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_debug.h"
  60 #include "lp_bld_arit.h"
  61
  62
  63 #define EXP_POLY_DEGREE 3
  64
  65 #define LOG_POLY_DEGREE 5
  66
  67
  68 /**
  69  * Generate min(a, b)
  70  * No checks for special case values of a or b = 1 or 0 are done.
  71  */
  72 static LLVMValueRef
  73 lp_build_min_simple(struct lp_build_context *bld,
  74                     LLVMValueRef a,
  75                     LLVMValueRef b)
  76 {
  77    const struct lp_type type = bld->type;
  78    const char *intrinsic = NULL;
  79    LLVMValueRef cond;
  80
  81    assert(lp_check_value(type, a));
  82    assert(lp_check_value(type, b));
  83
  84    /* TODO: optimize the constant case */
  85
  86    if(type.width * type.length == 128) {
  87       if(type.floating) {
  88          if(type.width == 32 && util_cpu_caps.has_sse)
  89             intrinsic = "llvm.x86.sse.min.ps";
  90          if(type.width == 64 && util_cpu_caps.has_sse2)
  91             intrinsic = "llvm.x86.sse2.min.pd";
  92       }
  93       else {
  94          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
  95             intrinsic = "llvm.x86.sse2.pminu.b";
  96          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
  97             intrinsic = "llvm.x86.sse41.pminsb";
  98          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
  99             intrinsic = "llvm.x86.sse41.pminuw";
 100          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 101             intrinsic = "llvm.x86.sse2.pmins.w";
 102          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 103             intrinsic = "llvm.x86.sse41.pminud";
 104          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 105             intrinsic = "llvm.x86.sse41.pminsd";
 106       }
 107    }
 108
 109    if(intrinsic)
 110       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 111
 112    cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
 113    return lp_build_select(bld, cond, a, b);
 114 }
 115
 116
 117 /**
 118  * Generate max(a, b)
 119  * No checks for special case values of a or b = 1 or 0 are done.
 120  */
 121 static LLVMValueRef
 122 lp_build_max_simple(struct lp_build_context *bld,
 123                     LLVMValueRef a,
 124                     LLVMValueRef b)
 125 {
 126    const struct lp_type type = bld->type;
 127    const char *intrinsic = NULL;
 128    LLVMValueRef cond;
 129
 130    assert(lp_check_value(type, a));
 131    assert(lp_check_value(type, b));
 132
 133    /* TODO: optimize the constant case */
 134
 135    if(type.width * type.length == 128) {
 136       if(type.floating) {
 137          if(type.width == 32 && util_cpu_caps.has_sse)
 138             intrinsic = "llvm.x86.sse.max.ps";
 139          if(type.width == 64 && util_cpu_caps.has_sse2)
 140             intrinsic = "llvm.x86.sse2.max.pd";
 141       }
 142       else {
 143          if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
 144             intrinsic = "llvm.x86.sse2.pmaxu.b";
 145          if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
 146             intrinsic = "llvm.x86.sse41.pmaxsb";
 147          if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
 148             intrinsic = "llvm.x86.sse41.pmaxuw";
 149          if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
 150             intrinsic = "llvm.x86.sse2.pmaxs.w";
 151          if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
 152             intrinsic = "llvm.x86.sse41.pmaxud";
 153          if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
 154             intrinsic = "llvm.x86.sse41.pmaxsd";
 155       }
 156    }
 157
 158    if(intrinsic)
 159       return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 160
 161    cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
 162    return lp_build_select(bld, cond, a, b);
 163 }
 164
 165
 166 /**
 167  * Generate 1 - a, or ~a depending on bld->type.
 168  */
 169 LLVMValueRef
 170 lp_build_comp(struct lp_build_context *bld,
 171               LLVMValueRef a)
 172 {
 173    const struct lp_type type = bld->type;
 174
 175    assert(lp_check_value(type, a));
 176
 177    if(a == bld->one)
 178       return bld->zero;
 179    if(a == bld->zero)
 180       return bld->one;
 181
 182    if(type.norm && !type.floating && !type.fixed && !type.sign) {
 183       if(LLVMIsConstant(a))
 184          return LLVMConstNot(a);
 185       else
 186          return LLVMBuildNot(bld->builder, a, "");
 187    }
 188
 189    if(LLVMIsConstant(a))
 190       if (type.floating)
 191           return LLVMConstFSub(bld->one, a);
 192       else
 193           return LLVMConstSub(bld->one, a);
 194    else
 195       if (type.floating)
 196          return LLVMBuildFSub(bld->builder, bld->one, a, "");
 197       else
 198          return LLVMBuildSub(bld->builder, bld->one, a, "");
 199 }
 200
 201
 202 /**
 203  * Generate a + b
 204  */
 205 LLVMValueRef
 206 lp_build_add(struct lp_build_context *bld,
 207              LLVMValueRef a,
 208              LLVMValueRef b)
 209 {
 210    const struct lp_type type = bld->type;
 211    LLVMValueRef res;
 212
 213    assert(lp_check_value(type, a));
 214    assert(lp_check_value(type, b));
 215
 216    if(a == bld->zero)
 217       return b;
 218    if(b == bld->zero)
 219       return a;
 220    if(a == bld->undef || b == bld->undef)
 221       return bld->undef;
 222
 223    if(bld->type.norm) {
 224       const char *intrinsic = NULL;
 225
 226       if(a == bld->one || b == bld->one)
 227         return bld->one;
 228
 229       if(util_cpu_caps.has_sse2 &&
 230          type.width * type.length == 128 &&
 231          !type.floating && !type.fixed) {
 232          if(type.width == 8)
 233             intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
 234          if(type.width == 16)
 235             intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
 236       }
 237
 238       if(intrinsic)
 239          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 240    }
 241
 242    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 243       if (type.floating)
 244          res = LLVMConstFAdd(a, b);
 245       else
 246          res = LLVMConstAdd(a, b);
 247    else
 248       if (type.floating)
 249          res = LLVMBuildFAdd(bld->builder, a, b, "");
 250       else
 251          res = LLVMBuildAdd(bld->builder, a, b, "");
 252
 253    /* clamp to ceiling of 1.0 */
 254    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 255       res = lp_build_min_simple(bld, res, bld->one);
 256
 257    /* XXX clamp to floor of -1 or 0??? */
 258
 259    return res;
 260 }
 261
 262
 263 /** Return the scalar sum of the elements of a */
 264 LLVMValueRef
 265 lp_build_sum_vector(struct lp_build_context *bld,
 266                     LLVMValueRef a)
 267 {
 268    const struct lp_type type = bld->type;
 269    LLVMValueRef index, res;
 270    unsigned i;
 271
 272    assert(lp_check_value(type, a));
 273
 274    if (type.length == 1) {
 275       return a;
 276    }
 277
 278    assert(!bld->type.norm);
 279
 280    index = LLVMConstInt(LLVMInt32Type(), 0, 0);
