// Copyright 2006-2008 the V8 project authors. All rights reserved. #include #include "cctest.h" #include "diy-fp.h" #include "ieee.h" #include "utils.h" #include "../../src/ieee.h" using namespace double_conversion; TEST(Uint64Conversions) { // Start by checking the byte-order. uint64_t ordered = UINT64_2PART_C(0x01234567, 89ABCDEF); CHECK_EQ(3512700564088504e-318, Double(ordered).value()); uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); CHECK_EQ(5e-324, Double(min_double64).value()); uint64_t max_double64 = UINT64_2PART_C(0x7fefffff, ffffffff); CHECK_EQ(1.7976931348623157e308, Double(max_double64).value()); } TEST(Uint32Conversions) { // Start by checking the byte-order. uint32_t ordered = 0x01234567; CHECK_EQ(2.9988165487136453e-38f, Single(ordered).value()); uint32_t min_float32 = 0x00000001; CHECK_EQ(1.4e-45f, Single(min_float32).value()); uint32_t max_float32 = 0x7f7fffff; CHECK_EQ(3.4028234e38f, Single(max_float32).value()); } TEST(Double_AsDiyFp) { uint64_t ordered = UINT64_2PART_C(0x01234567, 89ABCDEF); DiyFp diy_fp = Double(ordered).AsDiyFp(); CHECK_EQ(0x12 - 0x3FF - 52, diy_fp.e()); // The 52 mantissa bits, plus the implicit 1 in bit 52 as a UINT64. CHECK(UINT64_2PART_C(0x00134567, 89ABCDEF) == diy_fp.f()); // NOLINT uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); diy_fp = Double(min_double64).AsDiyFp(); CHECK_EQ(-0x3FF - 52 + 1, diy_fp.e()); // This is a denormal; so no hidden bit. CHECK(1 == diy_fp.f()); // NOLINT uint64_t max_double64 = UINT64_2PART_C(0x7fefffff, ffffffff); diy_fp = Double(max_double64).AsDiyFp(); CHECK_EQ(0x7FE - 0x3FF - 52, diy_fp.e()); CHECK(UINT64_2PART_C(0x001fffff, ffffffff) == diy_fp.f()); // NOLINT } TEST(Single_AsDiyFp) { uint32_t ordered = 0x01234567; DiyFp diy_fp = Single(ordered).AsDiyFp(); CHECK_EQ(0x2 - 0x7F - 23, diy_fp.e()); // The 23 mantissa bits, plus the implicit 1 in bit 24 as a uint32_t. CHECK_EQ(0xA34567, diy_fp.f()); uint32_t min_float32 = 0x00000001; diy_fp = Single(min_float32).AsDiyFp(); CHECK_EQ(-0x7F - 23 + 1, diy_fp.e()); // This is a denormal; so no hidden bit. CHECK_EQ(1, diy_fp.f()); uint32_t max_float32 = 0x7f7fffff; diy_fp = Single(max_float32).AsDiyFp(); CHECK_EQ(0xFE - 0x7F - 23, diy_fp.e()); CHECK_EQ(0x00ffffff, diy_fp.f()); } TEST(AsNormalizedDiyFp) { uint64_t ordered = UINT64_2PART_C(0x01234567, 89ABCDEF); DiyFp diy_fp = Double(ordered).AsNormalizedDiyFp(); CHECK_EQ(0x12 - 0x3FF - 52 - 11, diy_fp.e()); CHECK((UINT64_2PART_C(0x00134567, 89ABCDEF) << 11) == diy_fp.f()); // NOLINT uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); diy_fp = Double(min_double64).AsNormalizedDiyFp(); CHECK_EQ(-0x3FF - 52 + 1 - 63, diy_fp.e()); // This is a denormal; so no hidden bit. CHECK(UINT64_2PART_C(0x80000000, 00000000) == diy_fp.f()); // NOLINT uint64_t max_double64 = UINT64_2PART_C(0x7fefffff, ffffffff); diy_fp = Double(max_double64).AsNormalizedDiyFp(); CHECK_EQ(0x7FE - 0x3FF - 52 - 11, diy_fp.e()); CHECK((UINT64_2PART_C(0x001fffff, ffffffff) << 11) == diy_fp.f()); // NOLINT } TEST(Double_IsDenormal) { uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); CHECK(Double(min_double64).IsDenormal()); uint64_t bits = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); CHECK(Double(bits).IsDenormal()); bits = UINT64_2PART_C(0x00100000, 00000000); CHECK(!Double(bits).IsDenormal()); } TEST(Single_IsDenormal) { uint32_t min_float32 = 0x00000001; CHECK(Single(min_float32).IsDenormal()); uint32_t bits = 