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 958       return res;
 959    }
 960 }
 961
 962
 963 /**
 964  * Return float (vector) rounded to nearest integer (vector).  The returned
 965  * value is a float (vector).
 966  * Ex: round(0.9) = 1.0
 967  * Ex: round(-1.5) = -2.0
 968  */
 969 LLVMValueRef
 970 lp_build_round(struct lp_build_context *bld,
 971                LLVMValueRef a)
 972 {
 973    const struct lp_type type = bld->type;
 974
 975    assert(type.floating);
 976    assert(lp_check_value(type, a));
 977
 978    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 979       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 980    else {
 981       LLVMTypeRef vec_type = lp_build_vec_type(type);
 982       LLVMValueRef res;
 983       res = lp_build_iround(bld, a);
 984       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 985       return res;
 986    }
 987 }
 988
 989
 990 /**
 991  * Return floor of float (vector), result is a float (vector)
 992  * Ex: floor(1.1) = 1.0
 993  * Ex: floor(-1.1) = -2.0
 994  */
 995 LLVMValueRef
 996 lp_build_floor(struct lp_build_context *bld,
 997                LLVMValueRef a)
 998 {
 999    const struct lp_type type = bld->type;
1000
1001    assert(type.floating);
1002    assert(lp_check_value(type, a));
1003
1004    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1005       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1006    else {
1007       LLVMTypeRef vec_type = lp_build_vec_type(type);
1008       LLVMValueRef res;
1009       res = lp_build_ifloor(bld, a);
1010       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1011       return res;
1012    }
1013 }
1014
1015
1016 /**
1017  * Return ceiling of float (vector), returning float (vector).
1018  * Ex: ceil( 1.1) = 2.0
1019  * Ex: ceil(-1.1) = -1.0
1020  */
1021 LLVMValueRef
1022 lp_build_ceil(struct lp_build_context *bld,
1023               LLVMValueRef a)
1024 {
1025    const struct lp_type type = bld->type;
1026
1027    assert(type.floating);
1028    assert(lp_check_value(type, a));
1029
1030    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1031       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1032    else {
1033       LLVMTypeRef vec_type = lp_build_vec_type(type);
1034       LLVMValueRef res;
1035       res = lp_build_iceil(bld, a);
1036       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1037       return res;
1038    }
1039 }
1040
1041
1042 /**
1043  * Return fractional part of 'a' computed as a - floor(a)
1044  * Typically used in texture coord arithmetic.
1045  */
1046 LLVMValueRef
1047 lp_build_fract(struct lp_build_context *bld,
1048                LLVMValueRef a)
1049 {
1050    assert(bld->type.floating);
1051    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1052 }
1053
1054
1055 /**
1056  * Return the integer part of a float (vector) value.  The returned value is
1057  * an integer (vector).
1058  * Ex: itrunc(-1.5) = 1
1059  */
1060 LLVMValueRef
1061 lp_build_itrunc(struct lp_build_context *bld,
1062                 LLVMValueRef a)
1063 {
1064    const struct lp_type type = bld->type;
1065    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1066
1067    assert(type.floating);
1068    assert(lp_check_value(type, a));
1069
1070    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1071 }
1072
1073
1074 /**
1075  * Return float (vector) rounded to nearest integer (vector).  The returned
1076  * value is an integer (vector).
