src/gallium/auxiliary/gallivm/lp_bld_arit.c

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  27
  28
  29 /**
  30  * @file
  31  * Helper
  32  *
  33  * LLVM IR doesn't support all basic arithmetic operations we care about (most
  34  * notably min/max and saturated operations), and it is often necessary to
  35  * resort machine-specific intrinsics directly. The functions here hide all
  36  * these implementation details from the other modules.
  37  *
  38  * We also do simple expressions simplification here. Reasons are:
  39  * - it is very easy given we have all necessary information readily available
  40  * - LLVM optimization passes fail to simplify several vector expressions
  41  * - We often know value constraints which the optimization passes have no way
  42  *   of knowing, such as when source arguments are known to be in [0, 1] range.
  43  *
  44  * @author Jose Fonseca <jfonseca@vmware.com>
  45  */
  46
  47
  48 #include "util/u_memory.h"
  49 #include "util/u_debug.h"
  50 #include "util/u_math.h"
  51 #include "util/u_string.h"
  52 #include "util/u_cpu_detect.h"
  53
  54 #include "lp_bld_type.h"
  55 #include "lp_bld_const.h"
  56 #include "lp_bld_intr.h"
  57 #include "lp_bld_logic.h"
  58 #include "lp_bld_pack.h"
  59 #include "lp_bld_debug.h"
  60 #include "lp_bld_arit.h"
  61
  62
  63 /**
  64  * Generate min(a, b)
  65  * No checks for special case values of a or b = 1 or 0 are done.
  66  */
  67 static LLVMValueRef
  68 lp_build_min_simple(struct lp_build_context *bld,
  69                     LLVMValueRef a,
  70                     LLVMValueRef b)
  71 {
  72    const struct lp_type type = bld->type;
  73    const char *intrinsic = NULL;
  74    LLVMValueRef cond;
  75
  76    /* TODO: optimize the constant case */
  77
  78    if(type.width * type.length == 128) {
  79       if(type.floating) {
  80          if(type.width == 32 && util_cpu_caps.has_sse)
  81             intrinsic = "llvm.x86.sse.min.ps";
  82          if(type.width == 64 && util_cpu_caps.has_sse2)
  83             intrinsic = "llvm.x86.sse2.min.pd";
  84       }
  85       else {
  86          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  87             intrinsic = "llvm.x86.sse2.pminu.b";
  88          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  89             intrinsic = "llvm.x86.sse41.pminsb";
  90          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  91             intrinsic = "llvm.x86.sse41.pminuw";
  92          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
  93             intrinsic = "llvm.x86.sse2.pmins.w";
  94          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
  95             intrinsic = "llvm.x86.sse41.pminud";
  96          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
  97             intrinsic = "llvm.x86.sse41.pminsd";
  98       }
  99    }
 100
 101    if(intrinsic)
 102       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 103
 104    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 105    return lp_build_select(bld, cond, a, b);
 106 }
 107
 108
 109 /**
 110  * Generate max(a, b)
 111  * No checks for special case values of a or b = 1 or 0 are done.
 112  */
 113 static LLVMValueRef
 114 lp_build_max_simple(struct lp_build_context *bld,
 115                     LLVMValueRef a,
 116                     LLVMValueRef b)
 117 {
 118    const struct lp_type type = bld->type;
 119    const char *intrinsic = NULL;
 120    LLVMValueRef cond;
 121
 122    /* TODO: optimize the constant case */
 123
 124    if(type.width * type.length == 128) {
 125       if(type.floating) {
 126          if(type.width == 32 && util_cpu_caps.has_sse)
 127             intrinsic = "llvm.x86.sse.max.ps";
 128          if(type.width == 64 && util_cpu_caps.has_sse2)
 129             intrinsic = "llvm.x86.sse2.max.pd";
 130       }
 131       else {
 132          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 133             intrinsic = "llvm.x86.sse2.pmaxu.b";
 134          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 135             intrinsic = "llvm.x86.sse41.pmaxsb";
 136          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 137             intrinsic = "llvm.x86.sse41.pmaxuw";
 138          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 139             intrinsic = "llvm.x86.sse2.pmaxs.w";
 140          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 141             intrinsic = "llvm.x86.sse41.pmaxud";
 142          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 143             intrinsic = "llvm.x86.sse41.pmaxsd";
 144       }
 145    }
 146
 147    if(intrinsic)
 148       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 149
 150    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 151    return lp_build_select(bld, cond, a, b);
 152 }
 153
 154
 155 /**
 156  * Generate 1 - a, or ~a depending on bld->type.
