1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
// Copyright (c) 2015-2016 The Khronos Group Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#ifndef LIBSPIRV_UTIL_HEX_FLOAT_H_
#define LIBSPIRV_UTIL_HEX_FLOAT_H_

#include <cassert>
#include <cctype>
#include <cmath>
#include <cstdint>
#include <iomanip>
#include <limits>
#include <sstream>

#if defined(_MSC_VER) && _MSC_VER < 1800
namespace std {
bool isnan(double f)
{
  return ::_isnan(f) != 0;
}
bool isinf(double f)
{
  return ::_finite(f) == 0;
}
}
#endif

#include "bitutils.h"

namespace spvutils {

class Float16 {
 public:
  Float16(uint16_t v) : val(v) {}
  Float16() {}
  static bool isNan(const Float16& val) {
    return ((val.val & 0x7C00) == 0x7C00) && ((val.val & 0x3FF) != 0);
  }
  // Returns true if the given value is any kind of infinity.
  static bool isInfinity(const Float16& val) {
    return ((val.val & 0x7C00) == 0x7C00) && ((val.val & 0x3FF) == 0);
  }
  Float16(const Float16& other) { val = other.val; }
  uint16_t get_value() const { return val; }

  // Returns the maximum normal value.
  static Float16 max() { return Float16(0x7bff); }
  // Returns the lowest normal value.
  static Float16 lowest() { return Float16(0xfbff); }

 private:
  uint16_t val;
};

// To specialize this type, you must override uint_type to define
// an unsigned integer that can fit your floating point type.
// You must also add a isNan function that returns true if
// a value is Nan.
template <typename T>
struct FloatProxyTraits {
  typedef void uint_type;
};

template <>
struct FloatProxyTraits<float> {
  typedef uint32_t uint_type;
  static bool isNan(float f) { return std::isnan(f); }
  // Returns true if the given value is any kind of infinity.
  static bool isInfinity(float f) { return std::isinf(f); }
  // Returns the maximum normal value.
  static float max() { return std::numeric_limits<float>::max(); }
  // Returns the lowest normal value.
  static float lowest() { return std::numeric_limits<float>::lowest(); }
};

template <>
struct FloatProxyTraits<double> {
  typedef uint64_t uint_type;
  static bool isNan(double f) { return std::isnan(f); }
  // Returns true if the given value is any kind of infinity.
  static bool isInfinity(double f) { return std::isinf(f); }
  // Returns the maximum normal value.
  static double max() { return std::numeric_limits<double>::max(); }
  // Returns the lowest normal value.
  static double lowest() { return std::numeric_limits<double>::lowest(); }
};

template <>
struct FloatProxyTraits<Float16> {
  typedef uint16_t uint_type;
  static bool isNan(Float16 f) { return Float16::isNan(f); }
  // Returns true if the given value is any kind of infinity.
  static bool isInfinity(Float16 f) { return Float16::isInfinity(f); }
  // Returns the maximum normal value.
  static Float16 max() { return Float16::max(); }
  // Returns the lowest normal value.
  static Float16 lowest() { return Float16::lowest(); }
};

// Since copying a floating point number (especially if it is NaN)
// does not guarantee that bits are preserved, this class lets us
// store the type and use it as a float when necessary.
template <typename T>
class FloatProxy {
 public:
  typedef typename FloatProxyTraits<T>::uint_type uint_type;

  // Since this is to act similar to the normal floats,
  // do not initialize the data by default.
  FloatProxy() {}

  // Intentionally non-explicit. This is a proxy type so
  // implicit conversions allow us to use it more transparently.
  FloatProxy(T val) { data_ = BitwiseCast<uint_type>(val); }

  // Intentionally non-explicit. This is a proxy type so
  // implicit conversions allow us to use it more transparently.
  FloatProxy(uint_type val) { data_ = val; }

  // This is helpful to have and is guaranteed not to stomp bits.
  FloatProxy<T> operator-() const {
    return static_cast<uint_type>(data_ ^
                                  (uint_type(0x1) << (sizeof(T) * 8 - 1)));
  }

  // Returns the data as a floating point value.
  T getAsFloat() const { return BitwiseCast<T>(data_); }

  // Returns the raw data.
  uint_type data() const { return data_; }

  // Returns true if the value represents any type of NaN.
  bool isNan() { return FloatProxyTraits<T>::isNan(getAsFloat()); }
  // Returns true if the value represents any type of infinity.
  bool isInfinity() { return FloatProxyTraits<T>::isInfinity(getAsFloat()); }

  // Returns the maximum normal value.
  static FloatProxy<T> max() {
    return FloatProxy<T>(FloatProxyTraits<T>::max());
  }
  // Returns the lowest normal value.
  static FloatProxy<T> lowest() {
    return FloatProxy<T>(FloatProxyTraits<T>::lowest());
  }

 private:
  uint_type data_;
};

template <typename T>
bool operator==(const FloatProxy<T>& first, const FloatProxy<T>& second) {
  return first.data() == second.data();
}

