src/gallium/drivers/llvmpipe/lp_bld_arit.c

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  27
  28
  29 /**
  30  * @file
  31  * Helper
  32  *
  33  * LLVM IR doesn't support all basic arithmetic operations we care about (most
  34  * notably min/max and saturated operations), and it is often necessary to
  35  * resort machine-specific intrinsics directly. The functions here hide all
  36  * these implementation details from the other modules.
  37  *
  38  * We also do simple expressions simplification here. Reasons are:
  39  * - it is very easy given we have all necessary information readily available
  40  * - LLVM optimization passes fail to simplify several vector expressions
  41  * - We often know value constraints which the optimization passes have no way
  42  *   of knowing, such as when source arguments are known to be in [0, 1] range.
  43  *
  44  * @author Jose Fonseca <jfonseca@vmware.com>
  45  */
  46
  47
  48 #include "util/u_memory.h"
  49 #include "util/u_debug.h"
  50 #include "util/u_math.h"
  51 #include "util/u_string.h"
  52 #include "util/u_cpu_detect.h"
  53
  54 #include "lp_bld_type.h"
  55 #include "lp_bld_const.h"
  56 #include "lp_bld_intr.h"
  57 #include "lp_bld_logic.h"
  58 #include "lp_bld_pack.h"
  59 #include "lp_bld_arit.h"
  60
  61
  62 /**
  63  * Generate min(a, b)
  64  * No checks for special case values of a or b = 1 or 0 are done.
  65  */
  66 static LLVMValueRef
  67 lp_build_min_simple(struct lp_build_context *bld,
  68                     LLVMValueRef a,
  69                     LLVMValueRef b)
  70 {
  71    const struct lp_type type = bld->type;
  72    const char *intrinsic = NULL;
  73    LLVMValueRef cond;
  74
  75    /* TODO: optimize the constant case */
  76
  77    if(type.width * type.length == 128) {
  78       if(type.floating) {
  79          if(type.width == 32 && util_cpu_caps.has_sse)
  80             intrinsic = "llvm.x86.sse.min.ps";
  81          if(type.width == 64 && util_cpu_caps.has_sse2)
  82             intrinsic = "llvm.x86.sse2.min.pd";
  83       }
  84       else {
  85          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  86             intrinsic = "llvm.x86.sse2.pminu.b";
  87          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  88             intrinsic = "llvm.x86.sse41.pminsb";
  89          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  90             intrinsic = "llvm.x86.sse41.pminuw";
  91          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  92             intrinsic = "llvm.x86.sse2.pmins.w";
  93          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  94             intrinsic = "llvm.x86.sse41.pminud";
  95          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  96             intrinsic = "llvm.x86.sse41.pminsd";
  97       }
  98    }
  99
 100    if(intrinsic)
 101       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 102
 103    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 104    return lp_build_select(bld, cond, a, b);
 105 }
 106
 107
 108 /**
 109  * Generate max(a, b)
 110  * No checks for special case values of a or b = 1 or 0 are done.
 111  */
 112 static LLVMValueRef
 113 lp_build_max_simple(struct lp_build_context *bld,
 114                     LLVMValueRef a,
 115                     LLVMValueRef b)
 116 {
 117    const struct lp_type type = bld->type;
 118    const char *intrinsic = NULL;
 119    LLVMValueRef cond;
 120
 121    /* TODO: optimize the constant case */
 122
 123    if(type.width * type.length == 128) {
 124       if(type.floating) {
 125          if(type.width == 32 && util_cpu_caps.has_sse)
 126             intrinsic = "llvm.x86.sse.max.ps";
 127          if(type.width == 64 && util_cpu_caps.has_sse2)
 128             intrinsic = "llvm.x86.sse2.max.pd";
 129       }
 130       else {
 131          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 132             intrinsic = "llvm.x86.sse2.pmaxu.b";
 133          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 134             intrinsic = "llvm.x86.sse41.pmaxsb";
 135          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 136             intrinsic = "llvm.x86.sse41.pmaxuw";
 137          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 138             intrinsic = "llvm.x86.sse2.pmaxs.w";
 139          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 140             intrinsic = "llvm.x86.sse41.pmaxud";
 141          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 142             intrinsic = "llvm.x86.sse41.pmaxsd";
 143       }
 144    }
 145
 146    if(intrinsic)
 147       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 148
 149    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 150    return lp_build_select(bld, cond, a, b);
 151 }
 152
 153
 154 /**
 155  * Generate 1 - a, or ~a depending on bld->type.
