src/gallium/auxiliary/gallivm/lp_bld_arit.c

   1 /**************************************************************************
   2  *
   3  * Copyright 2009-2010 VMware, Inc.
   4  * All Rights Reserved.
   5  *
   6  * Permission is hereby granted, free of charge, to any person obtaining a
   7  * copy of this software and associated documentation files (the
   8  * "Software"), to deal in the Software without restriction, including
   9  * without limitation the rights to use, copy, modify, merge, publish,
  10  * distribute, sub license, and/or sell copies of the Software, and to
  11  * permit persons to whom the Software is furnished to do so, subject to
  12  * the following conditions:
  13  *
  14  * The above copyright notice and this permission notice (including the
  15  * next paragraph) shall be included in all copies or substantial portions
  16  * of the Software.
  17  *
  18  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  19  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  20  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
  21  * IN NO EVENT SHALL VMWARE AND/OR ITS SUPPLIERS BE LIABLE FOR
  22  * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  23  * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
  24  * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  25  *
  26  **************************************************************************/
  27
  28
  29 /**
  30  * @file
  31  * Helper
  32  *
  33  * LLVM IR doesn't support all basic arithmetic operations we care about (most
  34  * notably min/max and saturated operations), and it is often necessary to
  35  * resort machine-specific intrinsics directly. The functions here hide all
  36  * these implementation details from the other modules.
  37  *
  38  * We also do simple expressions simplification here. Reasons are:
  39  * - it is very easy given we have all necessary information readily available
  40  * - LLVM optimization passes fail to simplify several vector expressions
  41  * - We often know value constraints which the optimization passes have no way
  42  *   of knowing, such as when source arguments are known to be in [0, 1] range.
  43  *
  44  * @author Jose Fonseca <jfonseca@vmware.com>
  45  */
  46
  47
  48 #include "util/u_memory.h"
  49 #include "util/u_debug.h"
  50 #include "util/u_math.h"
  51 #include "util/u_string.h"
  52 #include "util/u_cpu_detect.h"
  53
  54 #include "lp_bld_type.h"
  55 #include "lp_bld_const.h"
  56 #include "lp_bld_intr.h"
  57 #include "lp_bld_logic.h"
  58 #include "lp_bld_pack.h"
  59 #include "lp_bld_arit.h"
  60
  61
  62 #define EXP_POLY_DEGREE 3
  63
  64 #define LOG_POLY_DEGREE 5
  65
  66
  67 /**
  68  * Generate min(a, b)
  69  * No checks for special case values of a or b = 1 or 0 are done.
  70  */
  71 static LLVMValueRef
  72 lp_build_min_simple(struct lp_build_context *bld,
  73                     LLVMValueRef a,
  74                     LLVMValueRef b)
  75 {
  76    const struct lp_type type = bld->type;
  77    const char *intrinsic = NULL;
  78    LLVMValueRef cond;
  79
  80    assert(lp_check_value(type, a));
  81    assert(lp_check_value(type, b));
  82
  83    /* TODO: optimize the constant case */
  84
  85    if(type.width * type.length == 128) {
  86       if(type.floating) {
  87          if(type.width == 32 && util_cpu_caps.has_sse)
  88             intrinsic = "llvm.x86.sse.min.ps";
  89          if(type.width == 64 && util_cpu_caps.has_sse2)
  90             intrinsic = "llvm.x86.sse2.min.pd";
  91       }
  92       else {
  93          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  94             intrinsic = "llvm.x86.sse2.pminu.b";
  95          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  96             intrinsic = "llvm.x86.sse41.pminsb";
  97          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  98             intrinsic = "llvm.x86.sse41.pminuw";
  99          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 100             intrinsic = "llvm.x86.sse2.pmins.w";
 101          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 102             intrinsic = "llvm.x86.sse41.pminud";
 103          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 104             intrinsic = "llvm.x86.sse41.pminsd";
 105       }
 106    }
 107
 108    if(intrinsic)
 109       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 110
 111    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 112    return lp_build_select(bld, cond, a, b);
 113 }
 114
 115
 116 /**
 117  * Generate max(a, b)
 118  * No checks for special case values of a or b = 1 or 0 are done.
 119  */
 120 static LLVMValueRef
 121 lp_build_max_simple(struct lp_build_context *bld,
 122                     LLVMValueRef a,
 123                     LLVMValueRef b)
 124 {
 125    const struct lp_type type = bld->type;
 126    const char *intrinsic = NULL;
 127    LLVMValueRef cond;
 128
 129    assert(lp_check_value(type, a));
 130    assert(lp_check_value(type, b));
 131
 132    /* TODO: optimize the constant case */
 133
 134    if(type.width * type.length == 128) {
 135       if(type.floating) {
 136          if(type.width == 32 && util_cpu_caps.has_sse)
 137             intrinsic = "llvm.x86.sse.max.ps";
 138          if(type.width == 64 && util_cpu_caps.has_sse2)
 139             intrinsic = "llvm.x86.sse2.max.pd";
 140       }
 141       else {
 142          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 143             intrinsic = "llvm.x86.sse2.pmaxu.b";
 144          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 145             intrinsic = "llvm.x86.sse41.pmaxsb";
 146          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 147             intrinsic = "llvm.x86.sse41.pmaxuw";
 148          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 149             intrinsic = "llvm.x86.sse2.pmaxs.w";
 150          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 151             intrinsic = "llvm.x86.sse41.pmaxud";
 152          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 153             intrinsic = "llvm.x86.sse41.pmaxsd";
 154       }
 155    }
 156
 157    if(intrinsic)
 158       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 159
 160    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 161    return lp_build_select(bld, cond, a, b);
 162 }
 163
 164
 165 /**
 166  * Generate 1 - a, or ~a depending on bld->type.