// Reads a FloatProxy value as a normal float from a stream.
template <typename T>
std::istream& operator>>(std::istream& is, FloatProxy<T>& value) {
  T float_val;
  is >> float_val;
  value = FloatProxy<T>(float_val);
  return is;
}

// This is an example traits. It is not meant to be used in practice, but will
// be the default for any non-specialized type.
template <typename T>
struct HexFloatTraits {
  // Integer type that can store this hex-float.
  typedef void uint_type;
  // Signed integer type that can store this hex-float.
  typedef void int_type;
  // The numerical type that this HexFloat represents.
  typedef void underlying_type;
  // The type needed to construct the underlying type.
  typedef void native_type;
  // The number of bits that are actually relevant in the uint_type.
  // This allows us to deal with, for example, 24-bit values in a 32-bit
  // integer.
  static const uint32_t num_used_bits = 0;
  // Number of bits that represent the exponent.
  static const uint32_t num_exponent_bits = 0;
  // Number of bits that represent the fractional part.
  static const uint32_t num_fraction_bits = 0;
  // The bias of the exponent. (How much we need to subtract from the stored
  // value to get the correct value.)
  static const uint32_t exponent_bias = 0;
};

// Traits for IEEE float.
// 1 sign bit, 8 exponent bits, 23 fractional bits.
template <>
struct HexFloatTraits<FloatProxy<float>> {
  typedef uint32_t uint_type;
  typedef int32_t int_type;
  typedef FloatProxy<float> underlying_type;
  typedef float native_type;
  static const uint_type num_used_bits = 32;
  static const uint_type num_exponent_bits = 8;
  static const uint_type num_fraction_bits = 23;
  static const uint_type exponent_bias = 127;
};

// Traits for IEEE double.
// 1 sign bit, 11 exponent bits, 52 fractional bits.
template <>
struct HexFloatTraits<FloatProxy<double>> {
  typedef uint64_t uint_type;
  typedef int64_t int_type;
  typedef FloatProxy<double> underlying_type;
  typedef double native_type;
  static const uint_type num_used_bits = 64;
  static const uint_type num_exponent_bits = 11;
  static const uint_type num_fraction_bits = 52;
  static const uint_type exponent_bias = 1023;
};

// Traits for IEEE half.
// 1 sign bit, 5 exponent bits, 10 fractional bits.
template <>
struct HexFloatTraits<FloatProxy<Float16>> {
  typedef uint16_t uint_type;
  typedef int16_t int_type;
  typedef uint16_t underlying_type;
  typedef uint16_t native_type;
  static const uint_type num_used_bits = 16;
  static const uint_type num_exponent_bits = 5;
  static const uint_type num_fraction_bits = 10;
  static const uint_type exponent_bias = 15;
};

enum round_direction {
  kRoundToZero,
  kRoundToNearestEven,
  kRoundToPositiveInfinity,
  kRoundToNegativeInfinity
};

// Template class that houses a floating pointer number.
// It exposes a number of constants based on the provided traits to
// assist in interpreting the bits of the value.
template <typename T, typename Traits = HexFloatTraits<T>>
class HexFloat {
 public:
  typedef typename Traits::uint_type uint_type;
  typedef typename Traits::int_type int_type;
  typedef typename Traits::underlying_type underlying_type;
  typedef typename Traits::native_type native_type;

  explicit HexFloat(T f) : value_(f) {}

  T value() const { return value_; }
  void set_value(T f) { value_ = f; }

  // These are all written like this because it is convenient to have
  // compile-time constants for all of these values.

  // Pass-through values to save typing.
  static const uint32_t num_used_bits = Traits::num_used_bits;
  static const uint32_t exponent_bias = Traits::exponent_bias;
  static const uint32_t num_exponent_bits = Traits::num_exponent_bits;
  static const uint32_t num_fraction_bits = Traits::num_fraction_bits;

  // Number of bits to shift left to set the highest relevant bit.
  static const uint32_t top_bit_left_shift = num_used_bits - 1;
  // How many nibbles (hex characters) the fractional part takes up.
  static const uint32_t fraction_nibbles = (num_fraction_bits + 3) / 4;
  // If the fractional part does not fit evenly into a hex character (4-bits)
  // then we have to left-shift to get rid of leading 0s. This is the amount
  // we have to shift (might be 0).
  static const uint32_t num_overflow_bits =
      fraction_nibbles * 4 - num_fraction_bits;

  // The representation of the fraction, not the actual bits. This
  // includes the leading bit that is usually implicit.
  static const uint_type fraction_represent_mask =
      spvutils::SetBits<uint_type, 0,
                        num_fraction_bits + num_overflow_bits>::get;