1077  * Ex: iround(0.9) = 1
1078  * Ex: iround(-1.5) = -2
1079  */
1080 LLVMValueRef
1081 lp_build_iround(struct lp_build_context *bld,
1082                 LLVMValueRef a)
1083 {
1084    const struct lp_type type = bld->type;
1085    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1086    LLVMValueRef res;
1087
1088    assert(type.floating);
1089
1090    assert(lp_check_value(type, a));
1091
1092    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1093       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1094    }
1095    else {
1096       LLVMTypeRef vec_type = lp_build_vec_type(type);
1097       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1098       LLVMValueRef sign;
1099       LLVMValueRef half;
1100
1101       /* get sign bit */
1102       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1103       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1104
1105       /* sign * 0.5 */
1106       half = lp_build_const_vec(type, 0.5);
1107       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1108       half = LLVMBuildOr(bld->builder, sign, half, "");
1109       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1110
1111       res = LLVMBuildFAdd(bld->builder, a, half, "");
1112    }
1113
1114    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1115
1116    return res;
1117 }
1118
1119
1120 /**
1121  * Return floor of float (vector), result is an int (vector)
1122  * Ex: ifloor(1.1) = 1.0
1123  * Ex: ifloor(-1.1) = -2.0
1124  */
1125 LLVMValueRef
1126 lp_build_ifloor(struct lp_build_context *bld,
1127                 LLVMValueRef a)
1128 {
1129    const struct lp_type type = bld->type;
1130    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1131    LLVMValueRef res;
1132
1133    assert(type.floating);
1134    assert(lp_check_value(type, a));
1135
1136    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1137       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1138    }
1139    else {
1140       /* Take the sign bit and add it to 1 constant */
1141       LLVMTypeRef vec_type = lp_build_vec_type(type);
1142       unsigned mantissa = lp_mantissa(type);
1143       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1144       LLVMValueRef sign;
1145       LLVMValueRef offset;
1146
1147       /* sign = a < 0 ? ~0 : 0 */
1148       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1149       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1150       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1151
1152       /* offset = -0.99999(9)f */
1153       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1154       offset = LLVMConstBitCast(offset, int_vec_type);
1155
1156       /* offset = a < 0 ? offset : 0.0f */
1157       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1158       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1159
1160       res = LLVMBuildFAdd(bld->builder, a, offset, "ifloor.res");
1161    }
1162
1163    /* round to nearest (toward zero) */
1164    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1165
1166    return res;
1167 }
1168
1169
1170 /**
1171  * Return ceiling of float (vector), returning int (vector).
1172  * Ex: iceil( 1.1) = 2
1173  * Ex: iceil(-1.1) = -1
1174  */
1175 LLVMValueRef
1176 lp_build_iceil(struct lp_build_context *bld,
1177                LLVMValueRef a)
1178 {
1179    const struct lp_type type = bld->type;
1180    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1181    LLVMValueRef res;
1182
1183    assert(type.floating);
1184    assert(lp_check_value(type, a));
1185
1186    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1187       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1188    }
1189    else {
1190       LLVMTypeRef vec_type = lp_build_vec_type(type);
1191       unsigned mantissa = lp_mantissa(type);
1192       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1193       LLVMValueRef sign;
1194       LLVMValueRef offset;
1195
1196       /* sign = a < 0 ? 0 : ~0 */
1197       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1198       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1199       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1200       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1201
1202       /* offset = 0.99999(9)f */
1203       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1204       offset = LLVMConstBitCast(offset, int_vec_type);
1205
1206       /* offset = a < 0 ? 0.0 : offset */
1207       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1208       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1209
1210       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1211    }
1212
1213    /* round to nearest (toward zero) */
1214    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1215
1216    return res;
1217 }
1218
1219
1220 LLVMValueRef
1221 lp_build_sqrt(struct lp_build_context *bld,
1222               LLVMValueRef a)
1223 {
1224    const struct lp_type type = bld->type;
1225    LLVMTypeRef vec_type = lp_build_vec_type(type);
1226    char intrinsic[32];
1227
1228    assert(lp_check_value(type, a));
1229
1230    /* TODO: optimize the constant case */
1231    /* TODO: optimize the constant case */
1232
1233    assert(type.floating);
1234    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1235
1236    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1237 }
1238
1239
1240 LLVMValueRef
1241 lp_build_rcp(struct lp_build_context *bld,
1242              LLVMValueRef a)
1243 {
1244    const struct lp_type type = bld->type;
1245
1246    assert(lp_check_value(type, a));
1247
1248    if(a == bld->zero)
1249       return bld->undef;
1250    if(a == bld->one)
1251       return bld->one;
1252    if(a == bld->undef)
1253       return bld->undef;
1254
1255    assert(type.floating);
1256
1257    if(LLVMIsConstant(a))
1258       return LLVMConstFDiv(bld->one, a);
1259
1260    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1261       /*
1262        * XXX: Added precision is not always necessary, so only enable this
1263        * when we have a better system in place to track minimum precision.