 156  */
 157 LLVMValueRef
 158 lp_build_comp(struct lp_build_context *bld,
 159               LLVMValueRef a)
 160 {
 161    const struct lp_type type = bld->type;
 162
 163    if(a == bld->one)
 164       return bld->zero;
 165    if(a == bld->zero)
 166       return bld->one;
 167
 168    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 169       if(LLVMIsConstant(a))
 170          return LLVMConstNot(a);
 171       else
 172          return LLVMBuildNot(bld->builder, a, "");
 173    }
 174
 175    if(LLVMIsConstant(a))
 176       return LLVMConstSub(bld->one, a);
 177    else
 178       return LLVMBuildSub(bld->builder, bld->one, a, "");
 179 }
 180
 181
 182 /**
 183  * Generate a + b
 184  */
 185 LLVMValueRef
 186 lp_build_add(struct lp_build_context *bld,
 187              LLVMValueRef a,
 188              LLVMValueRef b)
 189 {
 190    const struct lp_type type = bld->type;
 191    LLVMValueRef res;
 192
 193    if(a == bld->zero)
 194       return b;
 195    if(b == bld->zero)
 196       return a;
 197    if(a == bld->undef || b == bld->undef)
 198       return bld->undef;
 199
 200    if(bld->type.norm) {
 201       const char *intrinsic = NULL;
 202
 203       if(a == bld->one || b == bld->one)
 204         return bld->one;
 205
 206       if(util_cpu_caps.has_sse2 &&
 207          type.width * type.length == 128 &&
 208          !type.floating && !type.fixed) {
 209          if(type.width == 8)
 210             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 211          if(type.width == 16)
 212             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 213       }
 214
 215       if(intrinsic)
 216          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 217    }
 218
 219    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 220       res = LLVMConstAdd(a, b);
 221    else
 222       res = LLVMBuildAdd(bld->builder, a, b, "");
 223
 224    /* clamp to ceiling of 1.0 */
 225    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 226       res = lp_build_min_simple(bld, res, bld->one);
 227
 228    /* XXX clamp to floor of -1 or 0??? */
 229
 230    return res;
 231 }
 232
 233
 234 /**
 235  * Generate a - b
 236  */
 237 LLVMValueRef
 238 lp_build_sub(struct lp_build_context *bld,
 239              LLVMValueRef a,
 240              LLVMValueRef b)
 241 {
 242    const struct lp_type type = bld->type;
 243    LLVMValueRef res;
 244
 245    if(b == bld->zero)
 246       return a;
 247    if(a == bld->undef || b == bld->undef)
 248       return bld->undef;
 249    if(a == b)
 250       return bld->zero;
 251
 252    if(bld->type.norm) {
 253       const char *intrinsic = NULL;
 254
 255       if(b == bld->one)
 256         return bld->zero;
 257
 258       if(util_cpu_caps.has_sse2 &&
 259          type.width * type.length == 128 &&
 260          !type.floating && !type.fixed) {
 261          if(type.width == 8)
 262             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 263          if(type.width == 16)
 264             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 265       }
 266
 267       if(intrinsic)
 268          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 269    }
 270
 271    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 272       res = LLVMConstSub(a, b);
 273    else
 274       res = LLVMBuildSub(bld->builder, a, b, "");
 275
 276    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 277       res = lp_build_max_simple(bld, res, bld->zero);
 278
 279    return res;
 280 }
 281
 282
 283 /**
 284  * Normalized 8bit multiplication.
 285  *
 286  * - alpha plus one
 287  *
 288  *     makes the following approximation to the division (Sree)
 289  *
 290  *       a*b/255 ~= (a*(b + 1)) >> 256
 291  *
 292  *     which is the fastest method that satisfies the following OpenGL criteria
 293  *
 294  *       0*0 = 0 and 255*255 = 255
 295  *
 296  * - geometric series
 297  *
 298  *     takes the geometric series approximation to the division
 299  *
 300  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 301  *
 302  *     in this case just the first two terms to fit in 16bit arithmetic
 303  *
 304  *       t/255 ~= (t + (t >> 8)) >> 8
 305  *
 306  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 307  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 308  *     must be used
 309  *
 310  * - geometric series plus rounding
 311  *
 312  *     when using a geometric series division instead of truncating the result
 313  *     use roundoff in the approximation (Jim Blinn)
 314  *
 315  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 316  *
 317  *     achieving the exact results
 318  *
 319  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 320  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 321  * @sa Michael Herf, The "double blend trick", May 2000,
 322  *     http://www.stereopsis.com/doubleblend.html
 323  */
 324 static LLVMValueRef
 325 lp_build_mul_u8n(LLVMBuilderRef builder,
 326                  struct lp_type i16_type,
 327                  LLVMValueRef a, LLVMValueRef b)
 328 {
 329    LLVMValueRef c8;
 330    LLVMValueRef ab;
 331
 332    c8 = lp_build_int_const_scalar(i16_type, 8);
 333