 157  */
 158 LLVMValueRef
 159 lp_build_comp(struct lp_build_context *bld,
 160               LLVMValueRef a)
 161 {
 162    const struct lp_type type = bld->type;
 163
 164    if(a == bld->one)
 165       return bld->zero;
 166    if(a == bld->zero)
 167       return bld->one;
 168
 169    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 170       if(LLVMIsConstant(a))
 171          return LLVMConstNot(a);
 172       else
 173          return LLVMBuildNot(bld->builder, a, "");
 174    }
 175
 176    if(LLVMIsConstant(a))
 177       return LLVMConstSub(bld->one, a);
 178    else
 179       return LLVMBuildSub(bld->builder, bld->one, a, "");
 180 }
 181
 182
 183 /**
 184  * Generate a + b
 185  */
 186 LLVMValueRef
 187 lp_build_add(struct lp_build_context *bld,
 188              LLVMValueRef a,
 189              LLVMValueRef b)
 190 {
 191    const struct lp_type type = bld->type;
 192    LLVMValueRef res;
 193
 194    if(a == bld->zero)
 195       return b;
 196    if(b == bld->zero)
 197       return a;
 198    if(a == bld->undef || b == bld->undef)
 199       return bld->undef;
 200
 201    if(bld->type.norm) {
 202       const char *intrinsic = NULL;
 203
 204       if(a == bld->one || b == bld->one)
 205         return bld->one;
 206
 207       if(util_cpu_caps.has_sse2 &&
 208          type.width * type.length == 128 &&
 209          !type.floating && !type.fixed) {
 210          if(type.width == 8)
 211             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 212          if(type.width == 16)
 213             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 214       }
 215
 216       if(intrinsic)
 217          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 218    }
 219
 220    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 221       res = LLVMConstAdd(a, b);
 222    else
 223       res = LLVMBuildAdd(bld->builder, a, b, "");
 224
 225    /* clamp to ceiling of 1.0 */
 226    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 227       res = lp_build_min_simple(bld, res, bld->one);
 228
 229    /* XXX clamp to floor of -1 or 0??? */
 230
 231    return res;
 232 }
 233
 234
 235 /**
 236  * Generate a - b
 237  */
 238 LLVMValueRef
 239 lp_build_sub(struct lp_build_context *bld,
 240              LLVMValueRef a,
 241              LLVMValueRef b)
 242 {
 243    const struct lp_type type = bld->type;
 244    LLVMValueRef res;
 245
 246    if(b == bld->zero)
 247       return a;
 248    if(a == bld->undef || b == bld->undef)
 249       return bld->undef;
 250    if(a == b)
 251       return bld->zero;
 252
 253    if(bld->type.norm) {
 254       const char *intrinsic = NULL;
 255
 256       if(b == bld->one)
 257         return bld->zero;
 258
 259       if(util_cpu_caps.has_sse2 &&
 260          type.width * type.length == 128 &&
 261          !type.floating && !type.fixed) {
 262          if(type.width == 8)
 263             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 264          if(type.width == 16)
 265             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 266       }
 267
 268       if(intrinsic)
 269          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 270    }
 271
 272    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 273       res = LLVMConstSub(a, b);
 274    else
 275       res = LLVMBuildSub(bld->builder, a, b, "");
 276
 277    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 278       res = lp_build_max_simple(bld, res, bld->zero);
 279
 280    return res;
 281 }
 282
 283
 284 /**
 285  * Normalized 8bit multiplication.
 286  *
 287  * - alpha plus one
 288  *
 289  *     makes the following approximation to the division (Sree)
 290  *
 291  *       a*b/255 ~= (a*(b + 1)) >> 256
 292  *
 293  *     which is the fastest method that satisfies the following OpenGL criteria
 294  *
 295  *       0*0 = 0 and 255*255 = 255
 296  *
 297  * - geometric series
 298  *
 299  *     takes the geometric series approximation to the division
 300  *
 301  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 302  *
 303  *     in this case just the first two terms to fit in 16bit arithmetic
 304  *
 305  *       t/255 ~= (t + (t >> 8)) >> 8
 306  *
 307  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 308  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 309  *     must be used
 310  *
 311  * - geometric series plus rounding
 312  *
 313  *     when using a geometric series division instead of truncating the result
 314  *     use roundoff in the approximation (Jim Blinn)
 315  *
 316  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 317  *
 318  *     achieving the exact results
 319  *
 320  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 321  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 322  * @sa Michael Herf, The "double blend trick", May 2000,
 323  *     http://www.stereopsis.com/doubleblend.html
 324  */
 325 static LLVMValueRef
 326 lp_build_mul_u8n(LLVMBuilderRef builder,
 327                  struct lp_type i16_type,
 328                  LLVMValueRef a, LLVMValueRef b)
 329 {
 330    LLVMValueRef c8;
 331    LLVMValueRef ab;
 332
 333    c8 = lp_build_int_const_scalar(i16_type, 8);
 334
 335 #if 0
 336
