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Use Grisu2 for floating-point formatting

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This is an attempt to fix #360. The algorithm produces
decimal representations which are guaranteed to roundtrip
and in ~99.8% actually produces the shortest possible
representation. So this is a nice compromise between using
a precision of digits10 and max_digits10.

Note 1:

The implementation only works for IEEE single/double precision
numbers. So the old implementation is kept for compatibility
with non-IEEE implementations and 'long double'.

Note 2:

If number_float_t is 'float', not all serialized numbers can
be recovered using strtod (strtof works, though). (There is
exactly one such number and the result is off by 1 ulp.)
This can be avoided by changing the implementation (the fix
is trivial), but then the resulting decimal numbers are not
exactly short.

Note 3:

The code should be replaced by std::to_chars once it is available.
This commit is contained in:
abolz 2017-12-09 13:14:13 +01:00
parent 13160d93b2
commit 38e678d9f1
2 changed files with 1390 additions and 1 deletions
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921
src/json.hpp
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@ -6096,6 +6096,902 @@ class binary_writer
// serialization //
///////////////////
// Implements the Grisu2 algorithm for binary to decimal floating-point
// conversion.
//
// This implementation is a slightly modified version of the reference
// implementation by Florian Loitsch which can be obtained from
// http://florian.loitsch.com/publications (bench.tar.gz)
//
// References:
//
// [1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with Integers",
// Proceedings of the ACM SIGPLAN 2010 Conference on Programming Language Design and Implementation, PLDI 2010
// [2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately",
// Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language Design and Implementation, PLDI 1996
//
// Note:
// dtoa::to_short_string should be replaced with std::to_chars if available...
namespace dtoa {
template <typename Target, typename Source>
inline Target reinterpret_bits(Source source)
{
static_assert(sizeof(Target) == sizeof(Source), "Size mismatch");
Target target;
std::memcpy(&target, &source, sizeof(Source));
return target;
}
struct diyfp // f * 2^e
{
static constexpr int kPrecision = 64; // = q
uint64_t f;
int e;
constexpr diyfp() : f(0), e(0) {}
constexpr diyfp(uint64_t f_, int e_) : f(f_), e(e_) {}
// Returns x - y.
// PRE: x.e == y.e and x.f >= y.f
static diyfp sub(diyfp x, diyfp y);
// Returns x * y.
// The result is rounded. (Only the upper q bits are returned.)
static diyfp mul(diyfp x, diyfp y);
// Normalize x such that the significand is >= 2^(q-1).
// PRE: x.f != 0
static diyfp normalize(diyfp x);
// Normalize x such that the result has the exponent E.
// PRE: e >= x.e and the upper e - x.e bits of x.f must be zero.
static diyfp normalize_to(diyfp x, int e);
};
inline diyfp diyfp::sub(diyfp x, diyfp y)
{
assert(x.e == y.e);
assert(x.f >= y.f);
return diyfp(x.f - y.f, x.e);
}
inline diyfp diyfp::mul(diyfp x, diyfp y)
{
// Computes:
// f = round((x.f * y.f) / 2^q)
// e = x.e + y.e + q
// Emulate the 64-bit * 64-bit multiplication:
//
// p = u * v
// = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)
// = (u_lo v_lo ) + 2^32 ((u_lo v_hi ) + (u_hi v_lo )) + 2^64 (u_hi v_hi )
// = (p0 ) + 2^32 ((p1 ) + (p2 )) + 2^64 (p3 )
// = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3 )
// = (p0_lo ) + 2^32 (p0_hi + p1_lo + p2_lo ) + 2^64 (p1_hi + p2_hi + p3)
// = (p0_lo ) + 2^32 (Q ) + 2^64 (H )
// = (p0_lo ) + 2^32 (Q_lo + 2^32 Q_hi ) + 2^64 (H )
//
// (Since Q might be larger than 2^32 - 1)
//
// = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)
//
// (Q_hi + H does not overflow a 64-bit int)
//
// = p_lo + 2^64 p_hi
const uint64_t u_lo = x.f & 0xFFFFFFFF;
const uint64_t u_hi = x.f >> 32;
const uint64_t v_lo = y.f & 0xFFFFFFFF;
const uint64_t v_hi = y.f >> 32;
const uint64_t p0 = u_lo * v_lo;
const uint64_t p1 = u_lo * v_hi;
const uint64_t p2 = u_hi * v_lo;
const uint64_t p3 = u_hi * v_hi;
const uint64_t p0_hi = p0 >> 32;
const uint64_t p1_lo = p1 & 0xFFFFFFFF;
const uint64_t p1_hi = p1 >> 32;
const uint64_t p2_lo = p2 & 0xFFFFFFFF;
const uint64_t p2_hi = p2 >> 32;
uint64_t Q = p0_hi + p1_lo + p2_lo;
// The full product might now be computed as
//
// p_hi = p3 + p2_hi + p1_hi + (Q >> 32)
// p_lo = p0_lo + (Q << 32)
//
// But in this particular case here, the full p_lo is not required.
// Effectively we only need to add the highest bit in p_lo to p_hi (and
// Q_hi + 1 does not overflow).
Q += uint64_t{1} << (63 - 32); // round, ties up
const uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32);
return diyfp(h, x.e + y.e + 64);
}
inline diyfp diyfp::normalize(diyfp x)
{
assert(x.f != 0);
while ((x.f >> 63) == 0)
{
x.f <<= 1;
x.e--;
}
return x;
}
inline diyfp diyfp::normalize_to(diyfp x, int target_exponent)
{
const int delta = x.e - target_exponent;
assert(delta >= 0);
assert(((x.f << delta) >> delta) == x.f);
return diyfp(x.f << delta, target_exponent);
}
struct boundaries {
diyfp w;
diyfp minus;
diyfp plus;
};
// Compute the (normalized) diyfp representing the input number 'value' and its boundaries.
// PRE: value must be finite and positive
template <typename FloatType>
inline boundaries compute_boundaries(FloatType value)
{
assert(std::isfinite(value));
assert(value > 0);
// Convert the IEEE representation into a diyfp.
//
// If v is denormal:
// value = 0.F * 2^(1 - bias) = ( F) * 2^(1 - bias - (p-1))
// If v is normalized:
// value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))
static_assert(std::numeric_limits<FloatType>::is_iec559, "Requires an IEEE-754 floating-point implementation");
constexpr int kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
constexpr int kBias = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
constexpr int kMinExp = 1 - kBias;
constexpr uint64_t kHiddenBit = uint64_t{1} << (kPrecision - 1); // = 2^(p-1)
using bits_type = typename std::conditional<kPrecision == 24, uint32_t, uint64_t>::type;
const uint64_t bits = reinterpret_bits<bits_type>(value);
const uint64_t E = bits >> (kPrecision - 1);
const uint64_t F = bits & (kHiddenBit - 1);
const bool is_denormal = (E == 0);
const diyfp v
= is_denormal
? diyfp(F, 1 - kBias)
: diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);
// Compute the boundaries m- and m+ of the floating-point value
// v = f * 2^e.
//
// Determine v- and v+, the floating-point predecessor and successor if v,
// respectively.
//
// v- = v - 2^e if f != 2^(p-1) or e == e_min (A)
// = v - 2^(e-1) if f == 2^(p-1) and e > e_min (B)
//
// v+ = v + 2^e
//
// Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
// between m- and m+ round to v, regardless of how the input rounding
// algorithm breaks ties.