  // The topmost bit in the nibble-aligned fraction.
  static const uint_type fraction_top_bit =
      uint_type(1) << (num_fraction_bits + num_overflow_bits - 1);

  // The least significant bit in the exponent, which is also the bit
  // immediately to the left of the significand.
  static const uint_type first_exponent_bit = uint_type(1)
                                              << (num_fraction_bits);

  // The mask for the encoded fraction. It does not include the
  // implicit bit.
  static const uint_type fraction_encode_mask =
      spvutils::SetBits<uint_type, 0, num_fraction_bits>::get;

  // The bit that is used as a sign.
  static const uint_type sign_mask = uint_type(1) << top_bit_left_shift;

  // The bits that represent the exponent.
  static const uint_type exponent_mask =
      spvutils::SetBits<uint_type, num_fraction_bits, num_exponent_bits>::get;

  // How far left the exponent is shifted.
  static const uint32_t exponent_left_shift = num_fraction_bits;

  // How far from the right edge the fraction is shifted.
  static const uint32_t fraction_right_shift =
      static_cast<uint32_t>(sizeof(uint_type) * 8) - num_fraction_bits;

  // The maximum representable unbiased exponent.
  static const int_type max_exponent =
      (exponent_mask >> num_fraction_bits) - exponent_bias;
  // The minimum representable exponent for normalized numbers.
  static const int_type min_exponent = -static_cast<int_type>(exponent_bias);

  // Returns the bits associated with the value.
  uint_type getBits() const { return spvutils::BitwiseCast<uint_type>(value_); }

  // Returns the bits associated with the value, without the leading sign bit.
  uint_type getUnsignedBits() const {
    return static_cast<uint_type>(spvutils::BitwiseCast<uint_type>(value_) &
                                  ~sign_mask);
  }

  // Returns the bits associated with the exponent, shifted to start at the
  // lsb of the type.
  const uint_type getExponentBits() const {
    return static_cast<uint_type>((getBits() & exponent_mask) >>
                                  num_fraction_bits);
  }

  // Returns the exponent in unbiased form. This is the exponent in the
  // human-friendly form.
  const int_type getUnbiasedExponent() const {
    return static_cast<int_type>(getExponentBits() - exponent_bias);
  }

  // Returns just the significand bits from the value.
  const uint_type getSignificandBits() const {
    return getBits() & fraction_encode_mask;
  }

  // If the number was normalized, returns the unbiased exponent.
  // If the number was denormal, normalize the exponent first.
  const int_type getUnbiasedNormalizedExponent() const {
    if ((getBits() & ~sign_mask) == 0) {  // special case if everything is 0
      return 0;
    }
    int_type exp = getUnbiasedExponent();
    if (exp == min_exponent) {  // We are in denorm land.
      uint_type significand_bits = getSignificandBits();
      while ((significand_bits & (first_exponent_bit >> 1)) == 0) {
        significand_bits = static_cast<uint_type>(significand_bits << 1);
        exp = static_cast<int_type>(exp - 1);
      }
      significand_bits &= fraction_encode_mask;<--- Variable 'significand_bits' is assigned a value that is never used.
    }
    return exp;
  }

  // Returns the signficand after it has been normalized.
  const uint_type getNormalizedSignificand() const {
    int_type unbiased_exponent = getUnbiasedNormalizedExponent();
    uint_type significand = getSignificandBits();
    for (int_type i = unbiased_exponent; i <= min_exponent; ++i) {
      significand = static_cast<uint_type>(significand << 1);
    }
    significand &= fraction_encode_mask;
    return significand;
  }

  // Returns true if this number represents a negative value.
  bool isNegative() const { return (getBits() & sign_mask) != 0; }

  // Sets this HexFloat from the individual components.
  // Note this assumes EVERY significand is normalized, and has an implicit
  // leading one. This means that the only way that this method will set 0,
  // is if you set a number so denormalized that it underflows.
  // Do not use this method with raw bits extracted from a subnormal number,
  // since subnormals do not have an implicit leading 1 in the significand.
  // The significand is also expected to be in the
  // lowest-most num_fraction_bits of the uint_type.
  // The exponent is expected to be unbiased, meaning an exponent of
  // 0 actually means 0.
  // If underflow_round_up is set, then on underflow, if a number is non-0
  // and would underflow, we round up to the smallest denorm.
  void setFromSignUnbiasedExponentAndNormalizedSignificand(
      bool negative, int_type exponent, uint_type significand,
      bool round_denorm_up) {
    bool significand_is_zero = significand == 0;

    if (exponent <= min_exponent) {
      // If this was denormalized, then we have to shift the bit on, meaning
      // the significand is not zero.
      significand_is_zero = false;
      significand |= first_exponent_bit;
      significand = static_cast<uint_type>(significand >> 1);
    }

    while (exponent < min_exponent) {
      significand = static_cast<uint_type>(significand >> 1);
      ++exponent;
    }

    if (exponent == min_exponent) {
      if (significand == 0 && !significand_is_zero && round_denorm_up) {
        significand = static_cast<uint_type>(0x1);
      }
    }

    uint_type new_value = 0;
    if (negative) {
      new_value = static_cast<uint_type>(new_value | sign_mask);
    }
    exponent = static_cast<int_type>(exponent + exponent_bias);
    assert(exponent >= 0);