 337    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 338    b = LLVMBuildAdd(builder, b, lp_build_int_const_scalar(i16_type, 1), "");
 339    ab = LLVMBuildMul(builder, a, b, "");
 340
 341 #else
 342
 343    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 344    ab = LLVMBuildMul(builder, a, b, "");
 345    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 346    ab = LLVMBuildAdd(builder, ab, lp_build_int_const_scalar(i16_type, 0x80), "");
 347
 348 #endif
 349
 350    ab = LLVMBuildLShr(builder, ab, c8, "");
 351
 352    return ab;
 353 }
 354
 355
 356 /**
 357  * Generate a * b
 358  */
 359 LLVMValueRef
 360 lp_build_mul(struct lp_build_context *bld,
 361              LLVMValueRef a,
 362              LLVMValueRef b)
 363 {
 364    const struct lp_type type = bld->type;
 365    LLVMValueRef shift;
 366    LLVMValueRef res;
 367
 368    if(a == bld->zero)
 369       return bld->zero;
 370    if(a == bld->one)
 371       return b;
 372    if(b == bld->zero)
 373       return bld->zero;
 374    if(b == bld->one)
 375       return a;
 376    if(a == bld->undef || b == bld->undef)
 377       return bld->undef;
 378
 379    if(!type.floating && !type.fixed && type.norm) {
 380       if(type.width == 8) {
 381          struct lp_type i16_type = lp_wider_type(type);
 382          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 383
 384          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 385          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 386
 387          /* PMULLW, PSRLW, PADDW */
 388          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 389          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 390
 391          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 392
 393          return ab;
 394       }
 395
 396       /* FIXME */
 397       assert(0);
 398    }
 399
 400    if(type.fixed)
 401       shift = lp_build_int_const_scalar(type, type.width/2);
 402    else
 403       shift = NULL;
 404
 405    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 406       res =  LLVMConstMul(a, b);
 407       if(shift) {
 408          if(type.sign)
 409             res = LLVMConstAShr(res, shift);
 410          else
 411             res = LLVMConstLShr(res, shift);
 412       }
 413    }
 414    else {
 415       res = LLVMBuildMul(bld->builder, a, b, "");
 416       if(shift) {
 417          if(type.sign)
 418             res = LLVMBuildAShr(bld->builder, res, shift, "");
 419          else
 420             res = LLVMBuildLShr(bld->builder, res, shift, "");
 421       }
 422    }
 423
 424    return res;
 425 }
 426
 427
 428 /**
 429  * Small vector x scale multiplication optimization.
 430  */
 431 LLVMValueRef
 432 lp_build_mul_imm(struct lp_build_context *bld,
 433                  LLVMValueRef a,
 434                  int b)
 435 {
 436    LLVMValueRef factor;
 437
 438    if(b == 0)
 439       return bld->zero;
 440
 441    if(b == 1)
 442       return a;
 443
 444    if(b == -1)
 445       return LLVMBuildNeg(bld->builder, a, "");
 446
 447    if(b == 2 && bld->type.floating)
 448       return lp_build_add(bld, a, a);
 449
 450    if(util_is_pot(b)) {
 451       unsigned shift = ffs(b) - 1;
 452
 453       if(bld->type.floating) {
 454 #if 0
 455          /*
 456           * Power of two multiplication by directly manipulating the mantissa.
 457           *
 458           * XXX: This might not be always faster, it will introduce a small error
 459           * for multiplication by zero, and it will produce wrong results
 460           * for Inf and NaN.
 461           */
 462          unsigned mantissa = lp_mantissa(bld->type);
 463          factor = lp_build_int_const_scalar(bld->type, (unsigned long long)shift << mantissa);
 464          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 465          a = LLVMBuildAdd(bld->builder, a, factor, "");
 466          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 467          return a;
 468 #endif
 469       }
 470       else {
 471          factor = lp_build_const_scalar(bld->type, shift);
 472          return LLVMBuildShl(bld->builder, a, factor, "");
 473       }
 474    }
 475
 476    factor = lp_build_const_scalar(bld->type, (double)b);
 477    return lp_build_mul(bld, a, factor);
 478 }
 479
 480
 481 /**
 482  * Generate a / b
 483  */
 484 LLVMValueRef
 485 lp_build_div(struct lp_build_context *bld,
 486              LLVMValueRef a,
 487              LLVMValueRef b)
 488 {
 489    const struct lp_type type = bld->type;
 490
 491    if(a == bld->zero)
 492       return bld->zero;
 493    if(a == bld->one)
 494       return lp_build_rcp(bld, b);
 495    if(b == bld->zero)
 496       return bld->undef;
 497    if(b == bld->one)
 498       return a;
 499    if(a == bld->undef || b == bld->undef)
 500       return bld->undef;
 501
 502    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 503       return LLVMConstFDiv(a, b);
 504
 505    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 506       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 507
 508    return LLVMBuildFDiv(bld->builder, a, b, "");
 509 }
 510
 511
 512 /**
 513  * Linear interpolation.
 514  *
 515  * This also works for integer values with a few caveats.