 167  */
 168 LLVMValueRef
 169 lp_build_comp(struct lp_build_context *bld,
 170               LLVMValueRef a)
 171 {
 172    const struct lp_type type = bld->type;
 173
 174    assert(lp_check_value(type, a));
 175
 176    if(a == bld->one)
 177       return bld->zero;
 178    if(a == bld->zero)
 179       return bld->one;
 180
 181    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 182       if(LLVMIsConstant(a))
 183          return LLVMConstNot(a);
 184       else
 185          return LLVMBuildNot(bld->builder, a, "");
 186    }
 187
 188    if(LLVMIsConstant(a))
 189       if (type.floating)
 190           return LLVMConstFSub(bld->one, a);
 191       else
 192           return LLVMConstSub(bld->one, a);
 193    else
 194       if (type.floating)
 195          return LLVMBuildFSub(bld->builder, bld->one, a, "");
 196       else
 197          return LLVMBuildSub(bld->builder, bld->one, a, "");
 198 }
 199
 200
 201 /**
 202  * Generate a + b
 203  */
 204 LLVMValueRef
 205 lp_build_add(struct lp_build_context *bld,
 206              LLVMValueRef a,
 207              LLVMValueRef b)
 208 {
 209    const struct lp_type type = bld->type;
 210    LLVMValueRef res;
 211
 212    assert(lp_check_value(type, a));
 213    assert(lp_check_value(type, b));
 214
 215    if(a == bld->zero)
 216       return b;
 217    if(b == bld->zero)
 218       return a;
 219    if(a == bld->undef || b == bld->undef)
 220       return bld->undef;
 221
 222    if(bld->type.norm) {
 223       const char *intrinsic = NULL;
 224
 225       if(a == bld->one || b == bld->one)
 226         return bld->one;
 227
 228       if(util_cpu_caps.has_sse2 &&
 229          type.width * type.length == 128 &&
 230          !type.floating && !type.fixed) {
 231          if(type.width == 8)
 232             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 233          if(type.width == 16)
 234             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 235       }
 236
 237       if(intrinsic)
 238          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 239    }
 240
 241    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 242       if (type.floating)
 243          res = LLVMConstFAdd(a, b);
 244       else
 245          res = LLVMConstAdd(a, b);
 246    else
 247       if (type.floating)
 248          res = LLVMBuildFAdd(bld->builder, a, b, "");
 249       else
 250          res = LLVMBuildAdd(bld->builder, a, b, "");
 251
 252    /* clamp to ceiling of 1.0 */
 253    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 254       res = lp_build_min_simple(bld, res, bld->one);
 255
 256    /* XXX clamp to floor of -1 or 0??? */
 257
 258    return res;
 259 }
 260
 261
 262 /** Return the scalar sum of the elements of a */
 263 LLVMValueRef
 264 lp_build_sum_vector(struct lp_build_context *bld,
 265                     LLVMValueRef a)
 266 {
 267    const struct lp_type type = bld->type;
 268    LLVMValueRef index, res;
 269    unsigned i;
 270
 271    assert(lp_check_value(type, a));
 272
 273    if (type.length == 1) {
 274       return a;
 275    }
 276
 277    assert(!bld->type.norm);
 278
 279    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 280    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 281
 282    for (i = 1; i < type.length; i++) {
 283       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 284       if (type.floating)
 285          res = LLVMBuildFAdd(bld->builder, res,
 286                             LLVMBuildExtractElement(bld->builder,
 287                                                     a, index, ""),
 288                             "");
 289       else
 290          res = LLVMBuildAdd(bld->builder, res,
 291                             LLVMBuildExtractElement(bld->builder,
 292                                                     a, index, ""),
 293                             "");
 294    }
 295
 296    return res;
 297 }
 298
 299
 300 /**
 301  * Generate a - b
 302  */
 303 LLVMValueRef
 304 lp_build_sub(struct lp_build_context *bld,
 305              LLVMValueRef a,
 306              LLVMValueRef b)
 307 {
 308    const struct lp_type type = bld->type;
 309    LLVMValueRef res;
 310
 311    assert(lp_check_value(type, a));
 312    assert(lp_check_value(type, b));
 313
 314    if(b == bld->zero)
 315       return a;
 316    if(a == bld->undef || b == bld->undef)
 317       return bld->undef;
 318    if(a == b)
 319       return bld->zero;
 320
 321    if(bld->type.norm) {
 322       const char *intrinsic = NULL;
 323
 324       if(b == bld->one)
 325         return bld->zero;
 326
 327       if(util_cpu_caps.has_sse2 &&
 328          type.width * type.length == 128 &&
 329          !type.floating && !type.fixed) {
 330          if(type.width == 8)
 331             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 332          if(type.width == 16)
 333             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 334       }
 335
 336       if(intrinsic)
 337          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 338    }
 339
 340    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 341       if (type.floating)
 342          res = LLVMConstFSub(a, b);
 343       else
 344          res = LLVMConstSub(a, b);
 345    else
 346       if (type.floating)
 347          res = LLVMBuildFSub(bld->builder, a, b, "");
 348       else
 349          res = LLVMBuildSub(bld->builder, a, b, "");
 350
 351    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 352       res = lp_build_max_simple(bld, res, bld->zero);
 353
 354    return res;
 355 }
 356
 357
 358 /**
 359  * Normalized 8bit multiplication.
 360  *
 361  * - alpha plus one
 362  *
 363  *     makes the following approximation to the division (Sree)
 364  *
 365  *       a*b/255 ~= (a*(b + 1)) >> 256
 366  *
 367  *     which is the fastest method that satisfies the following OpenGL criteria
 368  *
 369  *       0*0 = 0 and 255*255 = 255
 370  *
 371  * - geometric series
 372  *
 373  *     takes the geometric series approximation to the division
 374  *
 375  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 376  *
 377  *     in this case just the first two terms to fit in 16bit arithmetic
 378  *
 379  *       t/255 ~= (t + (t >> 8)) >> 8
 380  *
 381  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 382  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 383  *     must be used
 384  *
 385  * - geometric series plus rounding
 386  *
 387  *     when using a geometric series division instead of truncating the result
 388  *     use roundoff in the approximation (Jim Blinn)
 389  *
 390  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 391  *
 392  *     achieving the exact results
 393  *
 394  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 395  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 396  * @sa Michael Herf, The "double blend trick", May 2000,
 397  *     http://www.stereopsis.com/doubleblend.html
 398  */
 399 static LLVMValueRef
 400 lp_build_mul_u8n(LLVMBuilderRef builder,
 401                  struct lp_type i16_type,
 402                  LLVMValueRef a, LLVMValueRef b)
 403 {
 404    LLVMValueRef c8;
 405    LLVMValueRef ab;
 406
 407    assert(!i16_type.floating);
 408    assert(lp_check_value(i16_type, a));
 409    assert(lp_check_value(i16_type, b));
 410
 411    c8 = lp_build_const_int_vec(i16_type, 8);
 412
 413 #if 0
 414
 415    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 416    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 417    ab = LLVMBuildMul(builder, a, b, "");
 418
 419 #else
 420
 421    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 422    ab = LLVMBuildMul(builder, a, b, "");
 423    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 424    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 425
 426 #endif
 427
 428    ab = LLVMBuildLShr(builder, ab, c8, "");
 429
 430    return ab;
 431 }
 432
 433
 434 /**
 435  * Generate a * b
 436  */
 437 LLVMValueRef
 438 lp_build_mul(struct lp_build_context *bld,
 439              LLVMValueRef a,
 440              LLVMValueRef b)
 441 {
 442    const struct lp_type type = bld->type;
 443    LLVMValueRef shift;
 444    LLVMValueRef res;
 445
 446    assert(lp_check_value(type, a));
 447    assert(lp_check_value(type, b));
 448
 449    if(a == bld->zero)
 450       return bld->zero;
 451    if(a == bld->one)
 452       return b;
 453    if(b == bld->zero)
 454       return bld->zero;
 455    if(b == bld->one)
 456       return a;
 457    if(a == bld->undef || b == bld->undef)
 458       return bld->undef;
 459
 460    if(!type.floating && !type.fixed && type.norm) {
 461       if(type.width == 8) {
 462          struct lp_type i16_type = lp_wider_type(type);
 463          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 464
 465          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 466          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 467
 468          /* PMULLW, PSRLW, PADDW */
 469          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 470          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 471
 472          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 473
 474          return ab;
 475       }
 476
 477       /* FIXME */
 478       assert(0);
 479    }
 480
 481    if(type.fixed)
 482       shift = lp_build_const_int_vec(type, type.width/2);
 483    else
 484       shift = NULL;
 485
 486    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 487       if (type.floating)
 488          res = LLVMConstFMul(a, b);
 489       else
 490          res = LLVMConstMul(a, b);
 491       if(shift) {
 492          if(type.sign)
 493             res = LLVMConstAShr(res, shift);
 494          else
 495             res = LLVMConstLShr(res, shift);
 496       }
 497    }
 498    else {
 499       if (type.floating)
 500          res = LLVMBuildFMul(bld->builder, a, b, "");
 501       else
 502          res = LLVMBuildMul(bld->builder, a, b, "");
 503       if(shift) {
 504          if(type.sign)
 505             res = LLVMBuildAShr(bld->builder, res, shift, "");
 506          else
 507             res = LLVMBuildLShr(bld->builder, res, shift, "");
 508       }
 509    }
 510
 511    return res;
 512 }
 513
 514
 515 /**
 516  * Small vector x scale multiplication optimization.