0x007FFFFF; CHECK(Single(bits).IsDenormal()); bits = 0x00800000; CHECK(!Single(bits).IsDenormal()); } TEST(Double_IsSpecial) { CHECK(Double(Double::Infinity()).IsSpecial()); CHECK(Double(-Double::Infinity()).IsSpecial()); CHECK(Double(Double::NaN()).IsSpecial()); uint64_t bits = UINT64_2PART_C(0xFFF12345, 00000000); CHECK(Double(bits).IsSpecial()); // Denormals are not special: CHECK(!Double(5e-324).IsSpecial()); CHECK(!Double(-5e-324).IsSpecial()); // And some random numbers: CHECK(!Double(0.0).IsSpecial()); CHECK(!Double(-0.0).IsSpecial()); CHECK(!Double(1.0).IsSpecial()); CHECK(!Double(-1.0).IsSpecial()); CHECK(!Double(1000000.0).IsSpecial()); CHECK(!Double(-1000000.0).IsSpecial()); CHECK(!Double(1e23).IsSpecial()); CHECK(!Double(-1e23).IsSpecial()); CHECK(!Double(1.7976931348623157e308).IsSpecial()); CHECK(!Double(-1.7976931348623157e308).IsSpecial()); } TEST(Single_IsSpecial) { CHECK(Single(Single::Infinity()).IsSpecial()); CHECK(Single(-Single::Infinity()).IsSpecial()); CHECK(Single(Single::NaN()).IsSpecial()); uint32_t bits = 0xFFF12345; CHECK(Single(bits).IsSpecial()); // Denormals are not special: CHECK(!Single(1.4e-45f).IsSpecial()); CHECK(!Single(-1.4e-45f).IsSpecial()); // And some random numbers: CHECK(!Single(0.0f).IsSpecial()); CHECK(!Single(-0.0f).IsSpecial()); CHECK(!Single(1.0f).IsSpecial()); CHECK(!Single(-1.0f).IsSpecial()); CHECK(!Single(1000000.0f).IsSpecial()); CHECK(!Single(-1000000.0f).IsSpecial()); CHECK(!Single(1e23f).IsSpecial()); CHECK(!Single(-1e23f).IsSpecial()); CHECK(!Single(1.18e-38f).IsSpecial()); CHECK(!Single(-1.18e-38f).IsSpecial()); } TEST(Double_IsInfinite) { CHECK(Double(Double::Infinity()).IsInfinite()); CHECK(Double(-Double::Infinity()).IsInfinite()); CHECK(!Double(Double::NaN()).IsInfinite()); CHECK(!Double(0.0).IsInfinite()); CHECK(!Double(-0.0).IsInfinite()); CHECK(!Double(1.0).IsInfinite()); CHECK(!Double(-1.0).IsInfinite()); uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); CHECK(!Double(min_double64).IsInfinite()); } TEST(Single_IsInfinite) { CHECK(Single(Single::Infinity()).IsInfinite()); CHECK(Single(-Single::Infinity()).IsInfinite()); CHECK(!Single(Single::NaN()).IsInfinite()); CHECK(!Single(0.0f).IsInfinite()); CHECK(!Single(-0.0f).IsInfinite()); CHECK(!Single(1.0f).IsInfinite()); CHECK(!Single(-1.0f).IsInfinite()); uint32_t min_float32 = 0x00000001; CHECK(!Single(min_float32).IsInfinite()); } TEST(Double_IsNan) { CHECK(Double(Double::NaN()).IsNan()); uint64_t other_nan = UINT64_2PART_C(0xFFFFFFFF, 00000001); CHECK(Double(other_nan).IsNan()); CHECK(!Double(Double::Infinity()).IsNan()); CHECK(!Double(-Double::Infinity()).IsNan()); CHECK(!Double(0.0).IsNan()); CHECK(!Double(-0.0).IsNan()); CHECK(!Double(1.0).IsNan()); CHECK(!Double(-1.0).IsNan()); uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); CHECK(!Double(min_double64).IsNan()); } TEST(Single_IsNan) { CHECK(Single(Single::NaN()).IsNan()); uint32_t other_nan = 0xFFFFF001; CHECK(Single(other_nan).IsNan()); CHECK(!Single(Single::Infinity()).IsNan()); CHECK(!Single(-Single::Infinity()).IsNan()); CHECK(!Single(0.0f).IsNan()); CHECK(!Single(-0.0f).IsNan()); CHECK(!Single(1.0f).IsNan()); CHECK(!Single(-1.0f).IsNan()); uint32_t min_float32 = 