//
// ---+-------------+-------------+-------------+-------------+--- (A)
// v- m- v m+ v+
//
// -----------------+------+------+-------------+-------------+--- (B)
// v- m- v m+ v+
// const bool lower_boundary_is_closer = (F == 0 and E > 1);
const bool lower_boundary_is_closer = (v.f == kHiddenBit and v.e > kMinExp);
const diyfp m_plus = diyfp(2*v.f + 1, v.e - 1);
const diyfp m_minus
= lower_boundary_is_closer
? diyfp(4*v.f - 1, v.e - 2) // (B)
: diyfp(2*v.f - 1, v.e - 1); // (A)
// Determine the normalized w+ = m+.
const diyfp w_plus = diyfp::normalize(m_plus);
// Determine w- = m- such that e_(w-) = e_(w+).
const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);
return {diyfp::normalize(v), w_minus, w_plus};
}
// Given normalized diyfp w, Grisu needs to find a (normalized) cached
// power-of-ten c, such that the exponent of the product c * w = f * 2^e lies
// within a certain range [alpha, gamma] (Definition 3.2 from [1])
//
// alpha <= e = e_c + e_w + q <= gamma
//
// The choice of (alpha,gamma) determines the size of the table and the digit
// generation procedure. Using (alpha,gamma)=(-60,-32) works out well in
// practice.
constexpr int kAlpha = -60;
constexpr int kGamma = -32;
struct cached_power { // c = f * 2^e ~= 10^k
uint64_t f;
int e;
int k;
};
inline cached_power get_cached_power_for_binary_exponent(int e)
{
// NB:
// Actually this function returns c, such that -60 <= e_c + e + 64 <= -34.
constexpr int kCachedPowersSize = 79;
constexpr int kCachedPowersMinDecExp = -300;
constexpr int kCachedPowersDecStep = 8;
static constexpr cached_power kCachedPowers[] = {
{ 0xAB70FE17C79AC6CA, -1060, -300 },
{ 0xFF77B1FCBEBCDC4F, -1034, -292 },
{ 0xBE5691EF416BD60C, -1007, -284 },
{ 0x8DD01FAD907FFC3C, -980, -276 },
{ 0xD3515C2831559A83, -954, -268 },
{ 0x9D71AC8FADA6C9B5, -927, -260 },
{ 0xEA9C227723EE8BCB, -901, -252 },
{ 0xAECC49914078536D, -874, -244 },
{ 0x823C12795DB6CE57, -847, -236 },
{ 0xC21094364DFB5637, -821, -228 },
{ 0x9096EA6F3848984F, -794, -220 },
{ 0xD77485CB25823AC7, -768, -212 },
{ 0xA086CFCD97BF97F4, -741, -204 },
{ 0xEF340A98172AACE5, -715, -196 },
{ 0xB23867FB2A35B28E, -688, -188 },
{ 0x84C8D4DFD2C63F3B, -661, -180 },
{ 0xC5DD44271AD3CDBA, -635, -172 },
{ 0x936B9FCEBB25C996, -608, -164 },
{ 0xDBAC6C247D62A584, -582, -156 },
{ 0xA3AB66580D5FDAF6, -555, -148 },
{ 0xF3E2F893DEC3F126, -529, -140 },
{ 0xB5B5ADA8AAFF80B8, -502, -132 },
{ 0x87625F056C7C4A8B, -475, -124 },
{ 0xC9BCFF6034C13053, -449, -116 },
{ 0x964E858C91BA2655, -422, -108 },
{ 0xDFF9772470297EBD, -396, -100 },
{ 0xA6DFBD9FB8E5B88F, -369, -92 },
{ 0xF8A95FCF88747D94, -343, -84 },
{ 0xB94470938FA89BCF, -316, -76 },
{ 0x8A08F0F8BF0F156B, -289, -68 },
{ 0xCDB02555653131B6, -263, -60 },
{ 0x993FE2C6D07B7FAC, -236, -52 },
{ 0xE45C10C42A2B3B06, -210, -44 },
{ 0xAA242499697392D3, -183, -36 },
{ 0xFD87B5F28300CA0E, -157, -28 },
{ 0xBCE5086492111AEB, -130, -20 },
{ 0x8CBCCC096F5088CC, -103, -12 },
{ 0xD1B71758E219652C, -77, -4 },
{ 0x9C40000000000000, -50, 4 },
{ 0xE8D4A51000000000, -24, 12 },
{ 0xAD78EBC5AC620000, 3, 20 },
{ 0x813F3978F8940984, 30, 28 },
{ 0xC097CE7BC90715B3, 56, 36 },
{ 0x8F7E32CE7BEA5C70, 83, 44 },
{ 0xD5D238A4ABE98068, 109, 52 },
{ 0x9F4F2726179A2245, 136, 60 },
{ 0xED63A231D4C4FB27, 162, 68 },
{ 0xB0DE65388CC8ADA8, 189, 76 },
{ 0x83C7088E1AAB65DB, 216, 84 },
{ 0xC45D1DF942711D9A, 242, 92 },
{ 0x924D692CA61BE758, 269, 100 },
{ 0xDA01EE641A708DEA, 295, 108 },
{ 0xA26DA3999AEF774A, 322, 116 },
{ 0xF209787BB47D6B85, 348, 124 },
{ 0xB454E4A179DD1877, 375, 132 },
{ 0x865B86925B9BC5C2, 402, 140 },
{ 0xC83553C5C8965D3D, 428, 148 },
{ 0x952AB45CFA97A0B3, 455, 156 },
{ 0xDE469FBD99A05FE3, 481, 164 },
{ 0xA59BC234DB398C25, 508, 172 },
{ 0xF6C69A72A3989F5C, 534, 180 },
{ 0xB7DCBF5354E9BECE, 561, 188 },
{ 0x88FCF317F22241E2, 588, 196 },
{ 0xCC20CE9BD35C78A5, 614, 204 },
{ 0x98165AF37B2153DF, 641, 212 },
{ 0xE2A0B5DC971F303A, 667, 220 },
{ 0xA8D9D1535CE3B396, 694, 228 },
{ 0xFB9B7CD9A4A7443C, 720, 236 },
{ 0xBB764C4CA7A44410, 747, 244 },
{ 0x8BAB8EEFB6409C1A, 774, 252 },
{ 0xD01FEF10A657842C, 800, 260 },
{ 0x9B10A4E5E9913129, 827, 268 },
{ 0xE7109BFBA19C0C9D, 853, 276 },
{ 0xAC2820D9623BF429, 880, 284 },
{ 0x80444B5E7AA7CF85, 907, 292 },
{ 0xBF21E44003ACDD2D, 933, 300 },
{ 0x8E679C2F5E44FF8F, 960, 308 },
{ 0xD433179D9C8CB841, 986, 316 },
{ 0x9E19DB92B4E31BA9, 1013, 324 },
};
// This computation gives exactly the same results for k as
// k = ceil((kAlpha - e - 1) * 0.30102999566398114)
// for |e| <= 1500, but doesn't require floating-point operations.
