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 -- without any checks.
 618  *
 619  * @sa http://www.stereopsis.com/doubleblend.html
 620  */
 621 static INLINE LLVMValueRef
 622 lp_build_lerp_simple(struct lp_build_context *bld,
 623                      LLVMValueRef x,
 624                      LLVMValueRef v0,
 625                      LLVMValueRef v1)
 626 {
 627    LLVMValueRef delta;
 628    LLVMValueRef res;
 629
 630    assert(lp_check_value(bld->type, x));
 631    assert(lp_check_value(bld->type, v0));
 632    assert(lp_check_value(bld->type, v1));
 633
 634    delta = lp_build_sub(bld, v1, v0);
 635
 636    res = lp_build_mul(bld, x, delta);
 637
 638    res = lp_build_add(bld, v0, res);
 639
 640    if (bld->type.fixed) {
 641       /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
 642        * but it will be wrong for other uses. Basically we need a more
 643        * powerful lp_type, capable of further distinguishing the values
 644        * interpretation from the value storage. */
 645       res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
 646    }
 647
 648    return res;
 649 }
 650
 651
 652 /**
 653  * Linear interpolation.
 654  */
 655 LLVMValueRef
 656 lp_build_lerp(struct lp_build_context *bld,
 657               LLVMValueRef x,
 658               LLVMValueRef v0,
 659               LLVMValueRef v1)
 660 {
 661    const struct lp_type type = bld->type;
 662    LLVMValueRef res;
 663
 664    assert(lp_check_value(type, x));
 665    assert(lp_check_value(type, v0));
 666    assert(lp_check_value(type, v1));
 667
 668    if (type.norm) {
 669       struct lp_type wide_type;
 670       struct lp_build_context wide_bld;
 671       LLVMValueRef xl, xh, v0l, v0h, v1l, v1h, resl, resh;
 672       LLVMValueRef shift;
 673
 674       assert(type.length >= 2);
 675       assert(!type.sign);
 676
 677       /*
 678        * Create a wider type, enough to hold the intermediate result of the
 679        * multiplication.
 680        */
 681       memset(&wide_type, 0, sizeof wide_type);
 682       wide_type.fixed  = TRUE;
 683       wide_type.width  = type.width*2;
 684       wide_type.length = type.length/2;
 685
 686       lp_build_context_init(&wide_bld, bld->builder, wide_type);
 687
 688       lp_build_unpack2(bld->builder, type, wide_type, x,  &xl,  &xh);
 689       lp_build_unpack2(bld->builder, type, wide_type, v0, &v0l, &v0h);
 690       lp_build_unpack2(bld->builder, type, wide_type, v1, &v1l, &v1h);
 691
 692       /*
 693        * Scale x from [0, 255] to [0, 256]
 694        */
 695
 696       shift = lp_build_const_int_vec(wide_type, type.width - 1);
 697
 698       xl = lp_build_add(&wide_bld, xl,
 699                         LLVMBuildAShr(bld->builder, xl, shift, ""));
 700       xh = lp_build_add(&wide_bld, xh,
 701                         LLVMBuildAShr(bld->builder, xh, shift, ""));
 702
 703       /*
 704        * Lerp both halves.
 705        */
 706
 707       resl = lp_build_lerp_simple(&wide_bld, xl, v0l, v1l);
 708       resh = lp_build_lerp_simple(&wide_bld, xh, v0h, v1h);
 709
 710       res = lp_build_pack2(bld->builder, wide_type, type, resl, resh);
 711    } else {
 712       res = lp_build_lerp_simple(bld, x, v0, v1);
 713    }
 714
 715    return res;
 716 }
 717
 718
 719 LLVMValueRef
 720 lp_build_lerp_2d(struct lp_build_context *bld,
 721                  LLVMValueRef x,
 722                  LLVMValueRef y,
 723                  LLVMValueRef v00,
 724                  LLVMValueRef v01,
 725                  LLVMValueRef v10,
 726                  LLVMValueRef v11)
 727 {
 728    LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
 729    LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
 730    return lp_build_lerp(bld, y, v0, v1);
 731 }
 732
 733
 734 /**
 735  * Generate min(a, b)
 736  * Do checks for special cases.
 737  */
 738 LLVMValueRef
 739 lp_build_min(struct lp_build_context *bld,
 740              LLVMValueRef a,
 741              LLVMValueRef b)
 742 {
 743    assert(lp_check_value(bld->type, a));
 744    assert(lp_check_value(bld->type, b));
 745
 746    if(a == bld->undef || b == bld->undef)
 747       return bld->undef;
 748
 749    if(a == b)
 750       return a;
 751
 752    if(bld->type.norm) {
 753       if(a == bld->zero || b == bld->zero)
 754          return bld->zero;
 755       if(a == bld->one)
 756          return b;
 757       if(b == bld->one)
 758          return a;
 759    }
 760
 761    return lp_build_min_simple(bld, a, b);
 762 }
 763
 764
 765 /**
 766  * Generate max(a, b)
 767  * Do checks for special cases.
 768  */
 769 LLVMValueRef
 770 lp_build_max(struct lp_build_context *bld,
 771              LLVMValueRef a,
 772              LLVMValueRef b)
 773 {
 774    assert(lp_check_value(bld->type, a));
 775    assert(lp_check_value(bld->type, b));
 776
 777    if(a == bld->undef || b == bld->undef)
 778       return bld->undef;
 779
 780    if(a == b)
 781       return a;
 782
 783    if(bld->type.norm) {
 784       if(a == bld->one || b == bld->one)
 785          return bld->one;
 786       if(a == bld->zero)
 787          return b;
 788       if(b == bld->zero)
 789          return a;
 790    }
 791
 792    return lp_build_max_simple(bld, a, b);
 793 }
 794
 795
 796 /**
 797  * Generate clamp(a, min, max)
 798  * Do checks for special cases.