 334 #if 0
 335
 336    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 337    b = LLVMBuildAdd(builder, b, lp_build_int_const_scalar(i16_type, 1), "");
 338    ab = LLVMBuildMul(builder, a, b, "");
 339
 340 #else
 341
 342    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 343    ab = LLVMBuildMul(builder, a, b, "");
 344    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 345    ab = LLVMBuildAdd(builder, ab, lp_build_int_const_scalar(i16_type, 0x80), "");
 346
 347 #endif
 348
 349    ab = LLVMBuildLShr(builder, ab, c8, "");
 350
 351    return ab;
 352 }
 353
 354
 355 /**
 356  * Generate a * b
 357  */
 358 LLVMValueRef
 359 lp_build_mul(struct lp_build_context *bld,
 360              LLVMValueRef a,
 361              LLVMValueRef b)
 362 {
 363    const struct lp_type type = bld->type;
 364    LLVMValueRef shift;
 365    LLVMValueRef res;
 366
 367    if(a == bld->zero)
 368       return bld->zero;
 369    if(a == bld->one)
 370       return b;
 371    if(b == bld->zero)
 372       return bld->zero;
 373    if(b == bld->one)
 374       return a;
 375    if(a == bld->undef || b == bld->undef)
 376       return bld->undef;
 377
 378    if(!type.floating && !type.fixed && type.norm) {
 379       if(type.width == 8) {
 380          struct lp_type i16_type = lp_wider_type(type);
 381          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 382
 383          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 384          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 385
 386          /* PMULLW, PSRLW, PADDW */
 387          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 388          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 389
 390          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 391
 392          return ab;
 393       }
 394
 395       /* FIXME */
 396       assert(0);
 397    }
 398
 399    if(type.fixed)
 400       shift = lp_build_int_const_scalar(type, type.width/2);
 401    else
 402       shift = NULL;
 403
 404    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 405       res =  LLVMConstMul(a, b);
 406       if(shift) {
 407          if(type.sign)
 408             res = LLVMConstAShr(res, shift);
 409          else
 410             res = LLVMConstLShr(res, shift);
 411       }
 412    }
 413    else {
 414       res = LLVMBuildMul(bld->builder, a, b, "");
 415       if(shift) {
 416          if(type.sign)
 417             res = LLVMBuildAShr(bld->builder, res, shift, "");
 418          else
 419             res = LLVMBuildLShr(bld->builder, res, shift, "");
 420       }
 421    }
 422
 423    return res;
 424 }
 425
 426
 427 /**
 428  * Small vector x scale multiplication optimization.
 429  */
 430 LLVMValueRef
 431 lp_build_mul_imm(struct lp_build_context *bld,
 432                  LLVMValueRef a,
 433                  int b)
 434 {
 435    LLVMValueRef factor;
 436
 437    if(b == 0)
 438       return bld->zero;
 439
 440    if(b == 1)
 441       return a;
 442
 443    if(b == -1)
 444       return LLVMBuildNeg(bld->builder, a, "");
 445
 446    if(b == 2 && bld->type.floating)
 447       return lp_build_add(bld, a, a);
 448
 449    if(util_is_pot(b)) {
 450       unsigned shift = ffs(b) - 1;
 451
 452       if(bld->type.floating) {
 453 #if 0
 454          /*
 455           * Power of two multiplication by directly manipulating the mantissa.
 456           *
 457           * XXX: This might not be always faster, it will introduce a small error
 458           * for multiplication by zero, and it will produce wrong results
 459           * for Inf and NaN.
 460           */
 461          unsigned mantissa = lp_mantissa(bld->type);
 462          factor = lp_build_int_const_scalar(bld->type, (unsigned long long)shift << mantissa);
 463          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 464          a = LLVMBuildAdd(bld->builder, a, factor, "");
 465          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 466          return a;
 467 #endif
 468       }
 469       else {
 470          factor = lp_build_const_scalar(bld->type, shift);
 471          return LLVMBuildShl(bld->builder, a, factor, "");
 472       }
 473    }
 474
 475    factor = lp_build_const_scalar(bld->type, (double)b);
 476    return lp_build_mul(bld, a, factor);
 477 }
 478
 479
 480 /**
 481  * Generate a / b
 482  */
 483 LLVMValueRef
 484 lp_build_div(struct lp_build_context *bld,
 485              LLVMValueRef a,
 486              LLVMValueRef b)
 487 {
 488    const struct lp_type type = bld->type;
 489
 490    if(a == bld->zero)
 491       return bld->zero;
 492    if(a == bld->one)
 493       return lp_build_rcp(bld, b);
 494    if(b == bld->zero)
 495       return bld->undef;
 496    if(b == bld->one)
 497       return a;
 498    if(a == bld->undef || b == bld->undef)
 499       return bld->undef;
 500
 501    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 502       return LLVMConstFDiv(a, b);
 503
 504    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 505       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 506
 507    return LLVMBuildFDiv(bld->builder, a, b, "");
 508 }
 509
 510
 511 /**
 512  * Linear interpolation.