// NB: log_10(2) ~= 78913 / 2^18
assert(e >= -1500);
assert(e <= 1500);
const int f = kAlpha - e - 1;
const int k = (f * 78913) / (1 << 18) + (f > 0);
const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;
assert(index >= 0);
assert(index < kCachedPowersSize);
static_cast<void>(kCachedPowersSize); // Fix warning.
const cached_power cached = kCachedPowers[index];
assert(kAlpha <= cached.e + e + 64);
assert(kGamma >= cached.e + e + 64);
return cached;
}
// For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
// For n == 0, returns 1 and sets pow10 := 1.
inline int find_largest_pow10(uint32_t n, uint32_t& pow10)
{
if (n >= 1000000000) { pow10 = 1000000000; return 10; }
if (n >= 100000000) { pow10 = 100000000; return 9; }
if (n >= 10000000) { pow10 = 10000000; return 8; }
if (n >= 1000000) { pow10 = 1000000; return 7; }
if (n >= 100000) { pow10 = 100000; return 6; }
if (n >= 10000) { pow10 = 10000; return 5; }
if (n >= 1000) { pow10 = 1000; return 4; }
if (n >= 100) { pow10 = 100; return 3; }
if (n >= 10) { pow10 = 10; return 2; }
pow10 = 1; return 1;
}
inline void grisu2_round(char* buf, int len, uint64_t dist, uint64_t delta, uint64_t rest, uint64_t ten_k)
{
assert(len >= 1);
assert(dist <= delta);
assert(rest <= delta);
assert(ten_k > 0);
// <--------------------------- delta ---->
// <---- dist --------->
// --------------[------------------+-------------------]--------------
// w- w w+
//
// ten_k
// <------>
// <---- rest ---->
// --------------[------------------+----+--------------]--------------
// w V
// = buf * 10^k
//
// ten_k represents a unit-in-the-last-place in the decimal representation
// stored in buf.
// Decrement buf by ten_k while this takes buf closer to w.
// The tests are written in this order to avoid overflow in unsigned
// integer arithmetic.
while (rest < dist
and delta - rest >= ten_k
and (rest + ten_k < dist or dist - rest > rest + ten_k - dist))
{
assert(buf[len - 1] != '0');
buf[len - 1]--;
rest += ten_k;
}
}
inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent, diyfp M_minus, diyfp w, diyfp M_plus)
{
static_assert(diyfp::kPrecision == 64, "invalid config");
static_assert(kAlpha >= -60, "invalid config");
static_assert(kGamma <= -32, "invalid config");
// Generates the digits (and the exponent) of a decimal floating-point
// number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
// w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
//
// <--------------------------- delta ---->
// <---- dist --------->
// --------------[------------------+-------------------]--------------
// M- w M+
//
// Grisu2 generates the digits of M+ from left to right and stops as soon as
// V is in [M-,M+].
assert(M_plus.e >= kAlpha);
assert(M_plus.e <= kGamma);
uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
uint64_t dist = diyfp::sub(M_plus, w ).f; // (significand of (M+ - w ), implicit exponent is e)
// Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
//
// M+ = f * 2^e
// = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
// = ((p1 ) * 2^-e + (p2 )) * 2^e
// = p1 + p2 * 2^e
const diyfp one(uint64_t{1} << -M_plus.e, M_plus.e);
uint32_t p1 = static_cast<uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
uint64_t p2 = M_plus.f & (one.f - 1); // p2 = f mod 2^-e
// 1)
//
// Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]
assert(p1 > 0);
uint32_t pow10;
const int k = find_largest_pow10(p1, pow10);
// 10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)
//
// p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))
// = (d[k-1] ) * 10^(k-1) + (p1 mod 10^(k-1))
//
// M+ = p1 + p2 * 2^e
// = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1)) + p2 * 2^e
// = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e
// = d[k-1] * 10^(k-1) + ( rest) * 2^e
//
// Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)
//
// p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]
//
// but stop as soon as
//
// rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e
int n = k;
while (n > 0)
{
// Invariants:
// M+ = buffer * 10^n + (p1 + p2 * 2^e) (buffer = 0 for n = k)
// pow10 = 10^(n-1) <= p1 < 10^n
//
const uint32_t d = p1 / pow10; // d = p1 div 10^(n-1)
const uint32_t r = p1 % pow10; // r = p1 mod 10^(n-1)
//
// M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e
// = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e)
//
assert(d <= 9);
buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
//
// M+ = buffer * 10^(n-1) + (r + p2 * 2^e)
//
p1 = r;
n--;
//
// M+ = buffer * 10^n + (p1 + p2 * 2^e)
// pow10 = 10^n
//
// Now check if enough digits have been generated.
// Compute
//
// p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e
//
// Note:
// Since rest and delta share the same exponent e, it suffices to
// compare the significands.
const uint64_t rest = (uint64_t{p1} << -one.e) + p2;
if (rest <= delta)
{
// V = buffer * 10^n, with M- <= V <= M+.
decimal_exponent += n;
// We may now just stop. But instead look if the buffer could be
// decremented to bring V closer to w.
//
// pow10 = 10^n is now 1 ulp in the decimal representation V.
// The rounding procedure works with diyfp's with an implicit
// exponent of e.
//
// 10^n = (10^n * 2^-e) * 2^e = ulp * 2^e
//
const uint64_t ten_n = uint64_t{pow10} << -one.e;
grisu2_round(buffer, length, dist, delta, rest, ten_n);
return;
}
pow10 /= 10;
//
// pow10 = 10^(n-1) <= p1 < 10^n
// Invariants restored.
}
// 2)
//
// The digits of the integral part have been generated:
//
// M+ = d[k-1]...d[1]d[0] + p2 * 2^e
// = buffer + p2 * 2^e
//
// Now generate the digits of the fractional part p2 * 2^e.
//
// Note:
// No decimal point is generated: the exponent is adjusted instead.
//
// p2 actually represents the fraction
//
// p2 * 2^e
// = p2 / 2^-e
// = d[-1] / 10^1 + d[-2] / 10^2 + ...
//
// Now generate the digits d[-m] of p1 from left to right (m = 1,2,...)
//
// p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m
// + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...)
//
// using
//
// 10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e)
// = ( d) * 2^-e + ( r)
//
// or
// 10^m * p2 * 2^e = d + r * 2^e
//
// i.e.
//
// M+ = buffer + p2 * 2^e
// = buffer + 10^-m * (d + r * 2^e)
// = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e
//
// and stop as soon as 10^-m * r * 2^e <= delta * 2^e
assert(p2 > delta);
int m = 0;
for (;;)
{
// Invariant:
// M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e
// = buffer * 10^-m + 10^-m * (p2 ) * 2^e
// = buffer * 10^-m + 10^-m * (1/10 * (10 * p2) ) * 2^e
// = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e
//
assert(p2 <= UINT64_MAX / 10);
p2 *= 10;
const uint64_t d = p2 >> -one.e; // d = (10 * p2) div 2^-e
const uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e
//
// M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e
// = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e))
// = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e
//
assert(d <= 9);
buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
//
// M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e
//
p2 = r;
m++;
//
// M+ = buffer * 10^-m + 10^-m * p2 * 2^e
// Invariant restored.
// Check if enough digits have been generated.
//
// 10^-m * p2 * 2^e <= delta * 2^e
// p2 * 2^e <= 10^m * delta * 2^e
// p2 <= 10^m * delta
delta *= 10;
dist *= 10;
if (p2 <= delta)
{
break;
}
}
// V = buffer * 10^-m, with M- <= V <= M+.
decimal_exponent -= m;
// 1 ulp in the decimal representation is now 10^-m.
// Since delta and dist are now scaled by 10^m, we need to do the
// same with ulp in order to keep the units in sync.
//
// 10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e
//
const uint64_t ten_m = one.f;
grisu2_round(buffer, length, dist, delta, p2, ten_m);
// By construction this algorithm generates the shortest possible decimal
// number (Loitsch, Theorem 6.2) which rounds back to w.