 517  */
 518 LLVMValueRef
 519 lp_build_mul_imm(struct lp_build_context *bld,
 520                  LLVMValueRef a,
 521                  int b)
 522 {
 523    LLVMValueRef factor;
 524
 525    assert(lp_check_value(bld->type, a));
 526
 527    if(b == 0)
 528       return bld->zero;
 529
 530    if(b == 1)
 531       return a;
 532
 533    if(b == -1)
 534       return lp_build_negate(bld, a);
 535
 536    if(b == 2 && bld->type.floating)
 537       return lp_build_add(bld, a, a);
 538
 539    if(util_is_power_of_two(b)) {
 540       unsigned shift = ffs(b) - 1;
 541
 542       if(bld->type.floating) {
 543 #if 0
 544          /*
 545           * Power of two multiplication by directly manipulating the mantissa.
 546           *
 547           * XXX: This might not be always faster, it will introduce a small error
 548           * for multiplication by zero, and it will produce wrong results
 549           * for Inf and NaN.
 550           */
 551          unsigned mantissa = lp_mantissa(bld->type);
 552          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 553          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 554          a = LLVMBuildAdd(bld->builder, a, factor, "");
 555          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 556          return a;
 557 #endif
 558       }
 559       else {
 560          factor = lp_build_const_vec(bld->type, shift);
 561          return LLVMBuildShl(bld->builder, a, factor, "");
 562       }
 563    }
 564
 565    factor = lp_build_const_vec(bld->type, (double)b);
 566    return lp_build_mul(bld, a, factor);
 567 }
 568
 569
 570 /**
 571  * Generate a / b
 572  */
 573 LLVMValueRef
 574 lp_build_div(struct lp_build_context *bld,
 575              LLVMValueRef a,
 576              LLVMValueRef b)
 577 {
 578    const struct lp_type type = bld->type;
 579
 580    assert(lp_check_value(type, a));
 581    assert(lp_check_value(type, b));
 582
 583    if(a == bld->zero)
 584       return bld->zero;
 585    if(a == bld->one)
 586       return lp_build_rcp(bld, b);
 587    if(b == bld->zero)
 588       return bld->undef;
 589    if(b == bld->one)
 590       return a;
 591    if(a == bld->undef || b == bld->undef)
 592       return bld->undef;
 593
 594    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 595       if (type.floating)
 596          return LLVMConstFDiv(a, b);
 597       else if (type.sign)
 598          return LLVMConstSDiv(a, b);
 599       else
 600          return LLVMConstUDiv(a, b);
 601    }
 602
 603    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 604       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 605
 606    if (type.floating)
 607       return LLVMBuildFDiv(bld->builder, a, b, "");
 608    else if (type.sign)
 609       return LLVMBuildSDiv(bld->builder, a, b, "");
 610    else
 611       return LLVMBuildUDiv(bld->builder, a, b, "");
 612 }
 613
 614
 615 /**
 616  * Linear interpolation.
 617  *
 618  * This also works for integer values with a few caveats.
 619  *
 620  * @sa http://www.stereopsis.com/doubleblend.html
 621  */
 622 LLVMValueRef
 623 lp_build_lerp(struct lp_build_context *bld,
 624               LLVMValueRef x,
 625               LLVMValueRef v0,
 626               LLVMValueRef v1)
 627 {
 628    LLVMValueRef delta;
 629    LLVMValueRef res;
 630
 631    assert(lp_check_value(bld->type, x));
 632    assert(lp_check_value(bld->type, v0));
 633    assert(lp_check_value(bld->type, v1));
 634
 635    delta = lp_build_sub(bld, v1, v0);
 636
 637    res = lp_build_mul(bld, x, delta);
 638
 639    res = lp_build_add(bld, v0, res);
 640
 641    if(bld->type.fixed)
 642       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 643        * but it will be wrong for other uses. Basically we need a more
 644        * powerful lp_type, capable of further distinguishing the values
 645        * interpretation from the value storage. */
 646       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 647
 648    return res;
 649 }
 650
 651
 652 LLVMValueRef
 653 lp_build_lerp_2d(struct lp_build_context *bld,
 654                  LLVMValueRef x,
 655                  LLVMValueRef y,
 656                  LLVMValueRef v00,
 657                  LLVMValueRef v01,
 658                  LLVMValueRef v10,
 659                  LLVMValueRef v11)
 660 {
 661    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 662    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 663    return lp_build_lerp(bld, y, v0, v1);
 664 }
 665
 666
 667 /**
 668  * Generate min(a, b)
 669  * Do checks for special cases.
 670  */
 671 LLVMValueRef
 672 lp_build_min(struct lp_build_context *bld,
 673              LLVMValueRef a,
 674              LLVMValueRef b)
 675 {
 676    assert(lp_check_value(bld->type, a));
 677    assert(lp_check_value(bld->type, b));
 678
 679    if(a == bld->undef || b == bld->undef)
 680       return bld->undef;
 681
 682    if(a == b)
 683       return a;
 684
 685    if(bld->type.norm) {
 686       if(a == bld->zero || b == bld->zero)
 687          return bld->zero;
 688       if(a == bld->one)
 689          return b;
 690       if(b == bld->one)
 691          return a;
 692    }
 693
 694    return lp_build_min_simple(bld, a, b);
 695 }
 696
 697
 698 /**
 699  * Generate max(a, b)
 700  * Do checks for special cases.
 701  */
 702 LLVMValueRef
 703 lp_build_max(struct lp_build_context *bld,
 704              LLVMValueRef a,
 705              LLVMValueRef b)
 706 {
 707    assert(lp_check_value(bld->type, a));
 708    assert(lp_check_value(bld->type, b));
 709
 710    if(a == bld->undef || b == bld->undef)
 711       return bld->undef;
 712
 713    if(a == b)
 714       return a;
 715
 716    if(bld->type.norm) {
 717       if(a == bld->one || b == bld->one)
 718          return bld->one;
 719       if(a == bld->zero)
 720          return b;
 721       if(b == bld->zero)
 722          return a;
 723    }
 724
 725    return lp_build_max_simple(bld, a, b);
 726 }
 727
 728
 729 /**
 730  * Generate clamp(a, min, max)
 731  * Do checks for special cases.
