external/spirv-tools/src/test/hex_float_test.cpp

   1 // Copyright (c) 2015-2016 The Khronos Group Inc.
   2 //
   3 // Licensed under the Apache License, Version 2.0 (the "License");
   4 // you may not use this file except in compliance with the License.
   5 // You may obtain a copy of the License at
   6 //
   7 //     http://www.apache.org/licenses/LICENSE-2.0
   8 //
   9 // Unless required by applicable law or agreed to in writing, software
  10 // distributed under the License is distributed on an "AS IS" BASIS,
  11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  12 // See the License for the specific language governing permissions and
  13 // limitations under the License.
  14
  15 #include <cfloat>
  16 #include <cmath>
  17 #include <cstdio>
  18 #include <sstream>
  19 #include <string>
  20 #include <tuple>
  21
  22 #include <gmock/gmock.h>
  23
  24 #include "source/util/hex_float.h"
  25 #include "unit_spirv.h"
  26
  27 namespace {
  28 using ::testing::Eq;
  29 using spvutils::BitwiseCast;
  30 using spvutils::Float16;
  31 using spvutils::FloatProxy;
  32 using spvutils::HexFloat;
  33 using spvutils::ParseNormalFloat;
  34
  35 // In this file "encode" means converting a number into a string,
  36 // and "decode" means converting a string into a number.
  37
  38 using HexFloatTest =
  39     ::testing::TestWithParam<std::pair<FloatProxy<float>, std::string>>;
  40 using DecodeHexFloatTest =
  41     ::testing::TestWithParam<std::pair<std::string, FloatProxy<float>>>;
  42 using HexDoubleTest =
  43     ::testing::TestWithParam<std::pair<FloatProxy<double>, std::string>>;
  44 using DecodeHexDoubleTest =
  45     ::testing::TestWithParam<std::pair<std::string, FloatProxy<double>>>;
  46
  47 // Hex-encodes a float value.
  48 template <typename T>
  49 std::string EncodeViaHexFloat(const T& value) {
  50   std::stringstream ss;
  51   ss << spvutils::HexFloat<T>(value);
  52   return ss.str();
  53 }
  54
  55 // The following two tests can't be DRY because they take different parameter
  56 // types.
  57
  58 TEST_P(HexFloatTest, EncodeCorrectly) {
  59   EXPECT_THAT(EncodeViaHexFloat(GetParam().first), Eq(GetParam().second));
  60 }
  61
  62 TEST_P(HexDoubleTest, EncodeCorrectly) {
  63   EXPECT_THAT(EncodeViaHexFloat(GetParam().first), Eq(GetParam().second));
  64 }
  65
  66 // Decodes a hex-float string.
  67 template <typename T>
  68 FloatProxy<T> Decode(const std::string& str) {
  69   spvutils::HexFloat<FloatProxy<T>> decoded(0.f);
  70   EXPECT_TRUE((std::stringstream(str) >> decoded).eof());
  71   return decoded.value();
  72 }
  73
  74 TEST_P(HexFloatTest, DecodeCorrectly) {
  75   EXPECT_THAT(Decode<float>(GetParam().second), Eq(GetParam().first));
  76 }
  77
  78 TEST_P(HexDoubleTest, DecodeCorrectly) {
  79   EXPECT_THAT(Decode<double>(GetParam().second), Eq(GetParam().first));
  80 }
  81
  82 INSTANTIATE_TEST_CASE_P(
  83     Float32Tests, HexFloatTest,
  84     ::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
  85         {0.f, "0x0p+0"},
  86         {1.f, "0x1p+0"},
  87         {2.f, "0x1p+1"},
  88         {3.f, "0x1.8p+1"},
  89         {0.5f, "0x1p-1"},
  90         {0.25f, "0x1p-2"},
  91         {0.75f, "0x1.8p-1"},
  92         {-0.f, "-0x0p+0"},
  93         {-1.f, "-0x1p+0"},
  94         {-0.5f, "-0x1p-1"},
  95         {-0.25f, "-0x1p-2"},
  96         {-0.75f, "-0x1.8p-1"},
  97
  98         // Larger numbers
  99         {512.f, "0x1p+9"},
 100         {-512.f, "-0x1p+9"},
 101         {1024.f, "0x1p+10"},
 102         {-1024.f, "-0x1p+10"},
 103         {1024.f + 8.f, "0x1.02p+10"},
 104         {-1024.f - 8.f, "-0x1.02p+10"},
 105
 106         // Small numbers
 107         {1.0f / 512.f, "0x1p-9"},
 108         {1.0f / -512.f, "-0x1p-9"},
 109         {1.0f / 1024.f, "0x1p-10"},
 110         {1.0f / -1024.f, "-0x1p-10"},
 111         {1.0f / 1024.f + 1.0f / 8.f, "0x1.02p-3"},
 112         {1.0f / -1024.f - 1.0f / 8.f, "-0x1.02p-3"},
 113
 114         // lowest non-denorm
 115         {float(ldexp(1.0f, -126)), "0x1p-126"},
 116         {float(ldexp(-1.0f, -126)), "-0x1p-126"},
 117
 118         // Denormalized values
 119         {float(ldexp(1.0f, -127)), "0x1p-127"},
 120         {float(ldexp(1.0f, -127) / 2.0f), "0x1p-128"},
 121         {float(ldexp(1.0f, -127) / 4.0f), "0x1p-129"},
 122         {float(ldexp(1.0f, -127) / 8.0f), "0x1p-130"},
 123         {float(ldexp(-1.0f, -127)), "-0x1p-127"},
 124         {float(ldexp(-1.0f, -127) / 2.0f), "-0x1p-128"},
 125         {float(ldexp(-1.0f, -127) / 4.0f), "-0x1p-129"},
 126         {float(ldexp(-1.0f, -127) / 8.0f), "-0x1p-130"},
 127
 128         {float(ldexp(1.0, -127) + (ldexp(1.0, -127) / 2.0f)), "0x1.8p-127"},
 129         {float(ldexp(1.0, -127) / 2.0 + (ldexp(1.0, -127) / 4.0f)),
 130          "0x1.8p-128"},
 131
 132     })),);
 133
 134 INSTANTIATE_TEST_CASE_P(
 135     Float32NanTests, HexFloatTest,
 136     ::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
 137         // Various NAN and INF cases
 138         {uint32_t(0xFF800000), "-0x1p+128"},         // -inf
 139         {uint32_t(0x7F800000), "0x1p+128"},          // inf
 140         {uint32_t(0xFFC00000), "-0x1.8p+128"},       // -nan
 141         {uint32_t(0xFF800100), "-0x1.0002p+128"},    // -nan
 142         {uint32_t(0xFF800c00), "-0x1.0018p+128"},    // -nan
 143         {uint32_t(0xFF80F000), "-0x1.01ep+128"},     // -nan
 144         {uint32_t(0xFFFFFFFF), "-0x1.fffffep+128"},  // -nan
 145         {uint32_t(0x7FC00000), "0x1.8p+128"},        // +nan
 146         {uint32_t(0x7F800100), "0x1.0002p+128"},     // +nan
 147         {uint32_t(0x7f800c00), "0x1.0018p+128"},     // +nan
 148         {uint32_t(0x7F80F000), "0x1.01ep+128"},      // +nan
 149         {uint32_t(0x7FFFFFFF), "0x1.fffffep+128"},   // +nan
 150     })),);
 151
 152 INSTANTIATE_TEST_CASE_P(
 153     Float64Tests, HexDoubleTest,
 154     ::testing::ValuesIn(
 155         std::vector<std::pair<FloatProxy<double>, std::string>>({