 281    res = LLVMBuildExtractElement(bld->builder, a, index, "");
 282
 283    for (i = 1; i < type.length; i++) {
 284       index = LLVMConstInt(LLVMInt32Type(), i, 0);
 285       if (type.floating)
 286          res = LLVMBuildFAdd(bld->builder, res,
 287                             LLVMBuildExtractElement(bld->builder,
 288                                                     a, index, ""),
 289                             "");
 290       else
 291          res = LLVMBuildAdd(bld->builder, res,
 292                             LLVMBuildExtractElement(bld->builder,
 293                                                     a, index, ""),
 294                             "");
 295    }
 296
 297    return res;
 298 }
 299
 300
 301 /**
 302  * Generate a - b
 303  */
 304 LLVMValueRef
 305 lp_build_sub(struct lp_build_context *bld,
 306              LLVMValueRef a,
 307              LLVMValueRef b)
 308 {
 309    const struct lp_type type = bld->type;
 310    LLVMValueRef res;
 311
 312    assert(lp_check_value(type, a));
 313    assert(lp_check_value(type, b));
 314
 315    if(b == bld->zero)
 316       return a;
 317    if(a == bld->undef || b == bld->undef)
 318       return bld->undef;
 319    if(a == b)
 320       return bld->zero;
 321
 322    if(bld->type.norm) {
 323       const char *intrinsic = NULL;
 324
 325       if(b == bld->one)
 326         return bld->zero;
 327
 328       if(util_cpu_caps.has_sse2 &&
 329          type.width * type.length == 128 &&
 330          !type.floating && !type.fixed) {
 331          if(type.width == 8)
 332             intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
 333          if(type.width == 16)
 334             intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
 335       }
 336
 337       if(intrinsic)
 338          return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
 339    }
 340
 341    if(LLVMIsConstant(a) && LLVMIsConstant(b))
 342       if (type.floating)
 343          res = LLVMConstFSub(a, b);
 344       else
 345          res = LLVMConstSub(a, b);
 346    else
 347       if (type.floating)
 348          res = LLVMBuildFSub(bld->builder, a, b, "");
 349       else
 350          res = LLVMBuildSub(bld->builder, a, b, "");
 351
 352    if(bld->type.norm && (bld->type.floating || bld->type.fixed))
 353       res = lp_build_max_simple(bld, res, bld->zero);
 354
 355    return res;
 356 }
 357
 358
 359 /**
 360  * Normalized 8bit multiplication.
 361  *
 362  * - alpha plus one
 363  *
 364  *     makes the following approximation to the division (Sree)
 365  *
 366  *       a*b/255 ~= (a*(b + 1)) >> 256
 367  *
 368  *     which is the fastest method that satisfies the following OpenGL criteria
 369  *
 370  *       0*0 = 0 and 255*255 = 255
 371  *
 372  * - geometric series
 373  *
 374  *     takes the geometric series approximation to the division
 375  *
 376  *       t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
 377  *
 378  *     in this case just the first two terms to fit in 16bit arithmetic
 379  *
 380  *       t/255 ~= (t + (t >> 8)) >> 8
 381  *
 382  *     note that just by itself it doesn't satisfies the OpenGL criteria, as
 383  *     255*255 = 254, so the special case b = 255 must be accounted or roundoff
 384  *     must be used
 385  *
 386  * - geometric series plus rounding
 387  *
 388  *     when using a geometric series division instead of truncating the result
 389  *     use roundoff in the approximation (Jim Blinn)
 390  *
 391  *       t/255 ~= (t + (t >> 8) + 0x80) >> 8
 392  *
 393  *     achieving the exact results
 394  *
 395  * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
 396  *     ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
 397  * @sa Michael Herf, The "double blend trick", May 2000,
 398  *     http://www.stereopsis.com/doubleblend.html
 399  */
 400 static LLVMValueRef
 401 lp_build_mul_u8n(LLVMBuilderRef builder,
 402                  struct lp_type i16_type,
 403                  LLVMValueRef a, LLVMValueRef b)
 404 {
 405    LLVMValueRef c8;
 406    LLVMValueRef ab;
 407
 408    assert(!i16_type.floating);
 409    assert(lp_check_value(i16_type, a));
 410    assert(lp_check_value(i16_type, b));
 411
 412    c8 = lp_build_const_int_vec(i16_type, 8);
 413
 414 #if 0
 415
 416    /* a*b/255 ~= (a*(b + 1)) >> 256 */
 417    b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
 418    ab = LLVMBuildMul(builder, a, b, "");
 419
 420 #else
 421
 422    /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
 423    ab = LLVMBuildMul(builder, a, b, "");
 424    ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
 425    ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
 426
 427 #endif
 428
 429    ab = LLVMBuildLShr(builder, ab, c8, "");
 430
 431    return ab;
 432 }
 433
 434
 435 /**
 436  * Generate a * b
 437  */
 438 LLVMValueRef
 439 lp_build_mul(struct lp_build_context *bld,
 440              LLVMValueRef a,
 441              LLVMValueRef b)
 442 {
 443    const struct lp_type type = bld->type;
 444    LLVMValueRef shift;
 445    LLVMValueRef res;
 446
 447    assert(lp_check_value(type, a));
 448    assert(lp_check_value(type, b));
 449
 450    if(a == bld->zero)
 451       return bld->zero;
 452    if(a == bld->one)
 453       return b;
 454    if(b == bld->zero)
 455       return bld->zero;
 456    if(b == bld->one)
 457       return a;
 458    if(a == bld->undef || b == bld->undef)
 459       return bld->undef;
 460
 461    if(!type.floating && !type.fixed && type.norm) {
 462       if(type.width == 8) {
 463          struct lp_type i16_type = lp_wider_type(type);
 464          LLVMValueRef al, ah, bl, bh, abl, abh, ab;
 465
 466          lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
 467          lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
 468
 469          /* PMULLW, PSRLW, PADDW */
 470          abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
 471          abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
 472
 473          ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
 474
 475          return ab;
 476       }
 477
 478       /* FIXME */
 479       assert(0);
 480    }
 481
 482    if(type.fixed)
 483       shift = lp_build_const_int_vec(type, type.width/2);
 484    else
 485       shift = NULL;
 486
 487    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 488       if (type.floating)
 489          res = LLVMConstFMul(a, b);
 490       else
 491          res = LLVMConstMul(a, b);
 492       if(shift) {
 493          if(type.sign)
 494             res = LLVMConstAShr(res, shift);
 495          else
 496             res = LLVMConstLShr(res, shift);
 497       }
 498    }
 499    else {
 500       if (type.floating)
 501          res = LLVMBuildFMul(bld->builder, a, b, "");
 502       else
 503          res = LLVMBuildMul(bld->builder, a, b, "");
 504       if(shift) {
 505          if(type.sign)
 506             res = LLVMBuildAShr(bld->builder, res, shift, "");
 507          else
 508             res = LLVMBuildLShr(bld->builder, res, shift, "");
 509       }
 510    }
 511
 512    return res;
 513 }
 514
 515
 516 /**
 517  * Small vector x scale multiplication optimization.