1264        */
1265
1266 #if 0
1267       /*
1268        * Do one Newton-Raphson step to improve precision:
1269        *
1270        *   x1 = (2 - a * rcp(a)) * rcp(a)
1271        */
1272
1273       LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1274       LLVMValueRef rcp_a;
1275       LLVMValueRef res;
1276
1277       rcp_a = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1278
1279       res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1280       res = LLVMBuildFSub(bld->builder, two, res, "");
1281       res = LLVMBuildFMul(bld->builder, res, rcp_a, "");
1282
1283       return rcp_a;
1284 #else
1285       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
1286 #endif
1287    }
1288
1289    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1290 }
1291
1292
1293 /**
1294  * Generate 1/sqrt(a)
1295  */
1296 LLVMValueRef
1297 lp_build_rsqrt(struct lp_build_context *bld,
1298                LLVMValueRef a)
1299 {
1300    const struct lp_type type = bld->type;
1301
1302    assert(lp_check_value(type, a));
1303
1304    assert(type.floating);
1305
1306    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1307       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1308
1309    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1310 }
1311
1312
1313 static inline LLVMValueRef
1314 lp_build_const_v4si(unsigned long value)
1315 {
1316    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1317    LLVMValueRef elements[4] = { element, element, element, element };
1318    return LLVMConstVector(elements, 4);
1319 }
1320
1321 static inline LLVMValueRef
1322 lp_build_const_v4sf(float value)
1323 {
1324    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1325    LLVMValueRef elements[4] = { element, element, element, element };
1326    return LLVMConstVector(elements, 4);
1327 }
1328
1329
1330 /**
1331  * Generate sin(a) using SSE2
1332  */
1333 LLVMValueRef
1334 lp_build_sin(struct lp_build_context *bld,
1335              LLVMValueRef a)
1336 {
1337    struct lp_type int_type = lp_int_type(bld->type);
1338    LLVMBuilderRef b = bld->builder;
1339    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1340    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1341
1342    /*
1343     *  take the absolute value,
1344     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1345     */
1346
1347    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1348    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1349
1350    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1351    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1352
1353    /*
1354     * extract the sign bit (upper one)
1355     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1356     */
1357    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1358    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1359
1360    /*
1361     * scale by 4/Pi
1362     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1363     */
1364
1365    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1366    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1367
1368    /*
1369     * store the integer part of y in mm0
1370     * emm2 = _mm_cvttps_epi32(y);
1371     */
1372
1373    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1374
1375    /*
1376     * j=(j+1) & (~1) (see the cephes sources)
1377     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1378     */
1379
1380    LLVMValueRef all_one = lp_build_const_v4si(1);
1381    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1382    /*
1383     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1384     */
1385    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1386    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1387
1388    /*
1389     * y = _mm_cvtepi32_ps(emm2);
1390     */
1391    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1392
1393    /* get the swap sign flag
1394     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1395     */
1396    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1397    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1398
1399    /*
1400     * emm2 = _mm_slli_epi32(emm0, 29);
1401     */
1402    LLVMValueRef const_29 = lp_build_const_v4si(29);
1403    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1404
1405    /*
1406     * get the polynom selection mask
1407     * there is one polynom for 0 <= x <= Pi/4
1408     * and another one for Pi/4<x<=Pi/2
1409     * Both branches will be computed.