    // put it all together
    exponent = static_cast<uint_type>((exponent << exponent_left_shift) &
                                      exponent_mask);
    significand = static_cast<uint_type>(significand & fraction_encode_mask);
    new_value = static_cast<uint_type>(new_value | (exponent | significand));
    value_ = BitwiseCast<T>(new_value);
  }

  // Increments the significand of this number by the given amount.
  // If this would spill the significand into the implicit bit,
  // carry is set to true and the significand is shifted to fit into
  // the correct location, otherwise carry is set to false.
  // All significands and to_increment are assumed to be within the bounds
  // for a valid significand.
  static uint_type incrementSignificand(uint_type significand,
                                        uint_type to_increment, bool* carry) {
    significand = static_cast<uint_type>(significand + to_increment);
    *carry = false;
    if (significand & first_exponent_bit) {
      *carry = true;
      // The implicit 1-bit will have carried, so we should zero-out the
      // top bit and shift back.
      significand = static_cast<uint_type>(significand & ~first_exponent_bit);
      significand = static_cast<uint_type>(significand >> 1);
    }
    return significand;
  }

  // These exist because MSVC throws warnings on negative right-shifts
  // even if they are not going to be executed. Eg:
  // constant_number < 0? 0: constant_number
  // These convert the negative left-shifts into right shifts.

  template <typename int_type>
  uint_type negatable_left_shift(int_type N, uint_type val)
  {
    if(N >= 0)
      return val << N;

    return val >> -N;
  }

  template <typename int_type>
  uint_type negatable_right_shift(int_type N, uint_type val)
  {
    if(N >= 0)
      return val >> N;

    return val << -N;
  }

  // Returns the significand, rounded to fit in a significand in
  // other_T. This is shifted so that the most significant
  // bit of the rounded number lines up with the most significant bit
  // of the returned significand.
  template <typename other_T>
  typename other_T::uint_type getRoundedNormalizedSignificand(
      round_direction dir, bool* carry_bit) {
    typedef typename other_T::uint_type other_uint_type;
    static const int_type num_throwaway_bits =
        static_cast<int_type>(num_fraction_bits) -
        static_cast<int_type>(other_T::num_fraction_bits);

    static const uint_type last_significant_bit =
        (num_throwaway_bits < 0)
            ? 0
            : negatable_left_shift(num_throwaway_bits, 1u);
    static const uint_type first_rounded_bit =
        (num_throwaway_bits < 1)
            ? 0
            : negatable_left_shift(num_throwaway_bits - 1, 1u);

    static const uint_type throwaway_mask_bits =
        num_throwaway_bits > 0 ? num_throwaway_bits : 0;
    static const uint_type throwaway_mask =
        spvutils::SetBits<uint_type, 0, throwaway_mask_bits>::get;

    *carry_bit = false;
    other_uint_type out_val = 0;
    uint_type significand = getNormalizedSignificand();
    // If we are up-casting, then we just have to shift to the right location.
    if (num_throwaway_bits <= 0) {
      out_val = static_cast<other_uint_type>(significand);
      uint_type shift_amount = static_cast<uint_type>(-num_throwaway_bits);
      out_val = static_cast<other_uint_type>(out_val << shift_amount);
      return out_val;
    }

    // If every non-representable bit is 0, then we don't have any casting to
    // do.
    if ((significand & throwaway_mask) == 0) {
      return static_cast<other_uint_type>(
          negatable_right_shift(num_throwaway_bits, significand));
    }

    bool round_away_from_zero = false;
    // We actually have to narrow the significand here, so we have to follow the
    // rounding rules.
    switch (dir) {
      case kRoundToZero:
        break;
      case kRoundToPositiveInfinity:
        round_away_from_zero = !isNegative();
        break;
      case kRoundToNegativeInfinity:
        round_away_from_zero = isNegative();
        break;
      case kRoundToNearestEven:
        // Have to round down, round bit is 0
        if ((first_rounded_bit & significand) == 0) {
          break;
        }
        if (((significand & throwaway_mask) & ~first_rounded_bit) != 0) {
          // If any subsequent bit of the rounded portion is non-0 then we round
          // up.
          round_away_from_zero = true;
          break;
        }
        // We are exactly half-way between 2 numbers, pick even.
        if ((significand & last_significant_bit) != 0) {
          // 1 for our last bit, round up.
          round_away_from_zero = true;
          break;
        }
        break;
    }

    if (round_away_from_zero) {
      return static_cast<other_uint_type>(
          negatable_right_shift(num_throwaway_bits, incrementSignificand(
              significand, last_significant_bit, carry_bit)));
    } else {
      return static_cast<other_uint_type>(
          negatable_right_shift(num_throwaway_bits, significand));
    }
  }