 516  *
 517  * @sa http://www.stereopsis.com/doubleblend.html
 518  */
 519 LLVMValueRef
 520 lp_build_lerp(struct lp_build_context *bld,
 521               LLVMValueRef x,
 522               LLVMValueRef v0,
 523               LLVMValueRef v1)
 524 {
 525    LLVMValueRef delta;
 526    LLVMValueRef res;
 527
 528    delta = lp_build_sub(bld, v1, v0);
 529
 530    res = lp_build_mul(bld, x, delta);
 531
 532    res = lp_build_add(bld, v0, res);
 533
 534    if(bld->type.fixed)
 535       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 536        * but it will be wrong for other uses. Basically we need a more
 537        * powerful lp_type, capable of further distinguishing the values
 538        * interpretation from the value storage. */
 539       res = LLVMBuildAnd(bld->builder, res, lp_build_int_const_scalar(bld->type, (1 << bld->type.width/2) - 1), "");
 540
 541    return res;
 542 }
 543
 544
 545 LLVMValueRef
 546 lp_build_lerp_2d(struct lp_build_context *bld,
 547                  LLVMValueRef x,
 548                  LLVMValueRef y,
 549                  LLVMValueRef v00,
 550                  LLVMValueRef v01,
 551                  LLVMValueRef v10,
 552                  LLVMValueRef v11)
 553 {
 554    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 555    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 556    return lp_build_lerp(bld, y, v0, v1);
 557 }
 558
 559
 560 /**
 561  * Generate min(a, b)
 562  * Do checks for special cases.
 563  */
 564 LLVMValueRef
 565 lp_build_min(struct lp_build_context *bld,
 566              LLVMValueRef a,
 567              LLVMValueRef b)
 568 {
 569    if(a == bld->undef || b == bld->undef)
 570       return bld->undef;
 571
 572    if(a == b)
 573       return a;
 574
 575    if(bld->type.norm) {
 576       if(a == bld->zero || b == bld->zero)
 577          return bld->zero;
 578       if(a == bld->one)
 579          return b;
 580       if(b == bld->one)
 581          return a;
 582    }
 583
 584    return lp_build_min_simple(bld, a, b);
 585 }
 586
 587
 588 /**
 589  * Generate max(a, b)
 590  * Do checks for special cases.
 591  */
 592 LLVMValueRef
 593 lp_build_max(struct lp_build_context *bld,
 594              LLVMValueRef a,
 595              LLVMValueRef b)
 596 {
 597    if(a == bld->undef || b == bld->undef)
 598       return bld->undef;
 599
 600    if(a == b)
 601       return a;
 602
 603    if(bld->type.norm) {
 604       if(a == bld->one || b == bld->one)
 605          return bld->one;
 606       if(a == bld->zero)
 607          return b;
 608       if(b == bld->zero)
 609          return a;
 610    }
 611
 612    return lp_build_max_simple(bld, a, b);
 613 }
 614
 615
 616 /**
 617  * Generate abs(a)
 618  */
 619 LLVMValueRef
 620 lp_build_abs(struct lp_build_context *bld,
 621              LLVMValueRef a)
 622 {
 623    const struct lp_type type = bld->type;
 624    LLVMTypeRef vec_type = lp_build_vec_type(type);
 625
 626    if(!type.sign)
 627       return a;
 628
 629    if(type.floating) {
 630       /* Mask out the sign bit */
 631       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 632       unsigned long long absMask = ~(1ULL << (type.width - 1));
 633       LLVMValueRef mask = lp_build_int_const_scalar(type, ((unsigned long long) absMask));
 634       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 635       a = LLVMBuildAnd(bld->builder, a, mask, "");
 636       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 637       return a;
 638    }
 639
 640    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 641       switch(type.width) {
 642       case 8:
 643          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 644       case 16:
 645          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 646       case 32:
 647          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 648       }
 649    }
 650
 651    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 652 }
 653
 654
 655 LLVMValueRef
 656 lp_build_sgn(struct lp_build_context *bld,
 657              LLVMValueRef a)
 658 {
 659    const struct lp_type type = bld->type;
 660    LLVMTypeRef vec_type = lp_build_vec_type(type);
 661    LLVMValueRef cond;
 662    LLVMValueRef res;
 663
 664    /* Handle non-zero case */
 665    if(!type.sign) {
 666       /* if not zero then sign must be positive */
 667       res = bld->one;
 668    }
 669    else if(type.floating) {
 670       /* Take the sign bit and add it to 1 constant */
 671       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 672       LLVMValueRef mask = lp_build_int_const_scalar(type, (unsigned long long)1 << (type.width - 1));
 673       LLVMValueRef sign;
 674       LLVMValueRef one;
 675       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 676       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 677       one = LLVMConstBitCast(bld->one, int_vec_type);
 678       res = LLVMBuildOr(bld->builder, sign, one, "");
 679       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 680    }
 681    else
 682    {
 683       LLVMValueRef minus_one = lp_build_const_scalar(type, -1.0);
 684       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 685       res = lp_build_select(bld, cond, bld->one, minus_one);
 686    }
 687
 688    /* Handle zero */
 689    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 690    res = lp_build_select(bld, cond, bld->zero, bld->one);
 691
 692    return res;
 693 }
 694
 695
 696 enum lp_build_round_sse41_mode