1410     *
1411     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1412     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1413     */
1414
1415    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1416    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1417    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1418                                              emm2_3, lp_build_const_v4si(0));
1419    /*
1420     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1421     */
1422    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1423
1424    /*
1425     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1426     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1427     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1428     */
1429    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1430    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1431    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1432
1433    /*
1434     * The magic pass: "Extended precision modular arithmetic"
1435     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1436     * xmm1 = _mm_mul_ps(y, xmm1);
1437     * xmm2 = _mm_mul_ps(y, xmm2);
1438     * xmm3 = _mm_mul_ps(y, xmm3);
1439     */
1440    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1441    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1442    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1443
1444    /*
1445     * x = _mm_add_ps(x, xmm1);
1446     * x = _mm_add_ps(x, xmm2);
1447     * x = _mm_add_ps(x, xmm3);
1448     */
1449
1450    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1451    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1452    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1453
1454    /*
1455     * Evaluate the first polynom  (0 <= x <= Pi/4)
1456     *
1457     * z = _mm_mul_ps(x,x);
1458     */
1459    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1460
1461    /*
1462     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1463     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1464     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1465     */
1466    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1467    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1468    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1469
1470    /*
1471     * y = *(v4sf*)_ps_coscof_p0;
1472     * y = _mm_mul_ps(y, z);
1473     */
1474    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1475    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1476    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1477    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1478    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1479    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1480
1481
1482    /*
1483     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1484     * y = _mm_sub_ps(y, tmp);
1485     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1486     */
1487    LLVMValueRef half = lp_build_const_v4sf(0.5);
1488    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1489    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1490    LLVMValueRef one = lp_build_const_v4sf(1.0);
1491    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1492
1493    /*
1494     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1495     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1496     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1497     */
1498    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1499    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1500    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1501
1502    /*
1503     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1504     *
1505     * y2 = *(v4sf*)_ps_sincof_p0;
1506     * y2 = _mm_mul_ps(y2, z);
1507     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1508     * y2 = _mm_mul_ps(y2, z);
1509     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1510     * y2 = _mm_mul_ps(y2, z);
1511     * y2 = _mm_mul_ps(y2, x);
1512     * y2 = _mm_add_ps(y2, x);
1513     */
1514
1515    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1516    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1517    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1518    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1519    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1520    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1521    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1522
1523    /*
1524     * select the correct result from the two polynoms
1525     * xmm3 = poly_mask;
1526     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1527     * y = _mm_andnot_ps(xmm3, y);
1528     * y = _mm_add_ps(y,y2);
1529     */
1530    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1531    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1532    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1533    LLVMValueRef inv = lp_build_const_v4si(~0);
1534    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1535    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1536    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1537
1538    /*
1539     * update the sign
1540     * y = _mm_xor_ps(y, sign_bit);
1541     */
1542    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1543    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1544    return y_result;
1545 }
1546
1547
1548 /**
1549  * Generate cos(a) using SSE2
1550  */
1551 LLVMValueRef
1552 lp_build_cos(struct lp_build_context *bld,
1553              LLVMValueRef a)
1554 {
1555    struct lp_type int_type = lp_int_type(bld->type);
1556    LLVMBuilderRef b = bld->builder;
1557    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1558    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1559
1560    /*
1561     *  take the absolute value,
1562     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1563     */
1564
1565    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1566    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1567
1568    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1569    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1570
1571    /*
1572     * scale by 4/Pi
1573     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1574     */
1575
1576    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1577    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1578
1579    /*
1580     * store the integer part of y in mm0
1581     * emm2 = _mm_cvttps_epi32(y);
1582     */
1583
1584    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1585
1586    /*
1587     * j=(j+1) & (~1) (see the cephes sources)
1588     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1589     */
1590
1591    LLVMValueRef all_one = lp_build_const_v4si(1);
1592    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1593    /*
1594     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1595     */
1596    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1597    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1598
1599    /*
1600     * y = _mm_cvtepi32_ps(emm2);
1601     */
1602    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1603
1604
1605    /*
1606     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1607     */
1608    LLVMValueRef const_2 = lp_build_const_v4si(2);
1609    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1610
1611
1612    /* get the swap sign flag
1613     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1614     */
1615    LLVMValueRef inv = lp_build_const_v4si(~0);
1616    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1617    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1618    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1619
1620    /*
1621     * emm2 = _mm_slli_epi32(emm0, 29);
1622     */
1623    LLVMValueRef const_29 = lp_build_const_v4si(29);
1624    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1625
1626    /*
1627     * get the polynom selection mask
1628     * there is one polynom for 0 <= x <= Pi/4
1629     * and another one for Pi/4<x<=Pi/2
1630     * Both branches will be computed.