 518  */
 519 LLVMValueRef
 520 lp_build_mul_imm(struct lp_build_context *bld,
 521                  LLVMValueRef a,
 522                  int b)
 523 {
 524    LLVMValueRef factor;
 525
 526    assert(lp_check_value(bld->type, a));
 527
 528    if(b == 0)
 529       return bld->zero;
 530
 531    if(b == 1)
 532       return a;
 533
 534    if(b == -1)
 535       return lp_build_negate(bld, a);
 536
 537    if(b == 2 && bld->type.floating)
 538       return lp_build_add(bld, a, a);
 539
 540    if(util_is_power_of_two(b)) {
 541       unsigned shift = ffs(b) - 1;
 542
 543       if(bld->type.floating) {
 544 #if 0
 545          /*
 546           * Power of two multiplication by directly manipulating the mantissa.
 547           *
 548           * XXX: This might not be always faster, it will introduce a small error
 549           * for multiplication by zero, and it will produce wrong results
 550           * for Inf and NaN.
 551           */
 552          unsigned mantissa = lp_mantissa(bld->type);
 553          factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
 554          a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
 555          a = LLVMBuildAdd(bld->builder, a, factor, "");
 556          a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
 557          return a;
 558 #endif
 559       }
 560       else {
 561          factor = lp_build_const_vec(bld->type, shift);
 562          return LLVMBuildShl(bld->builder, a, factor, "");
 563       }
 564    }
 565
 566    factor = lp_build_const_vec(bld->type, (double)b);
 567    return lp_build_mul(bld, a, factor);
 568 }
 569
 570
 571 /**
 572  * Generate a / b
 573  */
 574 LLVMValueRef
 575 lp_build_div(struct lp_build_context *bld,
 576              LLVMValueRef a,
 577              LLVMValueRef b)
 578 {
 579    const struct lp_type type = bld->type;
 580
 581    assert(lp_check_value(type, a));
 582    assert(lp_check_value(type, b));
 583
 584    if(a == bld->zero)
 585       return bld->zero;
 586    if(a == bld->one)
 587       return lp_build_rcp(bld, b);
 588    if(b == bld->zero)
 589       return bld->undef;
 590    if(b == bld->one)
 591       return a;
 592    if(a == bld->undef || b == bld->undef)
 593       return bld->undef;
 594
 595    if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
 596       if (type.floating)
 597          return LLVMConstFDiv(a, b);
 598       else if (type.sign)
 599          return LLVMConstSDiv(a, b);
 600       else
 601          return LLVMConstUDiv(a, b);
 602    }
 603
 604    if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
 605       return lp_build_mul(bld, a, lp_build_rcp(bld, b));
 606
 607    if (type.floating)
 608       return LLVMBuildFDiv(bld->builder, a, b, "");
 609    else if (type.sign)
 610       return LLVMBuildSDiv(bld->builder, a, b, "");
 611    else
 612       return LLVMBuildUDiv(bld->builder, a, b, "");
 613 }
 614
 615
 616 /**
 617  * Linear interpolation.
 618  *
 619  * This also works for integer values with a few caveats.
 620  *
 621  * @sa http://www.stereopsis.com/doubleblend.html
 622  */
 623 LLVMValueRef
 624 lp_build_lerp(struct lp_build_context *bld,
 625               LLVMValueRef x,
 626               LLVMValueRef v0,
 627               LLVMValueRef v1)
 628 {
 629    LLVMValueRef delta;
 630    LLVMValueRef res;
 631
 632    assert(lp_check_value(bld->type, x));
 633    assert(lp_check_value(bld->type, v0));
 634    assert(lp_check_value(bld->type, v1));
 635
 636    delta = lp_build_sub(bld, v1, v0);
 637
 638    res = lp_build_mul(bld, x, delta);
 639
 640    res = lp_build_add(bld, v0, res);
 641
 642    if(bld->type.fixed)
 643       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 644        * but it will be wrong for other uses. Basically we need a more
 645        * powerful lp_type, capable of further distinguishing the values
 646        * interpretation from the value storage. */
 647       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 648
 649    return res;
 650 }
 651
 652
 653 LLVMValueRef
 654 lp_build_lerp_2d(struct lp_build_context *bld,
 655                  LLVMValueRef x,
 656                  LLVMValueRef y,
 657                  LLVMValueRef v00,
 658                  LLVMValueRef v01,
 659                  LLVMValueRef v10,
 660                  LLVMValueRef v11)
 661 {
 662    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 663    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 664    return lp_build_lerp(bld, y, v0, v1);
 665 }
 666
 667
 668 /**
 669  * Generate min(a, b)
 670  * Do checks for special cases.
 671  */
 672 LLVMValueRef
 673 lp_build_min(struct lp_build_context *bld,
 674              LLVMValueRef a,
 675              LLVMValueRef b)
 676 {
 677    assert(lp_check_value(bld->type, a));
 678    assert(lp_check_value(bld->type, b));
 679
 680    if(a == bld->undef || b == bld->undef)
 681       return bld->undef;
 682
 683    if(a == b)
 684       return a;
 685
 686    if(bld->type.norm) {
 687       if(a == bld->zero || b == bld->zero)
 688          return bld->zero;
 689       if(a == bld->one)
 690          return b;
 691       if(b == bld->one)
 692          return a;
 693    }
 694
 695    return lp_build_min_simple(bld, a, b);
 696 }
 697
 698
 699 /**
 700  * Generate max(a, b)
 701  * Do checks for special cases.
 702  */
 703 LLVMValueRef
 704 lp_build_max(struct lp_build_context *bld,
 705              LLVMValueRef a,
 706              LLVMValueRef b)
 707 {
 708    assert(lp_check_value(bld->type, a));
 709    assert(lp_check_value(bld->type, b));
 710
 711    if(a == bld->undef || b == bld->undef)
 712       return bld->undef;
 713
 714    if(a == b)
 715       return a;
 716
 717    if(bld->type.norm) {
 718       if(a == bld->one || b == bld->one)
 719          return bld->one;
 720       if(a == bld->zero)
 721          return b;
 722       if(b == bld->zero)
 723          return a;
 724    }
 725
 726    return lp_build_max_simple(bld, a, b);
 727 }
 728
 729
 730 /**
 731  * Generate clamp(a, min, max)
 732  * Do checks for special cases.