// For an input number of precision p, at least
//
// N = 1 + ceil(p * log_10(2))
//
// decimal digits are sufficient to identify all binary floating-point
// numbers (Matula, "In-and-Out conversions").
// This implies that the algorithm does not produce more than N decimal
// digits.
//
// N = 17 for p = 53 (IEEE double precision)
// N = 9 for p = 24 (IEEE single precision)
}
// v = buf * 10^decimal_exponent
// len is the length of the buffer (number of decimal digits)
// The buffer must be large enough, i.e. >= max_digits10.
inline void grisu2(char* buf, int& len, int& decimal_exponent, diyfp m_minus, diyfp v, diyfp m_plus)
{
assert(m_plus.e == m_minus.e);
assert(m_plus.e == v.e);
// --------(-----------------------+-----------------------)-------- (A)
// m- v m+
//
// --------------------(-----------+-----------------------)-------- (B)
// m- v m+
//
// First scale v (and m- and m+) such that the exponent is in the range
// [alpha, gamma].
const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);
const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k
// The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]
const diyfp w = diyfp::mul(v, c_minus_k);
const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);
const diyfp w_plus = diyfp::mul(m_plus, c_minus_k);
// ----(---+---)---------------(---+---)---------------(---+---)----
// w- w w+
// = c*m- = c*v = c*m+
//
// diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and
// w+ are now off by a small amount.
// In fact:
//
// w - v * 10^k < 1 ulp
//
// To account for this inaccuracy, add resp. subtract 1 ulp.
//
// --------+---[---------------(---+---)---------------]---+--------
// w- M- w M+ w+
//
// Now any number in [M-, M+] (bounds included) will round to w when input,
// regardless of how the input rounding algorithm breaks ties.
//
// And digit_gen generates the shortest possible such number in [M-, M+].
// Note that this does not mean that Grisu2 always generates the shortest
// possible number in the interval (m-, m+).
const diyfp M_minus(w_minus.f + 1, w_minus.e);
const diyfp M_plus (w_plus.f - 1, w_plus.e );
decimal_exponent = -cached.k; // = -(-k) = k
grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);
}
// v = buf * 10^decimal_exponent
// len is the length of the buffer (number of decimal digits)
// The buffer must be large enough, i.e. >= max_digits10.
template <typename FloatType>
inline void grisu2(char* buf, int& len, int& decimal_exponent, FloatType value)
{
assert(std::isfinite(value));
assert(value > 0);
#if 0
// If the neighbors (and boundaries) of 'value' are always computed for
// double-precision numbers, all float's can be recovered using strtod
// (and strtof). However, the resulting decimal representations are not
// exactly "short".
//
// If the neighbors are computed for single-precision numbers, there is a
// single float (7.0385307e-26f) which can't be recovered using strtod.
// (The resulting double precision is off by 1 ulp.)
const boundaries w = compute_boundaries(static_cast<double>(value));
#else
const boundaries w = compute_boundaries(value);
#endif
grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus);
}
// Appends a decimal representation of e to buf.
// Returns a pointer to the element following the exponent.
// PRE: -1000 < e < 1000
inline char* append_exponent(char* buf, int e)
{
assert(e > -1000);
assert(e < 1000);
if (e < 0)
{
e = -e;
*buf++ = '-';
}
else
{
*buf++ = '+';
}
uint32_t k = static_cast<uint32_t>(e);
if (k < 10)
{
*buf++ = static_cast<char>('0' + k);
}
else if (k < 100)
{
*buf++ = static_cast<char>('0' + k / 10); k %= 10;
*buf++ = static_cast<char>('0' + k );
}
else
{
*buf++ = static_cast<char>('0' + k / 100); k %= 100;
*buf++ = static_cast<char>('0' + k / 10); k %= 10;
*buf++ = static_cast<char>('0' + k );
}
return buf;
}
// Prettify v = buf * 10^decimal_exponent
// If v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point notation.
// Otherwise it will be printed in exponential notation.
// PRE: min_exp < 0
// PRE: max_exp > 0
inline char* format_buffer(char* buf, int len, int decimal_exponent, int min_exp, int max_exp)
{
assert(min_exp < 0);
assert(max_exp > 0);
int k = len;
int n = len + decimal_exponent;
// v = buf * 10^(n-k)
// k is the length of the buffer (number of decimal digits)
// n is the position of the decimal point relative to the start of the buffer.
if (k <= n and n <= max_exp)
{
// digits[000]
// len <= max_exp
std::memset(buf + k, '0', static_cast<size_t>(n - k));
buf[n++] = '.';
buf[n++] = '0';
return buf + n;
}
if (0 < n and n <= max_exp)
{
// dig.its
// len <= max_digits10 + 1
assert(k > n);
std::memmove(buf + (n + 1), buf + n, static_cast<size_t>(k - n));
buf[n] = '.';
return buf + (k + 1);
}
if (min_exp < n and n <= 0)
{
// 0.[000]digits
// len <= 2 + (-min_exp - 1) + max_digits10
std::memmove(buf + (2 + -n), buf, static_cast<size_t>(k));
buf[0] = '0';
buf[1] = '.';
std::memset(buf + 2, '0', static_cast<size_t>(-n));
return buf + (2 + (-n) + k);
}
if (k == 1)
{
// dE+123
// len <= 1 + 5
buf += 1;
}
else
{
// d.igitsE+123
// len <= max_digits10 + 1 + 5
std::memmove(buf + 2, buf + 1, static_cast<size_t>(k - 1));
buf[1] = '.';
buf += 1 + k;
}
*buf++ = 'e';
return append_exponent(buf, n - 1);
}
// Generates a decimal representation of the floating-point number 'value' in
// [first, last).
//
// The input number must be finite, i.e. NaN's and Inf's are not supported.
// The buffer must be large enough.
//
// The result is _not_ null-terminated.
template <typename FloatType>
inline char* to_short_string(char* first, char* last, FloatType value)
{
static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3, "Not enough precision");
static_cast<void>(last); // maybe unused - fix warning
assert(!std::isnan(value));
assert(!std::isinf(value));
// Use signbit(value) instead of (value < 0) since signbit works for -0.
if (std::signbit(value))
{
value = -value;
*first++ = '-';
}
if (value == 0)
{
*first++ = '0';
*first++ = '.';
*first++ = '0';
return first;
}
assert(last - first >= std::numeric_limits<FloatType>::max_digits10);
// Compute v = buffer * 10^decimal_exponent.
// The decimal digits are stored in the buffer, which needs to be interpreted
// as an unsigned decimal integer.
// len is the length of the buffer, i.e. the number of decimal digits.
int len = 0;
int decimal_exponent = 0;
grisu2(first, len, decimal_exponent, value);
assert(len <= std::numeric_limits<FloatType>::max_digits10);
// Format the buffer like printf("%.*g", prec, value)
constexpr int kMinExp = -4;
#if 0
constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10;
#else
constexpr int kMaxExp = std::numeric_limits<FloatType>::max_digits10;
#endif
assert(last - first >=
std::max({
kMaxExp,
2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10,
std::numeric_limits<FloatType>::max_digits10 + 6}));
return format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp);
}
} // namespace dtoa
template<typename BasicJsonType>
class serializer
{
@ -6711,12 +7607,35 @@ class serializer
void dump_float(number_float_t x)
{
// NaN / inf
if (not std::isfinite(x) or std::isnan(x))
if (not std::isfinite(x))
{
o->write_characters("null", 4);
return;
}
// If number_float_t is an IEEE-754 single or double precision number,
// use the Grisu2 algorithm to produce short numbers which are guaranteed
// to round-trip.