 513  *
 514  * This also works for integer values with a few caveats.
 515  *
 516  * @sa http://www.stereopsis.com/doubleblend.html
 517  */
 518 LLVMValueRef
 519 lp_build_lerp(struct lp_build_context *bld,
 520               LLVMValueRef x,
 521               LLVMValueRef v0,
 522               LLVMValueRef v1)
 523 {
 524    LLVMValueRef delta;
 525    LLVMValueRef res;
 526
 527    delta = lp_build_sub(bld, v1, v0);
 528
 529    res = lp_build_mul(bld, x, delta);
 530
 531    res = lp_build_add(bld, v0, res);
 532
 533    if(bld->type.fixed)
 534       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 535        * but it will be wrong for other uses. Basically we need a more
 536        * powerful lp_type, capable of further distinguishing the values
 537        * interpretation from the value storage. */
 538       res = LLVMBuildAnd(bld->builder, res, lp_build_int_const_scalar(bld->type, (1 << bld->type.width/2) - 1), "");
 539
 540    return res;
 541 }
 542
 543
 544 LLVMValueRef
 545 lp_build_lerp_2d(struct lp_build_context *bld,
 546                  LLVMValueRef x,
 547                  LLVMValueRef y,
 548                  LLVMValueRef v00,
 549                  LLVMValueRef v01,
 550                  LLVMValueRef v10,
 551                  LLVMValueRef v11)
 552 {
 553    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 554    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 555    return lp_build_lerp(bld, y, v0, v1);
 556 }
 557
 558
 559 /**
 560  * Generate min(a, b)
 561  * Do checks for special cases.
 562  */
 563 LLVMValueRef
 564 lp_build_min(struct lp_build_context *bld,
 565              LLVMValueRef a,
 566              LLVMValueRef b)
 567 {
 568    if(a == bld->undef || b == bld->undef)
 569       return bld->undef;
 570
 571    if(a == b)
 572       return a;
 573
 574    if(bld->type.norm) {
 575       if(a == bld->zero || b == bld->zero)
 576          return bld->zero;
 577       if(a == bld->one)
 578          return b;
 579       if(b == bld->one)
 580          return a;
 581    }
 582
 583    return lp_build_min_simple(bld, a, b);
 584 }
 585
 586
 587 /**
 588  * Generate max(a, b)
 589  * Do checks for special cases.
 590  */
 591 LLVMValueRef
 592 lp_build_max(struct lp_build_context *bld,
 593              LLVMValueRef a,
 594              LLVMValueRef b)
 595 {
 596    if(a == bld->undef || b == bld->undef)
 597       return bld->undef;
 598
 599    if(a == b)
 600       return a;
 601
 602    if(bld->type.norm) {
 603       if(a == bld->one || b == bld->one)
 604          return bld->one;
 605       if(a == bld->zero)
 606          return b;
 607       if(b == bld->zero)
 608          return a;
 609    }
 610
 611    return lp_build_max_simple(bld, a, b);
 612 }
 613
 614
 615 /**
 616  * Generate abs(a)
 617  */
 618 LLVMValueRef
 619 lp_build_abs(struct lp_build_context *bld,
 620              LLVMValueRef a)
 621 {
 622    const struct lp_type type = bld->type;
 623    LLVMTypeRef vec_type = lp_build_vec_type(type);
 624
 625    if(!type.sign)
 626       return a;
 627
 628    if(type.floating) {
 629       /* Mask out the sign bit */
 630       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 631       unsigned long absMask = ~(1 << (type.width - 1));
 632       LLVMValueRef mask = lp_build_int_const_scalar(type, ((unsigned long long) absMask));
 633       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 634       a = LLVMBuildAnd(bld->builder, a, mask, "");
 635       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 636       return a;
 637    }
 638
 639    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 640       switch(type.width) {
 641       case 8:
 642          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 643       case 16:
 644          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 645       case 32:
 646          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 647       }
 648    }
 649
 650    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 651 }
 652
 653
 654 LLVMValueRef
 655 lp_build_sgn(struct lp_build_context *bld,
 656              LLVMValueRef a)
 657 {
 658    const struct lp_type type = bld->type;
 659    LLVMTypeRef vec_type = lp_build_vec_type(type);
 660    LLVMValueRef cond;
 661    LLVMValueRef res;
 662
 663    /* Handle non-zero case */
 664    if(!type.sign) {
 665       /* if not zero then sign must be positive */
 666       res = bld->one;
 667    }
 668    else if(type.floating) {
 669       /* Take the sign bit and add it to 1 constant */
 670       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 671       LLVMValueRef mask = lp_build_int_const_scalar(type, (unsigned long long)1 << (type.width - 1));
