detail::dtoa_impl Namespace Reference

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

Classes
struct	boundaries
struct	cached_power
struct	diyfp

Functions
JSON_HEDLEY_RETURNS_NON_NULL char *	append_exponent (char *buf, int e)
	appends a decimal representation of e to buf
template<typename FloatType >
boundaries	compute_boundaries (FloatType value)
	Compute the (normalized) diyfp representing the input number 'value' and its boundaries.
int	find_largest_pow10 (const std::uint32_t n, std::uint32_t &pow10)
	For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
JSON_HEDLEY_RETURNS_NON_NULL 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)
	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])
void	grisu2 (char *buf, int &len, int &decimal_exponent, diyfp m_minus, diyfp v, diyfp 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.
template<typename FloatType >
void	grisu2 (char *buf, int &len, int &decimal_exponent, FloatType value)
	v = buf * 10^decimal_exponent len is the length of the buffer (number of decimal digits) The buffer must be large enough, i.e.
void	grisu2_digit_gen (char *buffer, int &length, int &decimal_exponent, diyfp M_minus, diyfp w, diyfp M_plus)
	Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.
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).

The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.

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()

JSON_HEDLEY_RETURNS_NON_NULL char * 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 18639 of file json.h.

References JSON_ASSERT.

Referenced by format_buffer().

Here is the caller graph for this function:

compute_boundaries()

template<typename FloatType >

boundaries 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 17900 of file json.h.

References compute_boundaries(), detail::dtoa_impl::diyfp::e, E, detail::dtoa_impl::diyfp::f, and JSON_ASSERT.

Referenced by compute_boundaries(), and grisu2().

Here is the call graph for this function:

Here is the caller graph for this function:

find_largest_pow10()

int 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 18203 of file json.h.

References find_largest_pow10().

Referenced by find_largest_pow10(), and grisu2_digit_gen().

Here is the call graph for this function:

Here is the caller graph for this function:

format_buffer()

JSON_HEDLEY_RETURNS_NON_NULL char * 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 18691 of file json.h.

References append_exponent(), and JSON_ASSERT.

Here is the call graph for this function:

get_cached_power_for_binary_exponent()

cached_power 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 18039 of file json.h.

References 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().

Here is the call graph for this function:

Here is the caller graph for this function:

grisu2() [1/2]

void 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 18539 of file json.h.

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

Referenced by grisu2().

Here is the call graph for this function:

Here is the caller graph for this function:

grisu2() [2/2]

template<typename FloatType >

void 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 18599 of file json.h.

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

Here is the call graph for this function:

grisu2_digit_gen()

void 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 18298 of file json.h.

References detail::dtoa_impl::diyfp::e, 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().

Here is the call graph for this function:

Here is the caller graph for this function:

grisu2_round()

void 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  )

inlineprivate

Definition at line 18257 of file json.h.

References grisu2_round(), and JSON_ASSERT.

Referenced by grisu2_digit_gen(), and grisu2_round().

Here is the call graph for this function:

Here is the caller graph for this function:

reinterpret_bits()

template<typename Target , typename Source >

Target detail::dtoa_impl::reinterpret_bits ( const Source  source )

private

Definition at line 17759 of file json.h.

References reinterpret_bits().

Referenced by reinterpret_bits().

Here is the call graph for this function:

Here is the caller graph for this function:

Variable Documentation

kAlpha

constexpr int detail::dtoa_impl::kAlpha = -60

constexprprivate

Definition at line 18022 of file json.h.

Referenced by get_cached_power_for_binary_exponent(), and grisu2_digit_gen().

kGamma

constexpr int detail::dtoa_impl::kGamma = -32

constexprprivate

Definition at line 18023 of file json.h.

Referenced by get_cached_power_for_binary_exponent(), and grisu2_digit_gen().