 732  */
 733 LLVMValueRef
 734 lp_build_clamp(struct lp_build_context *bld,
 735                LLVMValueRef a,
 736                LLVMValueRef min,
 737                LLVMValueRef max)
 738 {
 739    assert(lp_check_value(bld->type, a));
 740    assert(lp_check_value(bld->type, min));
 741    assert(lp_check_value(bld->type, max));
 742
 743    a = lp_build_min(bld, a, max);
 744    a = lp_build_max(bld, a, min);
 745    return a;
 746 }
 747
 748
 749 /**
 750  * Generate abs(a)
 751  */
 752 LLVMValueRef
 753 lp_build_abs(struct lp_build_context *bld,
 754              LLVMValueRef a)
 755 {
 756    const struct lp_type type = bld->type;
 757    LLVMTypeRef vec_type = lp_build_vec_type(type);
 758
 759    assert(lp_check_value(type, a));
 760
 761    if(!type.sign)
 762       return a;
 763
 764    if(type.floating) {
 765       /* Mask out the sign bit */
 766       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 767       unsigned long long absMask = ~(1ULL << (type.width - 1));
 768       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 769       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 770       a = LLVMBuildAnd(bld->builder, a, mask, "");
 771       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 772       return a;
 773    }
 774
 775    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 776       switch(type.width) {
 777       case 8:
 778          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 779       case 16:
 780          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 781       case 32:
 782          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 783       }
 784    }
 785
 786    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 787 }
 788
 789
 790 LLVMValueRef
 791 lp_build_negate(struct lp_build_context *bld,
 792                 LLVMValueRef a)
 793 {
 794    assert(lp_check_value(bld->type, a));
 795
 796 #if HAVE_LLVM >= 0x0207
 797    if (bld->type.floating)
 798       a = LLVMBuildFNeg(bld->builder, a, "");
 799    else
 800 #endif
 801       a = LLVMBuildNeg(bld->builder, a, "");
 802
 803    return a;
 804 }
 805
 806
 807 /** Return -1, 0 or +1 depending on the sign of a */
 808 LLVMValueRef
 809 lp_build_sgn(struct lp_build_context *bld,
 810              LLVMValueRef a)
 811 {
 812    const struct lp_type type = bld->type;
 813    LLVMValueRef cond;
 814    LLVMValueRef res;
 815
 816    assert(lp_check_value(type, a));
 817
 818    /* Handle non-zero case */
 819    if(!type.sign) {
 820       /* if not zero then sign must be positive */
 821       res = bld->one;
 822    }
 823    else if(type.floating) {
 824       LLVMTypeRef vec_type;
 825       LLVMTypeRef int_type;
 826       LLVMValueRef mask;
 827       LLVMValueRef sign;
 828       LLVMValueRef one;
 829       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 830
 831       int_type = lp_build_int_vec_type(type);
 832       vec_type = lp_build_vec_type(type);
 833       mask = lp_build_const_int_vec(type, maskBit);
 834
 835       /* Take the sign bit and add it to 1 constant */
 836       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 837       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 838       one = LLVMConstBitCast(bld->one, int_type);
 839       res = LLVMBuildOr(bld->builder, sign, one, "");
 840       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 841    }
 842    else
 843    {
 844       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 845       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 846       res = lp_build_select(bld, cond, bld->one, minus_one);
 847    }
 848
 849    /* Handle zero */
 850    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 851    res = lp_build_select(bld, cond, bld->zero, res);
 852
 853    return res;
 854 }
 855
 856
 857 /**
 858  * Set the sign of float vector 'a' according to 'sign'.
 859  * If sign==0, return abs(a).
 860  * If sign==1, return -abs(a);
 861  * Other values for sign produce undefined results.
 862  */
 863 LLVMValueRef
 864 lp_build_set_sign(struct lp_build_context *bld,
 865                   LLVMValueRef a, LLVMValueRef sign)
 866 {
 867    const struct lp_type type = bld->type;
 868    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 869    LLVMTypeRef vec_type = lp_build_vec_type(type);
 870    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 871    LLVMValueRef mask = lp_build_const_int_vec(type,
 872                              ~((unsigned long long) 1 << (type.width - 1)));
 873    LLVMValueRef val, res;
 874
 875    assert(type.floating);
 876    assert(lp_check_value(type, a));
 877
 878    /* val = reinterpret_cast<int>(a) */
 879    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 880    /* val = val & mask */
 881    val = LLVMBuildAnd(bld->builder, val, mask, "");
 882    /* sign = sign << shift */
 883    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 884    /* res = val | sign */
 885    res = LLVMBuildOr(bld->builder, val, sign, "");
 886    /* res = reinterpret_cast<float>(res) */
 887    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 888
 889    return res;
 890 }
 891
 892
 893 /**
 894  * Convert vector of (or scalar) int to vector of (or scalar) float.
 895  */
 896 LLVMValueRef
 897 lp_build_int_to_float(struct lp_build_context *bld,
 898                       LLVMValueRef a)
 899 {
 900    const struct lp_type type = bld->type;
 901    LLVMTypeRef vec_type = lp_build_vec_type(type);
 902
 903    assert(type.floating);
 904
 905    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 906 }
 907
 908
 909
 910 enum lp_build_round_sse41_mode
 911 {
 912    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 913    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 914    LP_BUILD_ROUND_SSE41_CEIL = 2,
 915    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 916 };
 917
 918
 919 static INLINE LLVMValueRef
 920 lp_build_round_sse41(struct lp_build_context *bld,
 921                      LLVMValueRef a,
 922                      enum lp_build_round_sse41_mode mode)
 923 {
 924    const struct lp_type type = bld->type;
 925    LLVMTypeRef vec_type = lp_build_vec_type(type);
 926    const char *intrinsic;
 927
 928    assert(type.floating);
 929    assert(type.width*type.length == 128);
 930    assert(lp_check_value(type, a));
 931    assert(util_cpu_caps.has_sse4_1);
 932
 933    switch(type.width) {
 934    case 32:
 935       intrinsic = "llvm.x86.sse41.round.ps";
 936       break;
 937    case 64:
 938       intrinsic = "llvm.x86.sse41.round.pd";
 939       break;
 940    default:
 941       assert(0);
 942       return bld->undef;
 943    }
 944
 945    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 946                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 947 }
 948
 949
 950 /**
 951  * Return the integer part of a float (vector) value.  The returned value is
 952  * a float (vector).
 953  * Ex: trunc(-1.5) = 1.0
 954  */
 955 LLVMValueRef
 956 lp_build_trunc(struct lp_build_context *bld,
 957                LLVMValueRef a)
 958 {
 959    const struct lp_type type = bld->type;
 960
 961    assert(type.floating);
 962    assert(lp_check_value(type, a));
 963
 964    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 965       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 966    else {
 967       LLVMTypeRef vec_type = lp_build_vec_type(type);
 968       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 969       LLVMValueRef res;
 970       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 971       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 972       return res;
 973    }
 974 }
 975
 976
 977 /**
 978  * Return float (vector) rounded to nearest integer (vector).  The returned
 979  * value is a float (vector).