 672       LLVMValueRef sign;
 673       LLVMValueRef one;
 674       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 675       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 676       one = LLVMConstBitCast(bld->one, int_vec_type);
 677       res = LLVMBuildOr(bld->builder, sign, one, "");
 678       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 679    }
 680    else
 681    {
 682       LLVMValueRef minus_one = lp_build_const_scalar(type, -1.0);
 683       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 684       res = lp_build_select(bld, cond, bld->one, minus_one);
 685    }
 686
 687    /* Handle zero */
 688    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 689    res = lp_build_select(bld, cond, bld->zero, bld->one);
 690
 691    return res;
 692 }
 693
 694
 695 enum lp_build_round_sse41_mode
 696 {
 697    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 698    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 699    LP_BUILD_ROUND_SSE41_CEIL = 2,
 700    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 701 };
 702
 703
 704 static INLINE LLVMValueRef
 705 lp_build_round_sse41(struct lp_build_context *bld,
 706                      LLVMValueRef a,
 707                      enum lp_build_round_sse41_mode mode)
 708 {
 709    const struct lp_type type = bld->type;
 710    LLVMTypeRef vec_type = lp_build_vec_type(type);
 711    const char *intrinsic;
 712
 713    assert(type.floating);
 714    assert(type.width*type.length == 128);
 715    assert(lp_check_value(type, a));
 716    assert(util_cpu_caps.has_sse4_1);
 717
 718    switch(type.width) {
 719    case 32:
 720       intrinsic = "llvm.x86.sse41.round.ps";
 721       break;
 722    case 64:
 723       intrinsic = "llvm.x86.sse41.round.pd";
 724       break;
 725    default:
 726       assert(0);
 727       return bld->undef;
 728    }
 729
 730    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 731                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 732 }
 733
 734
 735 LLVMValueRef
 736 lp_build_trunc(struct lp_build_context *bld,
 737                LLVMValueRef a)
 738 {
 739    const struct lp_type type = bld->type;
 740
 741    assert(type.floating);
 742    assert(lp_check_value(type, a));
 743
 744    if(util_cpu_caps.has_sse4_1)
 745       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 746    else {
 747       LLVMTypeRef vec_type = lp_build_vec_type(type);
 748       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 749       LLVMValueRef res;
 750       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 751       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 752       return res;
 753    }
 754 }
 755
 756
 757 LLVMValueRef
 758 lp_build_round(struct lp_build_context *bld,
 759                LLVMValueRef a)
 760 {
 761    const struct lp_type type = bld->type;
 762
 763    assert(type.floating);
 764    assert(lp_check_value(type, a));
 765
 766    if(util_cpu_caps.has_sse4_1)
 767       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 768    else {
 769       LLVMTypeRef vec_type = lp_build_vec_type(type);
 770       LLVMValueRef res;
 771       res = lp_build_iround(bld, a);
 772       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 773       return res;
 774    }
 775 }
 776
 777
 778 LLVMValueRef
 779 lp_build_floor(struct lp_build_context *bld,
 780                LLVMValueRef a)
 781 {
 782    const struct lp_type type = bld->type;
 783
 784    assert(type.floating);
 785
 786    if(util_cpu_caps.has_sse4_1)
 787       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 788    else {
 789       LLVMTypeRef vec_type = lp_build_vec_type(type);
 790       LLVMValueRef res;
 791       res = lp_build_ifloor(bld, a);
 792       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 793       return res;
 794    }
 795 }
 796
 797
 798 LLVMValueRef
 799 lp_build_ceil(struct lp_build_context *bld,
 800               LLVMValueRef a)
 801 {
 802    const struct lp_type type = bld->type;
 803
 804    assert(type.floating);
 805    assert(lp_check_value(type, a));
 806
 807    if(util_cpu_caps.has_sse4_1)
 808       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 809    else {
 810       LLVMTypeRef vec_type = lp_build_vec_type(type);
 811       LLVMValueRef res;
 812       res = lp_build_iceil(bld, a);
 813       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 814       return res;
 815    }
 816 }
 817
 818
 819 /**
 820  * Convert to integer, through whichever rounding method that's fastest,
 821  * typically truncating to zero.