 156             {0., "0x0p+0"},
 157             {1., "0x1p+0"},
 158             {2., "0x1p+1"},
 159             {3., "0x1.8p+1"},
 160             {0.5, "0x1p-1"},
 161             {0.25, "0x1p-2"},
 162             {0.75, "0x1.8p-1"},
 163             {-0., "-0x0p+0"},
 164             {-1., "-0x1p+0"},
 165             {-0.5, "-0x1p-1"},
 166             {-0.25, "-0x1p-2"},
 167             {-0.75, "-0x1.8p-1"},
 168
 169             // Larger numbers
 170             {512., "0x1p+9"},
 171             {-512., "-0x1p+9"},
 172             {1024., "0x1p+10"},
 173             {-1024., "-0x1p+10"},
 174             {1024. + 8., "0x1.02p+10"},
 175             {-1024. - 8., "-0x1.02p+10"},
 176
 177             // Large outside the range of normal floats
 178             {ldexp(1.0, 128), "0x1p+128"},
 179             {ldexp(1.0, 129), "0x1p+129"},
 180             {ldexp(-1.0, 128), "-0x1p+128"},
 181             {ldexp(-1.0, 129), "-0x1p+129"},
 182             {ldexp(1.0, 128) + ldexp(1.0, 90), "0x1.0000000004p+128"},
 183             {ldexp(1.0, 129) + ldexp(1.0, 120), "0x1.008p+129"},
 184             {ldexp(-1.0, 128) + ldexp(1.0, 90), "-0x1.fffffffff8p+127"},
 185             {ldexp(-1.0, 129) + ldexp(1.0, 120), "-0x1.ffp+128"},
 186
 187             // Small numbers
 188             {1.0 / 512., "0x1p-9"},
 189             {1.0 / -512., "-0x1p-9"},
 190             {1.0 / 1024., "0x1p-10"},
 191             {1.0 / -1024., "-0x1p-10"},
 192             {1.0 / 1024. + 1.0 / 8., "0x1.02p-3"},
 193             {1.0 / -1024. - 1.0 / 8., "-0x1.02p-3"},
 194
 195             // Small outside the range of normal floats
 196             {ldexp(1.0, -128), "0x1p-128"},
 197             {ldexp(1.0, -129), "0x1p-129"},
 198             {ldexp(-1.0, -128), "-0x1p-128"},
 199             {ldexp(-1.0, -129), "-0x1p-129"},
 200             {ldexp(1.0, -128) + ldexp(1.0, -90), "0x1.0000000004p-90"},
 201             {ldexp(1.0, -129) + ldexp(1.0, -120), "0x1.008p-120"},
 202             {ldexp(-1.0, -128) + ldexp(1.0, -90), "0x1.fffffffff8p-91"},
 203             {ldexp(-1.0, -129) + ldexp(1.0, -120), "0x1.ffp-121"},
 204
 205             // lowest non-denorm
 206             {ldexp(1.0, -1022), "0x1p-1022"},
 207             {ldexp(-1.0, -1022), "-0x1p-1022"},
 208
 209             // Denormalized values
 210             {ldexp(1.0, -1023), "0x1p-1023"},
 211             {ldexp(1.0, -1023) / 2.0, "0x1p-1024"},
 212             {ldexp(1.0, -1023) / 4.0, "0x1p-1025"},
 213             {ldexp(1.0, -1023) / 8.0, "0x1p-1026"},
 214             {ldexp(-1.0, -1024), "-0x1p-1024"},
 215             {ldexp(-1.0, -1024) / 2.0, "-0x1p-1025"},
 216             {ldexp(-1.0, -1024) / 4.0, "-0x1p-1026"},
 217             {ldexp(-1.0, -1024) / 8.0, "-0x1p-1027"},
 218
 219             {ldexp(1.0, -1023) + (ldexp(1.0, -1023) / 2.0), "0x1.8p-1023"},
 220             {ldexp(1.0, -1023) / 2.0 + (ldexp(1.0, -1023) / 4.0),
 221              "0x1.8p-1024"},
 222
 223         })),);
 224
 225 INSTANTIATE_TEST_CASE_P(
 226     Float64NanTests, HexDoubleTest,
 227     ::testing::ValuesIn(std::vector<
 228                         std::pair<FloatProxy<double>, std::string>>({
 229         // Various NAN and INF cases
 230         {uint64_t(0xFFF0000000000000LL), "-0x1p+1024"},                //-inf
 231         {uint64_t(0x7FF0000000000000LL), "0x1p+1024"},                 //+inf
 232         {uint64_t(0xFFF8000000000000LL), "-0x1.8p+1024"},              // -nan
 233         {uint64_t(0xFFF0F00000000000LL), "-0x1.0fp+1024"},             // -nan
 234         {uint64_t(0xFFF0000000000001LL), "-0x1.0000000000001p+1024"},  // -nan
 235         {uint64_t(0xFFF0000300000000LL), "-0x1.00003p+1024"},          // -nan
 236         {uint64_t(0xFFFFFFFFFFFFFFFFLL), "-0x1.fffffffffffffp+1024"},  // -nan
 237         {uint64_t(0x7FF8000000000000LL), "0x1.8p+1024"},               // +nan
 238         {uint64_t(0x7FF0F00000000000LL), "0x1.0fp+1024"},              // +nan
 239         {uint64_t(0x7FF0000000000001LL), "0x1.0000000000001p+1024"},   // -nan
 240         {uint64_t(0x7FF0000300000000LL), "0x1.00003p+1024"},           // -nan
 241         {uint64_t(0x7FFFFFFFFFFFFFFFLL), "0x1.fffffffffffffp+1024"},   // -nan
 242     })),);
 243
 244 TEST(HexFloatStreamTest, OperatorLeftShiftPreservesFloatAndFill) {
 245   std::stringstream s;
 246   s << std::setw(4) << std::oct << std::setfill('x') << 8 << " "
 247     << FloatProxy<float>(uint32_t(0xFF800100)) << " " << std::setw(4) << 9;
 248   EXPECT_THAT(s.str(), Eq(std::string("xx10 -0x1.0002p+128 xx11")));
 249 }
 250
 251 TEST(HexDoubleStreamTest, OperatorLeftShiftPreservesFloatAndFill) {
 252   std::stringstream s;
 253   s << std::setw(4) << std::oct << std::setfill('x') << 8 << " "
 254     << FloatProxy<double>(uint64_t(0x7FF0F00000000000LL)) << " " << std::setw(4)
 255     << 9;
 256   EXPECT_THAT(s.str(), Eq(std::string("xx10 0x1.0fp+1024 xx11")));
 257 }
 258
 259 TEST_P(DecodeHexFloatTest, DecodeCorrectly) {
 260   EXPECT_THAT(Decode<float>(GetParam().first), Eq(GetParam().second));
 261 }
 262
 263 TEST_P(DecodeHexDoubleTest, DecodeCorrectly) {
 264   EXPECT_THAT(Decode<double>(GetParam().first), Eq(GetParam().second));
 265 }
 266
 267 INSTANTIATE_TEST_CASE_P(
 268     Float32DecodeTests, DecodeHexFloatTest,
 269     ::testing::ValuesIn(std::vector<std::pair<std::string, FloatProxy<float>>>({
 270         {"0x0p+000", 0.f},
 271         {"0x0p0", 0.f},
 272         {"0x0p-0", 0.f},
 273
 274         // flush to zero cases
 275         {"0x1p-500", 0.f},  // Exponent underflows.
 276         {"-0x1p-500", -0.f},
 277         {"0x0.00000000001p-126", 0.f},  // Fraction causes underflow.
 278         {"-0x0.0000000001p-127", -0.f},
 279         {"-0x0.01p-142", -0.f},  // Fraction causes additional underflow.
 280         {"0x0.01p-142", 0.f},
 281
 282         // Some floats that do not encode the same way as they decode.