 980  * Ex: round(0.9) = 1.0
 981  * Ex: round(-1.5) = -2.0
 982  */
 983 LLVMValueRef
 984 lp_build_round(struct lp_build_context *bld,
 985                LLVMValueRef a)
 986 {
 987    const struct lp_type type = bld->type;
 988
 989    assert(type.floating);
 990    assert(lp_check_value(type, a));
 991
 992    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 993       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 994    else {
 995       LLVMTypeRef vec_type = lp_build_vec_type(type);
 996       LLVMValueRef res;
 997       res = lp_build_iround(bld, a);
 998       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 999       return res;
1000    }
1001 }
1002
1003
1004 /**
1005  * Return floor of float (vector), result is a float (vector)
1006  * Ex: floor(1.1) = 1.0
1007  * Ex: floor(-1.1) = -2.0
1008  */
1009 LLVMValueRef
1010 lp_build_floor(struct lp_build_context *bld,
1011                LLVMValueRef a)
1012 {
1013    const struct lp_type type = bld->type;
1014
1015    assert(type.floating);
1016    assert(lp_check_value(type, a));
1017
1018    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1019       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1020    else {
1021       LLVMTypeRef vec_type = lp_build_vec_type(type);
1022       LLVMValueRef res;
1023       res = lp_build_ifloor(bld, a);
1024       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1025       return res;
1026    }
1027 }
1028
1029
1030 /**
1031  * Return ceiling of float (vector), returning float (vector).
1032  * Ex: ceil( 1.1) = 2.0
1033  * Ex: ceil(-1.1) = -1.0
1034  */
1035 LLVMValueRef
1036 lp_build_ceil(struct lp_build_context *bld,
1037               LLVMValueRef a)
1038 {
1039    const struct lp_type type = bld->type;
1040
1041    assert(type.floating);
1042    assert(lp_check_value(type, a));
1043
1044    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1045       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1046    else {
1047       LLVMTypeRef vec_type = lp_build_vec_type(type);
1048       LLVMValueRef res;
1049       res = lp_build_iceil(bld, a);
1050       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1051       return res;
1052    }
1053 }
1054
1055
1056 /**
1057  * Return fractional part of 'a' computed as a - floor(a)
1058  * Typically used in texture coord arithmetic.
1059  */
1060 LLVMValueRef
1061 lp_build_fract(struct lp_build_context *bld,
1062                LLVMValueRef a)
1063 {
1064    assert(bld->type.floating);
1065    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1066 }
1067
1068
1069 /**
1070  * Return the integer part of a float (vector) value.  The returned value is
1071  * an integer (vector).
1072  * Ex: itrunc(-1.5) = 1
1073  */
1074 LLVMValueRef
1075 lp_build_itrunc(struct lp_build_context *bld,
1076                 LLVMValueRef a)
1077 {
1078    const struct lp_type type = bld->type;
1079    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1080
1081    assert(type.floating);
1082    assert(lp_check_value(type, a));
1083
1084    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1085 }
1086
1087
1088 /**
1089  * Return float (vector) rounded to nearest integer (vector).  The returned
1090  * value is an integer (vector).
1091  * Ex: iround(0.9) = 1
1092  * Ex: iround(-1.5) = -2
1093  */
1094 LLVMValueRef
1095 lp_build_iround(struct lp_build_context *bld,
1096                 LLVMValueRef a)
1097 {
1098    const struct lp_type type = bld->type;
1099    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1100    LLVMValueRef res;
1101
1102    assert(type.floating);
1103
1104    assert(lp_check_value(type, a));
1105
1106    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1107       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1108    }
1109    else {
1110       LLVMTypeRef vec_type = lp_build_vec_type(type);
1111       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1112       LLVMValueRef sign;
1113       LLVMValueRef half;
1114
1115       /* get sign bit */
1116       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1117       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1118
1119       /* sign * 0.5 */
1120       half = lp_build_const_vec(type, 0.5);
1121       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1122       half = LLVMBuildOr(bld->builder, sign, half, "");
1123       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1124
1125       res = LLVMBuildFAdd(bld->builder, a, half, "");
1126    }
1127
1128    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1129
1130    return res;
1131 }
1132
1133
1134 /**
1135  * Return floor of float (vector), result is an int (vector)
1136  * Ex: ifloor(1.1) = 1.0
1137  * Ex: ifloor(-1.1) = -2.0
1138  */
1139 LLVMValueRef
1140 lp_build_ifloor(struct lp_build_context *bld,
1141                 LLVMValueRef a)
1142 {
1143    const struct lp_type type = bld->type;
1144    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1145    LLVMValueRef res;
1146
1147    assert(type.floating);
1148    assert(lp_check_value(type, a));
1149
1150    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1151       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1152    }
1153    else {
1154       /* Take the sign bit and add it to 1 constant */
1155       LLVMTypeRef vec_type = lp_build_vec_type(type);
1156       unsigned mantissa = lp_mantissa(type);
1157       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1158       LLVMValueRef sign;
1159       LLVMValueRef offset;
1160
1161       /* sign = a < 0 ? ~0 : 0 */
1162       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1163       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1164       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1165
1166       /* offset = -0.99999(9)f */
1167       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1168       offset = LLVMConstBitCast(offset, int_vec_type);
1169
1170       /* offset = a < 0 ? offset : 0.0f */
1171       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1172       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1173
1174       res = LLVMBuildFAdd(bld->builder, a, offset, "ifloor.res");
1175    }
1176
1177    /* round to nearest (toward zero) */
1178    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1179
1180    return res;
1181 }
1182
1183
1184 /**
1185  * Return ceiling of float (vector), returning int (vector).
1186  * Ex: iceil( 1.1) = 2
1187  * Ex: iceil(-1.1) = -1
1188  */
1189 LLVMValueRef
1190 lp_build_iceil(struct lp_build_context *bld,
1191                LLVMValueRef a)
1192 {
1193    const struct lp_type type = bld->type;
1194    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1195    LLVMValueRef res;
1196
1197    assert(type.floating);
1198    assert(lp_check_value(type, a));
1199
1200    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1201       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1202    }
1203    else {
1204       LLVMTypeRef vec_type = lp_build_vec_type(type);
1205       unsigned mantissa = lp_mantissa(type);
1206       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1207       LLVMValueRef sign;
1208       LLVMValueRef offset;
1209
1210       /* sign = a < 0 ? 0 : ~0 */
1211       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1212       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1213       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1214       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1215
1216       /* offset = 0.99999(9)f */
1217       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1218       offset = LLVMConstBitCast(offset, int_vec_type);
1219
1220       /* offset = a < 0 ? 0.0 : offset */
1221       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1222       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1223
1224       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1225    }
1226
1227    /* round to nearest (toward zero) */
1228    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1229
1230    return res;
1231 }
1232
1233
1234 LLVMValueRef
1235 lp_build_sqrt(struct lp_build_context *bld,
1236               LLVMValueRef a)
1237 {
1238    const struct lp_type type = bld->type;
1239    LLVMTypeRef vec_type = lp_build_vec_type(type);
1240    char intrinsic[32];
1241
1242    assert(lp_check_value(type, a));
1243
1244    /* TODO: optimize the constant case */
1245    /* TODO: optimize the constant case */
1246
1247    assert(type.floating);
1248    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1249
1250    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1251 }
1252
1253
1254 /**
1255  * Do one Newton-Raphson step to improve reciprocate precision:
1256  *
1257  *   x_{i+1} = x_i * (2 - a * x_i)
1258  *
1259  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
1260  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
1261  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
1262  * halo. It would be necessary to clamp the argument to prevent this.