 697 {
 698    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 699    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 700    LP_BUILD_ROUND_SSE41_CEIL = 2,
 701    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 702 };
 703
 704
 705 static INLINE LLVMValueRef
 706 lp_build_round_sse41(struct lp_build_context *bld,
 707                      LLVMValueRef a,
 708                      enum lp_build_round_sse41_mode mode)
 709 {
 710    const struct lp_type type = bld->type;
 711    LLVMTypeRef vec_type = lp_build_vec_type(type);
 712    const char *intrinsic;
 713
 714    assert(type.floating);
 715    assert(type.width*type.length == 128);
 716    assert(lp_check_value(type, a));
 717    assert(util_cpu_caps.has_sse4_1);
 718
 719    switch(type.width) {
 720    case 32:
 721       intrinsic = "llvm.x86.sse41.round.ps";
 722       break;
 723    case 64:
 724       intrinsic = "llvm.x86.sse41.round.pd";
 725       break;
 726    default:
 727       assert(0);
 728       return bld->undef;
 729    }
 730
 731    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 732                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 733 }
 734
 735
 736 LLVMValueRef
 737 lp_build_trunc(struct lp_build_context *bld,
 738                LLVMValueRef a)
 739 {
 740    const struct lp_type type = bld->type;
 741
 742    assert(type.floating);
 743    assert(lp_check_value(type, a));
 744
 745    if(util_cpu_caps.has_sse4_1)
 746       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 747    else {
 748       LLVMTypeRef vec_type = lp_build_vec_type(type);
 749       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 750       LLVMValueRef res;
 751       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 752       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 753       return res;
 754    }
 755 }
 756
 757
 758 LLVMValueRef
 759 lp_build_round(struct lp_build_context *bld,
 760                LLVMValueRef a)
 761 {
 762    const struct lp_type type = bld->type;
 763
 764    assert(type.floating);
 765    assert(lp_check_value(type, a));
 766
 767    if(util_cpu_caps.has_sse4_1)
 768       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 769    else {
 770       LLVMTypeRef vec_type = lp_build_vec_type(type);
 771       LLVMValueRef res;
 772       res = lp_build_iround(bld, a);
 773       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 774       return res;
 775    }
 776 }
 777
 778
 779 LLVMValueRef
 780 lp_build_floor(struct lp_build_context *bld,
 781                LLVMValueRef a)
 782 {
 783    const struct lp_type type = bld->type;
 784
 785    assert(type.floating);
 786
 787    if(util_cpu_caps.has_sse4_1)
 788       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 789    else {
 790       LLVMTypeRef vec_type = lp_build_vec_type(type);
 791       LLVMValueRef res;
 792       res = lp_build_ifloor(bld, a);
 793       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 794       return res;
 795    }
 796 }
 797
 798
 799 LLVMValueRef
 800 lp_build_ceil(struct lp_build_context *bld,
 801               LLVMValueRef a)
 802 {
 803    const struct lp_type type = bld->type;
 804
 805    assert(type.floating);
 806    assert(lp_check_value(type, a));
 807
 808    if(util_cpu_caps.has_sse4_1)
 809       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 810    else {
 811       LLVMTypeRef vec_type = lp_build_vec_type(type);
 812       LLVMValueRef res;
 813       res = lp_build_iceil(bld, a);
 814       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 815       return res;
 816    }
 817 }
 818
 819
 820 /**
 821  * Convert to integer, through whichever rounding method that's fastest,
 822  * typically truncating to zero.
 823  */
 824 LLVMValueRef
 825 lp_build_itrunc(struct lp_build_context *bld,
 826                 LLVMValueRef a)
 827 {
 828    const struct lp_type type = bld->type;
 829    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 830
 831    assert(type.floating);
 832    assert(lp_check_value(type, a));
 833
 834    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 835 }
 836
 837
 838 LLVMValueRef
 839 lp_build_iround(struct lp_build_context *bld,
 840                 LLVMValueRef a)
 841 {
 842    const struct lp_type type = bld->type;
 843    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 844    LLVMValueRef res;
 845
 846    assert(type.floating);
 847    assert(lp_check_value(type, a));
 848
 849    if(util_cpu_caps.has_sse4_1) {
 850       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 851    }
 852    else {
 853       LLVMTypeRef vec_type = lp_build_vec_type(type);
 854       LLVMValueRef mask = lp_build_int_const_scalar(type, (unsigned long long)1 << (type.width - 1));
 855       LLVMValueRef sign;
 856       LLVMValueRef half;
 857
 858       /* get sign bit */
 859       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 860       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 861
 862       /* sign * 0.5 */
 863       half = lp_build_const_scalar(type, 0.5);
 864       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
 865       half = LLVMBuildOr(bld->builder, sign, half, "");
 866       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
 867
 868       res = LLVMBuildAdd(bld->builder, a, half, "");
 869    }
 870
 871    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
 872
 873    return res;
 874 }
 875
 876
 877 /**
 878  * Convert float[] to int[] with floor().