1631     *
1632     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1633     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1634     */
1635
1636    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1637    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1638    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1639                                              emm2_3, lp_build_const_v4si(0));
1640
1641    /*
1642     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1643     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1644     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1645     */
1646    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1647    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1648    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1649
1650    /*
1651     * The magic pass: "Extended precision modular arithmetic"
1652     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1653     * xmm1 = _mm_mul_ps(y, xmm1);
1654     * xmm2 = _mm_mul_ps(y, xmm2);
1655     * xmm3 = _mm_mul_ps(y, xmm3);
1656     */
1657    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1658    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1659    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1660
1661    /*
1662     * x = _mm_add_ps(x, xmm1);
1663     * x = _mm_add_ps(x, xmm2);
1664     * x = _mm_add_ps(x, xmm3);
1665     */
1666
1667    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1668    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1669    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1670
1671    /*
1672     * Evaluate the first polynom  (0 <= x <= Pi/4)
1673     *
1674     * z = _mm_mul_ps(x,x);
1675     */
1676    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1677
1678    /*
1679     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1680     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1681     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1682     */
1683    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1684    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1685    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1686
1687    /*
1688     * y = *(v4sf*)_ps_coscof_p0;
1689     * y = _mm_mul_ps(y, z);
1690     */
1691    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1692    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1693    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1694    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1695    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1696    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1697
1698
1699    /*
1700     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1701     * y = _mm_sub_ps(y, tmp);
1702     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1703     */
1704    LLVMValueRef half = lp_build_const_v4sf(0.5);
1705    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1706    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1707    LLVMValueRef one = lp_build_const_v4sf(1.0);
1708    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1709
1710    /*
1711     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1712     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1713     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1714     */
1715    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1716    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1717    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1718
1719    /*
1720     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1721     *
1722     * y2 = *(v4sf*)_ps_sincof_p0;
1723     * y2 = _mm_mul_ps(y2, z);
1724     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1725     * y2 = _mm_mul_ps(y2, z);
1726     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1727     * y2 = _mm_mul_ps(y2, z);
1728     * y2 = _mm_mul_ps(y2, x);
1729     * y2 = _mm_add_ps(y2, x);
1730     */
1731
1732    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1733    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1734    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1735    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1736    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1737    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1738    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1739
1740    /*
1741     * select the correct result from the two polynoms
1742     * xmm3 = poly_mask;
1743     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1744     * y = _mm_andnot_ps(xmm3, y);
1745     * y = _mm_add_ps(y,y2);
1746     */
1747    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1748    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1749    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1750    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1751    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1752    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1753
1754    /*
1755     * update the sign
1756     * y = _mm_xor_ps(y, sign_bit);
1757     */
1758    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1759    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1760    return y_result;
1761 }
1762
1763
1764 /**
1765  * Generate pow(x, y)
1766  */
1767 LLVMValueRef
1768 lp_build_pow(struct lp_build_context *bld,
1769              LLVMValueRef x,
1770              LLVMValueRef y)
1771 {
1772    /* TODO: optimize the constant case */
1773    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1774       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1775                    __FUNCTION__);
1776
1777    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1778 }
1779
1780
1781 /**
1782  * Generate exp(x)
1783  */
1784 LLVMValueRef
1785 lp_build_exp(struct lp_build_context *bld,
1786              LLVMValueRef x)
1787 {
1788    /* log2(e) = 1/log(2) */
1789    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1790
1791    assert(lp_check_value(bld->type, x));
1792
1793    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1794 }
1795
1796
1797 /**
1798  * Generate log(x)
1799  */
1800 LLVMValueRef
1801 lp_build_log(struct lp_build_context *bld,
1802              LLVMValueRef x)
1803 {
1804    /* log(2) */
1805    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1806
1807    assert(lp_check_value(bld->type, x));
1808
1809    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1810 }
1811
1812
1813 #define EXP_POLY_DEGREE 3
1814 #define LOG_POLY_DEGREE 5
1815
1816
1817 /**
1818  * Generate polynomial.