 283         {"0x2p+0", 2.f},
 284         {"0xFFp+0", 255.f},
 285         {"0x0.8p+0", 0.5f},
 286         {"0x0.4p+0", 0.25f},
 287     })),);
 288
 289 INSTANTIATE_TEST_CASE_P(
 290     Float32DecodeInfTests, DecodeHexFloatTest,
 291     ::testing::ValuesIn(std::vector<std::pair<std::string, FloatProxy<float>>>({
 292         // inf cases
 293         {"-0x1p+128", uint32_t(0xFF800000)},   // -inf
 294         {"0x32p+127", uint32_t(0x7F800000)},   // inf
 295         {"0x32p+500", uint32_t(0x7F800000)},   // inf
 296         {"-0x32p+127", uint32_t(0xFF800000)},  // -inf
 297     })),);
 298
 299 INSTANTIATE_TEST_CASE_P(
 300     Float64DecodeTests, DecodeHexDoubleTest,
 301     ::testing::ValuesIn(
 302         std::vector<std::pair<std::string, FloatProxy<double>>>({
 303             {"0x0p+000", 0.},
 304             {"0x0p0", 0.},
 305             {"0x0p-0", 0.},
 306
 307             // flush to zero cases
 308             {"0x1p-5000", 0.},  // Exponent underflows.
 309             {"-0x1p-5000", -0.},
 310             {"0x0.0000000000000001p-1023", 0.},  // Fraction causes underflow.
 311             {"-0x0.000000000000001p-1024", -0.},
 312             {"-0x0.01p-1090", -0.f},  // Fraction causes additional underflow.
 313             {"0x0.01p-1090", 0.},
 314
 315             // Some floats that do not encode the same way as they decode.
 316             {"0x2p+0", 2.},
 317             {"0xFFp+0", 255.},
 318             {"0x0.8p+0", 0.5},
 319             {"0x0.4p+0", 0.25},
 320         })),);
 321
 322 INSTANTIATE_TEST_CASE_P(
 323     Float64DecodeInfTests, DecodeHexDoubleTest,
 324     ::testing::ValuesIn(
 325         std::vector<std::pair<std::string, FloatProxy<double>>>({
 326             // inf cases
 327             {"-0x1p+1024", uint64_t(0xFFF0000000000000)},   // -inf
 328             {"0x32p+1023", uint64_t(0x7FF0000000000000)},   // inf
 329             {"0x32p+5000", uint64_t(0x7FF0000000000000)},   // inf
 330             {"-0x32p+1023", uint64_t(0xFFF0000000000000)},  // -inf
 331         })),);
 332
 333 TEST(FloatProxy, ValidConversion) {
 334   EXPECT_THAT(FloatProxy<float>(1.f).getAsFloat(), Eq(1.0f));
 335   EXPECT_THAT(FloatProxy<float>(32.f).getAsFloat(), Eq(32.0f));
 336   EXPECT_THAT(FloatProxy<float>(-1.f).getAsFloat(), Eq(-1.0f));
 337   EXPECT_THAT(FloatProxy<float>(0.f).getAsFloat(), Eq(0.0f));
 338   EXPECT_THAT(FloatProxy<float>(-0.f).getAsFloat(), Eq(-0.0f));
 339   EXPECT_THAT(FloatProxy<float>(1.2e32f).getAsFloat(), Eq(1.2e32f));
 340
 341   EXPECT_TRUE(std::isinf(FloatProxy<float>(uint32_t(0xFF800000)).getAsFloat()));
 342   EXPECT_TRUE(std::isinf(FloatProxy<float>(uint32_t(0x7F800000)).getAsFloat()));
 343   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFFC00000)).getAsFloat()));
 344   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF800100)).getAsFloat()));
 345   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF800c00)).getAsFloat()));
 346   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFF80F000)).getAsFloat()));
 347   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0xFFFFFFFF)).getAsFloat()));
 348   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7FC00000)).getAsFloat()));
 349   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7F800100)).getAsFloat()));
 350   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7f800c00)).getAsFloat()));
 351   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7F80F000)).getAsFloat()));
 352   EXPECT_TRUE(std::isnan(FloatProxy<float>(uint32_t(0x7FFFFFFF)).getAsFloat()));
 353
 354   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800000)).data(), Eq(0xFF800000u));
 355   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F800000)).data(), Eq(0x7F800000u));
 356   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFFC00000)).data(), Eq(0xFFC00000u));
 357   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800100)).data(), Eq(0xFF800100u));
 358   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF800c00)).data(), Eq(0xFF800c00u));
 359   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFF80F000)).data(), Eq(0xFF80F000u));
 360   EXPECT_THAT(FloatProxy<float>(uint32_t(0xFFFFFFFF)).data(), Eq(0xFFFFFFFFu));
 361   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7FC00000)).data(), Eq(0x7FC00000u));
 362   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F800100)).data(), Eq(0x7F800100u));
 363   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7f800c00)).data(), Eq(0x7f800c00u));
 364   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7F80F000)).data(), Eq(0x7F80F000u));
 365   EXPECT_THAT(FloatProxy<float>(uint32_t(0x7FFFFFFF)).data(), Eq(0x7FFFFFFFu));
 366 }
 367
 368 TEST(FloatProxy, Nan) {
 369   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFFC00000)).isNan());
 370   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF800100)).isNan());
 371   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF800c00)).isNan());
 372   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFF80F000)).isNan());
 373   EXPECT_TRUE(FloatProxy<float>(uint32_t(0xFFFFFFFF)).isNan());
 374   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7FC00000)).isNan());
 375   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7F800100)).isNan());
 376   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7f800c00)).isNan());
 377   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7F80F000)).isNan());
 378   EXPECT_TRUE(FloatProxy<float>(uint32_t(0x7FFFFFFF)).isNan());
 379 }
 380
 381 TEST(FloatProxy, Negation) {
 382   EXPECT_THAT((-FloatProxy<float>(1.f)).getAsFloat(), Eq(-1.0f));
 383   EXPECT_THAT((-FloatProxy<float>(0.f)).getAsFloat(), Eq(-0.0f));
 384
 385   EXPECT_THAT((-FloatProxy<float>(-1.f)).getAsFloat(), Eq(1.0f));
 386   EXPECT_THAT((-FloatProxy<float>(-0.f)).getAsFloat(), Eq(0.0f));
 387
 388   EXPECT_THAT((-FloatProxy<float>(32.f)).getAsFloat(), Eq(-32.0f));
 389   EXPECT_THAT((-FloatProxy<float>(-32.f)).getAsFloat(), Eq(32.0f));
 390
 391   EXPECT_THAT((-FloatProxy<float>(1.2e32f)).getAsFloat(), Eq(-1.2e32f));
 392   EXPECT_THAT((-FloatProxy<float>(-1.2e32f)).getAsFloat(), Eq(1.2e32f));
 393
 394   EXPECT_THAT(
 395       (-FloatProxy<float>(std::numeric_limits<float>::infinity())).getAsFloat(),
 396       Eq(-std::numeric_limits<float>::infinity()));
 397   EXPECT_THAT((-FloatProxy<float>(-std::numeric_limits<float>::infinity()))
 398                   .getAsFloat(),
 399               Eq(std::numeric_limits<float>::infinity()));
 400 }
 401
 402 // Test conversion of FloatProxy values to strings.
 403 //
 404 // In previous cases, we always wrapped the FloatProxy value in a HexFloat
 405 // before conversion to a string.  In the following cases, the FloatProxy
 406 // decides for itself whether to print as a regular number or as a hex float.
 407
 408 using FloatProxyFloatTest =
 409     ::testing::TestWithParam<std::pair<FloatProxy<float>, std::string>>;
 410 using FloatProxyDoubleTest =
 411     ::testing::TestWithParam<std::pair<FloatProxy<double>, std::string>>;
 412
 413 // Converts a float value to a string via a FloatProxy.
 414 template <typename T>
 415 std::string EncodeViaFloatProxy(const T& value) {
 416   std::stringstream ss;
 417   ss << value;
 418   return ss.str();
 419 }
 420
 421 // Converts a floating point string so that the exponent prefix
 422 // is 'e', and the exponent value does not have leading zeros.
 423 // The Microsoft runtime library likes to write things like "2.5E+010".
 424 // Convert that to "2.5e+10".
 425 // We don't care what happens to strings that are not floating point
 426 // strings.
 427 std::string NormalizeExponentInFloatString(std::string in) {
 428   std::string result;
 429   // Reserve one spot for the terminating null, even when the sscanf fails.