 799  */
 800 LLVMValueRef
 801 lp_build_clamp(struct lp_build_context *bld,
 802                LLVMValueRef a,
 803                LLVMValueRef min,
 804                LLVMValueRef max)
 805 {
 806    assert(lp_check_value(bld->type, a));
 807    assert(lp_check_value(bld->type, min));
 808    assert(lp_check_value(bld->type, max));
 809
 810    a = lp_build_min(bld, a, max);
 811    a = lp_build_max(bld, a, min);
 812    return a;
 813 }
 814
 815
 816 /**
 817  * Generate abs(a)
 818  */
 819 LLVMValueRef
 820 lp_build_abs(struct lp_build_context *bld,
 821              LLVMValueRef a)
 822 {
 823    const struct lp_type type = bld->type;
 824    LLVMTypeRef vec_type = lp_build_vec_type(type);
 825
 826    assert(lp_check_value(type, a));
 827
 828    if(!type.sign)
 829       return a;
 830
 831    if(type.floating) {
 832       /* Mask out the sign bit */
 833       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 834       unsigned long long absMask = ~(1ULL << (type.width - 1));
 835       LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
 836       a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 837       a = LLVMBuildAnd(bld->builder, a, mask, "");
 838       a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
 839       return a;
 840    }
 841
 842    if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
 843       switch(type.width) {
 844       case 8:
 845          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
 846       case 16:
 847          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
 848       case 32:
 849          return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
 850       }
 851    }
 852
 853    return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
 854 }
 855
 856
 857 LLVMValueRef
 858 lp_build_negate(struct lp_build_context *bld,
 859                 LLVMValueRef a)
 860 {
 861    assert(lp_check_value(bld->type, a));
 862
 863 #if HAVE_LLVM >= 0x0207
 864    if (bld->type.floating)
 865       a = LLVMBuildFNeg(bld->builder, a, "");
 866    else
 867 #endif
 868       a = LLVMBuildNeg(bld->builder, a, "");
 869
 870    return a;
 871 }
 872
 873
 874 /** Return -1, 0 or +1 depending on the sign of a */
 875 LLVMValueRef
 876 lp_build_sgn(struct lp_build_context *bld,
 877              LLVMValueRef a)
 878 {
 879    const struct lp_type type = bld->type;
 880    LLVMValueRef cond;
 881    LLVMValueRef res;
 882
 883    assert(lp_check_value(type, a));
 884
 885    /* Handle non-zero case */
 886    if(!type.sign) {
 887       /* if not zero then sign must be positive */
 888       res = bld->one;
 889    }
 890    else if(type.floating) {
 891       LLVMTypeRef vec_type;
 892       LLVMTypeRef int_type;
 893       LLVMValueRef mask;
 894       LLVMValueRef sign;
 895       LLVMValueRef one;
 896       unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
 897
 898       int_type = lp_build_int_vec_type(type);
 899       vec_type = lp_build_vec_type(type);
 900       mask = lp_build_const_int_vec(type, maskBit);
 901
 902       /* Take the sign bit and add it to 1 constant */
 903       sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
 904       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
 905       one = LLVMConstBitCast(bld->one, int_type);
 906       res = LLVMBuildOr(bld->builder, sign, one, "");
 907       res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 908    }
 909    else
 910    {
 911       LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
 912       cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
 913       res = lp_build_select(bld, cond, bld->one, minus_one);
 914    }
 915
 916    /* Handle zero */
 917    cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
 918    res = lp_build_select(bld, cond, bld->zero, res);
 919
 920    return res;
 921 }
 922
 923
 924 /**
 925  * Set the sign of float vector 'a' according to 'sign'.
 926  * If sign==0, return abs(a).
 927  * If sign==1, return -abs(a);
 928  * Other values for sign produce undefined results.
 929  */
 930 LLVMValueRef
 931 lp_build_set_sign(struct lp_build_context *bld,
 932                   LLVMValueRef a, LLVMValueRef sign)
 933 {
 934    const struct lp_type type = bld->type;
 935    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
 936    LLVMTypeRef vec_type = lp_build_vec_type(type);
 937    LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
 938    LLVMValueRef mask = lp_build_const_int_vec(type,
 939                              ~((unsigned long long) 1 << (type.width - 1)));
 940    LLVMValueRef val, res;
 941
 942    assert(type.floating);
 943    assert(lp_check_value(type, a));
 944
 945    /* val = reinterpret_cast<int>(a) */
 946    val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
 947    /* val = val & mask */
 948    val = LLVMBuildAnd(bld->builder, val, mask, "");
 949    /* sign = sign << shift */
 950    sign = LLVMBuildShl(bld->builder, sign, shift, "");
 951    /* res = val | sign */
 952    res = LLVMBuildOr(bld->builder, val, sign, "");
 953    /* res = reinterpret_cast<float>(res) */
 954    res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
 955
 956    return res;
 957 }
 958
 959
 960 /**
 961  * Convert vector of (or scalar) int to vector of (or scalar) float.