 733  */
 734 LLVMValueRef
 735 lp_build_clamp(struct lp_build_context *bld,
 736                LLVMValueRef a,
 737                LLVMValueRef min,
 738                LLVMValueRef max)
 739 {
 740    assert(lp_check_value(bld->type, a));
 741    assert(lp_check_value(bld->type, min));
 742    assert(lp_check_value(bld->type, max));
 743
 744    a = lp_build_min(bld, a, max);
 745    a = lp_build_max(bld, a, min);
 746    return a;
 747 }
 748
 749
 750 /**
 751  * Generate abs(a)
 752  */
 753 LLVMValueRef
 754 lp_build_abs(struct lp_build_context *bld,
 755              LLVMValueRef a)
 756 {
 757    const struct lp_type type = bld->type;
 758    LLVMTypeRef vec_type = lp_build_vec_type(type);
 759
 760    assert(lp_check_value(type, a));
 761
 762    if(!type.sign)
 763       return a;
 764
 765    if(type.floating) {
 766       /* Mask out the sign bit */
 767       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 768       unsigned long long absMask = ~(1ULL << (type.width - 1));
 769       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 770       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 771       a = LLVMBuildAnd(bld->builder, a, mask, "");
 772       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 773       return a;
 774    }
 775
 776    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 777       switch(type.width) {
 778       case 8:
 779          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 780       case 16:
 781          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 782       case 32:
 783          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 784       }
 785    }
 786
 787    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 788 }
 789
 790
 791 LLVMValueRef
 792 lp_build_negate(struct lp_build_context *bld,
 793                 LLVMValueRef a)
 794 {
 795    assert(lp_check_value(bld->type, a));
 796
 797 #if HAVE_LLVM >= 0x0207
 798    if (bld->type.floating)
 799       a = LLVMBuildFNeg(bld->builder, a, "");
 800    else
 801 #endif
 802       a = LLVMBuildNeg(bld->builder, a, "");
 803
 804    return a;
 805 }
 806
 807
 808 /** Return -1, 0 or +1 depending on the sign of a */
 809 LLVMValueRef
 810 lp_build_sgn(struct lp_build_context *bld,
 811              LLVMValueRef a)
 812 {
 813    const struct lp_type type = bld->type;
 814    LLVMValueRef cond;
 815    LLVMValueRef res;
 816
 817    assert(lp_check_value(type, a));
 818
 819    /* Handle non-zero case */
 820    if(!type.sign) {
 821       /* if not zero then sign must be positive */
 822       res = bld->one;
 823    }
 824    else if(type.floating) {
 825       LLVMTypeRef vec_type;
 826       LLVMTypeRef int_type;
 827       LLVMValueRef mask;
 828       LLVMValueRef sign;
 829       LLVMValueRef one;
 830       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 831
 832       int_type = lp_build_int_vec_type(type);
 833       vec_type = lp_build_vec_type(type);
 834       mask = lp_build_const_int_vec(type, maskBit);
 835
 836       /* Take the sign bit and add it to 1 constant */
 837       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 838       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 839       one = LLVMConstBitCast(bld->one, int_type);
 840       res = LLVMBuildOr(bld->builder, sign, one, "");
 841       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 842    }
 843    else
 844    {
 845       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 846       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 847       res = lp_build_select(bld, cond, bld->one, minus_one);
 848    }
 849
 850    /* Handle zero */
 851    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 852    res = lp_build_select(bld, cond, bld->zero, res);
 853
 854    return res;
 855 }
 856
 857
 858 /**
 859  * Set the sign of float vector 'a' according to 'sign'.
 860  * If sign==0, return abs(a).
 861  * If sign==1, return -abs(a);
 862  * Other values for sign produce undefined results.
 863  */
 864 LLVMValueRef
 865 lp_build_set_sign(struct lp_build_context *bld,
 866                   LLVMValueRef a, LLVMValueRef sign)
 867 {
 868    const struct lp_type type = bld->type;
 869    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 870    LLVMTypeRef vec_type = lp_build_vec_type(type);
 871    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 872    LLVMValueRef mask = lp_build_const_int_vec(type,
 873                              ~((unsigned long long) 1 << (type.width - 1)));
 874    LLVMValueRef val, res;
 875
 876    assert(type.floating);
 877    assert(lp_check_value(type, a));
 878
 879    /* val = reinterpret_cast<int>(a) */
 880    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 881    /* val = val & mask */
 882    val = LLVMBuildAnd(bld->builder, val, mask, "");
 883    /* sign = sign << shift */
 884    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 885    /* res = val | sign */
 886    res = LLVMBuildOr(bld->builder, val, sign, "");
 887    /* res = reinterpret_cast<float>(res) */
 888    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 889
 890    return res;
 891 }
 892
 893
 894 /**
 895  * Convert vector of (or scalar) int to vector of (or scalar) float.
 896  */
 897 LLVMValueRef
 898 lp_build_int_to_float(struct lp_build_context *bld,
 899                       LLVMValueRef a)
 900 {
 901    const struct lp_type type = bld->type;
 902    LLVMTypeRef vec_type = lp_build_vec_type(type);
 903
 904    assert(type.floating);
 905
 906    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 907 }
 908
 909
 910
 911 enum lp_build_round_sse41_mode
 912 {
 913    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 914    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 915    LP_BUILD_ROUND_SSE41_CEIL = 2,
 916    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 917 };
 918
 919
 920 static INLINE LLVMValueRef
 921 lp_build_round_sse41(struct lp_build_context *bld,
 922                      LLVMValueRef a,
 923                      enum lp_build_round_sse41_mode mode)
 924 {
 925    const struct lp_type type = bld->type;
 926    LLVMTypeRef vec_type = lp_build_vec_type(type);
 927    const char *intrinsic;
 928
 929    assert(type.floating);
 930    assert(type.width*type.length == 128);
 931    assert(lp_check_value(type, a));
 932    assert(util_cpu_caps.has_sse4_1);
 933
 934    switch(type.width) {
 935    case 32:
 936       intrinsic = "llvm.x86.sse41.round.ps";
 937       break;
 938    case 64:
 939       intrinsic = "llvm.x86.sse41.round.pd";
 940       break;
 941    default:
 942       assert(0);
 943       return bld->undef;
 944    }
 945
 946    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
 947                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
 948 }
 949
 950
 951 /**
 952  * Return the integer part of a float (vector) value.  The returned value is
 953  * a float (vector).
 954  * Ex: trunc(-1.5) = 1.0
 955  */
 956 LLVMValueRef
 957 lp_build_trunc(struct lp_build_context *bld,
 958                LLVMValueRef a)
 959 {
 960    const struct lp_type type = bld->type;
 961
 962    assert(type.floating);
 963    assert(lp_check_value(type, a));
 964
 965    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 966       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
 967    else {
 968       LLVMTypeRef vec_type = lp_build_vec_type(type);
 969       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 970       LLVMValueRef res;
 971       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
 972       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
 973       return res;
 974    }
 975 }
 976
 977
 978 /**
 979  * Return float (vector) rounded to nearest integer (vector).  The returned
 980  * value is a float (vector).
 981  * Ex: round(0.9) = 1.0
 982  * Ex: round(-1.5) = -2.0
 983  */
 984 LLVMValueRef
 985 lp_build_round(struct lp_build_context *bld,
 986                LLVMValueRef a)
 987 {
 988    const struct lp_type type = bld->type;
 989
 990    assert(type.floating);
 991    assert(lp_check_value(type, a));
 992
 993    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
 994       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
 995    else {
 996       LLVMTypeRef vec_type = lp_build_vec_type(type);
 997       LLVMValueRef res;
 998       res = lp_build_iround(bld, a);
 999       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1000       return res;
1001    }
1002 }
1003
1004
1005 /**
1006  * Return floor of float (vector), result is a float (vector)
1007  * Ex: floor(1.1) = 1.0
1008  * Ex: floor(-1.1) = -2.0
1009  */
1010 LLVMValueRef
1011 lp_build_floor(struct lp_build_context *bld,
1012                LLVMValueRef a)
1013 {
1014    const struct lp_type type = bld->type;
1015
1016    assert(type.floating);
1017    assert(lp_check_value(type, a));
1018
1019    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1020       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1021    else {
1022       LLVMTypeRef vec_type = lp_build_vec_type(type);
1023       LLVMValueRef res;
1024       res = lp_build_ifloor(bld, a);
1025       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1026       return res;
1027    }
1028 }
1029
1030
1031 /**
1032  * Return ceiling of float (vector), returning float (vector).