  // Casts this value to another HexFloat. If the cast is widening,
  // then round_dir is ignored. If the cast is narrowing, then
  // the result is rounded in the direction specified.
  // This number will retain Nan and Inf values.
  // It will also saturate to Inf if the number overflows, and
  // underflow to (0 or min depending on rounding) if the number underflows.
  template <typename other_T>
  void castTo(other_T& other, round_direction round_dir) {
    other = other_T(static_cast<typename other_T::native_type>(0));
    bool negate = isNegative();
    if (getUnsignedBits() == 0) {
      if (negate) {
        other.set_value(-other.value());
      }
      return;
    }
    uint_type significand = getSignificandBits();
    bool carried = false;
    typename other_T::uint_type rounded_significand =
        getRoundedNormalizedSignificand<other_T>(round_dir, &carried);

    int_type exponent = getUnbiasedExponent();
    if (exponent == min_exponent) {
      // If we are denormal, normalize the exponent, so that we can encode
      // easily.
      exponent = static_cast<int_type>(exponent + 1);
      for (uint_type check_bit = first_exponent_bit >> 1; check_bit != 0;
           check_bit = static_cast<uint_type>(check_bit >> 1)) {
        exponent = static_cast<int_type>(exponent - 1);
        if (check_bit & significand) break;
      }
    }

    bool is_nan =
        (getBits() & exponent_mask) == exponent_mask && significand != 0;
    bool is_inf =
        !is_nan &&
        ((exponent + carried) > static_cast<int_type>(other_T::exponent_bias) ||
         (significand == 0 && (getBits() & exponent_mask) == exponent_mask));

    // If we are Nan or Inf we should pass that through.
    if (is_inf) {
      other.set_value(BitwiseCast<typename other_T::underlying_type>(
          static_cast<typename other_T::uint_type>(
              (negate ? other_T::sign_mask : 0) | other_T::exponent_mask)));
      return;
    }
    if (is_nan) {
      typename other_T::uint_type shifted_significand;
      shifted_significand = static_cast<typename other_T::uint_type>(
          negatable_left_shift(
              static_cast<int_type>(other_T::num_fraction_bits) -
              static_cast<int_type>(num_fraction_bits), significand));

      // We are some sort of Nan. We try to keep the bit-pattern of the Nan
      // as close as possible. If we had to shift off bits so we are 0, then we
      // just set the last bit.
      other.set_value(BitwiseCast<typename other_T::underlying_type>(
          static_cast<typename other_T::uint_type>(
              (negate ? other_T::sign_mask : 0) | other_T::exponent_mask |
              (shifted_significand == 0 ? 0x1 : shifted_significand))));
      return;
    }

    bool round_underflow_up =
        isNegative() ? round_dir == kRoundToNegativeInfinity
                     : round_dir == kRoundToPositiveInfinity;
    typedef typename other_T::int_type other_int_type;
    // setFromSignUnbiasedExponentAndNormalizedSignificand will
    // zero out any underflowing value (but retain the sign).
    other.setFromSignUnbiasedExponentAndNormalizedSignificand(
        negate, static_cast<other_int_type>(exponent), rounded_significand,
        round_underflow_up);
    return;
  }

 private:
  T value_;

  static_assert(num_used_bits ==
                    Traits::num_exponent_bits + Traits::num_fraction_bits + 1,
                "The number of bits do not fit");
  static_assert(sizeof(T) == sizeof(uint_type), "The type sizes do not match");
};

// Returns 4 bits represented by the hex character.
inline uint8_t get_nibble_from_character(int character) {
  const char* dec = "0123456789";
  const char* lower = "abcdef";
  const char* upper = "ABCDEF";
  const char* p = nullptr;
  if ((p = strchr(dec, character))) {
    return static_cast<uint8_t>(p - dec);
  } else if ((p = strchr(lower, character))) {
    return static_cast<uint8_t>(p - lower + 0xa);
  } else if ((p = strchr(upper, character))) {
    return static_cast<uint8_t>(p - upper + 0xa);
  }

  assert(false && "This was called with a non-hex character");
  return 0;
}

// Outputs the given HexFloat to the stream.
template <typename T, typename Traits>
std::ostream& operator<<(std::ostream& os, const HexFloat<T, Traits>& value) {
  typedef HexFloat<T, Traits> HF;
  typedef typename HF::uint_type uint_type;
  typedef typename HF::int_type int_type;

  static_assert(HF::num_used_bits != 0,
                "num_used_bits must be non-zero for a valid float");
  static_assert(HF::num_exponent_bits != 0,
                "num_exponent_bits must be non-zero for a valid float");
  static_assert(HF::num_fraction_bits != 0,
                "num_fractin_bits must be non-zero for a valid float");

  const uint_type bits = spvutils::BitwiseCast<uint_type>(value.value());
  const char* const sign = (bits & HF::sign_mask) ? "-" : "";
  const uint_type exponent = static_cast<uint_type>(
      (bits & HF::exponent_mask) >> HF::num_fraction_bits);

  uint_type fraction = static_cast<uint_type>((bits & HF::fraction_encode_mask)
                                              << HF::num_overflow_bits);

  const bool is_zero = exponent == 0 && fraction == 0;
  const bool is_denorm = exponent == 0 && !is_zero;