1819  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1820  */
1821 static LLVMValueRef
1822 lp_build_polynomial(struct lp_build_context *bld,
1823                     LLVMValueRef x,
1824                     const double *coeffs,
1825                     unsigned num_coeffs)
1826 {
1827    const struct lp_type type = bld->type;
1828    LLVMValueRef res = NULL;
1829    unsigned i;
1830
1831    assert(lp_check_value(bld->type, x));
1832
1833    /* TODO: optimize the constant case */
1834    if(LLVMIsConstant(x))
1835       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1836                    __FUNCTION__);
1837
1838    for (i = num_coeffs; i--; ) {
1839       LLVMValueRef coeff;
1840
1841       coeff = lp_build_const_vec(type, coeffs[i]);
1842
1843       if(res)
1844          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1845       else
1846          res = coeff;
1847    }
1848
1849    if(res)
1850       return res;
1851    else
1852       return bld->undef;
1853 }
1854
1855
1856 /**
1857  * Minimax polynomial fit of 2**x, in range [0, 1[
1858  */
1859 const double lp_build_exp2_polynomial[] = {
1860 #if EXP_POLY_DEGREE == 5
1861    0.999999999690134838155,
1862    0.583974334321735217258,
1863    0.164553105719676828492,
1864    0.0292811063701710962255,
1865    0.00354944426657875141846,
1866    0.000296253726543423377365
1867 #elif EXP_POLY_DEGREE == 4
1868    1.00000001502262084505,
1869    0.563586057338685991394,
1870    0.150436017652442413623,
1871    0.0243220604213317927308,
1872    0.0025359088446580436489
1873 #elif EXP_POLY_DEGREE == 3
1874    0.999925218562710312959,
1875    0.695833540494823811697,
1876    0.226067155427249155588,
1877    0.0780245226406372992967
1878 #elif EXP_POLY_DEGREE == 2
1879    1.00172476321474503578,
1880    0.657636275736077639316,
1881    0.33718943461968720704
1882 #else
1883 #error
1884 #endif
1885 };
1886
1887
1888 void
1889 lp_build_exp2_approx(struct lp_build_context *bld,
1890                      LLVMValueRef x,
1891                      LLVMValueRef *p_exp2_int_part,
1892                      LLVMValueRef *p_frac_part,
1893                      LLVMValueRef *p_exp2)
1894 {
1895    const struct lp_type type = bld->type;
1896    LLVMTypeRef vec_type = lp_build_vec_type(type);
1897    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1898    LLVMValueRef ipart = NULL;
1899    LLVMValueRef fpart = NULL;
1900    LLVMValueRef expipart = NULL;
1901    LLVMValueRef expfpart = NULL;
1902    LLVMValueRef res = NULL;
1903
1904    assert(lp_check_value(bld->type, x));
1905
1906    if(p_exp2_int_part || p_frac_part || p_exp2) {
1907       /* TODO: optimize the constant case */
1908       if(LLVMIsConstant(x))
1909          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1910                       __FUNCTION__);
1911
1912       assert(type.floating && type.width == 32);
1913
1914       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1915       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1916
1917       /* ipart = floor(x) */
1918       ipart = lp_build_floor(bld, x);
1919
1920       /* fpart = x - ipart */
1921       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
1922    }
1923
1924    if(p_exp2_int_part || p_exp2) {
1925       /* expipart = (float) (1 << ipart) */
1926       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1927       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
1928       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
1929       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1930    }
1931
1932    if(p_exp2) {
1933       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1934                                      Elements(lp_build_exp2_polynomial));
1935
1936       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
1937    }
1938
1939    if(p_exp2_int_part)
1940       *p_exp2_int_part = expipart;
1941
1942    if(p_frac_part)
1943       *p_frac_part = fpart;
1944
1945    if(p_exp2)
1946       *p_exp2 = res;
1947 }
1948
1949
