It's not a seven-headed beast. It's not rocket science.Cassio Neri Fast conversion from floating-point numbers CppCon 2024 - Aurora (Independent Researcher)MeMe O Neri's equationMe O Neri's equation fixed-point representation 23. 410 x 23. 4 1 Decimal floating-point representation (a) mantissa biased exponent10 x 23. 4 1 Decimal floating-point representation (a) mantissa 0 0 0 0 0 0 2 3 4 0 0 biased exponent10 x 23. 4 1 Decimal floating-point representation (a) mantissa 0 0 0 0 0 0 2 3 4 0 0 0 . , , , biased exponent10 x 23. 4 1 Decimal floating-point representation (a) exponent 0 mantissa's

refactoring, reviews Dmytro Ivanchykhin 🇺🇦 di@6it.dev Implementing fixed- point math with floating-point fallback Mykhailo Borovyk 🇺🇦 mbo@6it.dev Implementing support for RISC-V, including Algorithm Correctness_/30 8 ❌ On Algorithm Correctness_/30 9 ❌ Mathematically 1 Fixed-Point 2 Floating-Point 3 ✅ ✅ ❌ There are algorithms, which are: Can be usually made solid - but only within compiler flags 4 Making 3rd-party libs deterministic is a MAJOR effortP3375: Reproducible floating-point results Spearheaded by Guy Davidson 1 Our C++ Standard/WG21 Proposal_ Proposed: std::strict_float

✘literal (in C++) noun 1. a single token in a program that represents a value of an integer, floating-point, character, string, Boolean, pointer, or user-defined type. 10/26/21 Pablo Halpern, 2021 (CC u8"yes"_udl – No: 1.2.3_udl, nullptr_udl, false_udl ■ Numeric literals that do not fit in a native floating-point or integer type are OK (assuming an appropriate definition). ■ String-token concatenation: have up to 12 overloads. Each overload can potentially return a different type. – Integer and floating-point UDLs can each have their own overload – Character and string literals can each have up to 5

CppCon 2024: Improving our safety with a quantities and units library The proliferation of magic numbers 12#ifndef PI static const double PI = (4*atan(1)); #endif #define EARTH_DIAMETER 12733426.0 need to track units in the identifiers • The library knows all the conversion factors – no magic numbers – intermediate results not needed CppCon 2024: Improving our safety with a quantities and units // Compile-time error quantity, int> q2 = q1; // Compile-time error • Floating-point representation type is considered value-preserving quantity q1 = 5. * m; // source quantity

safety. First, it cannot be implicitly converted to an integer, nor can it be compared to integer numbers, and it is even less likely to compare enumerated values of different enumerated types. But if the explicitly specified as metacharacters. This includes all uppercase and lowercase letters, all numbers, all punctuation, and some other symbols. Special characters A special character is a character foooooo. o{0,1} is equivalent to o?. Note that there can be no spaces between the comma and the two numbers. With these two tables, we can usually read almost all regular expressions. 66 6.2 std::regex

overloading ■ invokes a different operation for the given operator ■ example: operator+() ● might add two numbers or concatenate two strings ■ implemented using the overload resolution process 8Overload Resolution Categories ○ numeric promotions (4) ■ integral promotion ■ floating-point promotion ○ conversions (5) ■ integral conversion ■ floating-point conversion ■ floating–integral conversion ■ pointer conversion

152437111001089Floating-Point Numbers Aren’t Real Chuck AllisonReal numbers have infinite precision and are therefore continuous and nonlossy; floating-point numbers have limited precision, so they

parameters had limitations, e.g. no string literals  C++20 relaxes these limitations  Allows floating-point types  Allows class types (but with some restrictions)  E.g. use-case: pass string literals Constants  <numbers>  Following mathematical constants are defined:  e, log2e, log10e  pi, inv_pi, inv_sqrtpi  ln2, ln10  sqrt2, sqrt3, inv_sqrt3  egamma  phi  In std::numbers78 std::source_location remove- erase-idiom83 Small Standard Library Additions  midpoint() to calculate the midpoint of two numbers  lerp() to do linear interpolation  New unsequenced_policy (execution::unseq): algorithm is allowed

type year = 365.25 ∗ 24 ∗ 60 ∗ 60; 14 constexpr type mpc = 1.E6 ∗ (180 ∗ 60 ∗ 60 ∗ au) / std :: numbers ::pi_v ; 15 // Parameters 16 const type h0 = (argc > 1) ? std:: stod(argv [1]) : 0.677; sparse Null coefficients should be optimized away Compilers may not be able to do it because of floating-point special values CppCon - Vincent Reverdy - September 20th, 2024 - Aurora, Colorado, USA 44 CC0

reliable concurrent code.Atomic Floating-Point Min/Max in C++ (P3008) Atomic min/max operations are crucial for concurrent algorithms Integer versions added in C++20 Floating-point versions were removed due due to concerns The Challenge of Floating-Point Corner Cases ● NaN (Not a Number): Represents undefined or unrepresentable values. ● Signed Zero: Both +0 and -0 exist, but their ordering can be ambiguous ambiguous Evolution of Floating-Point Min/Max in C++ ● std::min, std::max: Undefined behavior with NaNs. a. std::min(-0.0f, +0.0f); // Returns -0.0f b. std::min(NaN, 2.0f); // Undefined behavior