  // exponent contains the biased exponent we have to convert it back into
  // the normal range.
  int_type int_exponent = static_cast<int_type>(exponent - HF::exponent_bias);
  // If the number is all zeros, then we actually have to NOT shift the
  // exponent.
  int_exponent = is_zero ? 0 : int_exponent;

  // If we are denorm, then start shifting, and decreasing the exponent until
  // our leading bit is 1.

  if (is_denorm) {
    while ((fraction & HF::fraction_top_bit) == 0) {
      fraction = static_cast<uint_type>(fraction << 1);
      int_exponent = static_cast<int_type>(int_exponent - 1);
    }
    // Since this is denormalized, we have to consume the leading 1 since it
    // will end up being implicit.
    fraction = static_cast<uint_type>(fraction << 1);  // eat the leading 1
    fraction &= HF::fraction_represent_mask;
  }

  uint_type fraction_nibbles = HF::fraction_nibbles;
  // We do not have to display any trailing 0s, since this represents the
  // fractional part.
  while (fraction_nibbles > 0 && (fraction & 0xF) == 0) {
    // Shift off any trailing values;
    fraction = static_cast<uint_type>(fraction >> 4);
    --fraction_nibbles;
  }

  const auto saved_flags = os.flags();
  const auto saved_fill = os.fill();

  os << sign << "0x" << (is_zero ? '0' : '1');
  if (fraction_nibbles) {
    // Make sure to keep the leading 0s in place, since this is the fractional
    // part.
    os << "." << std::setw(static_cast<int>(fraction_nibbles))
       << std::setfill('0') << std::hex << fraction;
  }
  os << "p" << std::dec << (int_exponent >= 0 ? "+" : "") << int_exponent;

  os.flags(saved_flags);
  os.fill(saved_fill);

  return os;
}

// Returns true if negate_value is true and the next character on the
// input stream is a plus or minus sign.  In that case we also set the fail bit
// on the stream and set the value to the zero value for its type.
template <typename T, typename Traits>
inline bool RejectParseDueToLeadingSign(std::istream& is, bool negate_value,
                                        HexFloat<T, Traits>& value) {
  if (negate_value) {
    auto next_char = is.peek();
    if (next_char == '-' || next_char == '+') {
      // Fail the parse.  Emulate standard behaviour by setting the value to
      // the zero value, and set the fail bit on the stream.
      value = HexFloat<T, Traits>(typename HexFloat<T, Traits>::uint_type(0));
      is.setstate(std::ios_base::failbit);
      return true;
    }
  }
  return false;
}

// Parses a floating point number from the given stream and stores it into the
// value parameter.
// If negate_value is true then the number may not have a leading minus or
// plus, and if it successfully parses, then the number is negated before
// being stored into the value parameter.
// If the value cannot be correctly parsed or overflows the target floating
// point type, then set the fail bit on the stream.
// TODO(dneto): Promise C++11 standard behavior in how the value is set in
// the error case, but only after all target platforms implement it correctly.
// In particular, the Microsoft C++ runtime appears to be out of spec.
template <typename T, typename Traits>
inline std::istream& ParseNormalFloat(std::istream& is, bool negate_value,
                                      HexFloat<T, Traits>& value) {
  if (RejectParseDueToLeadingSign(is, negate_value, value)) {
    return is;
  }
  T val;
  is >> val;
  if (negate_value) {
    val = -val;
  }
  value.set_value(val);
  // In the failure case, map -0.0 to 0.0.
  if (is.fail() && value.getUnsignedBits() == 0u) {
    value = HexFloat<T, Traits>(typename HexFloat<T, Traits>::uint_type(0));
  }
  if (val.isInfinity()) {
    // Fail the parse.  Emulate standard behaviour by setting the value to
    // the closest normal value, and set the fail bit on the stream.
    value.set_value((value.isNegative() || negate_value) ? T::lowest()
                                                         : T::max());
    is.setstate(std::ios_base::failbit);
  }
  return is;
}