 430   std::vector<char> prefix(in.size() + 1);
 431   char e;
 432   char plus_or_minus;
 433   int exponent;  // in base 10
 434   if ((4 == std::sscanf(in.c_str(), "%[-+.0123456789]%c%c%d", prefix.data(), &e,
 435                         &plus_or_minus, &exponent)) &&
 436       (e == 'e' || e == 'E') &&
 437       (plus_or_minus == '-' || plus_or_minus == '+')) {
 438     // It looks like a floating point value with exponent.
 439     std::stringstream out;
 440     out << prefix.data() << 'e' << plus_or_minus << exponent;
 441     result = out.str();
 442   } else {
 443     result = in;
 444   }
 445   return result;
 446 }
 447
 448 TEST(NormalizeFloat, Sample) {
 449   EXPECT_THAT(NormalizeExponentInFloatString(""), Eq(""));
 450   EXPECT_THAT(NormalizeExponentInFloatString("1e-12"), Eq("1e-12"));
 451   EXPECT_THAT(NormalizeExponentInFloatString("1E+14"), Eq("1e+14"));
 452   EXPECT_THAT(NormalizeExponentInFloatString("1e-0012"), Eq("1e-12"));
 453   EXPECT_THAT(NormalizeExponentInFloatString("1.263E+014"), Eq("1.263e+14"));
 454 }
 455
 456 // The following two tests can't be DRY because they take different parameter
 457 // types.
 458 TEST_P(FloatProxyFloatTest, EncodeCorrectly) {
 459   EXPECT_THAT(
 460       NormalizeExponentInFloatString(EncodeViaFloatProxy(GetParam().first)),
 461       Eq(GetParam().second));
 462 }
 463
 464 TEST_P(FloatProxyDoubleTest, EncodeCorrectly) {
 465   EXPECT_THAT(
 466       NormalizeExponentInFloatString(EncodeViaFloatProxy(GetParam().first)),
 467       Eq(GetParam().second));
 468 }
 469
 470 INSTANTIATE_TEST_CASE_P(
 471     Float32Tests, FloatProxyFloatTest,
 472     ::testing::ValuesIn(std::vector<std::pair<FloatProxy<float>, std::string>>({
 473         // Zero
 474         {0.f, "0"},
 475         // Normal numbers
 476         {1.f, "1"},
 477         {-0.25f, "-0.25"},
 478         {1000.0f, "1000"},
 479
 480         // Still normal numbers, but with large magnitude exponents.
 481         {float(ldexp(1.f, 126)), "8.50706e+37"},
 482         {float(ldexp(-1.f, -126)), "-1.17549e-38"},
 483
 484         // denormalized values are printed as hex floats.
 485         {float(ldexp(1.0f, -127)), "0x1p-127"},
 486         {float(ldexp(1.5f, -128)), "0x1.8p-128"},
 487         {float(ldexp(1.25, -129)), "0x1.4p-129"},
 488         {float(ldexp(1.125, -130)), "0x1.2p-130"},
 489         {float(ldexp(-1.0f, -127)), "-0x1p-127"},
 490         {float(ldexp(-1.0f, -128)), "-0x1p-128"},
 491         {float(ldexp(-1.0f, -129)), "-0x1p-129"},
 492         {float(ldexp(-1.5f, -130)), "-0x1.8p-130"},
 493
 494         // NaNs
 495         {FloatProxy<float>(uint32_t(0xFFC00000)), "-0x1.8p+128"},
 496         {FloatProxy<float>(uint32_t(0xFF800100)), "-0x1.0002p+128"},
 497
 498         {std::numeric_limits<float>::infinity(), "0x1p+128"},
 499         {-std::numeric_limits<float>::infinity(), "-0x1p+128"},
 500     })),);
 501
 502 INSTANTIATE_TEST_CASE_P(
 503     Float64Tests, FloatProxyDoubleTest,
 504     ::testing::ValuesIn(
 505         std::vector<std::pair<FloatProxy<double>, std::string>>({
 506             {0., "0"},
 507             {1., "1"},
 508             {-0.25, "-0.25"},
 509             {1000.0, "1000"},
 510
 511             // Large outside the range of normal floats
 512             {ldexp(1.0, 128), "3.40282366920938e+38"},
 513             {ldexp(1.5, 129), "1.02084710076282e+39"},
 514             {ldexp(-1.0, 128), "-3.40282366920938e+38"},
 515             {ldexp(-1.5, 129), "-1.02084710076282e+39"},
 516
 517             // Small outside the range of normal floats
 518             {ldexp(1.5, -129), "2.20405190779179e-39"},
 519             {ldexp(-1.5, -129), "-2.20405190779179e-39"},
 520
 521             // lowest non-denorm
 522             {ldexp(1.0, -1022), "2.2250738585072e-308"},
 523             {ldexp(-1.0, -1022), "-2.2250738585072e-308"},
 524
 525             // Denormalized values
 526             {ldexp(1.125, -1023), "0x1.2p-1023"},
 527             {ldexp(-1.375, -1024), "-0x1.6p-1024"},
 528
 529             // NaNs
 530             {uint64_t(0x7FF8000000000000LL), "0x1.8p+1024"},
 531             {uint64_t(0xFFF0F00000000000LL), "-0x1.0fp+1024"},
 532
 533             // Infinity
 534             {std::numeric_limits<double>::infinity(), "0x1p+1024"},
 535             {-std::numeric_limits<double>::infinity(), "-0x1p+1024"},
 536
 537         })),);
 538
 539 // double is used so that unbiased_exponent can be used with the output
 540 // of ldexp directly.
 541 int32_t unbiased_exponent(double f) {
 542   return spvutils::HexFloat<spvutils::FloatProxy<float>>(
 543       static_cast<float>(f)).getUnbiasedNormalizedExponent();
 544 }
 545
 546 int16_t unbiased_half_exponent(uint16_t f) {
 547   return spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>(f)
 548       .getUnbiasedNormalizedExponent();
 549 }
 550
 551 TEST(HexFloatOperationTest, UnbiasedExponent) {
 552   // Float cases
 553   EXPECT_EQ(0, unbiased_exponent(ldexp(1.0f, 0)));
 554   EXPECT_EQ(-32, unbiased_exponent(ldexp(1.0f, -32)));
 555   EXPECT_EQ(42, unbiased_exponent(ldexp(1.0f, 42)));
 556   EXPECT_EQ(125, unbiased_exponent(ldexp(1.0f, 125)));
 557   // Saturates to 128
 558   EXPECT_EQ(128, unbiased_exponent(ldexp(1.0f, 256)));
 559
 560   EXPECT_EQ(-100, unbiased_exponent(ldexp(1.0f, -100)));
 561   EXPECT_EQ(-127, unbiased_exponent(ldexp(1.0f, -127))); // First denorm
 562   EXPECT_EQ(-128, unbiased_exponent(ldexp(1.0f, -128)));
 563   EXPECT_EQ(-129, unbiased_exponent(ldexp(1.0f, -129)));
 564   EXPECT_EQ(-140, unbiased_exponent(ldexp(1.0f, -140)));
 565   // Smallest representable number
 566   EXPECT_EQ(-126 - 23, unbiased_exponent(ldexp(1.0f, -126 - 23)));
 567   // Should get rounded to 0 first.
 568   EXPECT_EQ(0, unbiased_exponent(ldexp(1.0f, -127 - 23)));
 569
 570   // Float16 cases
 571   // The exponent is represented in the bits 0x7C00
 572   // The offset is -15
 573   EXPECT_EQ(0, unbiased_half_exponent(0x3C00));
 574   EXPECT_EQ(3, unbiased_half_exponent(0x4800));
 575   EXPECT_EQ(-1, unbiased_half_exponent(0x3800));
 576   EXPECT_EQ(-14, unbiased_half_exponent(0x0400));
 577   EXPECT_EQ(16, unbiased_half_exponent(0x7C00));
 578   EXPECT_EQ(10, unbiased_half_exponent(0x6400));
 579
 580   // Smallest representable number
 581   EXPECT_EQ(-24, unbiased_half_exponent(0x0001));
 582 }
 583
 584 // Creates a float that is the sum of 1/(2 ^ fractions[i]) for i in factions
 585 float float_fractions(const std::vector<uint32_t>& fractions) {
 586   float f = 0;
 587   for(int32_t i: fractions) {
 588     f += std::ldexp(1.0f, -i);
 589   }
 590   return f;
 591 }
 592
 593 // Returns the normalized significand of a HexFloat<FloatProxy<float>>
 594 // that was created by calling float_fractions with the input fractions,
 595 // raised to the power of exp.