1950 LLVMValueRef
1951 lp_build_exp2(struct lp_build_context *bld,
1952               LLVMValueRef x)
1953 {
1954    LLVMValueRef res;
1955    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1956    return res;
1957 }
1958
1959
1960 /**
1961  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1962  * These coefficients can be generate with
1963  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1964  */
1965 const double lp_build_log2_polynomial[] = {
1966 #if LOG_POLY_DEGREE == 6
1967    3.11578814719469302614,
1968    -3.32419399085241980044,
1969    2.59883907202499966007,
1970    -1.23152682416275988241,
1971    0.318212422185251071475,
1972    -0.0344359067839062357313
1973 #elif LOG_POLY_DEGREE == 5
1974    2.8882704548164776201,
1975    -2.52074962577807006663,
1976    1.48116647521213171641,
1977    -0.465725644288844778798,
1978    0.0596515482674574969533
1979 #elif LOG_POLY_DEGREE == 4
1980    2.61761038894603480148,
1981    -1.75647175389045657003,
1982    0.688243882994381274313,
1983    -0.107254423828329604454
1984 #elif LOG_POLY_DEGREE == 3
1985    2.28330284476918490682,
1986    -1.04913055217340124191,
1987    0.204446009836232697516
1988 #else
1989 #error
1990 #endif
1991 };
1992
1993
1994 /**
1995  * See http://www.devmaster.net/forums/showthread.php?p=43580
1996  */
1997 void
1998 lp_build_log2_approx(struct lp_build_context *bld,
1999                      LLVMValueRef x,
2000                      LLVMValueRef *p_exp,
2001                      LLVMValueRef *p_floor_log2,
2002                      LLVMValueRef *p_log2)
2003 {
2004    const struct lp_type type = bld->type;
2005    LLVMTypeRef vec_type = lp_build_vec_type(type);
2006    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2007
2008    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2009    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2010    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2011
2012    LLVMValueRef i = NULL;
2013    LLVMValueRef exp = NULL;
2014    LLVMValueRef mant = NULL;
2015    LLVMValueRef logexp = NULL;
2016    LLVMValueRef logmant = NULL;
2017    LLVMValueRef res = NULL;
2018
2019    assert(lp_check_value(bld->type, x));
2020
2021    if(p_exp || p_floor_log2 || p_log2) {
2022       /* TODO: optimize the constant case */
2023       if(LLVMIsConstant(x))
2024          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2025                       __FUNCTION__);
2026
2027       assert(type.floating && type.width == 32);
2028
2029       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2030
2031       /* exp = (float) exponent(x) */
2032       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2033    }
2034
2035    if(p_floor_log2 || p_log2) {
2036       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2037       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2038       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2039    }
2040
2041    if(p_log2) {
2042       /* mant = (float) mantissa(x) */
2043       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2044       mant = LLVMBuildOr(bld->builder, mant, one, "");
2045       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2046
2047       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2048                                     Elements(lp_build_log2_polynomial));
2049
2050       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2051       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2052
2053       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2054    }
2055
2056    if(p_exp) {
2057       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2058       *p_exp = exp;
2059    }
2060
2061    if(p_floor_log2)
2062       *p_floor_log2 = logexp;
2063
2064    if(p_log2)
2065       *p_log2 = res;
2066 }
2067
2068
2069 LLVMValueRef
2070 lp_build_log2(struct lp_build_context *bld,
2071               LLVMValueRef x)
2072 {
2073    LLVMValueRef res;
2074    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2075    return res;
2076 }