//
// NB: The test below works if <long double> == <double>.
static constexpr bool is_ieee_single_or_double
= (std::numeric_limits<number_float_t>::is_iec559 and std::numeric_limits<number_float_t>::digits == 24 and std::numeric_limits<number_float_t>::max_exponent == 128) or
(std::numeric_limits<number_float_t>::is_iec559 and std::numeric_limits<number_float_t>::digits == 53 and std::numeric_limits<number_float_t>::max_exponent == 1024);
dump_float(x, std::integral_constant<bool, is_ieee_single_or_double>());
}
private:
void dump_float(number_float_t x, std::true_type)
{
char* begin = number_buffer.data();
char* end = dtoa::to_short_string(begin, begin + number_buffer.size(), x);
o->write_characters(begin, static_cast<size_t>(end - begin));
}
void dump_float(number_float_t x, std::false_type)
{
// get number of digits for a text -> float -> text round-trip
static constexpr auto d = std::numeric_limits<number_float_t>::digits10;

470
test/src/unit-dtoa.cpp Normal file
View File

@ -0,0 +1,470 @@
/*
__ _____ _____ _____
__| | __| | | | JSON for Modern C++ (test suite)
| | |__ | | | | | | version 2.1.1
|_____|_____|_____|_|___| https://github.com/nlohmann/json
Licensed under the MIT License <http://opensource.org/licenses/MIT>.
Copyright (c) 2013-2017 Niels Lohmann <http://nlohmann.me>.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
// XXX:
// Only compile these tests if 'float' and 'double' are IEEE-754 single- and
// double-precision numbers, resp.
#include "catch.hpp"
#include "json.hpp"
using nlohmann::detail::dtoa::reinterpret_bits;
static float make_float(uint32_t sign_bit, uint32_t biased_exponent, uint32_t significand)
{
assert(sign_bit == 0 || sign_bit == 1);
assert(biased_exponent <= 0xFF);
assert(significand <= 0x007FFFFF);
uint32_t bits = 0;
bits |= sign_bit << 31;
bits |= biased_exponent << 23;
bits |= significand;
return reinterpret_bits<float>(bits);
}
// ldexp -- convert f * 2^e to IEEE single precision
static float make_float(uint64_t f, int e)
{
constexpr uint64_t kHiddenBit = 0x00800000;
constexpr uint64_t kSignificandMask = 0x007FFFFF;
constexpr int kPhysicalSignificandSize = 23; // Excludes the hidden bit.
constexpr int kExponentBias = 0x7F + kPhysicalSignificandSize;
constexpr int kDenormalExponent = 1 - kExponentBias;
constexpr int kMaxExponent = 0xFF - kExponentBias;
while (f > kHiddenBit + kSignificandMask) {
f >>= 1;
e++;
}
if (e >= kMaxExponent) {
return std::numeric_limits<float>::infinity();
}
if (e < kDenormalExponent) {
return 0.0;
}
while (e > kDenormalExponent && (f & kHiddenBit) == 0) {
f <<= 1;
e--;
}
uint64_t biased_exponent;
if (e == kDenormalExponent && (f & kHiddenBit) == 0)
biased_exponent = 0;
else
biased_exponent = static_cast<uint64_t>(e + kExponentBias);
uint64_t bits = (f & kSignificandMask) | (biased_exponent << kPhysicalSignificandSize);
return reinterpret_bits<float>(static_cast<uint32_t>(bits));
}
static double make_double(uint64_t sign_bit, uint64_t biased_exponent, uint64_t significand)
{
assert(sign_bit == 0 || sign_bit == 1);
assert(biased_exponent <= 0x7FF);
assert(significand <= 0x000FFFFFFFFFFFFF);
uint64_t bits = 0;
bits |= sign_bit << 63;
bits |= biased_exponent << 52;
bits |= significand;
return reinterpret_bits<double>(bits);
}
// ldexp -- convert f * 2^e to IEEE double precision
static double make_double(uint64_t f, int e)
{
constexpr uint64_t kHiddenBit = 0x0010000000000000;
constexpr uint64_t kSignificandMask = 0x000FFFFFFFFFFFFF;
constexpr int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
constexpr int kExponentBias = 0x3FF + kPhysicalSignificandSize;
constexpr int kDenormalExponent = 1 - kExponentBias;
constexpr int kMaxExponent = 0x7FF - kExponentBias;
while (f > kHiddenBit + kSignificandMask) {
f >>= 1;
e++;
}
if (e >= kMaxExponent) {
return std::numeric_limits<double>::infinity();
}
if (e < kDenormalExponent) {
return 0.0;
}
while (e > kDenormalExponent && (f & kHiddenBit) == 0) {
f <<= 1;
e--;
}
uint64_t biased_exponent;
if (e == kDenormalExponent && (f & kHiddenBit) == 0)
biased_exponent = 0;
else
biased_exponent = static_cast<uint64_t>(e + kExponentBias);
uint64_t bits = (f & kSignificandMask) | (biased_exponent << kPhysicalSignificandSize);
return reinterpret_bits<double>(bits);
}
TEST_CASE("digit gen")
{
SECTION("single precision")
{
auto check_float = [](float number, const std::string& digits, int expected_exponent)
{
CAPTURE(number);
CAPTURE(digits);
CAPTURE(expected_exponent);
char buf[32];
int len = 0;
int exponent = 0;
nlohmann::detail::dtoa::grisu2(buf, len, exponent, number);
CHECK(digits == std::string(buf, buf + len));
CHECK(expected_exponent == exponent);
};
check_float(make_float(0, 0, 0x00000001), "1", -45); // min denormal
check_float(make_float(0, 0, 0x007FFFFF), "11754942", -45); // max denormal
check_float(make_float(0, 1, 0x00000000), "11754944", -45); // min normal
check_float(make_float(0, 1, 0x00000001), "11754945", -45);
check_float(make_float(0, 1, 0x007FFFFF), "23509886", -45);
check_float(make_float(0, 2, 0x00000000), "23509887", -45);
check_float(make_float(0, 2, 0x00000001), "2350989", -44);
check_float(make_float(0, 24, 0x00000000), "98607613", -39); // fail if no special case in normalized boundaries
check_float(make_float(0, 30, 0x00000000), "63108872", -37); // fail if no special case in normalized boundaries
check_float(make_float(0, 31, 0x00000000), "12621775", -36); // fail if no special case in normalized boundaries
check_float(make_float(0, 57, 0x00000000), "84703295", -29); // fail if no special case in normalized boundaries
check_float(make_float(0, 254, 0x007FFFFE), "34028233", 31);
check_float(make_float(0, 254, 0x007FFFFF), "34028235", 31); // max normal
// V. Paxson and W. Kahan, "A Program for Testing IEEE Binary-Decimal Conversion", manuscript, May 1991,
// ftp://ftp.ee.lbl.gov/testbase-report.ps.Z (report)
// ftp://ftp.ee.lbl.gov/testbase.tar.Z (program)
// Table 16: Stress Inputs for Converting 24-bit Binary to Decimal, < 1/2 ULP
check_float(make_float(12676506, -102), "25", -25);
check_float(make_float(12676506, -103), "125", -26);
check_float(make_float(15445013, 86), "1195", 30);
check_float(make_float(13734123, -138), "39415", -39);
check_float(make_float(12428269, -130), "913085", -38);