 822  */
 823 LLVMValueRef
 824 lp_build_itrunc(struct lp_build_context *bld,
 825                 LLVMValueRef a)
 826 {
 827    const struct lp_type type = bld->type;
 828    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 829
 830    assert(type.floating);
 831    assert(lp_check_value(type, a));
 832
 833    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 834 }
 835
 836
 837 LLVMValueRef
 838 lp_build_iround(struct lp_build_context *bld,
 839                 LLVMValueRef a)
 840 {
 841    const struct lp_type type = bld->type;
 842    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 843    LLVMValueRef res;
 844
 845    assert(type.floating);
 846    assert(lp_check_value(type, a));
 847
 848    if(util_cpu_caps.has_sse4_1) {
 849       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 850    }
 851    else {
 852       LLVMTypeRef vec_type = lp_build_vec_type(type);
 853       LLVMValueRef mask = lp_build_int_const_scalar(type, (unsigned long long)1 << (type.width - 1));
 854       LLVMValueRef sign;
 855       LLVMValueRef half;
 856
 857       /* get sign bit */
 858       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 859       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 860
 861       /* sign * 0.5 */
 862       half = lp_build_const_scalar(type, 0.5);
 863       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
 864       half = LLVMBuildOr(bld->builder, sign, half, "");
 865       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
 866
 867       res = LLVMBuildAdd(bld->builder, a, half, "");
 868    }
 869
 870    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
 871
 872    return res;
 873 }
 874
 875
 876 LLVMValueRef
 877 lp_build_ifloor(struct lp_build_context *bld,
 878                 LLVMValueRef a)
 879 {
 880    const struct lp_type type = bld->type;
 881    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 882    LLVMValueRef res;
 883
 884    assert(type.floating);
 885    assert(lp_check_value(type, a));
 886
 887    if(util_cpu_caps.has_sse4_1) {
 888       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 889    }
 890    else {
 891       /* Take the sign bit and add it to 1 constant */
 892       LLVMTypeRef vec_type = lp_build_vec_type(type);
 893       unsigned mantissa = lp_mantissa(type);
 894       LLVMValueRef mask = lp_build_int_const_scalar(type, (unsigned long long)1 << (type.width - 1));
 895       LLVMValueRef sign;
 896       LLVMValueRef offset;
 897
 898       /* sign = a < 0 ? ~0 : 0 */
 899       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 900       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 901       sign = LLVMBuildAShr(bld->builder, sign, lp_build_int_const_scalar(type, type.width - 1), "");
 902
 903       /* offset = -0.99999(9)f */
 904       offset = lp_build_const_scalar(type, -(double)(((unsigned long long)1 << mantissa) - 1)/((unsigned long long)1 << mantissa));
 905       offset = LLVMConstBitCast(offset, int_vec_type);
 906
 907       /* offset = a < 0 ? -0.99999(9)f : 0.0f */
 908       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
 909       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "");
 910
 911       res = LLVMBuildAdd(bld->builder, a, offset, "");
 912    }
 913
 914    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
 915
 916    return res;
 917 }
 918
 919
 920 LLVMValueRef
 921 lp_build_iceil(struct lp_build_context *bld,
 922                LLVMValueRef a)
 923 {
 924    const struct lp_type type = bld->type;
 925    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 926    LLVMValueRef res;
 927
 928    assert(type.floating);
 929    assert(lp_check_value(type, a));
 930
 931    if(util_cpu_caps.has_sse4_1) {
 932       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 933    }
 934    else {
 935       assert(0);
 936       res = bld->undef;
 937    }
 938
 939    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
 940
 941    return res;
 942 }
 943
 944
 945 LLVMValueRef
 946 lp_build_sqrt(struct lp_build_context *bld,
 947               LLVMValueRef a)
 948 {
 949    const struct lp_type type = bld->type;
 950    LLVMTypeRef vec_type = lp_build_vec_type(type);
 951    char intrinsic[32];
 952
 953    /* TODO: optimize the constant case */
 954    /* TODO: optimize the constant case */
 955
 956    assert(type.floating);
 957    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
 958
 959    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
 960 }
 961
 962
 963 LLVMValueRef
 964 lp_build_rcp(struct lp_build_context *bld,
 965              LLVMValueRef a)
 966 {
 967    const struct lp_type type = bld->type;
 968
 969    if(a == bld->zero)
 970       return bld->undef;
 971    if(a == bld->one)
 972       return bld->one;
 973    if(a == bld->undef)
 974       return bld->undef;
 975
 976    assert(type.floating);
 977
 978    if(LLVMIsConstant(a))
 979       return LLVMConstFDiv(bld->one, a);
 980
 981    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 982       /* FIXME: improve precision */
 983       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
 984
 985    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
 986 }
 987
 988
 989 /**