 879  */
 880 LLVMValueRef
 881 lp_build_ifloor(struct lp_build_context *bld,
 882                 LLVMValueRef a)
 883 {
 884    const struct lp_type type = bld->type;
 885    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 886    LLVMValueRef res;
 887
 888    assert(type.floating);
 889    assert(lp_check_value(type, a));
 890
 891    if(util_cpu_caps.has_sse4_1) {
 892       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
 893    }
 894    else {
 895       /* Take the sign bit and add it to 1 constant */
 896       LLVMTypeRef vec_type = lp_build_vec_type(type);
 897       unsigned mantissa = lp_mantissa(type);
 898       LLVMValueRef mask = lp_build_int_const_scalar(type, (unsigned long long)1 << (type.width - 1));
 899       LLVMValueRef sign;
 900       LLVMValueRef offset;
 901
 902       /* sign = a < 0 ? ~0 : 0 */
 903       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 904       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 905       sign = LLVMBuildAShr(bld->builder, sign, lp_build_int_const_scalar(type, type.width - 1), "");
 906       lp_build_name(sign, "floor.sign");
 907
 908       /* offset = -0.99999(9)f */
 909       offset = lp_build_const_scalar(type, -(double)(((unsigned long long)1 << mantissa) - 1)/((unsigned long long)1 << mantissa));
 910       offset = LLVMConstBitCast(offset, int_vec_type);
 911
 912       /* offset = a < 0 ? -0.99999(9)f : 0.0f */
 913       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
 914       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "");
 915       lp_build_name(offset, "floor.offset");
 916
 917       res = LLVMBuildAdd(bld->builder, a, offset, "");
 918       lp_build_name(res, "floor.res");
 919    }
 920
 921    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
 922    lp_build_name(res, "floor");
 923
 924    return res;
 925 }
 926
 927
 928 LLVMValueRef
 929 lp_build_iceil(struct lp_build_context *bld,
 930                LLVMValueRef a)
 931 {
 932    const struct lp_type type = bld->type;
 933    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 934    LLVMValueRef res;
 935
 936    assert(type.floating);
 937    assert(lp_check_value(type, a));
 938
 939    if(util_cpu_caps.has_sse4_1) {
 940       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
 941    }
 942    else {
 943       assert(0);
 944       res = bld->undef;
 945    }
 946
 947    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
 948
 949    return res;
 950 }
 951
 952
 953 LLVMValueRef
 954 lp_build_sqrt(struct lp_build_context *bld,
 955               LLVMValueRef a)
 956 {
 957    const struct lp_type type = bld->type;
 958    LLVMTypeRef vec_type = lp_build_vec_type(type);
 959    char intrinsic[32];
 960
 961    /* TODO: optimize the constant case */
 962    /* TODO: optimize the constant case */
 963
 964    assert(type.floating);
 965    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
 966
 967    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
 968 }
 969
 970
 971 LLVMValueRef
 972 lp_build_rcp(struct lp_build_context *bld,
 973              LLVMValueRef a)
 974 {
 975    const struct lp_type type = bld->type;
 976
 977    if(a == bld->zero)
 978       return bld->undef;
 979    if(a == bld->one)
 980       return bld->one;
 981    if(a == bld->undef)
 982       return bld->undef;
 983
 984    assert(type.floating);
 985
 986    if(LLVMIsConstant(a))
 987       return LLVMConstFDiv(bld->one, a);
 988
 989    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 990       /* FIXME: improve precision */
 991       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", lp_build_vec_type(type), a);
 992
 993    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
 994 }
 995
 996
 997 /**
 998  * Generate 1/sqrt(a)
 999  */
1000 LLVMValueRef
1001 lp_build_rsqrt(struct lp_build_context *bld,
1002                LLVMValueRef a)
1003 {
1004    const struct lp_type type = bld->type;
1005
1006    assert(type.floating);
1007
1008    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
1009       return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a);
1010
1011    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1012 }
1013
1014
1015 /**
1016  * Generate cos(a)
1017  */
1018 LLVMValueRef
1019 lp_build_cos(struct lp_build_context *bld,
1020               LLVMValueRef a)
1021 {
1022    const struct lp_type type = bld->type;
1023    LLVMTypeRef vec_type = lp_build_vec_type(type);
1024    char intrinsic[32];
1025
1026    /* TODO: optimize the constant case */
1027
1028    assert(type.floating);
1029    util_snprintf(intrinsic, sizeof intrinsic, "llvm.cos.v%uf%u", type.length, type.width);
1030
1031    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1032 }
1033
1034
1035 /**