 962  */
 963 LLVMValueRef
 964 lp_build_int_to_float(struct lp_build_context *bld,
 965                       LLVMValueRef a)
 966 {
 967    const struct lp_type type = bld->type;
 968    LLVMTypeRef vec_type = lp_build_vec_type(type);
 969
 970    assert(type.floating);
 971
 972    return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
 973 }
 974
 975
 976
 977 enum lp_build_round_sse41_mode
 978 {
 979    LP_BUILD_ROUND_SSE41_NEAREST = 0,
 980    LP_BUILD_ROUND_SSE41_FLOOR = 1,
 981    LP_BUILD_ROUND_SSE41_CEIL = 2,
 982    LP_BUILD_ROUND_SSE41_TRUNCATE = 3
 983 };
 984
 985
 986 static INLINE LLVMValueRef
 987 lp_build_round_sse41(struct lp_build_context *bld,
 988                      LLVMValueRef a,
 989                      enum lp_build_round_sse41_mode mode)
 990 {
 991    const struct lp_type type = bld->type;
 992    LLVMTypeRef vec_type = lp_build_vec_type(type);
 993    const char *intrinsic;
 994
 995    assert(type.floating);
 996    assert(type.width*type.length == 128);
 997    assert(lp_check_value(type, a));
 998    assert(util_cpu_caps.has_sse4_1);
 999
1000    switch(type.width) {
1001    case 32:
1002       intrinsic = "llvm.x86.sse41.round.ps";
1003       break;
1004    case 64:
1005       intrinsic = "llvm.x86.sse41.round.pd";
1006       break;
1007    default:
1008       assert(0);
1009       return bld->undef;
1010    }
1011
1012    return lp_build_intrinsic_binary(bld->builder, intrinsic, vec_type, a,
1013                                     LLVMConstInt(LLVMInt32Type(), mode, 0));
1014 }
1015
1016
1017 /**
1018  * Return the integer part of a float (vector) value.  The returned value is
1019  * a float (vector).
1020  * Ex: trunc(-1.5) = 1.0
1021  */
1022 LLVMValueRef
1023 lp_build_trunc(struct lp_build_context *bld,
1024                LLVMValueRef a)
1025 {
1026    const struct lp_type type = bld->type;
1027
1028    assert(type.floating);
1029    assert(lp_check_value(type, a));
1030
1031    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1032       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
1033    else {
1034       LLVMTypeRef vec_type = lp_build_vec_type(type);
1035       LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1036       LLVMValueRef res;
1037       res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1038       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1039       return res;
1040    }
1041 }
1042
1043
1044 /**
1045  * Return float (vector) rounded to nearest integer (vector).  The returned
1046  * value is a float (vector).
1047  * Ex: round(0.9) = 1.0
1048  * Ex: round(-1.5) = -2.0
1049  */
1050 LLVMValueRef
1051 lp_build_round(struct lp_build_context *bld,
1052                LLVMValueRef a)
1053 {
1054    const struct lp_type type = bld->type;
1055
1056    assert(type.floating);
1057    assert(lp_check_value(type, a));
1058
1059    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1060       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1061    else {
1062       LLVMTypeRef vec_type = lp_build_vec_type(type);
1063       LLVMValueRef res;
1064       res = lp_build_iround(bld, a);
1065       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1066       return res;
1067    }
1068 }
1069
1070
1071 /**
1072  * Return floor of float (vector), result is a float (vector)
1073  * Ex: floor(1.1) = 1.0
1074  * Ex: floor(-1.1) = -2.0
1075  */
1076 LLVMValueRef
1077 lp_build_floor(struct lp_build_context *bld,
1078                LLVMValueRef a)
1079 {
1080    const struct lp_type type = bld->type;
1081
1082    assert(type.floating);
1083    assert(lp_check_value(type, a));
1084
1085    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1086       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1087    else {
1088       LLVMTypeRef vec_type = lp_build_vec_type(type);
1089       LLVMValueRef res;
1090       res = lp_build_ifloor(bld, a);
1091       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1092       return res;
1093    }
1094 }
1095
1096
1097 /**
1098  * Return ceiling of float (vector), returning float (vector).
1099  * Ex: ceil( 1.1) = 2.0
1100  * Ex: ceil(-1.1) = -1.0
1101  */
1102 LLVMValueRef
1103 lp_build_ceil(struct lp_build_context *bld,
1104               LLVMValueRef a)
1105 {
1106    const struct lp_type type = bld->type;
1107
1108    assert(type.floating);
1109    assert(lp_check_value(type, a));
1110
1111    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128)
1112       return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1113    else {
1114       LLVMTypeRef vec_type = lp_build_vec_type(type);
1115       LLVMValueRef res;
1116       res = lp_build_iceil(bld, a);
1117       res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
1118       return res;
1119    }
1120 }
1121
1122
1123 /**
1124  * Return fractional part of 'a' computed as a - floor(a)
1125  * Typically used in texture coord arithmetic.
1126  */
1127 LLVMValueRef
1128 lp_build_fract(struct lp_build_context *bld,
1129                LLVMValueRef a)
1130 {
1131    assert(bld->type.floating);
1132    return lp_build_sub(bld, a, lp_build_floor(bld, a));
1133 }
1134
1135
1136 /**
1137  * Return the integer part of a float (vector) value.  The returned value is
1138  * an integer (vector).
1139  * Ex: itrunc(-1.5) = 1
1140  */
1141 LLVMValueRef
1142 lp_build_itrunc(struct lp_build_context *bld,
1143                 LLVMValueRef a)
1144 {
1145    const struct lp_type type = bld->type;
1146    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1147
1148    assert(type.floating);
1149    assert(lp_check_value(type, a));
1150
1151    return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
1152 }
1153
1154
1155 /**
1156  * Return float (vector) rounded to nearest integer (vector).  The returned
1157  * value is an integer (vector).
