Implement std::numeric_limits<qfloat16>

This shall make it more nearly a first-class numeric type; in
particular, I need some of these for testlib's comparing and
formatting of float16 to handle NaNs and infinities sensibly.

Change-Id: Ic894dd0eb3e05653cd7645ab496463e7a884dff8
Reviewed-by: Qt CI Bot <qt_ci_bot@qt-project.org>
Reviewed-by: Thiago Macieira <thiago.macieira@intel.com>

1 files changed, 142 insertions, 0 deletions

diff --git a/tests/auto/corelib/global/qfloat16/tst_qfloat16.cpp b/tests/auto/corelib/global/qfloat16/tst_qfloat16.cpp
index 241dccb90e..b5a77a1de6 100644
--- a/tests/auto/corelib/global/qfloat16/tst_qfloat16.cpp
+++ b/tests/auto/corelib/global/qfloat16/tst_qfloat16.cpp
@@ -1,5 +1,6 @@
 /****************************************************************************
 **
+** Copyright (C) 2019 The Qt Company Ltd.
 ** Copyright (C) 2016 by Southwest Research Institute (R)
 ** Contact: https://www.qt.io/licensing/
 **
@@ -48,6 +49,7 @@ private slots:
     void arithOps();
     void floatToFloat16();
     void floatFromFloat16();
+    void limits();
 };
 
 void tst_qfloat16::fuzzyCompare_data()
@@ -345,5 +347,145 @@ void tst_qfloat16::floatFromFloat16()
         QCOMPARE(out[i], expected[i]);
 }
 
