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