1158  * Ex: iround(0.9) = 1
1159  * Ex: iround(-1.5) = -2
1160  */
1161 LLVMValueRef
1162 lp_build_iround(struct lp_build_context *bld,
1163                 LLVMValueRef a)
1164 {
1165    const struct lp_type type = bld->type;
1166    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1167    LLVMValueRef res;
1168
1169    assert(type.floating);
1170
1171    assert(lp_check_value(type, a));
1172
1173    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1174       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
1175    }
1176    else {
1177       LLVMTypeRef vec_type = lp_build_vec_type(type);
1178       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1179       LLVMValueRef sign;
1180       LLVMValueRef half;
1181
1182       /* get sign bit */
1183       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1184       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1185
1186       /* sign * 0.5 */
1187       half = lp_build_const_vec(type, 0.5);
1188       half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
1189       half = LLVMBuildOr(bld->builder, sign, half, "");
1190       half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
1191
1192       res = LLVMBuildFAdd(bld->builder, a, half, "");
1193    }
1194
1195    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
1196
1197    return res;
1198 }
1199
1200
1201 /**
1202  * Return floor of float (vector), result is an int (vector)
1203  * Ex: ifloor(1.1) = 1.0
1204  * Ex: ifloor(-1.1) = -2.0
1205  */
1206 LLVMValueRef
1207 lp_build_ifloor(struct lp_build_context *bld,
1208                 LLVMValueRef a)
1209 {
1210    const struct lp_type type = bld->type;
1211    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1212    LLVMValueRef res;
1213
1214    assert(type.floating);
1215    assert(lp_check_value(type, a));
1216
1217    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1218       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
1219    }
1220    else {
1221       /* Take the sign bit and add it to 1 constant */
1222       LLVMTypeRef vec_type = lp_build_vec_type(type);
1223       unsigned mantissa = lp_mantissa(type);
1224       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1225       LLVMValueRef sign;
1226       LLVMValueRef offset;
1227
1228       /* sign = a < 0 ? ~0 : 0 */
1229       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1230       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1231       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
1232
1233       /* offset = -0.99999(9)f */
1234       offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1235       offset = LLVMConstBitCast(offset, int_vec_type);
1236
1237       /* offset = a < 0 ? offset : 0.0f */
1238       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1239       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
1240
1241       res = LLVMBuildFAdd(bld->builder, a, offset, "ifloor.res");
1242    }
1243
1244    /* round to nearest (toward zero) */
1245    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
1246
1247    return res;
1248 }
1249
1250
1251 /**
1252  * Return ceiling of float (vector), returning int (vector).
1253  * Ex: iceil( 1.1) = 2
1254  * Ex: iceil(-1.1) = -1
1255  */
1256 LLVMValueRef
1257 lp_build_iceil(struct lp_build_context *bld,
1258                LLVMValueRef a)
1259 {
1260    const struct lp_type type = bld->type;
1261    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
1262    LLVMValueRef res;
1263
1264    assert(type.floating);
1265    assert(lp_check_value(type, a));
1266
1267    if (util_cpu_caps.has_sse4_1 && type.width*type.length == 128) {
1268       res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
1269    }
1270    else {
1271       LLVMTypeRef vec_type = lp_build_vec_type(type);
1272       unsigned mantissa = lp_mantissa(type);
1273       LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
1274       LLVMValueRef sign;
1275       LLVMValueRef offset;
1276
1277       /* sign = a < 0 ? 0 : ~0 */
1278       sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
1279       sign = LLVMBuildAnd(bld->builder, sign, mask, "");
1280       sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
1281       sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
1282
1283       /* offset = 0.99999(9)f */
1284       offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
1285       offset = LLVMConstBitCast(offset, int_vec_type);
1286
1287       /* offset = a < 0 ? 0.0 : offset */
1288       offset = LLVMBuildAnd(bld->builder, offset, sign, "");
1289       offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
1290
1291       res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
1292    }
1293
1294    /* round to nearest (toward zero) */
1295    res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
1296
1297    return res;
1298 }
1299
1300
1301 LLVMValueRef
1302 lp_build_sqrt(struct lp_build_context *bld,
1303               LLVMValueRef a)
1304 {
1305    const struct lp_type type = bld->type;
1306    LLVMTypeRef vec_type = lp_build_vec_type(type);
1307    char intrinsic[32];
1308
1309    assert(lp_check_value(type, a));
1310
1311    /* TODO: optimize the constant case */
1312    /* TODO: optimize the constant case */
1313
1314    assert(type.floating);
1315    util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
1316
1317    return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
1318 }
1319
1320
1321 /**
1322  * Do one Newton-Raphson step to improve reciprocate precision:
1323  *
1324  *   x_{i+1} = x_i * (2 - a * x_i)
1325  *
1326  * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
1327  * +/-Inf, giving NaN instead.  Certain applications rely on this behavior,
1328  * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
1329  * halo. It would be necessary to clamp the argument to prevent this.
1330  *
1331  * See also:
1332  * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
1333  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1334  */
1335 static INLINE LLVMValueRef
1336 lp_build_rcp_refine(struct lp_build_context *bld,
1337                     LLVMValueRef a,
1338                     LLVMValueRef rcp_a)
1339 {
1340    LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
1341    LLVMValueRef res;
1342
1343    res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
1344    res = LLVMBuildFSub(bld->builder, two, res, "");
1345    res = LLVMBuildFMul(bld->builder, rcp_a, res, "");
1346
1347    return res;
1348 }
1349
1350
1351 LLVMValueRef
1352 lp_build_rcp(struct lp_build_context *bld,
1353              LLVMValueRef a)
1354 {
1355    const struct lp_type type = bld->type;
1356
1357    assert(lp_check_value(type, a));
1358
1359    if(a == bld->zero)
1360       return bld->undef;
1361    if(a == bld->one)
1362       return bld->one;
1363    if(a == bld->undef)
1364       return bld->undef;
1365
1366    assert(type.floating);
1367
1368    if(LLVMIsConstant(a))
1369       return LLVMConstFDiv(bld->one, a);
1370
1371    /*
1372     * We don't use RCPPS because:
1373     * - it only has 10bits of precision
1374     * - it doesn't even get the reciprocate of 1.0 exactly
1375     * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
1376     * - for recent processors the benefit over DIVPS is marginal, a case
1377     *   depedent
1378     *
1379     * We could still use it on certain processors if benchmarks show that the
1380     * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
1381     * particular uses that require less workarounds.