check_float(make_float(15334037, -146), "1719005", -43);
check_float(make_float(11518287, -41), "52379105", -13);
check_float(make_float(12584953, -145), "2821644", -43);
check_float(make_float(15961084, -125), "37524328", -38);
check_float(make_float(14915817, -146), "16721209", -44);
check_float(make_float(10845484, -102), "21388946", -31);
check_float(make_float(16431059, -61), "7125836", -18);
// Table 17: Stress Inputs for Converting 24-bit Binary to Decimal, > 1/2 ULP
check_float(make_float(16093626, 69), "95", 26);
check_float(make_float( 9983778, 25), "335", 12);
check_float(make_float(12745034, 104), "2585", 35);
check_float(make_float(12706553, 72), "60005", 24);
check_float(make_float(11005028, 45), "387205", 15);
check_float(make_float(15059547, 71), "3555835", 22);
check_float(make_float(16015691, -99), "25268305", -30);
check_float(make_float( 8667859, 56), "6245851", 17);
check_float(make_float(14855922, -82), "30721327", -25);
check_float(make_float(14855922, -83), "15360663", -25);
check_float(make_float(10144164, -110), "781478", -32);
check_float(make_float(13248074, 95), "52481028", 28);
}
SECTION("double precision")
{
auto check_double = [](double number, const std::string& digits, int expected_exponent)
{
CAPTURE(number);
CAPTURE(digits);
CAPTURE(expected_exponent);
char buf[32];
int len = 0;
int exponent = 0;
nlohmann::detail::dtoa::grisu2(buf, len, exponent, number);
CHECK(digits == std::string(buf, buf + len));
CHECK(expected_exponent == exponent);
};
check_double(make_double(0, 0, 0x0000000000000001), "5", -324); // min denormal
check_double(make_double(0, 0, 0x000FFFFFFFFFFFFF), "2225073858507201", -323); // max denormal
check_double(make_double(0, 1, 0x0000000000000000), "22250738585072014", -324); // min normal
check_double(make_double(0, 1, 0x0000000000000001), "2225073858507202", -323);
check_double(make_double(0, 1, 0x000FFFFFFFFFFFFF), "44501477170144023", -324);
check_double(make_double(0, 2, 0x0000000000000000), "4450147717014403", -323);
check_double(make_double(0, 2, 0x0000000000000001), "4450147717014404", -323);
check_double(make_double(0, 4, 0x0000000000000000), "17800590868057611", -323); // fail if no special case in normalized boundaries
check_double(make_double(0, 5, 0x0000000000000000), "35601181736115222", -323); // fail if no special case in normalized boundaries
check_double(make_double(0, 6, 0x0000000000000000), "7120236347223045", -322); // fail if no special case in normalized boundaries
check_double(make_double(0, 10, 0x0000000000000000), "11392378155556871", -321); // fail if no special case in normalized boundaries
check_double(make_double(0, 2046, 0x000FFFFFFFFFFFFE), "17976931348623155", 292);
check_double(make_double(0, 2046, 0x000FFFFFFFFFFFFF), "17976931348623157", 292); // max normal
// Test different paths in DigitGen
check_double( 10000, "1", 4);
check_double( 1200000, "12", 5);
check_double(4.9406564584124654e-324, "5", -324); // exit integral loop
check_double(2.2250738585072009e-308, "2225073858507201", -323); // exit fractional loop
check_double( 1.82877982605164e-99, "182877982605164", -113);
check_double( 1.1505466208671903e-09, "11505466208671903", -25);
check_double( 5.5645893133766722e+20, "5564589313376672", 5);
check_double( 53.034830388866226, "53034830388866226", -15);
check_double( 0.0021066531670178605, "21066531670178605", -19);
// V. Paxson and W. Kahan, "A Program for Testing IEEE Binary-Decimal Conversion", manuscript, May 1991,
// ftp://ftp.ee.lbl.gov/testbase-report.ps.Z (report)
// ftp://ftp.ee.lbl.gov/testbase.tar.Z (program)
// Table 3: Stress Inputs for Converting 53-bit Binary to Decimal, < 1/2 ULP
check_double(make_double(8511030020275656, -342) /* 9.5e-088 */, "95", -89);
check_double(make_double(5201988407066741, -824) /* 4.65e-233 */, "465", -235);
check_double(make_double(6406892948269899, +237) /* 1.415e+087 */, "1415", 84);
check_double(make_double(8431154198732492, +72) /* 3.9815e+037 */, "39815", 33);
check_double(make_double(6475049196144587, +99) /* 4.10405e+045 */, "410405", 40);
check_double(make_double(8274307542972842, +726) /* 2.920845e+234 */, "2920845", 228);
check_double(make_double(5381065484265332, -456) /* 2.8919465e-122 */, "28919465", -129);
check_double(make_double(6761728585499734, -1057) /* 4.37877185e-303 */, "437877185", -311);
check_double(make_double(7976538478610756, +376) /* 1.227701635e+129 */, "1227701635", 120);
check_double(make_double(5982403858958067, +377) /* 1.8415524525e+129 */, "18415524525", 119);
check_double(make_double(5536995190630837, +93) /* 5.48357443505e+043 */, "548357443505", 32);
check_double(make_double(7225450889282194, +710) /* 3.891901811465e+229 */, "3891901811465", 217);
check_double(make_double(7225450889282194, +709) /* 1.9459509057325e+229 */, "19459509057325", 216);
check_double(make_double(8703372741147379, +117) /* 1.44609583816055e+051 */, "144609583816055", 37);
check_double(make_double(8944262675275217, -1001) /* 4.173677474585315e-286 */, "4173677474585315", -301);
check_double(make_double(7459803696087692, -707) /* 1.1079507728788885e-197 */, "11079507728788885", -213);
check_double(make_double(6080469016670379, -381) /* 1.234550136632744e-099 */, "1234550136632744", -114);
check_double(make_double(8385515147034757, +721) /* 9.2503171196036502e+232 */, "925031711960365", 218);
check_double(make_double(7514216811389786, -828) /* 4.1980471502848898e-234 */, "419804715028489", -248);
check_double(make_double(8397297803260511, -345) /* 1.1716315319786511e-088 */, "11716315319786511", -104);
check_double(make_double(6733459239310543, +202) /* 4.3281007284461249e+076 */, "4328100728446125", 61);
check_double(make_double(8091450587292794, -473) /* 3.3177101181600311e-127 */, "3317710118160031", -142);
// Table 4: Stress Inputs for Converting 53-bit Binary to Decimal, > 1/2 ULP
check_double(make_double(6567258882077402, +952) /* 2.5e+302 */, "25", 301);
check_double(make_double(6712731423444934, +535) /* 7.55e+176 */, "755", 174);
check_double(make_double(6712731423444934, +534) /* 3.775e+176 */, "3775", 173);
check_double(make_double(5298405411573037, -957) /* 4.3495e-273 */, "43495", -277);
check_double(make_double(5137311167659507, -144) /* 2.30365e-028 */, "230365", -33);
check_double(make_double(6722280709661868, +363) /* 1.263005e+125 */, "1263005", 119);