1033  * Ex: ceil( 1.1) = 2.0
1034  * Ex: ceil(-1.1) = -1.0
1035  */
1036 LLVMValueRef
1037 lp_build_ceil(struct lp_build_context *bld,
1038               LLVMValueRef a)
1039 {
1040    const struct lp_type type = bld->type;
1041
1042    assert(type.floating);
1043    assert(lp_check_value(type, a));
1044
1045    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1046       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1047    else {
1048       LLVMTypeRef vec_type = lp_build_vec_type(type);
1049       LLVMValueRef res;
1050       res = lp_build_iceil(bld, a);
1051       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1052       return res;
1053    }
1054 }
1055
1056
1057 /**
1058  * Return fractional part of 'a' computed as a - floor(a)
1059  * Typically used in texture coord arithmetic.
1060  */
1061 LLVMValueRef
1062 lp_build_fract(struct lp_build_context *bld,
1063                LLVMValueRef a)
1064 {
1065    assert(bld->type.floating);
1066    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1067 }
1068
1069
1070 /**
1071  * Return the integer part of a float (vector) value.  The returned value is
1072  * an integer (vector).
1073  * Ex: itrunc(-1.5) = 1
1074  */
1075 LLVMValueRef
1076 lp_build_itrunc(struct lp_build_context *bld,
1077                 LLVMValueRef a)
1078 {
1079    const struct lp_type type = bld->type;
1080    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1081
1082    assert(type.floating);
1083    assert(lp_check_value(type, a));
1084
1085    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1086 }
1087
1088
1089 /**
1090  * Return float (vector) rounded to nearest integer (vector).  The returned
1091  * value is an integer (vector).
1092  * Ex: iround(0.9) = 1
1093  * Ex: iround(-1.5) = -2
1094  */
1095 LLVMValueRef
1096 lp_build_iround(struct lp_build_context *bld,
1097                 LLVMValueRef a)
1098 {
1099    const struct lp_type type = bld->type;
1100    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1101    LLVMValueRef res;
1102
1103    assert(type.floating);
1104
1105    assert(lp_check_value(type, a));
1106
1107    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1108       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1109    }
1110    else {
1111       LLVMTypeRef vec_type = lp_build_vec_type(type);
1112       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1113       LLVMValueRef sign;
1114       LLVMValueRef half;
1115
1116       /* get sign bit */
1117       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1118       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1119
1120       /* sign * 0.5 */
1121       half = lp_build_const_vec(type, 0.5);
1122       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1123       half = LLVMBuildOr(bld->builder, sign, half, "");
1124       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1125
1126       res = LLVMBuildFAdd(bld->builder, a, half, "");
1127    }
1128
1129    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1130
1131    return res;
1132 }
1133
1134
1135 /**
1136  * Return floor of float (vector), result is an int (vector)
1137  * Ex: ifloor(1.1) = 1.0
1138  * Ex: ifloor(-1.1) = -2.0
1139  */
1140 LLVMValueRef
1141 lp_build_ifloor(struct lp_build_context *bld,
1142                 LLVMValueRef a)
1143 {
1144    const struct lp_type type = bld->type;
1145    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1146    LLVMValueRef res;
1147
1148    assert(type.floating);
1149    assert(lp_check_value(type, a));
1150
1151    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1152       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1153    }
1154    else {
1155       /* Take the sign bit and add it to 1 constant */
1156       LLVMTypeRef vec_type = lp_build_vec_type(type);
1157       unsigned mantissa = lp_mantissa(type);
1158       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1159       LLVMValueRef sign;
1160       LLVMValueRef offset;
1161
1162       /* sign = a < 0 ? ~0 : 0 */
1163       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1164       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1165       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1166
1167       /* offset = -0.99999(9)f */
1168       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1169       offset = LLVMConstBitCast(offset, int_vec_type);
1170
1171       /* offset = a < 0 ? offset : 0.0f */
1172       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1173       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1174
1175       res = LLVMBuildFAdd(bld->builder, a, offset, "ifloor.res");
1176    }
1177
1178    /* round to nearest (toward zero) */
1179    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1180
1181    return res;
1182 }
1183
1184
1185 /**
1186  * Return ceiling of float (vector), returning int (vector).
1187  * Ex: iceil( 1.1) = 2
1188  * Ex: iceil(-1.1) = -1
1189  */
1190 LLVMValueRef
1191 lp_build_iceil(struct lp_build_context *bld,
1192                LLVMValueRef a)
1193 {
1194    const struct lp_type type = bld->type;
1195    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1196    LLVMValueRef res;
1197
1198    assert(type.floating);
1199    assert(lp_check_value(type, a));
1200
1201    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1202       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1203    }
1204    else {
1205       LLVMTypeRef vec_type = lp_build_vec_type(type);
1206       unsigned mantissa = lp_mantissa(type);
1207       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1208       LLVMValueRef sign;
1209       LLVMValueRef offset;
1210
1211       /* sign = a < 0 ? 0 : ~0 */
1212       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1213       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1214       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1215       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1216
1217       /* offset = 0.99999(9)f */
1218       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1219       offset = LLVMConstBitCast(offset, int_vec_type);
1220
1221       /* offset = a < 0 ? 0.0 : offset */
1222       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1223       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1224
1225       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1226    }
1227
1228    /* round to nearest (toward zero) */
1229    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1230
1231    return res;
1232 }
1233
1234
1235 LLVMValueRef
1236 lp_build_sqrt(struct lp_build_context *bld,
1237               LLVMValueRef a)
1238 {
1239    const struct lp_type type = bld->type;
1240    LLVMTypeRef vec_type = lp_build_vec_type(type);
1241    char intrinsic[32];
1242
1243    assert(lp_check_value(type, a));
1244
1245    /* TODO: optimize the constant case */
1246    /* TODO: optimize the constant case */
1247
1248    assert(type.floating);
1249    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1250
1251    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1252 }
1253
1254
1255 /**
1256  * Do one Newton-Raphson step to improve reciprocate precision:
1257  *
1258  *   x_{i+1} = x_i * (2 - a * x_i)
1259  *
1260  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
1261  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
1262  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
1263  * halo. It would be necessary to clamp the argument to prevent this.