 596 uint32_t normalized_significand(const std::vector<uint32_t>& fractions, uint32_t exp) {
 597   return spvutils::HexFloat<spvutils::FloatProxy<float>>(
 598              static_cast<float>(ldexp(float_fractions(fractions), exp)))
 599       .getNormalizedSignificand();
 600 }
 601
 602 // Sets the bits from MSB to LSB of the significand part of a float.
 603 // For example 0 would set the bit 23 (counting from LSB to MSB),
 604 // and 1 would set the 22nd bit.
 605 uint32_t bits_set(const std::vector<uint32_t>& bits) {
 606   const uint32_t top_bit = 1u << 22u;
 607   uint32_t val= 0;
 608   for(uint32_t i: bits) {
 609     val |= top_bit >> i;
 610   }
 611   return val;
 612 }
 613
 614 // The same as bits_set but for a Float16 value instead of 32-bit floating
 615 // point.
 616 uint16_t half_bits_set(const std::vector<uint32_t>& bits) {
 617   const uint32_t top_bit = 1u << 9u;
 618   uint32_t val= 0;
 619   for(uint32_t i: bits) {
 620     val |= top_bit >> i;
 621   }
 622   return static_cast<uint16_t>(val);
 623 }
 624
 625 TEST(HexFloatOperationTest, NormalizedSignificand) {
 626   // For normalized numbers (the following) it should be a simple matter
 627   // of getting rid of the top implicit bit
 628   EXPECT_EQ(bits_set({}), normalized_significand({0}, 0));
 629   EXPECT_EQ(bits_set({0}), normalized_significand({0, 1}, 0));
 630   EXPECT_EQ(bits_set({0, 1}), normalized_significand({0, 1, 2}, 0));
 631   EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 0));
 632   EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 32));
 633   EXPECT_EQ(bits_set({1}), normalized_significand({0, 2}, 126));
 634
 635   // For denormalized numbers we expect the normalized significand to
 636   // shift as if it were normalized. This means, in practice that the
 637   // top_most set bit will be cut off. Looks very similar to above (on purpose)
 638   EXPECT_EQ(bits_set({}), normalized_significand({0}, -127));
 639   EXPECT_EQ(bits_set({3}), normalized_significand({0, 4}, -128));
 640   EXPECT_EQ(bits_set({3}), normalized_significand({0, 4}, -127));
 641   EXPECT_EQ(bits_set({}), normalized_significand({22}, -127));
 642   EXPECT_EQ(bits_set({0}), normalized_significand({21, 22}, -127));
 643 }
 644
 645 // Returns the 32-bit floating point value created by
 646 // calling setFromSignUnbiasedExponentAndNormalizedSignificand
 647 // on a HexFloat<FloatProxy<float>>
 648 float set_from_sign(bool negative, int32_t unbiased_exponent,
 649                    uint32_t significand, bool round_denorm_up) {
 650   spvutils::HexFloat<spvutils::FloatProxy<float>>  f(0.f);
 651   f.setFromSignUnbiasedExponentAndNormalizedSignificand(
 652       negative, unbiased_exponent, significand, round_denorm_up);
 653   return f.value().getAsFloat();
 654 }
 655
 656 TEST(HexFloatOperationTests,
 657      SetFromSignUnbiasedExponentAndNormalizedSignificand) {
 658
 659   EXPECT_EQ(1.f, set_from_sign(false, 0, 0, false));
 660
 661   // Tests insertion of various denormalized numbers with and without round up.
 662   EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)), set_from_sign(false, -149, 0, false));
 663   EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)), set_from_sign(false, -149, 0, true));
 664   EXPECT_EQ(0.f, set_from_sign(false, -150, 1, false));
 665   EXPECT_EQ(static_cast<float>(ldexp(1.f, -149)), set_from_sign(false, -150, 1, true));
 666
 667   EXPECT_EQ(ldexp(1.0f, -127), set_from_sign(false, -127, 0, false));
 668   EXPECT_EQ(ldexp(1.0f, -128), set_from_sign(false, -128, 0, false));
 669   EXPECT_EQ(float_fractions({0, 1, 2, 5}),
 670             set_from_sign(false, 0, bits_set({0, 1, 4}), false));
 671   EXPECT_EQ(ldexp(float_fractions({0, 1, 2, 5}), -32),
 672             set_from_sign(false, -32, bits_set({0, 1, 4}), false));
 673   EXPECT_EQ(ldexp(float_fractions({0, 1, 2, 5}), -128),
 674             set_from_sign(false, -128, bits_set({0, 1, 4}), false));
 675
 676   // The negative cases from above.
 677   EXPECT_EQ(-1.f, set_from_sign(true, 0, 0, false));
 678   EXPECT_EQ(-ldexp(1.0, -127), set_from_sign(true, -127, 0, false));
 679   EXPECT_EQ(-ldexp(1.0, -128), set_from_sign(true, -128, 0, false));
 680   EXPECT_EQ(-float_fractions({0, 1, 2, 5}),
 681             set_from_sign(true, 0, bits_set({0, 1, 4}), false));
 682   EXPECT_EQ(-ldexp(float_fractions({0, 1, 2, 5}), -32),
 683             set_from_sign(true, -32, bits_set({0, 1, 4}), false));
 684   EXPECT_EQ(-ldexp(float_fractions({0, 1, 2, 5}), -128),
 685             set_from_sign(true, -128, bits_set({0, 1, 4}), false));
 686 }
 687
 688 TEST(HexFloatOperationTests, NonRounding) {
 689   // Rounding from 32-bit hex-float to 32-bit hex-float should be trivial,
 690   // except in the denorm case which is a bit more complex.