// Specialization of ParseNormalFloat for FloatProxy<Float16> values.
// This will parse the float as it were a 32-bit floating point number,
// and then round it down to fit into a Float16 value.
// The number is rounded towards zero.
// If negate_value is true then the number may not have a leading minus or
// plus, and if it successfully parses, then the number is negated before
// being stored into the value parameter.
// If the value cannot be correctly parsed or overflows the target floating
// point type, then set the fail bit on the stream.
// TODO(dneto): Promise C++11 standard behavior in how the value is set in
// the error case, but only after all target platforms implement it correctly.
// In particular, the Microsoft C++ runtime appears to be out of spec.
template <>
inline std::istream&
ParseNormalFloat<FloatProxy<Float16>, HexFloatTraits<FloatProxy<Float16>>>(
    std::istream& is, bool negate_value,
    HexFloat<FloatProxy<Float16>, HexFloatTraits<FloatProxy<Float16>>>& value) {
  // First parse as a 32-bit float.
  HexFloat<FloatProxy<float>> float_val(0.0f);
  ParseNormalFloat(is, negate_value, float_val);

  // Then convert to 16-bit float, saturating at infinities, and
  // rounding toward zero.
  float_val.castTo(value, kRoundToZero);

  // Overflow on 16-bit behaves the same as for 32- and 64-bit: set the
  // fail bit and set the lowest or highest value.
  if (Float16::isInfinity(value.value().getAsFloat())) {
    value.set_value(value.isNegative() ? Float16::lowest() : Float16::max());
    is.setstate(std::ios_base::failbit);
  }
  return is;
}

// Reads a HexFloat from the given stream.
// If the float is not encoded as a hex-float then it will be parsed
// as a regular float.
// This may fail if your stream does not support at least one unget.
// Nan values can be encoded with "0x1.<not zero>p+exponent_bias".
// This would normally overflow a float and round to
// infinity but this special pattern is the exact representation for a NaN,
// and therefore is actually encoded as the correct NaN. To encode inf,
// either 0x0p+exponent_bias can be specified or any exponent greater than
// exponent_bias.
// Examples using IEEE 32-bit float encoding.
//    0x1.0p+128 (+inf)
//    -0x1.0p-128 (-inf)
//
//    0x1.1p+128 (+Nan)
//    -0x1.1p+128 (-Nan)
//
//    0x1p+129 (+inf)
//    -0x1p+129 (-inf)
template <typename T, typename Traits>
std::istream& operator>>(std::istream& is, HexFloat<T, Traits>& value) {
  using HF = HexFloat<T, Traits>;
  using uint_type = typename HF::uint_type;
  using int_type = typename HF::int_type;

  value.set_value(static_cast<typename HF::native_type>(0.f));

  if (is.flags() & std::ios::skipws) {
    // If the user wants to skip whitespace , then we should obey that.
    while (std::isspace(is.peek())) {
      is.get();
    }
  }

  auto next_char = is.peek();
  bool negate_value = false;

  if (next_char != '-' && next_char != '0') {
    return ParseNormalFloat(is, negate_value, value);
  }

  if (next_char == '-') {
    negate_value = true;
    is.get();
    next_char = is.peek();
  }

  if (next_char == '0') {
    is.get();  // We may have to unget this.
    auto maybe_hex_start = is.peek();
    if (maybe_hex_start != 'x' && maybe_hex_start != 'X') {
      is.unget();
      return ParseNormalFloat(is, negate_value, value);
    } else {
      is.get();  // Throw away the 'x';
    }
  } else {
    return ParseNormalFloat(is, negate_value, value);
  }

  // This "looks" like a hex-float so treat it as one.
  bool seen_p = false;
  bool seen_dot = false;
  uint_type fraction_index = 0;

  uint_type fraction = 0;
  int_type exponent = HF::exponent_bias;

  // Strip off leading zeros so we don't have to special-case them later.
  while ((next_char = is.peek()) == '0') {
    is.get();
  }