0x00000001; CHECK(!Single(min_float32).IsNan()); } TEST(Double_Sign) { CHECK_EQ(1, Double(1.0).Sign()); CHECK_EQ(1, Double(Double::Infinity()).Sign()); CHECK_EQ(-1, Double(-Double::Infinity()).Sign()); CHECK_EQ(1, Double(0.0).Sign()); CHECK_EQ(-1, Double(-0.0).Sign()); uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); CHECK_EQ(1, Double(min_double64).Sign()); } TEST(Single_Sign) { CHECK_EQ(1, Single(1.0f).Sign()); CHECK_EQ(1, Single(Single::Infinity()).Sign()); CHECK_EQ(-1, Single(-Single::Infinity()).Sign()); CHECK_EQ(1, Single(0.0f).Sign()); CHECK_EQ(-1, Single(-0.0f).Sign()); uint32_t min_float32 = 0x00000001; CHECK_EQ(1, Single(min_float32).Sign()); } TEST(Double_NormalizedBoundaries) { DiyFp boundary_plus; DiyFp boundary_minus; DiyFp diy_fp = Double(1.5).AsNormalizedDiyFp(); Double(1.5).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // 1.5 does not have a significand of the form 2^p (for some p). // Therefore its boundaries are at the same distance. CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((1 << 10) == diy_fp.f() - boundary_minus.f()); // NOLINT diy_fp = Double(1.0).AsNormalizedDiyFp(); Double(1.0).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // 1.0 does have a significand of the form 2^p (for some p). // Therefore its lower boundary is twice as close as the upper boundary. CHECK(boundary_plus.f() - diy_fp.f() > diy_fp.f() - boundary_minus.f()); CHECK((1 << 9) == diy_fp.f() - boundary_minus.f()); // NOLINT CHECK((1 << 10) == boundary_plus.f() - diy_fp.f()); // NOLINT uint64_t min_double64 = UINT64_2PART_C(0x00000000, 00000001); diy_fp = Double(min_double64).AsNormalizedDiyFp(); Double(min_double64).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // min-value does not have a significand of the form 2^p (for some p). // Therefore its boundaries are at the same distance. CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); // Denormals have their boundaries much closer. CHECK((static_cast(1) << 62) == diy_fp.f() - boundary_minus.f()); // NOLINT uint64_t smallest_normal64 = UINT64_2PART_C(0x00100000, 00000000); diy_fp = Double(smallest_normal64).AsNormalizedDiyFp(); Double(smallest_normal64).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // Even though the significand is of the form 2^p (for some p), its boundaries // are at the same distance. (This is the only exception). CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((1 << 10) == diy_fp.f() - boundary_minus.f()); // NOLINT uint64_t largest_denormal64 = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); diy_fp = Double(largest_denormal64).AsNormalizedDiyFp(); Double(largest_denormal64).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((1 << 11) == diy_fp.f() - boundary_minus.f()); // NOLINT uint64_t max_double64 = UINT64_2PART_C(0x7fefffff, ffffffff); diy_fp = Double(max_double64).AsNormalizedDiyFp(); Double(max_double64).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // max-value does not have a significand of the form 2^p (for some p). // Therefore its boundaries are at the same distance. CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((1 << 10) == diy_fp.f() - boundary_minus.f()); // NOLINT } TEST(Single_NormalizedBoundaries) { uint64_t kOne64 = 1; DiyFp boundary_plus; DiyFp boundary_minus; DiyFp diy_fp = Single(1.5f).AsDiyFp(); diy_fp.Normalize(); Single(1.5f).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // 1.5 does not have a significand of the form 2^p (for some p). // Therefore its boundaries are at the same distance. CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); // Normalization shifts the significand by 8 bits. Add 32 bits for the bigger // data-type, and remove 1 because boundaries are at half a ULP. CHECK((kOne64 << 39) == diy_fp.f() - boundary_minus.f()); diy_fp = Single(1.0f).AsDiyFp(); diy_fp.Normalize(); Single(1.0f).