+static qfloat16 powf16(qfloat16 base, int raise)
+{
+    const qfloat16 one(1.f);
+    if (raise < 0) {
+        raise = -raise;
+        base = one / base;
+    }
+    qfloat16 answer = (raise & 1) ? base : one;
+    while (raise > 0) {
+        raise >>= 1;
+        base *= base;
+        if (raise & 1)
+            answer *= base;
+    }
+    return answer;
+}
+
+void tst_qfloat16::limits()
+{
+    // *NOT* using QCOMPARE() on finite qfloat16 values, since that uses fuzzy
+    // comparison, and we need exact here.
+    using Bounds = std::numeric_limits<qfloat16>;
+    QVERIFY(Bounds::is_specialized);
+    QVERIFY(Bounds::is_signed);
+    QVERIFY(!Bounds::is_integer);
+    QVERIFY(!Bounds::is_exact);
+    QVERIFY(Bounds::is_iec559);
+    QVERIFY(Bounds::is_bounded);
+    QVERIFY(!Bounds::is_modulo);
+    QVERIFY(!Bounds::traps);
+    QVERIFY(Bounds::has_infinity);
+    QVERIFY(Bounds::has_quiet_NaN);
+    QVERIFY(Bounds::has_signaling_NaN);
+    QCOMPARE(Bounds::has_denorm, std::denorm_present);
+    QCOMPARE(Bounds::round_style, std::round_to_nearest);
+    QCOMPARE(Bounds::radix, 2);
+    // Untested: has_denorm_loss
+
+    // A few common values:
+    const qfloat16 zero(0), one(1), ten(10);
+    QVERIFY(qIsFinite(zero));
+    QVERIFY(!qIsInf(zero));
+    QVERIFY(!qIsNaN(zero));
+    QVERIFY(qIsFinite(one));
+    QVERIFY(!qIsInf(one));
+    QVERIFY(!qIsNaN(one));
+    QVERIFY(qIsFinite(ten));
+    QVERIFY(!qIsInf(ten));
+    QVERIFY(!qIsNaN(ten));
+
+    // digits in the mantissa, including the implicit 1 before the binary dot at its left:
+    QVERIFY(qfloat16(1 << (Bounds::digits - 1)) + one > qfloat16(1 << (Bounds::digits - 1)));
+    QVERIFY(qfloat16(1 << Bounds::digits) + one == qfloat16(1 << Bounds::digits));
+
+    // There is a wilful of-by-one in how m(ax|in)_exponent are defined; they're
+    // the lowest and highest n for which radix^{n-1} are normal and finite.
+    const qfloat16 two(Bounds::radix);
+    qfloat16 bit = powf16(two, Bounds::max_exponent - 1);
+    QVERIFY(qIsFinite(bit));
+    QVERIFY(qIsInf(bit * two));
+    bit = powf16(two, Bounds::min_exponent - 1);
+    QVERIFY(bit.isNormal());
+    QVERIFY(!(bit / two).isNormal());
+    QVERIFY(bit / two > zero);
+
+    // Base ten (with no matching off-by-one idiocy):
+    // the lowest negative number n such that 10^n is a valid normalized value
+    qfloat16 low10(powf16(ten, Bounds::min_exponent10));
+    QVERIFY(low10 > zero);
+    QVERIFY(low10.isNormal());
+    low10 /= ten;
+    QVERIFY(low10 == zero || !low10.isNormal());
+    // the largest positive number n such that 10^n is a representable finite value
+    qfloat16 high10(powf16(ten, Bounds::max_exponent10));
+    QVERIFY(high10 > zero);
+    QVERIFY(qIsFinite(high10));
+    QVERIFY(!qIsFinite(high10 * ten));
+
+    // How many digits are significant ?  (Casts avoid linker errors ...)
+    QCOMPARE(int(Bounds::digits10), 3); // 9.79e-4 has enough sigificant digits:
+    qfloat16 below(9.785e-4f), above(9.794e-4f);
+#if 0 // Sadly, the QEMU x-compile for arm64 "optimises" comparisons:
+    const bool overOptimised = false;
+#else
+    const bool overOptimised = (below != above);
+    if (overOptimised)
+        QEXPECT_FAIL("", "Over-optimised on QEMU", Continue);
+#endif // (but it did, so should, pass everywhere else, confirming digits10 is indeed 3).
+    QVERIFY(below == above);
+    QCOMPARE(int(Bounds::max_digits10), 5); // we need 5 to distinguish these two:
+    QVERIFY(qfloat16(1000.5f) != qfloat16(1001.4f));
+
+    // Actual limiting values of the type:
+    const qfloat16 rose(one + Bounds::epsilon());
+    QVERIFY(rose > one);
+    if (overOptimised)
+        QEXPECT_FAIL("", "Over-optimised on QEMU", Continue);
+    QVERIFY(one + Bounds::epsilon() / rose == one);
+    QVERIFY(qIsInf(Bounds::infinity()));
+    QVERIFY(!qIsNaN(Bounds::infinity()));
+    QVERIFY(!qIsFinite(Bounds::infinity()));
+    // QCOMPARE(Bounds::infinity(), Bounds::infinity());
+    QVERIFY(Bounds::infinity() > -Bounds::infinity());
+    QVERIFY(Bounds::infinity() > zero);
+    QVERIFY(qIsInf(-Bounds::infinity()));
+    QVERIFY(!qIsNaN(-Bounds::infinity()));
+    QVERIFY(!qIsFinite(-Bounds::infinity()));
+    // QCOMPARE(-Bounds::infinity(), -Bounds::infinity());
+    QVERIFY(-Bounds::infinity() < zero);
+    QVERIFY(qIsNaN(Bounds::quiet_NaN()));
+    QVERIFY(!qIsInf(Bounds::quiet_NaN()));
+    QVERIFY(!qIsFinite(Bounds::quiet_NaN()));
+    QVERIFY(!(Bounds::quiet_NaN() == Bounds::quiet_NaN()));
+    // QCOMPARE(Bounds::quiet_NaN(), Bounds::quiet_NaN());
+    QVERIFY(Bounds::max() > zero);
+    QVERIFY(qIsFinite(Bounds::max()));
+    QVERIFY(!qIsInf(Bounds::max()));
+    QVERIFY(!qIsNaN(Bounds::max()));
+    QVERIFY(qIsInf(Bounds::max() * rose));
+    QVERIFY(Bounds::lowest() < zero);
+    QVERIFY(qIsFinite(Bounds::lowest()));
+    QVERIFY(!qIsInf(Bounds::lowest()));
+    QVERIFY(!qIsNaN(Bounds::lowest()));
+    QVERIFY(qIsInf(Bounds::lowest() * rose));
+    QVERIFY(Bounds::min() > zero);
+    QVERIFY(Bounds::min().isNormal());
+    QVERIFY(!(Bounds::min() / rose).isNormal());
+    QVERIFY(qIsFinite(Bounds::min()));
+    QVERIFY(!qIsInf(Bounds::min()));
+    QVERIFY(!qIsNaN(Bounds::min()));
+    QVERIFY(Bounds::denorm_min() > zero);
+    QVERIFY(!Bounds::denorm_min().isNormal());
+    QVERIFY(qIsFinite(Bounds::denorm_min()));
+    QVERIFY(!qIsInf(Bounds::denorm_min()));
+    QVERIFY(!qIsNaN(Bounds::denorm_min()));
+    if (overOptimised)
+        QEXPECT_FAIL("", "Over-optimised on QEMU", Continue);
+    QCOMPARE(Bounds::denorm_min() / rose, zero);
+}
+
 QTEST_APPLESS_MAIN(tst_qfloat16)
 #include "tst_qfloat16.moc"