Q:

How to convert between a Unicode/UCS codepoint and a UTF16 surrogate pair? 

How to convert back and forth between a Unicode/UCS codepoint and a UTF16 surrogate pair in C++14 and later? 
EDIT: Removed mention of UCS-2 surrogates, as there is no such thing.  Thanks @remy-lebeau! 

A:

The surrogate-pairs tag info page explains (better than specified by the Unicode Standard 9.0 in §3.9, Table 3-5.)  the algorithm to convert from codepoint to surrogate pair as follows:

Unicode characters outside the Basic Multilingual Plane, that is characters with code above 0xFFFF, are encoded in UTF-16 by pairs of 16-bit code units called surrogate pairs, by the following scheme:

0x010000 is subtracted from the code point, leaving a 20-bit number in the range 0..0x0FFFFF;
the top ten bits (a number in the range 0..0x03FF) are added to 0xD800 to give the first code unit or high surrogate, which will be in the range 0xD800..0xDBFF;
the low ten bits (also in the range 0..0x03FF) are added to 0xDC00 to give the second code unit or low surrogate, which will be in the range 0xDC00..0xDFFF. 

In C++14 and later this could be written as:
#include <cstdint>

using codepoint = std::uint32_t;
using utf16 = std::uint16_t;

struct surrogate {
    utf16 high; // Leading
    utf16 low;  // Trailing
};

constexpr surrogate split(codepoint const in) noexcept {
    auto const inMinus0x10000 = (in - 0x10000);
    surrogate const r{
            static_cast<utf16>((inMinus0x10000 / 0x400) + 0xd800), // High
            static_cast<utf16>((inMinus0x10000 % 0x400) + 0xdc00)}; // Low
    return r;
}

In the reverse direction one just has to combine the last 10 bits from the high surrogate and the last 10 bits from the low surrogate, and add 0x10000:
constexpr codepoint combine(surrogate const s) noexcept {
    return static_cast<codepoint>(
            ((s.high - 0xd800) * 0x400) + (s.low - 0xdc00) + 0x10000);
}

Here's a test for these conversions:
#include <cassert>

constexpr bool isValidUtf16Surrogate(utf16 v) noexcept
{ return (v & 0xf800) == 0xd800; }

constexpr bool isValidCodePoint(codepoint v) noexcept {
    return (v <= 0x10ffff)
        && ((v >= 0x10000) || ! isValidUtf16Surrogate(static_cast<utf16>(v)));
}

constexpr bool isValidUtf16HighSurrogate(utf16 v) noexcept
{ return (v & 0xfc00) == 0xd800; }

constexpr bool isValidUtf16LowSurrogate(utf16 v) noexcept
{ return (v & 0xfc00) == 0xdc00; }

constexpr bool codePointNeedsUtf16Surrogates(codepoint v) noexcept
{ return (v >= 0x10000) && (v <= 0x10ffff); }

void test(codepoint const in) {
    assert(isValidCodePoint(in));
    assert(codePointNeedsUtf16Surrogates(in));
    auto const s = split(in);
    assert(isValidUtf16HighSurrogate(s.high));
    assert(isValidUtf16LowSurrogate(s.low));
    auto const out = combine(s);
    assert(isValidCodePoint(out));
    assert(in == out);
}

int main() {
    for (codepoint c = 0x10000; c <= 0x10ffff; ++c)
        test(c);
}

A:

In C++11 and later, you can use std::wstring_convert to convert between various UTF/UCS encodings, using the following std::codecvt types:

UTF-8 <-> UCS-2:
std::codecvt_utf8<char16_t>
UTF-8 <-> UTF-16:
std::codecvt_utf8_utf16
UTF-8 <-> UTF-32/UCS-4:
std::codecvt_utf8<char32_t>
UCS-2 <-> UTF-16:
std::codecvt_utf16<char16_t>
UTF-16 <-> UTF-32/UCS-4:
std::codecvt_utf16<char32_t>
UCS-2 <-> UTF-32/UCS-4:
no standard conversion, but you can write your own std::codecvt class for it if needed.   Otherwise, use one of the above conversions in between:
UCS-2 <-> UTF-X <-> UTF-32/UCS-4

You don't need to handle surrogates manually. 
You can use std::u32string to hold your codepoint(s), and std::u16string to hold your UTF-16/UCS-2 codeunits. 
For example:
using convert_utf16_uf32 = std::wstring_convert<std::codecvt_utf16<char32_t>, char16_t>;

std::u16string CodepointToUTF16(const char32_t codepoint)
{
    const char32_t *p = &codepoint;
    return convert_utf16_uf32{}.from_bytes(
        reinterpret_cast<const char*>(p),
        reinterpret_cast<const char*>(p+1)
    );
}

std::u16string UTF32toUTF16(const std::u32string &str)
{
    return convert_utf16_uf32{}.from_bytes(
        reinterpret_cast<const char*>(str.data()),
        reinterpret_cast<const char*>(str.data()+str.size())
    );
}

char32_t UTF16toCodepoint(const std::u16string &str)
{
    std::string bytes = convert_utf16_uf32{}.to_bytes(str);
    return *(reinterpret_cast<const char32_t*>(bytes.data()));
}

std::u32string UTF16toUTF32(const std::u16string &str)
{
    std::string bytes = convert_utf16_uf32{}.to_bytes(str);
    return std::u32string(
       reinterpret_cast<const char32_t*>(bytes.data()),
       bytes.size() / sizeof(char32_t)
    );
}