 990  * Generate 1/sqrt(a)
 991  */
 992 LLVMValueRef
 993 lp_build_rsqrt(struct lp_build_context *bld,
 994                LLVMValueRef a)
 995 {
 996    const struct lp_type type = bld->type;
 997
 998    assert(type.floating);
 999
1000    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1001       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1002
1003    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1004 }
1005
1006
1007 /**
1008  * Generate cos(a)
1009  */
1010 LLVMValueRef
1011 lp_build_cos(struct lp_build_context *bld,
1012               LLVMValueRef a)
1013 {
1014    const struct lp_type type = bld->type;
1015    LLVMTypeRef vec_type = lp_build_vec_type(type);
1016    char intrinsic[32];
1017
1018    /* TODO: optimize the constant case */
1019
1020    assert(type.floating);
1021    util_snprintf(intrinsic, sizeof intrinsic, "llvm.cos.v%uf%u", type.length, type.width);
1022
1023    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1024 }
1025
1026
1027 /**
1028  * Generate sin(a)
1029  */
1030 LLVMValueRef
1031 lp_build_sin(struct lp_build_context *bld,
1032               LLVMValueRef a)
1033 {
1034    const struct lp_type type = bld->type;
1035    LLVMTypeRef vec_type = lp_build_vec_type(type);
1036    char intrinsic[32];
1037
1038    /* TODO: optimize the constant case */
1039
1040    assert(type.floating);
1041    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sin.v%uf%u", type.length, type.width);
1042
1043    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1044 }
1045
1046
1047 /**
1048  * Generate pow(x, y)
1049  */
1050 LLVMValueRef
1051 lp_build_pow(struct lp_build_context *bld,
1052              LLVMValueRef x,
1053              LLVMValueRef y)
1054 {
1055    /* TODO: optimize the constant case */
1056    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1057       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1058                    __FUNCTION__);
1059
1060    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1061 }
1062
1063
1064 /**
1065  * Generate exp(x)
1066  */
1067 LLVMValueRef
1068 lp_build_exp(struct lp_build_context *bld,
1069              LLVMValueRef x)
1070 {
1071    /* log2(e) = 1/log(2) */
1072    LLVMValueRef log2e = lp_build_const_scalar(bld->type, 1.4426950408889634);
1073
1074    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1075 }
1076
1077
1078 /**
1079  * Generate log(x)
1080  */
1081 LLVMValueRef
1082 lp_build_log(struct lp_build_context *bld,
1083              LLVMValueRef x)
1084 {
1085    /* log(2) */
1086    LLVMValueRef log2 = lp_build_const_scalar(bld->type, 0.69314718055994529);
1087
1088    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1089 }
1090
1091
1092 #define EXP_POLY_DEGREE 3
1093 #define LOG_POLY_DEGREE 5
1094
1095
1096 /**
1097  * Generate polynomial.
1098  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1099  */
1100 static LLVMValueRef
1101 lp_build_polynomial(struct lp_build_context *bld,
1102                     LLVMValueRef x,
1103                     const double *coeffs,
1104                     unsigned num_coeffs)
1105 {
1106    const struct lp_type type = bld->type;
1107    LLVMValueRef res = NULL;
1108    unsigned i;
1109
1110    /* TODO: optimize the constant case */
1111    if(LLVMIsConstant(x))
1112       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1113                    __FUNCTION__);
1114
1115    for (i = num_coeffs; i--; ) {
1116       LLVMValueRef coeff = lp_build_const_scalar(type, coeffs[i]);
1117       if(res)
1118          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1119       else
1120          res = coeff;
1121    }
1122
1123    if(res)
1124       return res;
1125    else
1126       return bld->undef;
1127 }
1128
1129
1130 /**
1131  * Minimax polynomial fit of 2**x, in range [-0.5, 0.5[
1132  */
1133 const double lp_build_exp2_polynomial[] = {
1134 #if EXP_POLY_DEGREE == 5
1135    9.9999994e-1, 6.9315308e-1, 2.4015361e-1, 5.5826318e-2, 8.9893397e-3, 1.8775767e-3
1136 #elif EXP_POLY_DEGREE == 4
1137    1.0000026, 6.9300383e-1, 2.4144275e-1, 5.2011464e-2, 1.3534167e-2
1138 #elif EXP_POLY_DEGREE == 3
1139    9.9992520e-1, 6.9583356e-1, 2.2606716e-1, 7.8024521e-2
1140 #elif EXP_POLY_DEGREE == 2
1141    1.0017247, 6.5763628e-1, 3.3718944e-1
1142 #else
1143 #error
1144 #endif
1145 };
1146
1147
1148 void
1149 lp_build_exp2_approx(struct lp_build_context *bld,
1150                      LLVMValueRef x,
1151                      LLVMValueRef *p_exp2_int_part,
1152                      LLVMValueRef *p_frac_part,
1153                      LLVMValueRef *p_exp2)
1154 {
1155    const struct lp_type type = bld->type;
1156    LLVMTypeRef vec_type = lp_build_vec_type(type);
1157    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1158    LLVMValueRef ipart = NULL;
1159    LLVMValueRef fpart = NULL;
1160    LLVMValueRef expipart = NULL;
1161    LLVMValueRef expfpart = NULL;
1162    LLVMValueRef res = NULL;
1163
1164    if(p_exp2_int_part || p_frac_part || p_exp2) {
1165       /* TODO: optimize the constant case */
1166       if(LLVMIsConstant(x))
1167          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1168                       __FUNCTION__);
1169
1170       assert(type.floating && type.width == 32);