 691   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 692   bool carry_bit = false;
 693
 694   spvutils::round_direction rounding[] = {
 695       spvutils::round_direction::kToZero,
 696       spvutils::round_direction::kToNearestEven,
 697       spvutils::round_direction::kToPositiveInfinity,
 698       spvutils::round_direction::kToNegativeInfinity};
 699
 700   // Everything fits, so this should be straight-forward
 701   for (spvutils::round_direction round : rounding) {
 702     EXPECT_EQ(bits_set({}), HF(0.f).getRoundedNormalizedSignificand<HF>(
 703                                 round, &carry_bit));
 704     EXPECT_FALSE(carry_bit);
 705
 706     EXPECT_EQ(bits_set({0}),
 707               HF(float_fractions({0, 1}))
 708                   .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 709     EXPECT_FALSE(carry_bit);
 710
 711     EXPECT_EQ(bits_set({1, 3}),
 712               HF(float_fractions({0, 2, 4}))
 713                   .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 714     EXPECT_FALSE(carry_bit);
 715
 716     EXPECT_EQ(
 717         bits_set({0, 1, 4}),
 718         HF(static_cast<float>(-ldexp(float_fractions({0, 1, 2, 5}), -128)))
 719             .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 720     EXPECT_FALSE(carry_bit);
 721
 722     EXPECT_EQ(
 723         bits_set({0, 1, 4, 22}),
 724         HF(static_cast<float>(float_fractions({0, 1, 2, 5, 23})))
 725             .getRoundedNormalizedSignificand<HF>(round, &carry_bit));
 726     EXPECT_FALSE(carry_bit);
 727   }
 728 }
 729
 730 using RD = spvutils::round_direction;
 731 struct RoundSignificandCase {
 732   float source_float;
 733   std::pair<int16_t, bool> expected_results;
 734   spvutils::round_direction round;
 735 };
 736
 737 using HexFloatRoundTest =
 738     ::testing::TestWithParam<RoundSignificandCase>;
 739
 740 TEST_P(HexFloatRoundTest, RoundDownToFP16) {
 741   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 742   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 743
 744   HF input_value(GetParam().source_float);
 745   bool carry_bit = false;
 746   EXPECT_EQ(GetParam().expected_results.first,
 747             input_value.getRoundedNormalizedSignificand<HF16>(
 748                 GetParam().round, &carry_bit));
 749   EXPECT_EQ(carry_bit, GetParam().expected_results.second);
 750 }
 751
 752 // clang-format off
 753 INSTANTIATE_TEST_CASE_P(F32ToF16, HexFloatRoundTest,
 754   ::testing::ValuesIn(std::vector<RoundSignificandCase>(
 755   {
 756     {float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToZero},
 757     {float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToNearestEven},
 758     {float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToPositiveInfinity},
 759     {float_fractions({0}), std::make_pair(half_bits_set({}), false), RD::kToNegativeInfinity},
 760     {float_fractions({0, 1}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
 761
 762     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
 763     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
 764     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
 765     {float_fractions({0, 1, 11}), std::make_pair(half_bits_set({0}), false), RD::kToNearestEven},
 766
 767     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 9}), false), RD::kToZero},
 768     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 8}), false), RD::kToPositiveInfinity},
 769     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNegativeInfinity},
 770     {float_fractions({0, 1, 10, 11}), std::make_pair(half_bits_set({0, 8}), false), RD::kToNearestEven},
 771
 772     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
 773     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
 774     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
 775     {float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
 776
 777     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
 778     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0}), false), RD::kToPositiveInfinity},
 779     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNegativeInfinity},
 780     {-float_fractions({0, 1, 11, 12}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
 781
 782     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0}), false), RD::kToZero},
 783     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
 784     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
 785     {float_fractions({0, 1, 11, 22}), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
 786
 787     // Carries
 788     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), false), RD::kToZero},
 789     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({}), true), RD::kToPositiveInfinity},
 790     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), false), RD::kToNegativeInfinity},
 791     {float_fractions({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}), std::make_pair(half_bits_set({}), true), RD::kToNearestEven},
 792
 793     // Cases where original number was denorm. Note: this should have no effect
 794     // the number is pre-normalized.
 795     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -128)), std::make_pair(half_bits_set({0}), false), RD::kToZero},
 796     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -129)), std::make_pair(half_bits_set({0, 9}), false), RD::kToPositiveInfinity},
 797     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -131)), std::make_pair(half_bits_set({0}), false), RD::kToNegativeInfinity},
 798     {static_cast<float>(ldexp(float_fractions({0, 1, 11, 13}), -130)), std::make_pair(half_bits_set({0, 9}), false), RD::kToNearestEven},
 799   })),);
 800 // clang-format on
 801
 802 struct UpCastSignificandCase {
 803   uint16_t source_half;
 804   uint32_t expected_result;
 805 };
 806
 807 using HexFloatRoundUpSignificandTest =
 808     ::testing::TestWithParam<UpCastSignificandCase>;
 809 TEST_P(HexFloatRoundUpSignificandTest, Widening) {
 810   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 811   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 812   bool carry_bit = false;
 813
 814   spvutils::round_direction rounding[] = {
 815       spvutils::round_direction::kToZero,
 816       spvutils::round_direction::kToNearestEven,
 817       spvutils::round_direction::kToPositiveInfinity,
 818       spvutils::round_direction::kToNegativeInfinity};
 819
 820   // Everything fits, so everything should just be bit-shifts.
 821   for (spvutils::round_direction round : rounding) {
 822     carry_bit = false;
 823     HF16 input_value(GetParam().source_half);
 824     EXPECT_EQ(
 825         GetParam().expected_result,
 826         input_value.getRoundedNormalizedSignificand<HF>(round, &carry_bit))
 827         << std::hex << "0x"
 828         << input_value.getRoundedNormalizedSignificand<HF>(round, &carry_bit)
 829         << "  0x" << GetParam().expected_result;
 830     EXPECT_FALSE(carry_bit);
 831   }
 832 }
 833
 834 INSTANTIATE_TEST_CASE_P(F16toF32, HexFloatRoundUpSignificandTest,
 835   // 0xFC00 of the source 16-bit hex value cover the sign and the exponent.
 836   // They are ignored for this test.
 837   ::testing::ValuesIn(std::vector<UpCastSignificandCase>(
 838   {
 839     {0x3F00, 0x600000},
 840     {0x0F00, 0x600000},
 841     {0x0F01, 0x602000},
 842     {0x0FFF, 0x7FE000},
 843   })),);
 844
 845 struct DownCastTest {
 846   float source_float;
 847   uint16_t expected_half;
 848   std::vector<spvutils::round_direction> directions;
 849 };
 850
 851 std::string get_round_text(spvutils::round_direction direction) {
 852 #define CASE(round_direction) \
 853   case round_direction:      \
 854     return #round_direction
 855
 856   switch (direction) {
 857     CASE(spvutils::round_direction::kToZero);
 858     CASE(spvutils::round_direction::kToPositiveInfinity);
 859     CASE(spvutils::round_direction::kToNegativeInfinity);
 860     CASE(spvutils::round_direction::kToNearestEven);
 861   }
 862 #undef CASE
 863   return "";
 864 }
 865
 866 using HexFloatFP32To16Tests = ::testing::TestWithParam<DownCastTest>;
 867
 868 TEST_P(HexFloatFP32To16Tests, NarrowingCasts) {
 869   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 870   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 871   HF f(GetParam().source_float);
 872   for (auto round : GetParam().directions) {
 873     HF16 half(0);
 874     f.castTo(half, round);
 875     EXPECT_EQ(GetParam().expected_half, half.value().getAsFloat().get_value())
 876         << get_round_text(round) << "  " << std::hex
 877         << spvutils::BitwiseCast<uint32_t>(GetParam().source_float)
 878         << " cast to: " << half.value().getAsFloat().get_value();
 879   }
 880 }
 881
 882 const uint16_t positive_infinity = 0x7C00;
 883 const uint16_t negative_infinity = 0xFC00;
 884
 885 INSTANTIATE_TEST_CASE_P(F32ToF16, HexFloatFP32To16Tests,
 886   ::testing::ValuesIn(std::vector<DownCastTest>(
 887   {
 888     // Exactly representable as half.
 889     {0.f, 0x0, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 890     {-0.f, 0x8000, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 891     {1.0f, 0x3C00, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 892     {-1.0f, 0xBC00, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 893
 894     {float_fractions({0, 1, 10}) , 0x3E01, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 895     {-float_fractions({0, 1, 10}) , 0xBE01, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 896     {static_cast<float>(ldexp(float_fractions({0, 1, 10}), 3)), 0x4A01, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 897     {static_cast<float>(-ldexp(float_fractions({0, 1, 10}), 3)), 0xCA01, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 898
 899
 900     // Underflow
 901     {static_cast<float>(ldexp(1.0f, -25)), 0x0, {RD::kToZero, RD::kToNegativeInfinity, RD::kToNearestEven}},
 902     {static_cast<float>(ldexp(1.0f, -25)), 0x1, {RD::kToPositiveInfinity}},
 903     {static_cast<float>(-ldexp(1.0f, -25)), 0x8000, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNearestEven}},
 904     {static_cast<float>(-ldexp(1.0f, -25)), 0x8001, {RD::kToNegativeInfinity}},
 905     {static_cast<float>(ldexp(1.0f, -24)), 0x1, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 906
 907     // Overflow
 908     {static_cast<float>(ldexp(1.0f, 16)), positive_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 909     {static_cast<float>(ldexp(1.0f, 18)), positive_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 910     {static_cast<float>(ldexp(1.3f, 16)), positive_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 911     {static_cast<float>(-ldexp(1.0f, 16)), negative_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 912     {static_cast<float>(-ldexp(1.0f, 18)), negative_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 913     {static_cast<float>(-ldexp(1.3f, 16)), negative_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 914
 915     // Transfer of Infinities
 916     {std::numeric_limits<float>::infinity(), positive_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 917     {-std::numeric_limits<float>::infinity(), negative_infinity, {RD::kToZero, RD::kToPositiveInfinity, RD::kToNegativeInfinity, RD::kToNearestEven}},
 918
 919     // Nans are below because we cannot test for equality.