1264  *
1265  * See also:
1266  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
1267  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1268  */
1269 static INLINE LLVMValueRef
1270 lp_build_rcp_refine(struct lp_build_context *bld,
1271                     LLVMValueRef a,
1272                     LLVMValueRef rcp_a)
1273 {
1274    LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1275    LLVMValueRef res;
1276
1277    res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1278    res = LLVMBuildFSub(bld->builder, two, res, "");
1279    res = LLVMBuildFMul(bld->builder, rcp_a, res, "");
1280
1281    return res;
1282 }
1283
1284
1285 LLVMValueRef
1286 lp_build_rcp(struct lp_build_context *bld,
1287              LLVMValueRef a)
1288 {
1289    const struct lp_type type = bld->type;
1290
1291    assert(lp_check_value(type, a));
1292
1293    if(a == bld->zero)
1294       return bld->undef;
1295    if(a == bld->one)
1296       return bld->one;
1297    if(a == bld->undef)
1298       return bld->undef;
1299
1300    assert(type.floating);
1301
1302    if(LLVMIsConstant(a))
1303       return LLVMConstFDiv(bld->one, a);
1304
1305    /*
1306     * We don't use RCPPS because:
1307     * - it only has 10bits of precision
1308     * - it doesn't even get the reciprocate of 1.0 exactly
1309     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
1310     * - for recent processors the benefit over DIVPS is marginal, a case
1311     *   depedent
1312     *
1313     * We could still use it on certain processors if benchmarks show that the
1314     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
1315     * particular uses that require less workarounds.
1316     */
1317
1318    if (FALSE && util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1319       const unsigned num_iterations = 0;
1320       LLVMValueRef res;
1321       unsigned i;
1322
1323       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", bld->vec_type, a);
1324
1325       for (i = 0; i < num_iterations; ++i) {
1326          res = lp_build_rcp_refine(bld, a, res);
1327       }
1328
1329       return res;
1330    }
1331
1332    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1333 }
1334
1335
1336 /**
1337  * Do one Newton-Raphson step to improve rsqrt precision:
1338  *
1339  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
1340  *
1341  * See also:
1342  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1343  */
1344 static INLINE LLVMValueRef
1345 lp_build_rsqrt_refine(struct lp_build_context *bld,
1346                       LLVMValueRef a,
1347                       LLVMValueRef rsqrt_a)
1348 {
1349    LLVMValueRef half = lp_build_const_vec(bld->type, 0.5);
1350    LLVMValueRef three = lp_build_const_vec(bld->type, 3.0);
1351    LLVMValueRef res;
1352
1353    res = LLVMBuildFMul(bld->builder, rsqrt_a, rsqrt_a, "");
1354    res = LLVMBuildFMul(bld->builder, a, res, "");
1355    res = LLVMBuildFSub(bld->builder, three, res, "");
1356    res = LLVMBuildFMul(bld->builder, rsqrt_a, res, "");
1357    res = LLVMBuildFMul(bld->builder, half, res, "");
1358
1359    return res;
1360 }
1361
1362
1363 /**
1364  * Generate 1/sqrt(a)
1365  */
1366 LLVMValueRef
1367 lp_build_rsqrt(struct lp_build_context *bld,
1368                LLVMValueRef a)
1369 {
1370    const struct lp_type type = bld->type;
1371
1372    assert(lp_check_value(type, a));
1373
1374    assert(type.floating);
1375
1376    if (util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1377       const unsigned num_iterations = 0;
1378       LLVMValueRef res;
1379       unsigned i;
1380
1381       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", bld->vec_type, a);
1382
1383       for (i = 0; i < num_iterations; ++i) {
1384          res = lp_build_rsqrt_refine(bld, a, res);
1385       }
1386
1387       return res;
1388    }
1389
1390    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1391 }
1392
1393
1394 static inline LLVMValueRef
1395 lp_build_const_v4si(unsigned long value)
1396 {
1397    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1398    LLVMValueRef elements[4] = { element, element, element, element };
1399    return LLVMConstVector(elements, 4);
1400 }
1401
1402 static inline LLVMValueRef
1403 lp_build_const_v4sf(float value)
1404 {
1405    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1406    LLVMValueRef elements[4] = { element, element, element, element };
1407    return LLVMConstVector(elements, 4);
1408 }
1409
1410
1411 /**
1412  * Generate sin(a) using SSE2
1413  */
1414 LLVMValueRef
1415 lp_build_sin(struct lp_build_context *bld,
1416              LLVMValueRef a)
1417 {
1418    struct lp_type int_type = lp_int_type(bld->type);
1419    LLVMBuilderRef b = bld->builder;
1420    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1421    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1422
1423    /*
1424     *  take the absolute value,
1425     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1426     */
1427
1428    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1429    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1430
1431    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1432    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1433
1434    /*
1435     * extract the sign bit (upper one)
1436     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1437     */
1438    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1439    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1440
1441    /*
1442     * scale by 4/Pi
1443     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1444     */
1445
1446    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1447    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1448
1449    /*
1450     * store the integer part of y in mm0
1451     * emm2 = _mm_cvttps_epi32(y);
1452     */
1453
1454    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1455
1456    /*
1457     * j=(j+1) & (~1) (see the cephes sources)
1458     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1459     */
1460
1461    LLVMValueRef all_one = lp_build_const_v4si(1);
1462    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1463    /*
1464     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1465     */
1466    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1467    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1468
1469    /*
1470     * y = _mm_cvtepi32_ps(emm2);
1471     */
1472    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1473
1474    /* get the swap sign flag
1475     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1476     */
1477    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1478    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1479
1480    /*
1481     * emm2 = _mm_slli_epi32(emm0, 29);
1482     */
1483    LLVMValueRef const_29 = lp_build_const_v4si(29);
1484    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1485
1486    /*
1487     * get the polynom selection mask
1488     * there is one polynom for 0 <= x <= Pi/4
1489     * and another one for Pi/4<x<=Pi/2
1490     * Both branches will be computed.