check_double(make_double(5344436398034927, -169) /* 7.1422105e-036 */, "71422105", -43);
check_double(make_double(8369123604277281, -853) /* 1.39345735e-241 */, "139345735", -249);
check_double(make_double(8995822108487663, -780) /* 1.414634485e-219 */, "1414634485", -228);
check_double(make_double(8942832835564782, -383) /* 4.5392779195e-100 */, "45392779195", -110);
check_double(make_double(8942832835564782, -384) /* 2.26963895975e-100 */, "226963895975", -111);
check_double(make_double(8942832835564782, -385) /* 1.134819479875e-100 */, "1134819479875", -112);
check_double(make_double(6965949469487146, -249) /* 7.7003665618895e-060 */, "77003665618895", -73);
check_double(make_double(6965949469487146, -250) /* 3.85018328094475e-060 */, "385018328094475", -74);
check_double(make_double(6965949469487146, -251) /* 1.925091640472375e-060 */, "1925091640472375", -75);
check_double(make_double(7487252720986826, +548) /* 6.8985865317742005e+180 */, "68985865317742005", 164);
check_double(make_double(5592117679628511, +164) /* 1.3076622631878654e+065 */, "13076622631878654", 49);
check_double(make_double(8887055249355788, +665) /* 1.3605202075612124e+216 */, "13605202075612124", 200);
check_double(make_double(6994187472632449, +690) /* 3.5928102174759597e+223 */, "35928102174759597", 207);
check_double(make_double(8797576579012143, +588) /* 8.9125197712484552e+192 */, "8912519771248455", 177);
check_double(make_double(7363326733505337, +272) /* 5.5876975736230114e+097 */, "55876975736230114", 81);
check_double(make_double(8549497411294502, -448) /* 1.1762578307285404e-119 */, "11762578307285404", -135);
// Table 20: Stress Inputs for Converting 56-bit Binary to Decimal, < 1/2 ULP
check_double(make_double(50883641005312716, -172) /* 8.4999999999999993e-036 */, "8499999999999999", -51);
check_double(make_double(38162730753984537, -170) /* 2.5499999999999999e-035 */, "255", -37);
check_double(make_double(50832789069151999, -101) /* 2.0049999999999997e-014 */, "20049999999999997", -30);
check_double(make_double(51822367833714164, -109) /* 7.9844999999999994e-017 */, "7984499999999999", -32);
check_double(make_double(66840152193508133, -172) /* 1.1165499999999999e-035 */, "11165499999999999", -51);
check_double(make_double(55111239245584393, -138) /* 1.581615e-025 */, "1581615", -31);
check_double(make_double(71704866733321482, -112) /* 1.3809855e-017 */, "13809855", -24);
check_double(make_double(67160949328233173, -142) /* 1.2046404499999999e-026 */, "12046404499999999", -42);
check_double(make_double(53237141308040189, -152) /* 9.3251405449999991e-030 */, "9325140544999999", -45);
check_double(make_double(62785329394975786, -112) /* 1.2092014595e-017 */, "12092014595", -27);
check_double(make_double(48367680154689523, -77) /* 3.2007045838499998e-007 */, "320070458385", -18);
check_double(make_double(42552223180606797, -102) /* 8.391946324354999e-015 */, "8391946324354999", -30);
check_double(make_double(63626356173011241, -112) /* 1.2253990460585e-017 */, "12253990460585", -30);
check_double(make_double(43566388595783643, -99) /* 6.8735641489760495e-014 */, "687356414897605", -28);
check_double(make_double(54512669636675272, -159) /* 7.459816430480385e-032 */, "7459816430480385", -47);
check_double(make_double(52306490527514614, -167) /* 2.7960588398142552e-034 */, "2796058839814255", -49);
check_double(make_double(52306490527514614, -168) /* 1.3980294199071276e-034 */, "13980294199071276", -50);
check_double(make_double(41024721590449423, -89) /* 6.6279012373057359e-011 */, "6627901237305736", -26);
check_double(make_double(37664020415894738, -132) /* 6.9177880043968072e-024 */, "6917788004396807", -39);
check_double(make_double(37549883692866294, -93) /* 3.7915693108349708e-012 */, "3791569310834971", -27);
check_double(make_double(69124110374399839, -104) /* 3.4080817676591365e-015 */, "34080817676591365", -31);
check_double(make_double(69124110374399839, -105) /* 1.7040408838295683e-015 */, "17040408838295683", -31);
// Table 21: Stress Inputs for Converting 56-bit Binary to Decimal, > 1/2 ULP
check_double(make_double(49517601571415211, -94) /* 2.4999999999999998e-012 */, "25", -13);
check_double(make_double(49517601571415211, -95) /* 1.2499999999999999e-012 */, "125", -14);
check_double(make_double(54390733528642804, -133) /* 4.9949999999999996e-024 */, "49949999999999996", -40); // shortest: 4995e-27
check_double(make_double(71805402319113924, -157) /* 3.9304999999999998e-031 */, "39304999999999998", -47); // shortest: 39305e-35
check_double(make_double(40435277969631694, -179) /* 5.2770499999999992e-038 */, "5277049999999999", -53);
check_double(make_double(57241991568619049, -165) /* 1.223955e-033 */, "1223955", -39);
check_double(make_double(65224162876242886, +58) /* 1.8799584999999998e+034 */, "18799584999999998", 18);
check_double(make_double(70173376848895368, -138) /* 2.01387715e-025 */, "201387715", -33);
check_double(make_double(37072848117383207, -99) /* 5.8490641049999989e-014 */, "5849064104999999", -29);
check_double(make_double(56845051585389697, -176) /* 5.9349003054999999e-037 */, "59349003055", -47);
check_double(make_double(54791673366936431, -145) /* 1.2284718039499998e-027 */, "12284718039499998", -43);
check_double(make_double(66800318669106231, -169) /* 8.9270767180849991e-035 */, "8927076718084999", -50);
check_double(make_double(66800318669106231, -170) /* 4.4635383590424995e-035 */, "44635383590424995", -51);
check_double(make_double(66574323440112438, -119) /* 1.0016990862549499e-019 */, "10016990862549499", -35);
check_double(make_double(65645179969330963, -173) /* 5.4829412628024647e-036 */, "5482941262802465", -51);
check_double(make_double(61847254334681076, -109) /* 9.5290783281036439e-017 */, "9529078328103644", -32);
check_double(make_double(39990712921393606, -145) /* 8.9662279366405553e-028 */, "8966227936640555", -43);
check_double(make_double(59292318184400283, -149) /* 8.3086234418058538e-029 */, "8308623441805854", -44);
check_double(make_double(69116558615326153, -143) /* 6.1985873566126555e-027 */, "61985873566126555", -43);
check_double(make_double(69116558615326153, -144) /* 3.0992936783063277e-027 */, "30992936783063277", -43);