1263  *
1264  * See also:
1265  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
1266  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1267  */
1268 static INLINE LLVMValueRef
1269 lp_build_rcp_refine(struct lp_build_context *bld,
1270                     LLVMValueRef a,
1271                     LLVMValueRef rcp_a)
1272 {
1273    LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1274    LLVMValueRef res;
1275
1276    res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1277    res = LLVMBuildFSub(bld->builder, two, res, "");
1278    res = LLVMBuildFMul(bld->builder, rcp_a, res, "");
1279
1280    return res;
1281 }
1282
1283
1284 LLVMValueRef
1285 lp_build_rcp(struct lp_build_context *bld,
1286              LLVMValueRef a)
1287 {
1288    const struct lp_type type = bld->type;
1289
1290    assert(lp_check_value(type, a));
1291
1292    if(a == bld->zero)
1293       return bld->undef;
1294    if(a == bld->one)
1295       return bld->one;
1296    if(a == bld->undef)
1297       return bld->undef;
1298
1299    assert(type.floating);
1300
1301    if(LLVMIsConstant(a))
1302       return LLVMConstFDiv(bld->one, a);
1303
1304    /*
1305     * We don't use RCPPS because:
1306     * - it only has 10bits of precision
1307     * - it doesn't even get the reciprocate of 1.0 exactly
1308     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
1309     * - for recent processors the benefit over DIVPS is marginal, a case
1310     *   depedent
1311     *
1312     * We could still use it on certain processors if benchmarks show that the
1313     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
1314     * particular uses that require less workarounds.
1315     */
1316
1317    if (FALSE && util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1318       const unsigned num_iterations = 0;
1319       LLVMValueRef res;
1320       unsigned i;
1321
1322       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", bld->vec_type, a);
1323
1324       for (i = 0; i < num_iterations; ++i) {
1325          res = lp_build_rcp_refine(bld, a, res);
1326       }
1327
1328       return res;
1329    }
1330
1331    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1332 }
1333
1334
1335 /**
1336  * Do one Newton-Raphson step to improve rsqrt precision:
1337  *
1338  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
1339  *
1340  * See also:
1341  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1342  */
1343 static INLINE LLVMValueRef
1344 lp_build_rsqrt_refine(struct lp_build_context *bld,
1345                       LLVMValueRef a,
1346                       LLVMValueRef rsqrt_a)
1347 {
1348    LLVMValueRef half = lp_build_const_vec(bld->type, 0.5);
1349    LLVMValueRef three = lp_build_const_vec(bld->type, 3.0);
1350    LLVMValueRef res;
1351
1352    res = LLVMBuildFMul(bld->builder, rsqrt_a, rsqrt_a, "");
1353    res = LLVMBuildFMul(bld->builder, a, res, "");
1354    res = LLVMBuildFSub(bld->builder, three, res, "");
1355    res = LLVMBuildFMul(bld->builder, rsqrt_a, res, "");
1356    res = LLVMBuildFMul(bld->builder, half, res, "");
1357
1358    return res;
1359 }
1360
1361
1362 /**
1363  * Generate 1/sqrt(a)
1364  */
1365 LLVMValueRef
1366 lp_build_rsqrt(struct lp_build_context *bld,
1367                LLVMValueRef a)
1368 {
1369    const struct lp_type type = bld->type;
1370
1371    assert(lp_check_value(type, a));
1372
1373    assert(type.floating);
1374
1375    if (util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1376       const unsigned num_iterations = 0;
1377       LLVMValueRef res;
1378       unsigned i;
1379
1380       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", bld->vec_type, a);
1381
1382       for (i = 0; i < num_iterations; ++i) {
1383          res = lp_build_rsqrt_refine(bld, a, res);
1384       }
1385
1386       return res;
1387    }
1388
1389    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1390 }
1391
1392
1393 static inline LLVMValueRef
1394 lp_build_const_v4si(unsigned long value)
1395 {
1396    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1397    LLVMValueRef elements[4] = { element, element, element, element };
1398    return LLVMConstVector(elements, 4);
1399 }
1400
1401 static inline LLVMValueRef
1402 lp_build_const_v4sf(float value)
1403 {
1404    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1405    LLVMValueRef elements[4] = { element, element, element, element };
1406    return LLVMConstVector(elements, 4);
1407 }
1408
1409
1410 /**
1411  * Generate sin(a) using SSE2
1412  */
1413 LLVMValueRef
1414 lp_build_sin(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     * extract the sign bit (upper one)
1435     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1436     */
1437    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1438    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1439
1440    /*
1441     * scale by 4/Pi
1442     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1443     */
1444
1445    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1446    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1447
1448    /*
1449     * store the integer part of y in mm0
1450     * emm2 = _mm_cvttps_epi32(y);
1451     */
1452
1453    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1454
1455    /*
1456     * j=(j+1) & (~1) (see the cephes sources)
1457     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1458     */
1459
1460    LLVMValueRef all_one = lp_build_const_v4si(1);
1461    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1462    /*
1463     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1464     */
1465    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1466    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1467
1468    /*
1469     * y = _mm_cvtepi32_ps(emm2);
1470     */
1471    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1472
1473    /* get the swap sign flag
1474     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1475     */
1476    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1477    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1478
1479    /*
1480     * emm2 = _mm_slli_epi32(emm0, 29);
1481     */
1482    LLVMValueRef const_29 = lp_build_const_v4si(29);
1483    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1484
1485    /*
1486     * get the polynom selection mask
1487     * there is one polynom for 0 <= x <= Pi/4
1488     * and another one for Pi/4<x<=Pi/2
1489     * Both branches will be computed.