1382     */
1383
1384    if (FALSE && util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1385       const unsigned num_iterations = 0;
1386       LLVMValueRef res;
1387       unsigned i;
1388
1389       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", bld->vec_type, a);
1390
1391       for (i = 0; i < num_iterations; ++i) {
1392          res = lp_build_rcp_refine(bld, a, res);
1393       }
1394
1395       return res;
1396    }
1397
1398    return LLVMBuildFDiv(bld->builder, bld->one, a, "");
1399 }
1400
1401
1402 /**
1403  * Do one Newton-Raphson step to improve rsqrt precision:
1404  *
1405  *   x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
1406  *
1407  * See also:
1408  * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1409  */
1410 static INLINE LLVMValueRef
1411 lp_build_rsqrt_refine(struct lp_build_context *bld,
1412                       LLVMValueRef a,
1413                       LLVMValueRef rsqrt_a)
1414 {
1415    LLVMValueRef half = lp_build_const_vec(bld->type, 0.5);
1416    LLVMValueRef three = lp_build_const_vec(bld->type, 3.0);
1417    LLVMValueRef res;
1418
1419    res = LLVMBuildFMul(bld->builder, rsqrt_a, rsqrt_a, "");
1420    res = LLVMBuildFMul(bld->builder, a, res, "");
1421    res = LLVMBuildFSub(bld->builder, three, res, "");
1422    res = LLVMBuildFMul(bld->builder, rsqrt_a, res, "");
1423    res = LLVMBuildFMul(bld->builder, half, res, "");
1424
1425    return res;
1426 }
1427
1428
1429 /**
1430  * Generate 1/sqrt(a)
1431  */
1432 LLVMValueRef
1433 lp_build_rsqrt(struct lp_build_context *bld,
1434                LLVMValueRef a)
1435 {
1436    const struct lp_type type = bld->type;
1437
1438    assert(lp_check_value(type, a));
1439
1440    assert(type.floating);
1441
1442    if (util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
1443       const unsigned num_iterations = 0;
1444       LLVMValueRef res;
1445       unsigned i;
1446
1447       res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", bld->vec_type, a);
1448
1449       for (i = 0; i < num_iterations; ++i) {
1450          res = lp_build_rsqrt_refine(bld, a, res);
1451       }
1452
1453       return res;
1454    }
1455
1456    return lp_build_rcp(bld, lp_build_sqrt(bld, a));
1457 }
1458
1459
1460 static inline LLVMValueRef
1461 lp_build_const_v4si(unsigned long value)
1462 {
1463    LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
1464    LLVMValueRef elements[4] = { element, element, element, element };
1465    return LLVMConstVector(elements, 4);
1466 }
1467
1468 static inline LLVMValueRef
1469 lp_build_const_v4sf(float value)
1470 {
1471    LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
1472    LLVMValueRef elements[4] = { element, element, element, element };
1473    return LLVMConstVector(elements, 4);
1474 }
1475
1476
1477 /**
1478  * Generate sin(a) using SSE2
1479  */
1480 LLVMValueRef
1481 lp_build_sin(struct lp_build_context *bld,
1482              LLVMValueRef a)
1483 {
1484    struct lp_type int_type = lp_int_type(bld->type);
1485    LLVMBuilderRef b = bld->builder;
1486    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1487    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1488
1489    /*
1490     *  take the absolute value,
1491     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1492     */
1493
1494    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1495    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1496
1497    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1498    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1499
1500    /*
1501     * extract the sign bit (upper one)
1502     * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1503     */
1504    LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
1505    LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
1506
1507    /*
1508     * scale by 4/Pi
1509     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1510     */
1511
1512    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1513    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1514
1515    /*
1516     * store the integer part of y in mm0
1517     * emm2 = _mm_cvttps_epi32(y);
1518     */
1519
1520    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1521
1522    /*
1523     * j=(j+1) & (~1) (see the cephes sources)
1524     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1525     */
1526
1527    LLVMValueRef all_one = lp_build_const_v4si(1);
1528    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1529    /*
1530     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1531     */
1532    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1533    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1534
1535    /*
1536     * y = _mm_cvtepi32_ps(emm2);
1537     */
1538    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1539
1540    /* get the swap sign flag
1541     * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1542     */
1543    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1544    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
1545
1546    /*
1547     * emm2 = _mm_slli_epi32(emm0, 29);
1548     */
1549    LLVMValueRef const_29 = lp_build_const_v4si(29);
1550    LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
1551
1552    /*
1553     * get the polynom selection mask
1554     * there is one polynom for 0 <= x <= Pi/4
1555     * and another one for Pi/4<x<=Pi/2
1556     * Both branches will be computed.