 920   })),);
 921
 922 struct UpCastCase{
 923   uint16_t source_half;
 924   float expected_float;
 925 };
 926
 927 using HexFloatFP16To32Tests = ::testing::TestWithParam<UpCastCase>;
 928 TEST_P(HexFloatFP16To32Tests, WideningCasts) {
 929   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 930   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 931   HF16 f(GetParam().source_half);
 932
 933   spvutils::round_direction rounding[] = {
 934       spvutils::round_direction::kToZero,
 935       spvutils::round_direction::kToNearestEven,
 936       spvutils::round_direction::kToPositiveInfinity,
 937       spvutils::round_direction::kToNegativeInfinity};
 938
 939   // Everything fits, so everything should just be bit-shifts.
 940   for (spvutils::round_direction round : rounding) {
 941     HF flt(0.f);
 942     f.castTo(flt, round);
 943     EXPECT_EQ(GetParam().expected_float, flt.value().getAsFloat())
 944         << get_round_text(round) << "  " << std::hex
 945         << spvutils::BitwiseCast<uint16_t>(GetParam().source_half)
 946         << " cast to: " << flt.value().getAsFloat();
 947   }
 948 }
 949
 950 INSTANTIATE_TEST_CASE_P(F16ToF32, HexFloatFP16To32Tests,
 951   ::testing::ValuesIn(std::vector<UpCastCase>(
 952   {
 953     {0x0000, 0.f},
 954     {0x8000, -0.f},
 955     {0x3C00, 1.0f},
 956     {0xBC00, -1.0f},
 957     {0x3F00, float_fractions({0, 1, 2})},
 958     {0xBF00, -float_fractions({0, 1, 2})},
 959     {0x3F01, float_fractions({0, 1, 2, 10})},
 960     {0xBF01, -float_fractions({0, 1, 2, 10})},
 961
 962     // denorm
 963     {0x0001, static_cast<float>(ldexp(1.0, -24))},
 964     {0x0002, static_cast<float>(ldexp(1.0, -23))},
 965     {0x8001, static_cast<float>(-ldexp(1.0, -24))},
 966     {0x8011, static_cast<float>(-ldexp(1.0, -20) + -ldexp(1.0, -24))},
 967
 968     // inf
 969     {0x7C00, std::numeric_limits<float>::infinity()},
 970     {0xFC00, -std::numeric_limits<float>::infinity()},
 971   })),);
 972
 973 TEST(HexFloatOperationTests, NanTests) {
 974   using HF = spvutils::HexFloat<spvutils::FloatProxy<float>>;
 975   using HF16 = spvutils::HexFloat<spvutils::FloatProxy<spvutils::Float16>>;
 976   spvutils::round_direction rounding[] = {
 977       spvutils::round_direction::kToZero,
 978       spvutils::round_direction::kToNearestEven,
 979       spvutils::round_direction::kToPositiveInfinity,
 980       spvutils::round_direction::kToNegativeInfinity};
 981
 982   // Everything fits, so everything should just be bit-shifts.
 983   for (spvutils::round_direction round : rounding) {
 984     HF16 f16(0);
 985     HF f(0.f);
 986     HF(std::numeric_limits<float>::quiet_NaN()).castTo(f16, round);
 987     EXPECT_TRUE(f16.value().isNan());
 988     HF(std::numeric_limits<float>::signaling_NaN()).castTo(f16, round);
 989     EXPECT_TRUE(f16.value().isNan());
 990
 991     HF16(0x7C01).castTo(f, round);
 992     EXPECT_TRUE(f.value().isNan());
 993     HF16(0x7C11).castTo(f, round);
 994     EXPECT_TRUE(f.value().isNan());
 995     HF16(0xFC01).castTo(f, round);
 996     EXPECT_TRUE(f.value().isNan());
 997     HF16(0x7C10).castTo(f, round);
 998     EXPECT_TRUE(f.value().isNan());
 999     HF16(0xFF00).castTo(f, round);
1000     EXPECT_TRUE(f.value().isNan());
1001   }
1002 }
1003
1004 // A test case for parsing good and bad HexFloat<FloatProxy<T>> literals.
1005 template <typename T>
1006 struct FloatParseCase {
1007   std::string literal;
1008   bool negate_value;
1009   bool expect_success;
1010   HexFloat<FloatProxy<T>> expected_value;
1011 };
1012
1013 using ParseNormalFloatTest = ::testing::TestWithParam<FloatParseCase<float>>;
1014
1015 TEST_P(ParseNormalFloatTest, Samples) {
1016   std::stringstream input(GetParam().literal);
1017   HexFloat<FloatProxy<float>> parsed_value(0.0f);
1018   ParseNormalFloat(input, GetParam().negate_value, parsed_value);
1019   EXPECT_NE(GetParam().expect_success, input.fail())
1020       << " literal: " << GetParam().literal
1021       << " negate: " << GetParam().negate_value;
1022   if (GetParam().expect_success) {
1023     EXPECT_THAT(parsed_value.value(), Eq(GetParam().expected_value.value()))
1024         << " literal: " << GetParam().literal
1025         << " negate: " << GetParam().negate_value;
1026   }
1027 }
1028
1029 // Returns a FloatParseCase with expected failure.
1030 template <typename T>
1031 FloatParseCase<T> BadFloatParseCase(std::string literal, bool negate_value,
1032                                     T expected_value) {
1033   HexFloat<FloatProxy<T>> proxy_expected_value(expected_value);
1034   return FloatParseCase<T>{literal, negate_value, false, proxy_expected_value};
1035 }
1036
1037 // Returns a FloatParseCase that should successfully parse to a given value.
1038 template <typename T>
1039 FloatParseCase<T> GoodFloatParseCase(std::string literal, bool negate_value,
1040                                      T expected_value) {
1041   HexFloat<FloatProxy<T>> proxy_expected_value(expected_value);
1042   return FloatParseCase<T>{literal, negate_value, true, proxy_expected_value};
1043 }
1044
1045 INSTANTIATE_TEST_CASE_P(
1046     FloatParse, ParseNormalFloatTest,
1047     ::testing::ValuesIn(std::vector<FloatParseCase<float>>{
1048         // Failing cases due to trivially incorrect syntax.
1049         BadFloatParseCase("abc", false, 0.0f),
1050         BadFloatParseCase("abc", true, 0.0f),
1051
1052         // Valid cases.
1053         GoodFloatParseCase("0", false, 0.0f),
1054         GoodFloatParseCase("0.0", false, 0.0f),
1055         GoodFloatParseCase("-0.0", false, -0.0f),
1056         GoodFloatParseCase("2.0", false, 2.0f),
1057         GoodFloatParseCase("-2.0", false, -2.0f),
1058         GoodFloatParseCase("+2.0", false, 2.0f),
1059         // Cases with negate_value being true.
1060         GoodFloatParseCase("0.0", true, -0.0f),
1061         GoodFloatParseCase("2.0", true, -2.0f),
1062
1063         // When negate_value is true, we should not accept a
1064         // leading minus or plus.
1065         BadFloatParseCase("-0.0", true, 0.0f),
1066         BadFloatParseCase("-2.0", true, 0.0f),
1067         BadFloatParseCase("+0.0", true, 0.0f),
1068         BadFloatParseCase("+2.0", true, 0.0f),
1069
1070         // Overflow is an error for 32-bit float parsing.
1071         BadFloatParseCase("1e40", false, FLT_MAX),
1072         BadFloatParseCase("1e40", true, -FLT_MAX),
1073         BadFloatParseCase("-1e40", false, -FLT_MAX),
1074         // We can't have -1e40 and negate_value == true since
1075         // that represents an original case of "--1e40" which
1076         // is invalid.