1491     *
1492     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1493     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1494     */
1495
1496    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1497    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1498    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1499                                              emm2_3, lp_build_const_v4si(0));
1500    /*
1501     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1502     */
1503    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1504
1505    /*
1506     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1507     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1508     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1509     */
1510    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1511    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1512    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1513
1514    /*
1515     * The magic pass: "Extended precision modular arithmetic"
1516     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1517     * xmm1 = _mm_mul_ps(y, xmm1);
1518     * xmm2 = _mm_mul_ps(y, xmm2);
1519     * xmm3 = _mm_mul_ps(y, xmm3);
1520     */
1521    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1522    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1523    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1524
1525    /*
1526     * x = _mm_add_ps(x, xmm1);
1527     * x = _mm_add_ps(x, xmm2);
1528     * x = _mm_add_ps(x, xmm3);
1529     */
1530
1531    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1532    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1533    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1534
1535    /*
1536     * Evaluate the first polynom  (0 <= x <= Pi/4)
1537     *
1538     * z = _mm_mul_ps(x,x);
1539     */
1540    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1541
1542    /*
1543     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1544     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1545     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1546     */
1547    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1548    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1549    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1550
1551    /*
1552     * y = *(v4sf*)_ps_coscof_p0;
1553     * y = _mm_mul_ps(y, z);
1554     */
1555    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1556    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1557    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1558    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1559    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1560    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1561
1562
1563    /*
1564     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1565     * y = _mm_sub_ps(y, tmp);
1566     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1567     */
1568    LLVMValueRef half = lp_build_const_v4sf(0.5);
1569    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1570    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1571    LLVMValueRef one = lp_build_const_v4sf(1.0);
1572    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1573
1574    /*
1575     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1576     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1577     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1578     */
1579    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1580    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1581    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1582
1583    /*
1584     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1585     *
1586     * y2 = *(v4sf*)_ps_sincof_p0;
1587     * y2 = _mm_mul_ps(y2, z);
1588     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1589     * y2 = _mm_mul_ps(y2, z);
1590     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1591     * y2 = _mm_mul_ps(y2, z);
1592     * y2 = _mm_mul_ps(y2, x);
1593     * y2 = _mm_add_ps(y2, x);
1594     */
1595
1596    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1597    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1598    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1599    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1600    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1601    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1602    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1603
1604    /*
1605     * select the correct result from the two polynoms
1606     * xmm3 = poly_mask;
1607     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1608     * y = _mm_andnot_ps(xmm3, y);
1609     * y = _mm_add_ps(y,y2);
1610     */
1611    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1612    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1613    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1614    LLVMValueRef inv = lp_build_const_v4si(~0);
1615    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1616    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1617    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1618
1619    /*
1620     * update the sign
1621     * y = _mm_xor_ps(y, sign_bit);
1622     */
1623    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1624    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1625    return y_result;
1626 }
1627
1628
1629 /**
1630  * Generate cos(a) using SSE2
1631  */
1632 LLVMValueRef
1633 lp_build_cos(struct lp_build_context *bld,
1634              LLVMValueRef a)
1635 {
1636    struct lp_type int_type = lp_int_type(bld->type);
1637    LLVMBuilderRef b = bld->builder;
1638    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1639    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1640
1641    /*
1642     *  take the absolute value,
1643     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1644     */
1645
1646    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1647    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1648
1649    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1650    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1651
1652    /*
1653     * scale by 4/Pi
1654     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1655     */
1656
1657    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1658    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1659
1660    /*
1661     * store the integer part of y in mm0
1662     * emm2 = _mm_cvttps_epi32(y);
1663     */
1664
1665    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1666
1667    /*
1668     * j=(j+1) & (~1) (see the cephes sources)
1669     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1670     */
1671
1672    LLVMValueRef all_one = lp_build_const_v4si(1);
1673    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1674    /*
1675     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1676     */
1677    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1678    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1679
1680    /*
1681     * y = _mm_cvtepi32_ps(emm2);
1682     */
1683    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1684
1685
1686    /*
1687     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1688     */
1689    LLVMValueRef const_2 = lp_build_const_v4si(2);
1690    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1691
1692
1693    /* get the swap sign flag
1694     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1695     */
1696    LLVMValueRef inv = lp_build_const_v4si(~0);
1697    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1698    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1699    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1700
1701    /*
1702     * emm2 = _mm_slli_epi32(emm0, 29);
1703     */
1704    LLVMValueRef const_29 = lp_build_const_v4si(29);
1705    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1706
1707    /*
1708     * get the polynom selection mask
1709     * there is one polynom for 0 <= x <= Pi/4
1710     * and another one for Pi/4<x<=Pi/2
1711     * Both branches will be computed.
1712     *
1713     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1714     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1715     */
1716
1717    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1718    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1719    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1720                                              emm2_3, lp_build_const_v4si(0));
1721
1722    /*
1723     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1724     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1725     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1726     */
1727    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1728    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1729    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1730
1731    /*
1732     * The magic pass: "Extended precision modular arithmetic"
1733     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1734     * xmm1 = _mm_mul_ps(y, xmm1);
1735     * xmm2 = _mm_mul_ps(y, xmm2);
1736     * xmm3 = _mm_mul_ps(y, xmm3);
1737     */
1738    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1739    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1740    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1741
1742    /*
1743     * x = _mm_add_ps(x, xmm1);
1744     * x = _mm_add_ps(x, xmm2);
1745     * x = _mm_add_ps(x, xmm3);
1746     */
1747
1748    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1749    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1750    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1751
1752    /*
1753     * Evaluate the first polynom  (0 <= x <= Pi/4)
1754     *
1755     * z = _mm_mul_ps(x,x);
1756     */
1757    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1758
1759    /*
1760     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1761     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1762     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1763     */
1764    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1765    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1766    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1767
1768    /*
1769     * y = *(v4sf*)_ps_coscof_p0;
1770     * y = _mm_mul_ps(y, z);
1771     */
1772    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1773    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1774    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1775    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1776    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1777    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1778
1779
1780    /*
1781     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1782     * y = _mm_sub_ps(y, tmp);
1783     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1784     */
1785    LLVMValueRef half = lp_build_const_v4sf(0.5);
1786    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1787    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1788    LLVMValueRef one = lp_build_const_v4sf(1.0);
1789    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1790
1791    /*
1792     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1793     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1794     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1795     */
1796    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1797    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1798    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1799
1800    /*
1801     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1802     *
1803     * y2 = *(v4sf*)_ps_sincof_p0;
1804     * y2 = _mm_mul_ps(y2, z);
1805     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1806     * y2 = _mm_mul_ps(y2, z);
1807     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1808     * y2 = _mm_mul_ps(y2, z);
1809     * y2 = _mm_mul_ps(y2, x);
1810     * y2 = _mm_add_ps(y2, x);
1811     */
1812
1813    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1814    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1815    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1816    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1817    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1818    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1819    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1820
1821    /*
1822     * select the correct result from the two polynoms
1823     * xmm3 = poly_mask;
1824     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1825     * y = _mm_andnot_ps(xmm3, y);
1826     * y = _mm_add_ps(y,y2);
1827     */
1828    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1829    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1830    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1831    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1832    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1833    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1834
1835    /*
1836     * update the sign
1837     * y = _mm_xor_ps(y, sign_bit);
1838     */
1839    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1840    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1841    return y_result;
1842 }
1843
1844
1845 /**
1846  * Generate pow(x, y)
1847  */
1848 LLVMValueRef
1849 lp_build_pow(struct lp_build_context *bld,
1850              LLVMValueRef x,
1851              LLVMValueRef y)
1852 {
1853    /* TODO: optimize the constant case */
1854    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
1855        LLVMIsConstant(x) && LLVMIsConstant(y)) {
1856       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1857                    __FUNCTION__);
1858    }
1859
1860    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1861 }
1862
1863
1864 /**
1865  * Generate exp(x)
1866  */
1867 LLVMValueRef
1868 lp_build_exp(struct lp_build_context *bld,
1869              LLVMValueRef x)
1870 {
1871    /* log2(e) = 1/log(2) */
1872    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1873
1874    assert(lp_check_value(bld->type, x));
1875
1876    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1877 }
1878
1879
1880 /**
1881  * Generate log(x)
1882  */
1883 LLVMValueRef
1884 lp_build_log(struct lp_build_context *bld,
1885              LLVMValueRef x)
1886 {
1887    /* log(2) */
1888    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1889
1890    assert(lp_check_value(bld->type, x));
1891
1892    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1893 }
1894
1895
1896 /**
1897  * Generate polynomial.