1557     *
1558     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1559     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1560     */
1561
1562    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1563    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
1564    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1565                                              emm2_3, lp_build_const_v4si(0));
1566    /*
1567     *   sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1568     */
1569    LLVMValueRef sign_bit_1 =  LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
1570
1571    /*
1572     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1573     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1574     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1575     */
1576    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1577    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1578    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1579
1580    /*
1581     * The magic pass: "Extended precision modular arithmetic"
1582     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1583     * xmm1 = _mm_mul_ps(y, xmm1);
1584     * xmm2 = _mm_mul_ps(y, xmm2);
1585     * xmm3 = _mm_mul_ps(y, xmm3);
1586     */
1587    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1588    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1589    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1590
1591    /*
1592     * x = _mm_add_ps(x, xmm1);
1593     * x = _mm_add_ps(x, xmm2);
1594     * x = _mm_add_ps(x, xmm3);
1595     */
1596
1597    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1598    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1599    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1600
1601    /*
1602     * Evaluate the first polynom  (0 <= x <= Pi/4)
1603     *
1604     * z = _mm_mul_ps(x,x);
1605     */
1606    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1607
1608    /*
1609     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1610     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1611     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1612     */
1613    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1614    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1615    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1616
1617    /*
1618     * y = *(v4sf*)_ps_coscof_p0;
1619     * y = _mm_mul_ps(y, z);
1620     */
1621    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1622    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1623    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1624    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1625    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1626    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1627
1628
1629    /*
1630     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1631     * y = _mm_sub_ps(y, tmp);
1632     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1633     */
1634    LLVMValueRef half = lp_build_const_v4sf(0.5);
1635    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1636    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1637    LLVMValueRef one = lp_build_const_v4sf(1.0);
1638    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1639
1640    /*
1641     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1642     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1643     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1644     */
1645    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1646    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1647    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1648
1649    /*
1650     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1651     *
1652     * y2 = *(v4sf*)_ps_sincof_p0;
1653     * y2 = _mm_mul_ps(y2, z);
1654     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1655     * y2 = _mm_mul_ps(y2, z);
1656     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1657     * y2 = _mm_mul_ps(y2, z);
1658     * y2 = _mm_mul_ps(y2, x);
1659     * y2 = _mm_add_ps(y2, x);
1660     */
1661
1662    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1663    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1664    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1665    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1666    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1667    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1668    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1669
1670    /*
1671     * select the correct result from the two polynoms
1672     * xmm3 = poly_mask;
1673     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1674     * y = _mm_andnot_ps(xmm3, y);
1675     * y = _mm_add_ps(y,y2);
1676     */
1677    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1678    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1679    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1680    LLVMValueRef inv = lp_build_const_v4si(~0);
1681    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1682    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1683    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1684
1685    /*
1686     * update the sign
1687     * y = _mm_xor_ps(y, sign_bit);
1688     */
1689    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
1690    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1691    return y_result;
1692 }
1693
1694
1695 /**
1696  * Generate cos(a) using SSE2
1697  */
1698 LLVMValueRef
1699 lp_build_cos(struct lp_build_context *bld,
1700              LLVMValueRef a)
1701 {
1702    struct lp_type int_type = lp_int_type(bld->type);
1703    LLVMBuilderRef b = bld->builder;
1704    LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
1705    LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
1706
1707    /*
1708     *  take the absolute value,
1709     *  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1710     */
1711
1712    LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
1713    LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
1714
1715    LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
1716    LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
1717
1718    /*
1719     * scale by 4/Pi
1720     * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1721     */
1722
1723    LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
1724    LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
1725
1726    /*
1727     * store the integer part of y in mm0
1728     * emm2 = _mm_cvttps_epi32(y);
1729     */
1730
1731    LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
1732
1733    /*
1734     * j=(j+1) & (~1) (see the cephes sources)
1735     * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1736     */
1737
1738    LLVMValueRef all_one = lp_build_const_v4si(1);
1739    LLVMValueRef emm2_add =  LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
1740    /*
1741     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1742     */
1743    LLVMValueRef inv_one = lp_build_const_v4si(~1);
1744    LLVMValueRef emm2_and =  LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
1745
1746    /*
1747     * y = _mm_cvtepi32_ps(emm2);
1748     */
1749    LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
1750
1751
1752    /*
1753     * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1754     */
1755    LLVMValueRef const_2 = lp_build_const_v4si(2);
1756    LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
1757
1758
1759    /* get the swap sign flag
1760     * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1761     */
1762    LLVMValueRef inv = lp_build_const_v4si(~0);
1763    LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
1764    LLVMValueRef pi32_4 = lp_build_const_v4si(4);
1765    LLVMValueRef emm0_and =  LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
1766
1767    /*
1768     * emm2 = _mm_slli_epi32(emm0, 29);
1769     */
1770    LLVMValueRef const_29 = lp_build_const_v4si(29);
1771    LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
1772
1773    /*
1774     * get the polynom selection mask
1775     * there is one polynom for 0 <= x <= Pi/4
1776     * and another one for Pi/4<x<=Pi/2
1777     * Both branches will be computed.