check_double(make_double(39462549494468513, -152) /* 6.9123512506176015e-030 */, "6912351250617602", -45);
check_double(make_double(39462549494468513, -153) /* 3.4561756253088008e-030 */, "3456175625308801", -45);
}
}
TEST_CASE("formatting")
{
SECTION("single precision")
{
auto check_float = [](float number, const std::string& expected)
{
char buf[32];
char* end = nlohmann::detail::dtoa::to_short_string(buf, buf + 32, number);
std::string actual(buf, end);
CHECK(actual == expected);
};
// %.9g
check_float( -1.2345e-22f, "-1.2345e-22" ); // -1.23450004e-22
check_float( -1.2345e-21f, "-1.2345e-21" ); // -1.23450002e-21
check_float( -1.2345e-20f, "-1.2345e-20" ); // -1.23450002e-20
check_float( -1.2345e-19f, "-1.2345e-19" ); // -1.23449999e-19
check_float( -1.2345e-18f, "-1.2345e-18" ); // -1.23449996e-18
check_float( -1.2345e-17f, "-1.2345e-17" ); // -1.23449998e-17
check_float( -1.2345e-16f, "-1.2345e-16" ); // -1.23449996e-16
check_float( -1.2345e-15f, "-1.2345e-15" ); // -1.23450002e-15
check_float( -1.2345e-14f, "-1.2345e-14" ); // -1.23450004e-14
check_float( -1.2345e-13f, "-1.2345e-13" ); // -1.23449997e-13
check_float( -1.2345e-12f, "-1.2345e-12" ); // -1.23450002e-12
check_float( -1.2345e-11f, "-1.2345e-11" ); // -1.2345e-11
check_float( -1.2345e-10f, "-1.2345e-10" ); // -1.2345e-10
check_float( -1.2345e-9f, "-1.2345e-9" ); // -1.23449995e-09
check_float( -1.2345e-8f, "-1.2345e-8" ); // -1.23449997e-08
check_float( -1.2345e-7f, "-1.2345e-7" ); // -1.23449993e-07
check_float( -1.2345e-6f, "-1.2345e-6" ); // -1.23450002e-06
check_float( -1.2345e-5f, "-1.2345e-5" ); // -1.2345e-05
check_float( -1.2345e-4f, "-0.00012345" ); // -0.000123449994
check_float( -1.2345e-3f, "-0.0012345" ); // -0.00123449997
check_float( -1.2345e-2f, "-0.012345" ); // -0.0123450002
check_float( -1.2345e-1f, "-0.12345" ); // -0.123450004
check_float( -0.0f, "-0.0" ); // -0
check_float( 0.0f, "0.0" ); // 0
check_float( 1.2345e+0f, "1.2345" ); // 1.23450005
check_float( 1.2345e+1f, "12.345" ); // 12.3450003
check_float( 1.2345e+2f, "123.45" ); // 123.449997
check_float( 1.2345e+3f, "1234.5" ); // 1234.5
check_float( 1.2345e+4f, "12345.0" ); // 12345
check_float( 1.2345e+5f, "123450.0" ); // 123450
check_float( 1.2345e+6f, "1234500.0" ); // 1234500
check_float( 1.2345e+7f, "12345000.0" ); // 12345000
check_float( 1.2345e+8f, "123450000.0" ); // 123450000
check_float( 1.2345e+9f, "1.2345e+9" ); // 1.23449997e+09
check_float( 1.2345e+10f, "1.2345e+10" ); // 1.23449999e+10
check_float( 1.2345e+11f, "1.2345e+11" ); // 1.23449999e+11
check_float( 1.2345e+12f, "1.2345e+12" ); // 1.23450006e+12
check_float( 1.2345e+13f, "1.2345e+13" ); // 1.23449995e+13
check_float( 1.2345e+14f, "1.2345e+14" ); // 1.23450002e+14
check_float( 1.2345e+15f, "1.2345e+15" ); // 1.23450003e+15
check_float( 1.2345e+16f, "1.2345e+16" ); // 1.23449998e+16
check_float( 1.2345e+17f, "1.2345e+17" ); // 1.23449996e+17
check_float( 1.2345e+18f, "1.2345e+18" ); // 1.23450004e+18
check_float( 1.2345e+19f, "1.2345e+19" ); // 1.23449999e+19
check_float( 1.2345e+20f, "1.2345e+20" ); // 1.23449999e+20
check_float( 1.2345e+21f, "1.2345e+21" ); // 1.23449999e+21
check_float( 1.2345e+22f, "1.2345e+22" ); // 1.23450005e+22
}
SECTION("double precision")
{
auto check_double = [](double number, const std::string& expected)
{
char buf[32];
char* end = nlohmann::detail::dtoa::to_short_string(buf, buf + 32, number);
std::string actual(buf, end);
CHECK(actual == expected);
};
// %.17g
check_double( -1.2345e-22, "-1.2345e-22" ); // -1.2345000000000001e-22
check_double( -1.2345e-21, "-1.2345e-21" ); // -1.2345000000000001e-21
check_double( -1.2345e-20, "-1.2345e-20" ); // -1.2345e-20
check_double( -1.2345e-19, "-1.2345e-19" ); // -1.2345000000000001e-19
check_double( -1.2345e-18, "-1.2345e-18" ); // -1.2345000000000001e-18
check_double( -1.2345e-17, "-1.2345e-17" ); // -1.2345e-17
check_double( -1.2345e-16, "-1.2345e-16" ); // -1.2344999999999999e-16
check_double( -1.2345e-15, "-1.2345e-15" ); // -1.2345e-15
check_double( -1.2345e-14, "-1.2345e-14" ); // -1.2345e-14
check_double( -1.2345e-13, "-1.2345e-13" ); // -1.2344999999999999e-13
check_double( -1.2345e-12, "-1.2345e-12" ); // -1.2345e-12
check_double( -1.2345e-11, "-1.2345e-11" ); // -1.2345e-11
check_double( -1.2345e-10, "-1.2345e-10" ); // -1.2345e-10
check_double( -1.2345e-9, "-1.2345e-9" ); // -1.2345e-09
check_double( -1.2345e-8, "-1.2345e-8" ); // -1.2345000000000001e-08
check_double( -1.2345e-7, "-1.2345e-7" ); // -1.2345000000000001e-07
check_double( -1.2345e-6, "-1.2345e-6" ); // -1.2345e-06
check_double( -1.2345e-5, "-1.2345e-5" ); // -1.2345e-05
check_double( -1.2345e-4, "-0.00012345" ); // -0.00012344999999999999
check_double( -1.2345e-3, "-0.0012345" ); // -0.0012344999999999999
check_double( -1.2345e-2, "-0.012345" ); // -0.012345
check_double( -1.2345e-1, "-0.12345" ); // -0.12345
check_double( -0.0, "-0.0" ); // -0
check_double( 0.0, "0.0" ); // 0
check_double( 1.2345e+0, "1.2345" ); // 1.2344999999999999
check_double( 1.2345e+1, "12.345" ); // 12.345000000000001
check_double( 1.2345e+2, "123.45" ); // 123.45
check_double( 1.2345e+3, "1234.5" ); // 1234.5
check_double( 1.2345e+4, "12345.0" ); // 12345
check_double( 1.2345e+5, "123450.0" ); // 123450
check_double( 1.2345e+6, "1234500.0" ); // 1234500
check_double( 1.2345e+7, "12345000.0" ); // 12345000
check_double( 1.2345e+8, "123450000.0" ); // 123450000
check_double( 1.2345e+9, "1234500000.0" ); // 1234500000
check_double( 1.2345e+10, "12345000000.0" ); // 12345000000
check_double( 1.2345e+11, "123450000000.0" ); // 123450000000
check_double( 1.2345e+12, "1234500000000.0" ); // 1234500000000
check_double( 1.2345e+13, "12345000000000.0" ); // 12345000000000
check_double( 1.2345e+14, "123450000000000.0" ); // 123450000000000
check_double( 1.2345e+15, "1234500000000000.0" ); // 1234500000000000
check_double( 1.2345e+16, "12345000000000000.0" ); // 12345000000000000
check_double( 1.2345e+17, "1.2345e+17" ); // 1.2345e+17
check_double( 1.2345e+18, "1.2345e+18" ); // 1.2345e+18
check_double( 1.2345e+19, "1.2345e+19" ); // 1.2345e+19
check_double( 1.2345e+20, "1.2345e+20" ); // 1.2345e+20
check_double( 1.2345e+21, "1.2344999999999999e+21" ); // 1.2344999999999999e+21 (shortest: 1.2345e+21)
check_double( 1.2345e+22, "1.2345e+22" ); // 1.2345e+22
}
}