1490     *
1491     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1492     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1493     */
1494
1495    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1496    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1497    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1498                                              emm2_3, lp_build_const_v4si(0));
1499    /*
1500     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1501     */
1502    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1503
1504    /*
1505     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1506     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1507     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1508     */
1509    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1510    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1511    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1512
1513    /*
1514     * The magic pass: "Extended precision modular arithmetic"
1515     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1516     * xmm1 = _mm_mul_ps(y, xmm1);
1517     * xmm2 = _mm_mul_ps(y, xmm2);
1518     * xmm3 = _mm_mul_ps(y, xmm3);
1519     */
1520    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1521    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1522    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1523
1524    /*
1525     * x = _mm_add_ps(x, xmm1);
1526     * x = _mm_add_ps(x, xmm2);
1527     * x = _mm_add_ps(x, xmm3);
1528     */
1529
1530    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1531    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1532    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1533
1534    /*
1535     * Evaluate the first polynom  (0 <= x <= Pi/4)
1536     *
1537     * z = _mm_mul_ps(x,x);
1538     */
1539    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1540
1541    /*
1542     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1543     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1544     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1545     */
1546    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1547    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1548    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1549
1550    /*
1551     * y = *(v4sf*)_ps_coscof_p0;
1552     * y = _mm_mul_ps(y, z);
1553     */
1554    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1555    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1556    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1557    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1558    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1559    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1560
1561
1562    /*
1563     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1564     * y = _mm_sub_ps(y, tmp);
1565     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1566     */
1567    LLVMValueRef half = lp_build_const_v4sf(0.5);
1568    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1569    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1570    LLVMValueRef one = lp_build_const_v4sf(1.0);
1571    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1572
1573    /*
1574     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1575     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1576     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1577     */
1578    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1579    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1580    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1581
1582    /*
1583     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1584     *
1585     * y2 = *(v4sf*)_ps_sincof_p0;
1586     * y2 = _mm_mul_ps(y2, z);
1587     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1588     * y2 = _mm_mul_ps(y2, z);
1589     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1590     * y2 = _mm_mul_ps(y2, z);
1591     * y2 = _mm_mul_ps(y2, x);
1592     * y2 = _mm_add_ps(y2, x);
1593     */
1594
1595    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1596    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1597    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1598    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1599    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1600    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1601    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1602
1603    /*
1604     * select the correct result from the two polynoms
1605     * xmm3 = poly_mask;
1606     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1607     * y = _mm_andnot_ps(xmm3, y);
1608     * y = _mm_add_ps(y,y2);
1609     */
1610    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1611    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1612    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1613    LLVMValueRef inv = lp_build_const_v4si(~0);
1614    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1615    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1616    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1617
1618    /*
1619     * update the sign
1620     * y = _mm_xor_ps(y, sign_bit);
1621     */
1622    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1623    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1624    return y_result;
1625 }
1626
1627
1628 /**
1629  * Generate cos(a) using SSE2
1630  */
1631 LLVMValueRef
1632 lp_build_cos(struct lp_build_context *bld,
1633              LLVMValueRef a)
1634 {
1635    struct lp_type int_type = lp_int_type(bld->type);
1636    LLVMBuilderRef b = bld->builder;
1637    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1638    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1639
1640    /*
1641     *  take the absolute value,
1642     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1643     */
1644
1645    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1646    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1647
1648    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1649    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1650
1651    /*
1652     * scale by 4/Pi
1653     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1654     */
1655
1656    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1657    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1658
1659    /*
1660     * store the integer part of y in mm0
1661     * emm2 = _mm_cvttps_epi32(y);
1662     */
1663
1664    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1665
1666    /*
1667     * j=(j+1) & (~1) (see the cephes sources)
1668     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1669     */
1670
1671    LLVMValueRef all_one = lp_build_const_v4si(1);
1672    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1673    /*
1674     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1675     */
1676    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1677    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1678
1679    /*
1680     * y = _mm_cvtepi32_ps(emm2);
1681     */
1682    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1683
1684
1685    /*
1686     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1687     */
1688    LLVMValueRef const_2 = lp_build_const_v4si(2);
1689    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1690
1691
1692    /* get the swap sign flag
1693     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1694     */
1695    LLVMValueRef inv = lp_build_const_v4si(~0);
1696    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1697    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1698    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1699
1700    /*
1701     * emm2 = _mm_slli_epi32(emm0, 29);
1702     */
1703    LLVMValueRef const_29 = lp_build_const_v4si(29);
1704    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1705
1706    /*
1707     * get the polynom selection mask
1708     * there is one polynom for 0 <= x <= Pi/4
1709     * and another one for Pi/4<x<=Pi/2
1710     * Both branches will be computed.
1711     *
1712     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1713     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1714     */
1715
1716    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1717    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1718    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1719                                              emm2_3, lp_build_const_v4si(0));
1720
1721    /*
1722     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1723     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1724     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1725     */
1726    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1727    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1728    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1729
1730    /*
1731     * The magic pass: "Extended precision modular arithmetic"
1732     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1733     * xmm1 = _mm_mul_ps(y, xmm1);
1734     * xmm2 = _mm_mul_ps(y, xmm2);
1735     * xmm3 = _mm_mul_ps(y, xmm3);
1736     */
1737    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1738    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1739    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1740
1741    /*
1742     * x = _mm_add_ps(x, xmm1);
1743     * x = _mm_add_ps(x, xmm2);
1744     * x = _mm_add_ps(x, xmm3);
1745     */
1746
1747    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1748    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1749    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1750
1751    /*
1752     * Evaluate the first polynom  (0 <= x <= Pi/4)
1753     *
1754     * z = _mm_mul_ps(x,x);
1755     */
1756    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1757
1758    /*
1759     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1760     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1761     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1762     */
1763    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1764    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1765    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1766
1767    /*
1768     * y = *(v4sf*)_ps_coscof_p0;
1769     * y = _mm_mul_ps(y, z);
1770     */
1771    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1772    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1773    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1774    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1775    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1776    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1777
1778
1779    /*
1780     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1781     * y = _mm_sub_ps(y, tmp);
1782     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1783     */
1784    LLVMValueRef half = lp_build_const_v4sf(0.5);
1785    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1786    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1787    LLVMValueRef one = lp_build_const_v4sf(1.0);
1788    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1789
1790    /*
1791     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1792     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1793     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1794     */
1795    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1796    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1797    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1798
1799    /*
1800     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1801     *
1802     * y2 = *(v4sf*)_ps_sincof_p0;
1803     * y2 = _mm_mul_ps(y2, z);
1804     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1805     * y2 = _mm_mul_ps(y2, z);
1806     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1807     * y2 = _mm_mul_ps(y2, z);
1808     * y2 = _mm_mul_ps(y2, x);
1809     * y2 = _mm_add_ps(y2, x);
1810     */
1811
1812    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1813    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1814    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1815    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1816    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1817    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1818    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1819
1820    /*
1821     * select the correct result from the two polynoms
1822     * xmm3 = poly_mask;
1823     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1824     * y = _mm_andnot_ps(xmm3, y);
1825     * y = _mm_add_ps(y,y2);
1826     */
1827    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1828    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1829    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1830    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1831    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1832    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1833
1834    /*
1835     * update the sign
1836     * y = _mm_xor_ps(y, sign_bit);
1837     */
1838    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1839    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1840    return y_result;
1841 }
1842
1843
1844 /**
1845  * Generate pow(x, y)
1846  */
1847 LLVMValueRef
1848 lp_build_pow(struct lp_build_context *bld,
1849              LLVMValueRef x,
1850              LLVMValueRef y)
1851 {
1852    /* TODO: optimize the constant case */
1853    if(LLVMIsConstant(x) && LLVMIsConstant(y))
1854       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1855                    __FUNCTION__);
1856
1857    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1858 }
1859
1860
1861 /**
1862  * Generate exp(x)
1863  */
1864 LLVMValueRef
1865 lp_build_exp(struct lp_build_context *bld,
1866              LLVMValueRef x)
1867 {
1868    /* log2(e) = 1/log(2) */
1869    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1870
1871    assert(lp_check_value(bld->type, x));
1872
1873    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1874 }
1875
1876
1877 /**
1878  * Generate log(x)
1879  */
1880 LLVMValueRef
1881 lp_build_log(struct lp_build_context *bld,
1882              LLVMValueRef x)
1883 {
1884    /* log(2) */
1885    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1886
1887    assert(lp_check_value(bld->type, x));
1888
1889    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1890 }
1891
1892
1893 /**
1894  * Generate polynomial.