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // 1.0 does have a significand of the form 2^p (for some p). // Therefore its lower boundary is twice as close as the upper boundary. CHECK(boundary_plus.f() - diy_fp.f() > diy_fp.f() - boundary_minus.f()); CHECK((kOne64 << 38) == diy_fp.f() - boundary_minus.f()); // NOLINT CHECK((kOne64 << 39) == boundary_plus.f() - diy_fp.f()); // NOLINT uint32_t min_float32 = 0x00000001; diy_fp = Single(min_float32).AsDiyFp(); diy_fp.Normalize(); Single(min_float32).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // min-value does not have a significand of the form 2^p (for some p). // Therefore its boundaries are at the same distance. CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); // Denormals have their boundaries much closer. CHECK((kOne64 << 62) == diy_fp.f() - boundary_minus.f()); // NOLINT uint32_t smallest_normal32 = 0x00800000; diy_fp = Single(smallest_normal32).AsDiyFp(); diy_fp.Normalize(); Single(smallest_normal32).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // Even though the significand is of the form 2^p (for some p), its boundaries // are at the same distance. (This is the only exception). CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((kOne64 << 39) == diy_fp.f() - boundary_minus.f()); // NOLINT uint32_t largest_denormal32 = 0x007FFFFF; diy_fp = Single(largest_denormal32).AsDiyFp(); diy_fp.Normalize(); Single(largest_denormal32).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((kOne64 << 40) == diy_fp.f() - boundary_minus.f()); // NOLINT uint32_t max_float32 = 0x7f7fffff; diy_fp = Single(max_float32).AsDiyFp(); diy_fp.Normalize(); Single(max_float32).NormalizedBoundaries(&boundary_minus, &boundary_plus); CHECK_EQ(diy_fp.e(), boundary_minus.e()); CHECK_EQ(diy_fp.e(), boundary_plus.e()); // max-value does not have a significand of the form 2^p (for some p). // Therefore its boundaries are at the same distance. CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f()); CHECK((kOne64 << 39) == diy_fp.f() - boundary_minus.f()); // NOLINT } TEST(NextDouble) { CHECK_EQ(4e-324, Double(0.0).NextDouble()); CHECK_EQ(0.0, Double(-0.0).NextDouble()); CHECK_EQ(-0.0, Double(-4e-324).NextDouble()); CHECK(Double(Double(-0.0).NextDouble()).Sign() > 0); CHECK(Double(Double(-4e-324).NextDouble()).Sign() < 0); Double d0(-4e-324); Double d1(d0.NextDouble()); Double d2(d1.NextDouble()); CHECK_EQ(-0.0, d1.value()); CHECK(d1.Sign() < 0); CHECK_EQ(0.0, d2.value()); CHECK(d2.Sign() > 0); CHECK_EQ(4e-324, d2.NextDouble()); CHECK_EQ(-1.7976931348623157e308, Double(-Double::Infinity()).NextDouble()); CHECK_EQ(Double::Infinity(), Double(UINT64_2PART_C(0x7fefffff, ffffffff)).NextDouble()); } TEST(PreviousDouble) { CHECK_EQ(0.0, Double(4e-324).PreviousDouble()); CHECK_EQ(-0.0, Double(0.0).PreviousDouble()); CHECK(Double(Double(0.0).PreviousDouble()).Sign() < 0); CHECK_EQ(-4e-324, Double(-0.0).PreviousDouble()); Double d0(4e-324); Double d1(d0.PreviousDouble()); Double d2(d1.PreviousDouble()); CHECK_EQ(0.0, d1.value()); CHECK(d1.Sign() > 0); CHECK_EQ(-0.0, d2.value()); CHECK(d2.Sign() < 0); CHECK_EQ(-4e-324, d2.PreviousDouble()); CHECK_EQ(1.7976931348623157e308, Double(Double::Infinity()).PreviousDouble()); CHECK_EQ(-Double::Infinity(), Double(UINT64_2PART_C(0xffefffff, ffffffff)).PreviousDouble()); }