  bool is_denorm =
      true;  // Assume denorm "representation" until we hear otherwise.
             // NB: This does not mean the value is actually denorm,
             // it just means that it was written 0.
  bool bits_written = false;  // Stays false until we write a bit.
  while (!seen_p && !seen_dot) {
    // Handle characters that are left of the fractional part.
    if (next_char == '.') {
      seen_dot = true;
    } else if (next_char == 'p') {
      seen_p = true;
    } else if (::isxdigit(next_char)) {
      // We know this is not denormalized since we have stripped all leading
      // zeroes and we are not a ".".
      is_denorm = false;
      int number = get_nibble_from_character(next_char);
      for (int i = 0; i < 4; ++i, number <<= 1) {
        uint_type write_bit = (number & 0x8) ? 0x1 : 0x0;
        if (bits_written) {
          // If we are here the bits represented belong in the fractional
          // part of the float, and we have to adjust the exponent accordingly.
          fraction = static_cast<uint_type>(
              fraction |
              static_cast<uint_type>(
                  write_bit << (HF::top_bit_left_shift - fraction_index++)));
          exponent = static_cast<int_type>(exponent + 1);
        }
        bits_written |= write_bit != 0;
      }
    } else {
      // We have not found our exponent yet, so we have to fail.
      is.setstate(std::ios::failbit);
      return is;
    }
    is.get();
    next_char = is.peek();
  }
  bits_written = false;
  while (seen_dot && !seen_p) {
    // Handle only fractional parts now.
    if (next_char == 'p') {
      seen_p = true;
    } else if (::isxdigit(next_char)) {
      int number = get_nibble_from_character(next_char);
      for (int i = 0; i < 4; ++i, number <<= 1) {
        uint_type write_bit = (number & 0x8) ? 0x01 : 0x00;
        bits_written |= write_bit != 0;
        if (is_denorm && !bits_written) {
          // Handle modifying the exponent here this way we can handle
          // an arbitrary number of hex values without overflowing our
          // integer.
          exponent = static_cast<int_type>(exponent - 1);
        } else {
          fraction = static_cast<uint_type>(
              fraction |
              static_cast<uint_type>(
                  write_bit << (HF::top_bit_left_shift - fraction_index++)));
        }
      }
    } else {
      // We still have not found our 'p' exponent yet, so this is not a valid
      // hex-float.
      is.setstate(std::ios::failbit);
      return is;
    }
    is.get();
    next_char = is.peek();
  }

  bool seen_sign = false;
  int8_t exponent_sign = 1;
  int_type written_exponent = 0;
  while (true) {
    if ((next_char == '-' || next_char == '+')) {
      if (seen_sign) {
        is.setstate(std::ios::failbit);
        return is;
      }
      seen_sign = true;
      exponent_sign = (next_char == '-') ? -1 : 1;
    } else if (::isdigit(next_char)) {
      // Hex-floats express their exponent as decimal.
      written_exponent = static_cast<int_type>(written_exponent * 10);
      written_exponent =
          static_cast<int_type>(written_exponent + (next_char - '0'));
    } else {
      break;
    }
    is.get();
    next_char = is.peek();
  }

  written_exponent = static_cast<int_type>(written_exponent * exponent_sign);
  exponent = static_cast<int_type>(exponent + written_exponent);

  bool is_zero = is_denorm && (fraction == 0);
  if (is_denorm && !is_zero) {
    fraction = static_cast<uint_type>(fraction << 1);
    exponent = static_cast<int_type>(exponent - 1);
  } else if (is_zero) {
    exponent = 0;
  }

  if (exponent <= 0 && !is_zero) {
    fraction = static_cast<uint_type>(fraction >> 1);
    fraction |= static_cast<uint_type>(1) << HF::top_bit_left_shift;
  }

  fraction = (fraction >> HF::fraction_right_shift) & HF::fraction_encode_mask;

  const int_type max_exponent =
      SetBits<uint_type, 0, HF::num_exponent_bits>::get;

  // Handle actual denorm numbers
  while (exponent < 0 && !is_zero) {
    fraction = static_cast<uint_type>(fraction >> 1);
    exponent = static_cast<int_type>(exponent + 1);

    fraction &= HF::fraction_encode_mask;
    if (fraction == 0) {
      // We have underflowed our fraction. We should clamp to zero.
      is_zero = true;
      exponent = 0;
    }
  }

  // We have overflowed so we should be inf/-inf.
  if (exponent > max_exponent) {
    exponent = max_exponent;
    fraction = 0;
  }

  uint_type output_bits = static_cast<uint_type>(
      static_cast<uint_type>(negate_value ? 1 : 0) << HF::top_bit_left_shift);
  output_bits |= fraction;

  uint_type shifted_exponent = static_cast<uint_type>(
      static_cast<uint_type>(exponent << HF::exponent_left_shift) &
      HF::exponent_mask);
  output_bits |= shifted_exponent;

  T output_float = spvutils::BitwiseCast<T>(output_bits);
  value.set_value(output_float);

  return is;
}

// Writes a FloatProxy value to a stream.
// Zero and normal numbers are printed in the usual notation, but with
// enough digits to fully reproduce the value.  Other values (subnormal,
// NaN, and infinity) are printed as a hex float.
template <typename T>
std::ostream& operator<<(std::ostream& os, const FloatProxy<T>& value) {
  auto float_val = value.getAsFloat();
  switch (std::fpclassify(float_val)) {
    case FP_ZERO:
    case FP_NORMAL: {
      auto saved_precision = os.precision();
      os.precision(std::numeric_limits<T>::digits10);
      os << float_val;
      os.precision(saved_precision);
    } break;
    default:
      os << HexFloat<FloatProxy<T>>(value);
      break;
  }
  return os;
}

template <>
inline std::ostream& operator<<<Float16>(std::ostream& os,
                                         const FloatProxy<Float16>& value) {
  os << HexFloat<FloatProxy<Float16>>(value);
  return os;
}
}

#endif  // LIBSPIRV_UTIL_HEX_FLOAT_H_