1895  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1896  */
1897 static LLVMValueRef
1898 lp_build_polynomial(struct lp_build_context *bld,
1899                     LLVMValueRef x,
1900                     const double *coeffs,
1901                     unsigned num_coeffs)
1902 {
1903    const struct lp_type type = bld->type;
1904    LLVMValueRef res = NULL;
1905    unsigned i;
1906
1907    assert(lp_check_value(bld->type, x));
1908
1909    /* TODO: optimize the constant case */
1910    if(LLVMIsConstant(x))
1911       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1912                    __FUNCTION__);
1913
1914    for (i = num_coeffs; i--; ) {
1915       LLVMValueRef coeff;
1916
1917       coeff = lp_build_const_vec(type, coeffs[i]);
1918
1919       if(res)
1920          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1921       else
1922          res = coeff;
1923    }
1924
1925    if(res)
1926       return res;
1927    else
1928       return bld->undef;
1929 }
1930
1931
1932 /**
1933  * Minimax polynomial fit of 2**x, in range [0, 1[
1934  */
1935 const double lp_build_exp2_polynomial[] = {
1936 #if EXP_POLY_DEGREE == 5
1937    0.999999999690134838155,
1938    0.583974334321735217258,
1939    0.164553105719676828492,
1940    0.0292811063701710962255,
1941    0.00354944426657875141846,
1942    0.000296253726543423377365
1943 #elif EXP_POLY_DEGREE == 4
1944    1.00000001502262084505,
1945    0.563586057338685991394,
1946    0.150436017652442413623,
1947    0.0243220604213317927308,
1948    0.0025359088446580436489
1949 #elif EXP_POLY_DEGREE == 3
1950    0.999925218562710312959,
1951    0.695833540494823811697,
1952    0.226067155427249155588,
1953    0.0780245226406372992967
1954 #elif EXP_POLY_DEGREE == 2
1955    1.00172476321474503578,
1956    0.657636275736077639316,
1957    0.33718943461968720704
1958 #else
1959 #error
1960 #endif
1961 };
1962
1963
1964 void
1965 lp_build_exp2_approx(struct lp_build_context *bld,
1966                      LLVMValueRef x,
1967                      LLVMValueRef *p_exp2_int_part,
1968                      LLVMValueRef *p_frac_part,
1969                      LLVMValueRef *p_exp2)
1970 {
1971    const struct lp_type type = bld->type;
1972    LLVMTypeRef vec_type = lp_build_vec_type(type);
1973    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1974    LLVMValueRef ipart = NULL;
1975    LLVMValueRef fpart = NULL;
1976    LLVMValueRef expipart = NULL;
1977    LLVMValueRef expfpart = NULL;
1978    LLVMValueRef res = NULL;
1979
1980    assert(lp_check_value(bld->type, x));
1981
1982    if(p_exp2_int_part || p_frac_part || p_exp2) {
1983       /* TODO: optimize the constant case */
1984       if(LLVMIsConstant(x))
1985          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1986                       __FUNCTION__);
1987
1988       assert(type.floating && type.width == 32);
1989
1990       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1991       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1992
1993       /* ipart = floor(x) */
1994       ipart = lp_build_floor(bld, x);
1995
1996       /* fpart = x - ipart */
1997       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
1998    }
1999
2000    if(p_exp2_int_part || p_exp2) {
2001       /* expipart = (float) (1 << ipart) */
2002       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
2003       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
2004       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
2005       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
2006    }
2007
2008    if(p_exp2) {
2009       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
2010                                      Elements(lp_build_exp2_polynomial));
2011
2012       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
2013    }
2014
2015    if(p_exp2_int_part)
2016       *p_exp2_int_part = expipart;
2017
2018    if(p_frac_part)
2019       *p_frac_part = fpart;
2020
2021    if(p_exp2)
2022       *p_exp2 = res;
2023 }
2024
2025
2026 LLVMValueRef
2027 lp_build_exp2(struct lp_build_context *bld,
2028               LLVMValueRef x)
2029 {
2030    LLVMValueRef res;
2031    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
2032    return res;
2033 }
2034
2035
2036 /**
2037  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
2038  * These coefficients can be generate with
2039  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2040  */
2041 const double lp_build_log2_polynomial[] = {
2042 #if LOG_POLY_DEGREE == 6
2043    3.11578814719469302614,
2044    -3.32419399085241980044,
2045    2.59883907202499966007,
2046    -1.23152682416275988241,
2047    0.318212422185251071475,
2048    -0.0344359067839062357313
2049 #elif LOG_POLY_DEGREE == 5
2050    2.8882704548164776201,
2051    -2.52074962577807006663,
2052    1.48116647521213171641,
2053    -0.465725644288844778798,
2054    0.0596515482674574969533
2055 #elif LOG_POLY_DEGREE == 4
2056    2.61761038894603480148,
2057    -1.75647175389045657003,
2058    0.688243882994381274313,
2059    -0.107254423828329604454
2060 #elif LOG_POLY_DEGREE == 3
2061    2.28330284476918490682,
2062    -1.04913055217340124191,
2063    0.204446009836232697516
2064 #else
2065 #error
2066 #endif
2067 };
2068
2069
2070 /**
2071  * See http://www.devmaster.net/forums/showthread.php?p=43580
2072  */
2073 void
2074 lp_build_log2_approx(struct lp_build_context *bld,
2075                      LLVMValueRef x,
2076                      LLVMValueRef *p_exp,
2077                      LLVMValueRef *p_floor_log2,
2078                      LLVMValueRef *p_log2)
2079 {
2080    const struct lp_type type = bld->type;
2081    LLVMTypeRef vec_type = lp_build_vec_type(type);
2082    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2083
2084    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2085    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2086    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2087
2088    LLVMValueRef i = NULL;
2089    LLVMValueRef exp = NULL;
2090    LLVMValueRef mant = NULL;
2091    LLVMValueRef logexp = NULL;
2092    LLVMValueRef logmant = NULL;
2093    LLVMValueRef res = NULL;
2094
2095    assert(lp_check_value(bld->type, x));
2096
2097    if(p_exp || p_floor_log2 || p_log2) {
2098       /* TODO: optimize the constant case */
2099       if(LLVMIsConstant(x))
2100          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2101                       __FUNCTION__);
2102
2103       assert(type.floating && type.width == 32);
2104
2105       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2106
2107       /* exp = (float) exponent(x) */
2108       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2109    }
2110
2111    if(p_floor_log2 || p_log2) {
2112       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2113       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2114       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2115    }
2116
2117    if(p_log2) {
2118       /* mant = (float) mantissa(x) */
2119       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2120       mant = LLVMBuildOr(bld->builder, mant, one, "");
2121       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2122
2123       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2124                                     Elements(lp_build_log2_polynomial));
2125
2126       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2127       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2128
2129       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2130    }
2131
2132    if(p_exp) {
2133       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2134       *p_exp = exp;
2135    }
2136
2137    if(p_floor_log2)
2138       *p_floor_log2 = logexp;
2139
2140    if(p_log2)
2141       *p_log2 = res;
2142 }
2143
2144
2145 LLVMValueRef
2146 lp_build_log2(struct lp_build_context *bld,
2147               LLVMValueRef x)
2148 {
2149    LLVMValueRef res;
2150    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2151    return res;
2152 }