implements the Grisu2 algorithm for binary to decimal floating-point conversion. More...

Classes
struct	boundaries

struct	cached_power

struct	diyfp

Functions
char *	append_exponent (char *buf, int e)
	appends a decimal representation of e to buf

template<typename FloatType >
boundaries	compute_boundaries (FloatType value)

int	find_largest_pow10 (const std::uint32_t n, std::uint32_t &pow10)

char *	format_buffer (char *buf, int len, int decimal_exponent, int min_exp, int max_exp)
	prettify v = buf * 10^decimal_exponent

cached_power	get_cached_power_for_binary_exponent (int e)

void	grisu2 (char *buf, int &len, int &decimal_exponent, diyfp m_minus, diyfp v, diyfp m_plus)

template<typename FloatType >
void	grisu2 (char *buf, int &len, int &decimal_exponent, FloatType value)

void	grisu2_digit_gen (char *buffer, int &length, int &decimal_exponent, diyfp M_minus, diyfp w, diyfp M_plus)

void	grisu2_round (char *buf, int len, std::uint64_t dist, std::uint64_t delta, std::uint64_t rest, std::uint64_t ten_k)

template<typename Target , typename Source >
Target	reinterpret_bits (const Source source)

Variables
constexpr int	kAlpha = -60

constexpr int	kGamma = -32

Detailed Description

implements the Grisu2 algorithm for binary to decimal floating-point conversion.

This implementation is a slightly modified version of the reference implementation which may be obtained from http://florian.loitsch.com/publications (bench.tar.gz).

For a detailed description of the algorithm see:

[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

Function Documentation

◆ append_exponent()

char * nlohmann::json_abi_v3_11_3::detail::dtoa_impl::append_exponent	(	char *	buf,
		int	e
	)

inlineprivate

appends a decimal representation of e to buf

Returns: a pointer to the element following the exponent.

Precondition: -1000 < e < 1000

Definition at line 17835 of file json.hpp.

References JSON_ASSERT.

Referenced by format_buffer().

◆ compute_boundaries()

template<typename FloatType >

boundaries nlohmann::json_abi_v3_11_3::detail::dtoa_impl::compute_boundaries ( FloatType value )

private

Compute the (normalized) diyfp representing the input number 'value' and its boundaries.

Precondition: value must be finite and positive

Definition at line 17096 of file json.hpp.

References compute_boundaries(), nlohmann::json_abi_v3_11_3::detail::dtoa_impl::diyfp::e, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::diyfp::f, JSON_ASSERT, and nlohmann::json_abi_v3_11_3::detail::value.

Referenced by compute_boundaries(), and grisu2().

◆ find_largest_pow10()

int nlohmann::json_abi_v3_11_3::detail::dtoa_impl::find_largest_pow10	(	const std::uint32_t	n,
		std::uint32_t &	pow10
	)

inlineprivate

For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k. For n == 0, returns 1 and sets pow10 := 1.

Definition at line 17399 of file json.hpp.

References find_largest_pow10().

Referenced by find_largest_pow10(), and grisu2_digit_gen().

◆ format_buffer()

char * nlohmann::json_abi_v3_11_3::detail::dtoa_impl::format_buffer	(	char *	buf,
		int	len,
		int	decimal_exponent,
		int	min_exp,
		int	max_exp
	)

inlineprivate

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.

Precondition: min_exp < 0; max_exp > 0

Definition at line 17887 of file json.hpp.

References append_exponent(), and JSON_ASSERT.

◆ get_cached_power_for_binary_exponent()

cached_power nlohmann::json_abi_v3_11_3::detail::dtoa_impl::get_cached_power_for_binary_exponent ( int e )

inlineprivate

For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c satisfies (Definition 3.2 from [1])

 alpha <= e_c + e + q <= gamma.

Definition at line 17235 of file json.hpp.

References nlohmann::json_abi_v3_11_3::detail::dtoa_impl::cached_power::e, get_cached_power_for_binary_exponent(), JSON_ASSERT, kAlpha, and kGamma.

Referenced by get_cached_power_for_binary_exponent(), and grisu2().

◆ grisu2() [1/2]

void nlohmann::json_abi_v3_11_3::detail::dtoa_impl::grisu2	(	char *	buf,
		int &	len,
		int &	decimal_exponent,
		diyfp	m_minus,
		diyfp	v,
		diyfp	m_plus
	)

inlineprivate

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.

Definition at line 17735 of file json.hpp.

References nlohmann::json_abi_v3_11_3::detail::dtoa_impl::diyfp::e, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::cached_power::e, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::diyfp::f, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::cached_power::f, get_cached_power_for_binary_exponent(), grisu2_digit_gen(), JSON_ASSERT, and nlohmann::json_abi_v3_11_3::detail::dtoa_impl::cached_power::k.

Referenced by grisu2().

◆ grisu2() [2/2]

template<typename FloatType >

void nlohmann::json_abi_v3_11_3::detail::dtoa_impl::grisu2	(	char *	buf,
		int &	len,
		int &	decimal_exponent,
		FloatType	value
	)

private

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.

Definition at line 17795 of file json.hpp.

References compute_boundaries(), grisu2(), JSON_ASSERT, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::boundaries::minus, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::boundaries::plus, nlohmann::json_abi_v3_11_3::detail::value, and nlohmann::json_abi_v3_11_3::detail::dtoa_impl::boundaries::w.

◆ grisu2_digit_gen()

void nlohmann::json_abi_v3_11_3::detail::dtoa_impl::grisu2_digit_gen	(	char *	buffer,
		int &	length,
		int &	decimal_exponent,
		diyfp	M_minus,
		diyfp	w,
		diyfp	M_plus
	)

inlineprivate

Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+. M- and M+ must be normalized and share the same exponent -60 <= e <= -32.

Definition at line 17494 of file json.hpp.

References nlohmann::json_abi_v3_11_3::detail::dtoa_impl::diyfp::e, nlohmann::json_abi_v3_11_3::detail::dtoa_impl::diyfp::f, find_largest_pow10(), grisu2_digit_gen(), grisu2_round(), JSON_ASSERT, kAlpha, and kGamma.

Referenced by grisu2(), and grisu2_digit_gen().

◆ grisu2_round()

void nlohmann::json_abi_v3_11_3::detail::dtoa_impl::grisu2_round	(	char *	buf,
		int	len,
		std::uint64_t	dist,
		std::uint64_t	delta,
		std::uint64_t	rest,
		std::uint64_t	ten_k
	)