1036  * Generate sin(a)
1037  */
1038 LLVMValueRef
1039 lp_build_sin(struct lp_build_context *bld,
1040               LLVMValueRef a)
1041 {
1042    const struct lp_type type = bld->type;
1043    LLVMTypeRef vec_type = lp_build_vec_type(type);
1044    char intrinsic[32];
1045
1046    /* TODO: optimize the constant case */
1047
1048    assert(type.floating);
1049    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sin.v%uf%u", type.length, type.width);
1050
1051    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1052 }
1053
1054
1055 /**
1056  * Generate pow(x, y)
1057  */
1058 LLVMValueRef
1059 lp_build_pow(struct lp_build_context *bld,
1060              LLVMValueRef x,
1061              LLVMValueRef y)
1062 {
1063    /* TODO: optimize the constant case */
1064    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1065       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1066                    __FUNCTION__);
1067
1068    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1069 }
1070
1071
1072 /**
1073  * Generate exp(x)
1074  */
1075 LLVMValueRef
1076 lp_build_exp(struct lp_build_context *bld,
1077              LLVMValueRef x)
1078 {
1079    /* log2(e) = 1/log(2) */
1080    LLVMValueRef log2e = lp_build_const_scalar(bld->type, 1.4426950408889634);
1081
1082    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1083 }
1084
1085
1086 /**
1087  * Generate log(x)
1088  */
1089 LLVMValueRef
1090 lp_build_log(struct lp_build_context *bld,
1091              LLVMValueRef x)
1092 {
1093    /* log(2) */
1094    LLVMValueRef log2 = lp_build_const_scalar(bld->type, 0.69314718055994529);
1095
1096    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1097 }
1098
1099
1100 #define EXP_POLY_DEGREE 3
1101 #define LOG_POLY_DEGREE 5
1102
1103
1104 /**
1105  * Generate polynomial.
1106  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1107  */
1108 static LLVMValueRef
1109 lp_build_polynomial(struct lp_build_context *bld,
1110                     LLVMValueRef x,
1111                     const double *coeffs,
1112                     unsigned num_coeffs)
1113 {
1114    const struct lp_type type = bld->type;
1115    LLVMValueRef res = NULL;
1116    unsigned i;
1117
1118    /* TODO: optimize the constant case */
1119    if(LLVMIsConstant(x))
1120       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1121                    __FUNCTION__);
1122
1123    for (i = num_coeffs; i--; ) {
1124       LLVMValueRef coeff = lp_build_const_scalar(type, coeffs[i]);
1125       if(res)
1126          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1127       else
1128          res = coeff;
1129    }
1130
1131    if(res)
1132       return res;
1133    else
1134       return bld->undef;
1135 }
1136
1137
1138 /**
1139  * Minimax polynomial fit of 2**x, in range [-0.5, 0.5[
1140  */
1141 const double lp_build_exp2_polynomial[] = {
1142 #if EXP_POLY_DEGREE == 5
1143    9.9999994e-1, 6.9315308e-1, 2.4015361e-1, 5.5826318e-2, 8.9893397e-3, 1.8775767e-3
1144 #elif EXP_POLY_DEGREE == 4
1145    1.0000026, 6.9300383e-1, 2.4144275e-1, 5.2011464e-2, 1.3534167e-2
1146 #elif EXP_POLY_DEGREE == 3
1147    9.9992520e-1, 6.9583356e-1, 2.2606716e-1, 7.8024521e-2
1148 #elif EXP_POLY_DEGREE == 2
1149    1.0017247, 6.5763628e-1, 3.3718944e-1
1150 #else
1151 #error
1152 #endif
1153 };
1154
1155
1156 void
1157 lp_build_exp2_approx(struct lp_build_context *bld,
1158                      LLVMValueRef x,
1159                      LLVMValueRef *p_exp2_int_part,
1160                      LLVMValueRef *p_frac_part,
1161                      LLVMValueRef *p_exp2)
1162 {
1163    const struct lp_type type = bld->type;
1164    LLVMTypeRef vec_type = lp_build_vec_type(type);
1165    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1166    LLVMValueRef ipart = NULL;
1167    LLVMValueRef fpart = NULL;
1168    LLVMValueRef expipart = NULL;
1169    LLVMValueRef expfpart = NULL;
1170    LLVMValueRef res = NULL;
1171
1172    if(p_exp2_int_part || p_frac_part || p_exp2) {
1173       /* TODO: optimize the constant case */
1174       if(LLVMIsConstant(x))
1175          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1176                       __FUNCTION__);
1177
1178       assert(type.floating && type.width == 32);
1179
1180       x = lp_build_min(bld, x, lp_build_const_scalar(type,  129.0));
1181       x = lp_build_max(bld, x, lp_build_const_scalar(type, -126.99999));
1182
1183       /* ipart = int(x - 0.5) */
1184       ipart = LLVMBuildSub(bld->builder, x, lp_build_const_scalar(type, 0.5f), "");
1185       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
1186
1187       /* fpart = x - ipart */
1188       fpart = LLVMBuildSIToFP(bld->builder, ipart, vec_type, "");
1189       fpart = LLVMBuildSub(bld->builder, x, fpart, "");