1778     *
1779     * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1780     * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1781     */
1782
1783    LLVMValueRef pi32_2 = lp_build_const_v4si(2);
1784    LLVMValueRef emm2_3 =  LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
1785    LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
1786                                              emm2_3, lp_build_const_v4si(0));
1787
1788    /*
1789     * _PS_CONST(minus_cephes_DP1, -0.78515625);
1790     * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1791     * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1792     */
1793    LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
1794    LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
1795    LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
1796
1797    /*
1798     * The magic pass: "Extended precision modular arithmetic"
1799     * x = ((x - y * DP1) - y * DP2) - y * DP3;
1800     * xmm1 = _mm_mul_ps(y, xmm1);
1801     * xmm2 = _mm_mul_ps(y, xmm2);
1802     * xmm3 = _mm_mul_ps(y, xmm3);
1803     */
1804    LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
1805    LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
1806    LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
1807
1808    /*
1809     * x = _mm_add_ps(x, xmm1);
1810     * x = _mm_add_ps(x, xmm2);
1811     * x = _mm_add_ps(x, xmm3);
1812     */
1813
1814    LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
1815    LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
1816    LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
1817
1818    /*
1819     * Evaluate the first polynom  (0 <= x <= Pi/4)
1820     *
1821     * z = _mm_mul_ps(x,x);
1822     */
1823    LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
1824
1825    /*
1826     * _PS_CONST(coscof_p0,  2.443315711809948E-005);
1827     * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1828     * _PS_CONST(coscof_p2,  4.166664568298827E-002);
1829     */
1830    LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
1831    LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
1832    LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
1833
1834    /*
1835     * y = *(v4sf*)_ps_coscof_p0;
1836     * y = _mm_mul_ps(y, z);
1837     */
1838    LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
1839    LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
1840    LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
1841    LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
1842    LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
1843    LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
1844
1845
1846    /*
1847     * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1848     * y = _mm_sub_ps(y, tmp);
1849     * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1850     */
1851    LLVMValueRef half = lp_build_const_v4sf(0.5);
1852    LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
1853    LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
1854    LLVMValueRef one = lp_build_const_v4sf(1.0);
1855    LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
1856
1857    /*
1858     * _PS_CONST(sincof_p0, -1.9515295891E-4);
1859     * _PS_CONST(sincof_p1,  8.3321608736E-3);
1860     * _PS_CONST(sincof_p2, -1.6666654611E-1);
1861     */
1862    LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
1863    LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
1864    LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
1865
1866    /*
1867     * Evaluate the second polynom  (Pi/4 <= x <= 0)
1868     *
1869     * y2 = *(v4sf*)_ps_sincof_p0;
1870     * y2 = _mm_mul_ps(y2, z);
1871     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1872     * y2 = _mm_mul_ps(y2, z);
1873     * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1874     * y2 = _mm_mul_ps(y2, z);
1875     * y2 = _mm_mul_ps(y2, x);
1876     * y2 = _mm_add_ps(y2, x);
1877     */
1878
1879    LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
1880    LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
1881    LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
1882    LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
1883    LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
1884    LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
1885    LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
1886
1887    /*
1888     * select the correct result from the two polynoms
1889     * xmm3 = poly_mask;
1890     * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1891     * y = _mm_andnot_ps(xmm3, y);
1892     * y = _mm_add_ps(y,y2);
1893     */
1894    LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
1895    LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
1896    LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
1897    LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
1898    LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
1899    LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
1900
1901    /*
1902     * update the sign
1903     * y = _mm_xor_ps(y, sign_bit);
1904     */
1905    LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
1906    LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
1907    return y_result;
1908 }
1909
1910
1911 /**
1912  * Generate pow(x, y)
1913  */
1914 LLVMValueRef
1915 lp_build_pow(struct lp_build_context *bld,
1916              LLVMValueRef x,
1917              LLVMValueRef y)
1918 {
1919    /* TODO: optimize the constant case */
1920    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
1921        LLVMIsConstant(x) && LLVMIsConstant(y)) {
1922       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1923                    __FUNCTION__);
1924    }
1925
1926    return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
1927 }
1928
1929
1930 /**
1931  * Generate exp(x)
1932  */
1933 LLVMValueRef
1934 lp_build_exp(struct lp_build_context *bld,
1935              LLVMValueRef x)
1936 {
1937    /* log2(e) = 1/log(2) */
1938    LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
1939
1940    assert(lp_check_value(bld->type, x));
1941
1942    return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
1943 }
1944
1945
1946 /**
1947  * Generate log(x)
1948  */
1949 LLVMValueRef
1950 lp_build_log(struct lp_build_context *bld,
1951              LLVMValueRef x)
1952 {
1953    /* log(2) */
1954    LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
1955
1956    assert(lp_check_value(bld->type, x));
1957
1958    return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
1959 }
1960
1961
1962 /**
1963  * Generate polynomial.
1964  * Ex:  coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
1965  */
1966 static LLVMValueRef
1967 lp_build_polynomial(struct lp_build_context *bld,
1968                     LLVMValueRef x,
1969                     const double *coeffs,
1970                     unsigned num_coeffs)
1971 {
1972    const struct lp_type type = bld->type;
1973    LLVMValueRef res = NULL;
1974    unsigned i;
1975
1976    assert(lp_check_value(bld->type, x));
1977
1978    /* TODO: optimize the constant case */
1979    if (gallivm_debug & GALLIVM_DEBUG_PERF &&
1980        LLVMIsConstant(x)) {
1981       debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1982                    __FUNCTION__);
1983    }
1984
1985    for (i = num_coeffs; i--; ) {
1986       LLVMValueRef coeff;
1987
1988       coeff = lp_build_const_vec(type, coeffs[i]);
1989