1077   }),);
1078
1079 using ParseNormalFloat16Test =
1080     ::testing::TestWithParam<FloatParseCase<Float16>>;
1081
1082 TEST_P(ParseNormalFloat16Test, Samples) {
1083   std::stringstream input(GetParam().literal);
1084   HexFloat<FloatProxy<Float16>> parsed_value(0);
1085   ParseNormalFloat(input, GetParam().negate_value, parsed_value);
1086   EXPECT_NE(GetParam().expect_success, input.fail())
1087       << " literal: " << GetParam().literal
1088       << " negate: " << GetParam().negate_value;
1089   if (GetParam().expect_success) {
1090     EXPECT_THAT(parsed_value.value(), Eq(GetParam().expected_value.value()))
1091         << " literal: " << GetParam().literal
1092         << " negate: " << GetParam().negate_value;
1093   }
1094 }
1095
1096 INSTANTIATE_TEST_CASE_P(
1097     Float16Parse, ParseNormalFloat16Test,
1098     ::testing::ValuesIn(std::vector<FloatParseCase<Float16>>{
1099         // Failing cases due to trivially incorrect syntax.
1100         BadFloatParseCase<Float16>("abc", false, uint16_t{0}),
1101         BadFloatParseCase<Float16>("abc", true, uint16_t{0}),
1102
1103         // Valid cases.
1104         GoodFloatParseCase<Float16>("0", false, uint16_t{0}),
1105         GoodFloatParseCase<Float16>("0.0", false, uint16_t{0}),
1106         GoodFloatParseCase<Float16>("-0.0", false, uint16_t{0x8000}),
1107         GoodFloatParseCase<Float16>("2.0", false, uint16_t{0x4000}),
1108         GoodFloatParseCase<Float16>("-2.0", false, uint16_t{0xc000}),
1109         GoodFloatParseCase<Float16>("+2.0", false, uint16_t{0x4000}),
1110         // Cases with negate_value being true.
1111         GoodFloatParseCase<Float16>("0.0", true, uint16_t{0x8000}),
1112         GoodFloatParseCase<Float16>("2.0", true, uint16_t{0xc000}),
1113
1114         // When negate_value is true, we should not accept a leading minus or
1115         // plus.
1116         BadFloatParseCase<Float16>("-0.0", true, uint16_t{0}),
1117         BadFloatParseCase<Float16>("-2.0", true, uint16_t{0}),
1118         BadFloatParseCase<Float16>("+0.0", true, uint16_t{0}),
1119         BadFloatParseCase<Float16>("+2.0", true, uint16_t{0}),
1120     }),);
1121
1122 // A test case for detecting infinities.
1123 template <typename T>
1124 struct OverflowParseCase {
1125   std::string input;
1126   bool expect_success;
1127   T expected_value;
1128 };
1129
1130 using FloatProxyParseOverflowFloatTest =
1131     ::testing::TestWithParam<OverflowParseCase<float>>;
1132
1133 TEST_P(FloatProxyParseOverflowFloatTest, Sample) {
1134   std::istringstream input(GetParam().input);
1135   HexFloat<FloatProxy<float>> value(0.0f);
1136   input >> value;
1137   EXPECT_NE(GetParam().expect_success, input.fail());
1138   if (GetParam().expect_success) {
1139     EXPECT_THAT(value.value().getAsFloat(), GetParam().expected_value);
1140   }
1141 }
1142
1143 INSTANTIATE_TEST_CASE_P(
1144     FloatOverflow, FloatProxyParseOverflowFloatTest,
1145     ::testing::ValuesIn(std::vector<OverflowParseCase<float>>({
1146         {"0", true, 0.0f},
1147         {"0.0", true, 0.0f},
1148         {"1.0", true, 1.0f},
1149         {"1e38", true, 1e38f},
1150         {"-1e38", true, -1e38f},
1151         {"1e40", false, FLT_MAX},
1152         {"-1e40", false, -FLT_MAX},
1153         {"1e400", false, FLT_MAX},
1154         {"-1e400", false, -FLT_MAX},
1155     })),);
1156
1157 using FloatProxyParseOverflowDoubleTest =
1158     ::testing::TestWithParam<OverflowParseCase<double>>;
1159
1160 TEST_P(FloatProxyParseOverflowDoubleTest, Sample) {
1161   std::istringstream input(GetParam().input);
1162   HexFloat<FloatProxy<double>> value(0.0);
1163   input >> value;
1164   EXPECT_NE(GetParam().expect_success, input.fail());
1165   if (GetParam().expect_success) {
1166     EXPECT_THAT(value.value().getAsFloat(), Eq(GetParam().expected_value));
1167   }
1168 }
1169
1170 INSTANTIATE_TEST_CASE_P(
1171     DoubleOverflow, FloatProxyParseOverflowDoubleTest,
1172     ::testing::ValuesIn(std::vector<OverflowParseCase<double>>({
1173         {"0", true, 0.0},
1174         {"0.0", true, 0.0},
1175         {"1.0", true, 1.0},
1176         {"1e38", true, 1e38},
1177         {"-1e38", true, -1e38},
1178         {"1e40", true, 1e40},
1179         {"-1e40", true, -1e40},
1180         {"1e400", false, DBL_MAX},
1181         {"-1e400", false, -DBL_MAX},
1182     })),);
1183
1184 using FloatProxyParseOverflowFloat16Test =
1185     ::testing::TestWithParam<OverflowParseCase<uint16_t>>;
1186
1187 TEST_P(FloatProxyParseOverflowFloat16Test, Sample) {
1188   std::istringstream input(GetParam().input);
1189   HexFloat<FloatProxy<Float16>> value(0);
1190   input >> value;
1191   EXPECT_NE(GetParam().expect_success, input.fail()) << " literal: "
1192                                                      << GetParam().input;
1193   if (GetParam().expect_success) {
1194     EXPECT_THAT(value.value().data(), Eq(GetParam().expected_value))
1195         << " literal: " << GetParam().input;
1196   }
1197 }
1198
1199 INSTANTIATE_TEST_CASE_P(
1200     Float16Overflow, FloatProxyParseOverflowFloat16Test,
1201     ::testing::ValuesIn(std::vector<OverflowParseCase<uint16_t>>({
1202         {"0", true, uint16_t{0}},
1203         {"0.0", true, uint16_t{0}},
1204         {"1.0", true, uint16_t{0x3c00}},
1205         // Overflow for 16-bit float is an error, and returns max or
1206         // lowest value.
1207         {"1e38", false, uint16_t{0x7bff}},
1208         {"1e40", false, uint16_t{0x7bff}},
1209         {"1e400", false, uint16_t{0x7bff}},
1210         {"-1e38", false, uint16_t{0xfbff}},
1211         {"-1e40", false, uint16_t{0xfbff}},
1212         {"-1e400", false, uint16_t{0xfbff}},
1213     })),);
1214
1215 TEST(FloatProxy, Max) {
1216   EXPECT_THAT(FloatProxy<Float16>::max().getAsFloat().get_value(),
1217               Eq(uint16_t{0x7bff}));
1218   EXPECT_THAT(FloatProxy<float>::max().getAsFloat(),
1219               Eq(std::numeric_limits<float>::max()));
1220   EXPECT_THAT(FloatProxy<double>::max().getAsFloat(),
1221               Eq(std::numeric_limits<double>::max()));
1222 }
1223
1224 TEST(FloatProxy, Lowest) {
1225   EXPECT_THAT(FloatProxy<Float16>::lowest().getAsFloat().get_value(),
1226               Eq(uint16_t{0xfbff}));
1227   EXPECT_THAT(FloatProxy<float>::lowest().getAsFloat(),
1228               Eq(std::numeric_limits<float>::lowest()));
1229   EXPECT_THAT(FloatProxy<double>::lowest().getAsFloat(),
1230               Eq(std::numeric_limits<double>::lowest()));
1231 }
1232
1233 // TODO(awoloszyn): Add fp16 tests and HexFloatTraits.
1234 }  // anonymous namespace