1190    }
1191
1192    if(p_exp2_int_part || p_exp2) {
1193       /* expipart = (float) (1 << ipart) */
1194       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_int_const_scalar(type, 127), "");
1195       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_int_const_scalar(type, 23), "");
1196       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
1197    }
1198
1199    if(p_exp2) {
1200       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
1201                                      Elements(lp_build_exp2_polynomial));
1202
1203       res = LLVMBuildMul(bld->builder, expipart, expfpart, "");
1204    }
1205
1206    if(p_exp2_int_part)
1207       *p_exp2_int_part = expipart;
1208
1209    if(p_frac_part)
1210       *p_frac_part = fpart;
1211
1212    if(p_exp2)
1213       *p_exp2 = res;
1214 }
1215
1216
1217 LLVMValueRef
1218 lp_build_exp2(struct lp_build_context *bld,
1219               LLVMValueRef x)
1220 {
1221    LLVMValueRef res;
1222    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
1223    return res;
1224 }
1225
1226
1227 /**
1228  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
1229  * These coefficients can be generate with
1230  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
1231  */
1232 const double lp_build_log2_polynomial[] = {
1233 #if LOG_POLY_DEGREE == 6
1234    3.11578814719469302614, -3.32419399085241980044, 2.59883907202499966007, -1.23152682416275988241, 0.318212422185251071475, -0.0344359067839062357313
1235 #elif LOG_POLY_DEGREE == 5
1236    2.8882704548164776201, -2.52074962577807006663, 1.48116647521213171641, -0.465725644288844778798, 0.0596515482674574969533
1237 #elif LOG_POLY_DEGREE == 4
1238    2.61761038894603480148, -1.75647175389045657003, 0.688243882994381274313, -0.107254423828329604454
1239 #elif LOG_POLY_DEGREE == 3
1240    2.28330284476918490682, -1.04913055217340124191, 0.204446009836232697516
1241 #else
1242 #error
1243 #endif
1244 };
1245
1246
1247 /**
1248  * See http://www.devmaster.net/forums/showthread.php?p=43580
1249  */
1250 void
1251 lp_build_log2_approx(struct lp_build_context *bld,
1252                      LLVMValueRef x,
1253                      LLVMValueRef *p_exp,
1254                      LLVMValueRef *p_floor_log2,
1255                      LLVMValueRef *p_log2)
1256 {
1257    const struct lp_type type = bld->type;
1258    LLVMTypeRef vec_type = lp_build_vec_type(type);
1259    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1260
1261    LLVMValueRef expmask = lp_build_int_const_scalar(type, 0x7f800000);
1262    LLVMValueRef mantmask = lp_build_int_const_scalar(type, 0x007fffff);
1263    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
1264
1265    LLVMValueRef i = NULL;
1266    LLVMValueRef exp = NULL;
1267    LLVMValueRef mant = NULL;
1268    LLVMValueRef logexp = NULL;
1269    LLVMValueRef logmant = NULL;
1270    LLVMValueRef res = NULL;
1271
1272    if(p_exp || p_floor_log2 || p_log2) {
1273       /* TODO: optimize the constant case */
1274       if(LLVMIsConstant(x))
1275          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1276                       __FUNCTION__);
1277
1278       assert(type.floating && type.width == 32);
1279
1280       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
1281
1282       /* exp = (float) exponent(x) */
1283       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
1284    }
1285
1286    if(p_floor_log2 || p_log2) {
1287       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_int_const_scalar(type, 23), "");
1288       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_int_const_scalar(type, 127), "");
1289       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
1290    }
1291
1292    if(p_log2) {
1293       /* mant = (float) mantissa(x) */
1294       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
1295       mant = LLVMBuildOr(bld->builder, mant, one, "");
1296       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
1297
1298       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
1299                                     Elements(lp_build_log2_polynomial));
1300
1301       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
1302       logmant = LLVMBuildMul(bld->builder, logmant, LLVMBuildSub(bld->builder, mant, bld->one, ""), "");
1303
1304       res = LLVMBuildAdd(bld->builder, logmant, logexp, "");
1305    }
1306
1307    if(p_exp)
1308       *p_exp = exp;
1309
1310    if(p_floor_log2)
1311       *p_floor_log2 = logexp;
1312
1313    if(p_log2)
1314       *p_log2 = res;
1315 }
1316
1317
1318 LLVMValueRef
1319 lp_build_log2(struct lp_build_context *bld,
1320               LLVMValueRef x)
1321 {
1322    LLVMValueRef res;
1323    lp_build_log2_approx(bld, x, NULL, NULL, &res);
1324    return res;
1325 }