1990       if(res)
1991          res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
1992       else
1993          res = coeff;
1994    }
1995
1996    if(res)
1997       return res;
1998    else
1999       return bld->undef;
2000 }
2001
2002
2003 /**
2004  * Minimax polynomial fit of 2**x, in range [0, 1[
2005  */
2006 const double lp_build_exp2_polynomial[] = {
2007 #if EXP_POLY_DEGREE == 5
2008    0.999999999690134838155,
2009    0.583974334321735217258,
2010    0.164553105719676828492,
2011    0.0292811063701710962255,
2012    0.00354944426657875141846,
2013    0.000296253726543423377365
2014 #elif EXP_POLY_DEGREE == 4
2015    1.00000001502262084505,
2016    0.563586057338685991394,
2017    0.150436017652442413623,
2018    0.0243220604213317927308,
2019    0.0025359088446580436489
2020 #elif EXP_POLY_DEGREE == 3
2021    0.999925218562710312959,
2022    0.695833540494823811697,
2023    0.226067155427249155588,
2024    0.0780245226406372992967
2025 #elif EXP_POLY_DEGREE == 2
2026    1.00172476321474503578,
2027    0.657636275736077639316,
2028    0.33718943461968720704
2029 #else
2030 #error
2031 #endif
2032 };
2033
2034
2035 void
2036 lp_build_exp2_approx(struct lp_build_context *bld,
2037                      LLVMValueRef x,
2038                      LLVMValueRef *p_exp2_int_part,
2039                      LLVMValueRef *p_frac_part,
2040                      LLVMValueRef *p_exp2)
2041 {
2042    const struct lp_type type = bld->type;
2043    LLVMTypeRef vec_type = lp_build_vec_type(type);
2044    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2045    LLVMValueRef ipart = NULL;
2046    LLVMValueRef fpart = NULL;
2047    LLVMValueRef expipart = NULL;
2048    LLVMValueRef expfpart = NULL;
2049    LLVMValueRef res = NULL;
2050
2051    assert(lp_check_value(bld->type, x));
2052
2053    if(p_exp2_int_part || p_frac_part || p_exp2) {
2054       /* TODO: optimize the constant case */
2055       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2056           LLVMIsConstant(x)) {
2057          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2058                       __FUNCTION__);
2059       }
2060
2061       assert(type.floating && type.width == 32);
2062
2063       x = lp_build_min(bld, x, lp_build_const_vec(type,  129.0));
2064       x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
2065
2066       /* ipart = floor(x) */
2067       ipart = lp_build_floor(bld, x);
2068
2069       /* fpart = x - ipart */
2070       fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
2071    }
2072
2073    if(p_exp2_int_part || p_exp2) {
2074       /* expipart = (float) (1 << ipart) */
2075       ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
2076       expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
2077       expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
2078       expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
2079    }
2080
2081    if(p_exp2) {
2082       expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
2083                                      Elements(lp_build_exp2_polynomial));
2084
2085       res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
2086    }
2087
2088    if(p_exp2_int_part)
2089       *p_exp2_int_part = expipart;
2090
2091    if(p_frac_part)
2092       *p_frac_part = fpart;
2093
2094    if(p_exp2)
2095       *p_exp2 = res;
2096 }
2097
2098
2099 LLVMValueRef
2100 lp_build_exp2(struct lp_build_context *bld,
2101               LLVMValueRef x)
2102 {
2103    LLVMValueRef res;
2104    lp_build_exp2_approx(bld, x, NULL, NULL, &res);
2105    return res;
2106 }
2107
2108
2109 /**
2110  * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
2111  * These coefficients can be generate with
2112  * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2113  */
2114 const double lp_build_log2_polynomial[] = {
2115 #if LOG_POLY_DEGREE == 6
2116    3.11578814719469302614,
2117    -3.32419399085241980044,
2118    2.59883907202499966007,
2119    -1.23152682416275988241,
2120    0.318212422185251071475,
2121    -0.0344359067839062357313
2122 #elif LOG_POLY_DEGREE == 5
2123    2.8882704548164776201,
2124    -2.52074962577807006663,
2125    1.48116647521213171641,
2126    -0.465725644288844778798,
2127    0.0596515482674574969533
2128 #elif LOG_POLY_DEGREE == 4
2129    2.61761038894603480148,
2130    -1.75647175389045657003,
2131    0.688243882994381274313,
2132    -0.107254423828329604454
2133 #elif LOG_POLY_DEGREE == 3
2134    2.28330284476918490682,
2135    -1.04913055217340124191,
2136    0.204446009836232697516
2137 #else
2138 #error
2139 #endif
2140 };
2141
2142
2143 /**
2144  * See http://www.devmaster.net/forums/showthread.php?p=43580
2145  */
2146 void
2147 lp_build_log2_approx(struct lp_build_context *bld,
2148                      LLVMValueRef x,
2149                      LLVMValueRef *p_exp,
2150                      LLVMValueRef *p_floor_log2,
2151                      LLVMValueRef *p_log2)
2152 {
2153    const struct lp_type type = bld->type;
2154    LLVMTypeRef vec_type = lp_build_vec_type(type);
2155    LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
2156
2157    LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
2158    LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
2159    LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
2160
2161    LLVMValueRef i = NULL;
2162    LLVMValueRef exp = NULL;
2163    LLVMValueRef mant = NULL;
2164    LLVMValueRef logexp = NULL;
2165    LLVMValueRef logmant = NULL;
2166    LLVMValueRef res = NULL;
2167
2168    assert(lp_check_value(bld->type, x));
2169
2170    if(p_exp || p_floor_log2 || p_log2) {
2171       /* TODO: optimize the constant case */
2172       if (gallivm_debug & GALLIVM_DEBUG_PERF &&
2173           LLVMIsConstant(x)) {
2174          debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2175                       __FUNCTION__);
2176       }
2177
2178       assert(type.floating && type.width == 32);
2179
2180       i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
2181
2182       /* exp = (float) exponent(x) */
2183       exp = LLVMBuildAnd(bld->builder, i, expmask, "");
2184    }
2185
2186    if(p_floor_log2 || p_log2) {
2187       logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
2188       logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
2189       logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
2190    }
2191
2192    if(p_log2) {
2193       /* mant = (float) mantissa(x) */
2194       mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
2195       mant = LLVMBuildOr(bld->builder, mant, one, "");
2196       mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
2197
2198       logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
2199                                     Elements(lp_build_log2_polynomial));
2200
2201       /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2202       logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
2203
2204       res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
2205    }
2206
2207    if(p_exp) {
2208       exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
2209       *p_exp = exp;
2210    }
2211
2212    if(p_floor_log2)
2213       *p_floor_log2 = logexp;
2214
2215    if(p_log2)
2216       *p_log2 = res;
2217 }
2218
2219
2220 LLVMValueRef
2221 lp_build_log2(struct lp_build_context *bld,
2222               LLVMValueRef x)
2223 {
2224    LLVMValueRef res;
2225    lp_build_log2_approx(bld, x, NULL, NULL, &res);
2226    return res;
2227 }