1898  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1899  */
1900 static LLVMValueRef
1901 lp_build_polynomial(struct lp_build_context *bld,
1902                     LLVMValueRef x,
1903                     const double *coeffs,
1904                     unsigned num_coeffs)
1905 {
1906    const struct lp_type type = bld->type;
1907    LLVMValueRef res = NULL;
1908    unsigned i;
1909
1910    assert(lp_check_value(bld->type, x));
1911
1912    /* TODO: optimize the constant case */
1913    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
1914        LLVMIsConstant(x)) {
1915       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1916                    __FUNCTION__);
1917    }
1918
1919    for (i = num_coeffs; i--; ) {
1920       LLVMValueRef coeff;
1921
1922       coeff = lp_build_const_vec(type, coeffs[i]);
1923
1924       if(res)
1925          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1926       else
1927          res = coeff;
1928    }
1929
1930    if(res)
1931       return res;
1932    else
1933       return bld->undef;
1934 }
1935
1936
1937 /**
1938  * Minimax polynomial fit of 2**x, in range [0, 1[
1939  */
1940 const double lp_build_exp2_polynomial[] = {
1941 #if EXP_POLY_DEGREE == 5
1942    0.999999999690134838155,
1943    0.583974334321735217258,
1944    0.164553105719676828492,
1945    0.0292811063701710962255,
1946    0.00354944426657875141846,
1947    0.000296253726543423377365
1948 #elif EXP_POLY_DEGREE == 4
1949    1.00000001502262084505,
1950    0.563586057338685991394,
1951    0.150436017652442413623,
1952    0.0243220604213317927308,
1953    0.0025359088446580436489
1954 #elif EXP_POLY_DEGREE == 3
1955    0.999925218562710312959,
1956    0.695833540494823811697,
1957    0.226067155427249155588,
1958    0.0780245226406372992967
1959 #elif EXP_POLY_DEGREE == 2
1960    1.00172476321474503578,
1961    0.657636275736077639316,
1962    0.33718943461968720704
1963 #else
1964 #error
1965 #endif
1966 };
1967
1968
1969 void
1970 lp_build_exp2_approx(struct lp_build_context *bld,
1971                      LLVMValueRef x,
1972                      LLVMValueRef *p_exp2_int_part,
1973                      LLVMValueRef *p_frac_part,
1974                      LLVMValueRef *p_exp2)
1975 {
1976    const struct lp_type type = bld->type;
1977    LLVMTypeRef vec_type = lp_build_vec_type(type);
1978    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1979    LLVMValueRef ipart = NULL;
1980    LLVMValueRef fpart = NULL;
1981    LLVMValueRef expipart = NULL;
1982    LLVMValueRef expfpart = NULL;
1983    LLVMValueRef res = NULL;
1984
1985    assert(lp_check_value(bld->type, x));
1986
1987    if(p_exp2_int_part || p_frac_part || p_exp2) {
1988       /* TODO: optimize the constant case */
1989       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
1990           LLVMIsConstant(x)) {
1991          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1992                       __FUNCTION__);
1993       }
1994
1995       assert(type.floating && type.width == 32);
1996
1997       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
1998       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
1999
2000       /* ipart = floor(x) */
2001       ipart = lp_build_floor(bld, x);
2002
2003       /* fpart = x - ipart */
2004       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
2005    }
2006
2007    if(p_exp2_int_part || p_exp2) {
2008       /* expipart = (float) (1 << ipart) */
2009       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
2010       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
2011       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
2012       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
2013    }
2014
2015    if(p_exp2) {
2016       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
2017                                      Elements(lp_build_exp2_polynomial));
2018
2019       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
2020    }
2021
2022    if(p_exp2_int_part)
2023       *p_exp2_int_part = expipart;
2024
2025    if(p_frac_part)
2026       *p_frac_part = fpart;
2027
2028    if(p_exp2)
2029       *p_exp2 = res;
2030 }
2031
2032
2033 LLVMValueRef
2034 lp_build_exp2(struct lp_build_context *bld,
2035               LLVMValueRef x)
2036 {
2037    LLVMValueRef res;
2038    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
2039    return res;
2040 }
2041
2042
2043 /**
2044  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
2045  * These coefficients can be generate with
2046  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2047  */
2048 const double lp_build_log2_polynomial[] = {
2049 #if LOG_POLY_DEGREE == 6
2050    3.11578814719469302614,
2051    -3.32419399085241980044,
2052    2.59883907202499966007,
2053    -1.23152682416275988241,
2054    0.318212422185251071475,
2055    -0.0344359067839062357313
2056 #elif LOG_POLY_DEGREE == 5
2057    2.8882704548164776201,
2058    -2.52074962577807006663,
2059    1.48116647521213171641,
2060    -0.465725644288844778798,
2061    0.0596515482674574969533
2062 #elif LOG_POLY_DEGREE == 4
2063    2.61761038894603480148,
2064    -1.75647175389045657003,
2065    0.688243882994381274313,
2066    -0.107254423828329604454
2067 #elif LOG_POLY_DEGREE == 3
2068    2.28330284476918490682,
2069    -1.04913055217340124191,
2070    0.204446009836232697516
2071 #else
2072 #error
2073 #endif
2074 };
2075
2076
2077 /**
2078  * See http://www.devmaster.net/forums/showthread.php?p=43580
2079  */
2080 void
2081 lp_build_log2_approx(struct lp_build_context *bld,
2082                      LLVMValueRef x,
2083                      LLVMValueRef *p_exp,
2084                      LLVMValueRef *p_floor_log2,
2085                      LLVMValueRef *p_log2)
2086 {
2087    const struct lp_type type = bld->type;
2088    LLVMTypeRef vec_type = lp_build_vec_type(type);
2089    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2090
2091    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2092    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2093    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2094
2095    LLVMValueRef i = NULL;
2096    LLVMValueRef exp = NULL;
2097    LLVMValueRef mant = NULL;
2098    LLVMValueRef logexp = NULL;
2099    LLVMValueRef logmant = NULL;
2100    LLVMValueRef res = NULL;
2101
2102    assert(lp_check_value(bld->type, x));
2103
2104    if(p_exp || p_floor_log2 || p_log2) {
2105       /* TODO: optimize the constant case */
2106       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2107           LLVMIsConstant(x)) {
2108          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2109                       __FUNCTION__);
2110       }
2111
2112       assert(type.floating && type.width == 32);
2113
2114       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2115
2116       /* exp = (float) exponent(x) */
2117       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2118    }
2119
2120    if(p_floor_log2 || p_log2) {
2121       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2122       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2123       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2124    }
2125
2126    if(p_log2) {
2127       /* mant = (float) mantissa(x) */
2128       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2129       mant = LLVMBuildOr(bld->builder, mant, one, "");
2130       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2131
2132       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2133                                     Elements(lp_build_log2_polynomial));
2134
2135       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2136       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2137
2138       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2139    }
2140
2141    if(p_exp) {
2142       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2143       *p_exp = exp;
2144    }
2145
2146    if(p_floor_log2)
2147       *p_floor_log2 = logexp;
2148
2149    if(p_log2)
2150       *p_log2 = res;
2151 }
2152
2153
2154 LLVMValueRef
2155 lp_build_log2(struct lp_build_context *bld,
2156               LLVMValueRef x)
2157 {
2158    LLVMValueRef res;
2159    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2160    return res;
2161 }