1171
1172       x = lp_build_min(bld, x, lp_build_const_scalar(type,  129.0));
1173       x = lp_build_max(bld, x, lp_build_const_scalar(type, -126.99999));
1174
1175       /* ipart = int(x - 0.5) */
1176       ipart = LLVMBuildSub(bld->builder, x, lp_build_const_scalar(type, 0.5f), "");
1177       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1178
1179       /* fpart = x - ipart */
1180       fpart = LLVMBuildSIToFP(bld->builder, ipart, vec_type, "");
1181       fpart = LLVMBuildSub(bld->builder, x, fpart, "");
1182    }
1183
1184    if(p_exp2_int_part || p_exp2) {
1185       /* expipart = (float) (1 << ipart) */
1186       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_int_const_scalar(type, 127), "");
1187       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_int_const_scalar(type, 23), "");
1188       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1189    }
1190
1191    if(p_exp2) {
1192       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1193                                      Elements(lp_build_exp2_polynomial));
1194
1195       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1196    }
1197
1198    if(p_exp2_int_part)
1199       *p_exp2_int_part = expipart;
1200
1201    if(p_frac_part)
1202       *p_frac_part = fpart;
1203
1204    if(p_exp2)
1205       *p_exp2 = res;
1206 }
1207
1208
1209 LLVMValueRef
1210 lp_build_exp2(struct lp_build_context *bld,
1211               LLVMValueRef x)
1212 {
1213    LLVMValueRef res;
1214    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1215    return res;
1216 }
1217
1218
1219 /**
1220  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1221  * These coefficients can be generate with
1222  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1223  */
1224 const double lp_build_log2_polynomial[] = {
1225 #if LOG_POLY_DEGREE == 6
1226    3.11578814719469302614, -3.32419399085241980044, 2.59883907202499966007, -1.23152682416275988241, 0.318212422185251071475, -0.0344359067839062357313
1227 #elif LOG_POLY_DEGREE == 5
1228    2.8882704548164776201, -2.52074962577807006663, 1.48116647521213171641, -0.465725644288844778798, 0.0596515482674574969533
1229 #elif LOG_POLY_DEGREE == 4
1230    2.61761038894603480148, -1.75647175389045657003, 0.688243882994381274313, -0.107254423828329604454
1231 #elif LOG_POLY_DEGREE == 3
1232    2.28330284476918490682, -1.04913055217340124191, 0.204446009836232697516
1233 #else
1234 #error
1235 #endif
1236 };
1237
1238
1239 /**
1240  * See http://www.devmaster.net/forums/showthread.php?p=43580
1241  */
1242 void
1243 lp_build_log2_approx(struct lp_build_context *bld,
1244                      LLVMValueRef x,
1245                      LLVMValueRef *p_exp,
1246                      LLVMValueRef *p_floor_log2,
1247                      LLVMValueRef *p_log2)
1248 {
1249    const struct lp_type type = bld->type;
1250    LLVMTypeRef vec_type = lp_build_vec_type(type);
1251    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1252
1253    LLVMValueRef expmask = lp_build_int_const_scalar(type, 0x7f800000);
1254    LLVMValueRef mantmask = lp_build_int_const_scalar(type, 0x007fffff);
1255    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1256
1257    LLVMValueRef i = NULL;
1258    LLVMValueRef exp = NULL;
1259    LLVMValueRef mant = NULL;
1260    LLVMValueRef logexp = NULL;
1261    LLVMValueRef logmant = NULL;
1262    LLVMValueRef res = NULL;
1263
1264    if(p_exp || p_floor_log2 || p_log2) {
1265       /* TODO: optimize the constant case */
1266       if(LLVMIsConstant(x))
1267          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1268                       __FUNCTION__);
1269
1270       assert(type.floating && type.width == 32);
1271
1272       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1273
1274       /* exp = (float) exponent(x) */
1275       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1276    }
1277
1278    if(p_floor_log2 || p_log2) {
1279       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_int_const_scalar(type, 23), "");
1280       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_int_const_scalar(type, 127), "");
1281       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1282    }
1283
1284    if(p_log2) {
1285       /* mant = (float) mantissa(x) */
1286       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1287       mant = LLVMBuildOr(bld->builder, mant, one, "");
1288       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1289
1290       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1291                                     Elements(lp_build_log2_polynomial));
1292
1293       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1294       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1295
1296       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1297    }
1298
1299    if(p_exp)
1300       *p_exp = exp;
1301
1302    if(p_floor_log2)
1303       *p_floor_log2 = logexp;
1304
1305    if(p_log2)
1306       *p_log2 = res;
1307 }
1308
1309
1310 LLVMValueRef
1311 lp_build_log2(struct lp_build_context *bld,
1312               LLVMValueRef x)
1313 {
1314    LLVMValueRef res;
1315    lp_build_log2_approx(bld, x, NULL, NULL, &res);
1316    return res;
1317 }