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py/formatfloat: Improve accuracy of float formatting code.

Browse source 
Following discussions in PR #16666, this commit updates the float
formatting code to improve the `repr` reversibility, i.e. the percentage of
valid floating point numbers that do parse back to the same number when
formatted by `repr` (in CPython it's 100%).

This new code offers a choice of 3 float conversion methods, depending on
the desired tradeoff between code size and conversion precision:

- BASIC method is the smallest code footprint

- APPROX method uses an iterative method to approximate the exact
  representation, which is a bit slower but but does not have a big impact
  on code size.  It provides `repr` reversibility on >99.8% of the cases in
  double precision, and on >98.5% in single precision (except with REPR_C,
  where reversibility is 100% as the last two bits are not taken into
  account).

- EXACT method uses higher-precision floats during conversion, which
  provides perfect results but has a higher impact on code size.  It is
  faster than APPROX method, and faster than the CPython equivalent
  implementation.  It is however not available on all compilers when using
  FLOAT_IMPL_DOUBLE.

Here is the table comparing the impact of the three conversion methods on
code footprint on PYBV10 (using single-precision floats) and reversibility
rate for both single-precision and double-precision floats.  The table
includes current situation as a baseline for the comparison:

              PYBV10  REPR_C   FLOAT  DOUBLE
    current = 364688   12.9%   27.6%   37.9%
    basic   = 364812   85.6%   60.5%   85.7%
    approx  = 365080  100.0%   98.5%   99.8%
    exact   = 366408  100.0%  100.0%  100.0%

Signed-off-by: Yoctopuce dev <dev@yoctopuce.com>
This commit is contained in:
Yoctopuce dev 2025-06-06 14:55:21 +02:00 committed by Damien George
parent e4e1c9f413
commit dbbaa959c8
24 changed files with 807 additions and 427 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

1
ports/esp8266/mpconfigport.h
View file

@ -106,6 +106,7 @@
#define MICROPY_PY_OS_URANDOM (1)
#define MICROPY_LONGINT_IMPL (MICROPY_LONGINT_IMPL_MPZ)
#define MICROPY_FLOAT_IMPL (MICROPY_FLOAT_IMPL_FLOAT)
#define MICROPY_FLOAT_FORMAT_IMPL (MICROPY_FLOAT_FORMAT_IMPL_BASIC)
#define MICROPY_WARNINGS (1)
#define MICROPY_PY_STR_BYTES_CMP_WARN (1)
#define MICROPY_STREAMS_POSIX_API (1)

20
ports/unix/coverage.c
View file

@ -612,26 +612,6 @@ static mp_obj_t extra_coverage(void) {
mp_emitter_warning(MP_PASS_CODE_SIZE, "test");
}
// format float
{
mp_printf(&mp_plat_print, "# format float\n");
// format with inadequate buffer size
char buf[5];
mp_format_float(1, buf, sizeof(buf), 'g', 0, '+');
mp_printf(&mp_plat_print, "%s\n", buf);
// format with just enough buffer so that precision must be
// set from 0 to 1 twice
char buf2[8];
mp_format_float(1, buf2, sizeof(buf2), 'g', 0, '+');
mp_printf(&mp_plat_print, "%s\n", buf2);
// format where precision is trimmed to avoid buffer overflow
mp_format_float(1, buf2, sizeof(buf2), 'e', 0, '+');
mp_printf(&mp_plat_print, "%s\n", buf2);
}
// binary
{
mp_printf(&mp_plat_print, "# binary\n");

819
py/formatfloat.c
View file

@ -33,369 +33,212 @@
#include <stdint.h>
#include <math.h>
#include "py/formatfloat.h"
#include "py/parsenum.h"
/***********************************************************************
Routine for converting a arbitrary floating
point number into a string.
The code in this function was inspired from Fred Bayer's pdouble.c.
Since pdouble.c was released as Public Domain, I'm releasing this
code as public domain as well.
The code in this function was inspired from Dave Hylands's previous
version, which was itself inspired from Fred Bayer's pdouble.c.
The original code can be found in https://github.com/dhylands/format-float
Dave Hylands
***********************************************************************/
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
// 1 sign bit, 8 exponent bits, and 23 mantissa bits.
// exponent values 0 and 255 are reserved, exponent can be 1 to 254.
// exponent is stored with a bias of 127.
// The min and max floats are on the order of 1x10^37 and 1x10^-37
// Float formatting debug code is intended for use in ports/unix only,
// as it uses the libc float printing function as a reference.
#define DEBUG_FLOAT_FORMATTING 0
#define FPTYPE float
#define FPCONST(x) x##F
#define FPROUND_TO_ONE 0.9999995F
#define FPDECEXP 32
#define FPMIN_BUF_SIZE 6 // +9e+99
#if DEBUG_FLOAT_FORMATTING
#define DEBUG_PRINTF(...) fprintf(stderr, __VA_ARGS__)
#else
#define DEBUG_PRINTF(...)
#endif
#define FLT_SIGN_MASK 0x80000000
#if MICROPY_FLOAT_FORMAT_IMPL == MICROPY_FLOAT_FORMAT_IMPL_EXACT || MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
#define MP_FFUINT_FMT "%lu"
#else
#define MP_FFUINT_FMT "%u"
#endif
static inline int fp_signbit(float x) {
mp_float_union_t fb = {x};
return fb.i & FLT_SIGN_MASK;
static inline int fp_expval(mp_float_t x) {
mp_float_union_t fb = { x };
return (int)fb.p.exp - MP_FLOAT_EXP_OFFSET;
}
#define fp_isnan(x) isnan(x)
#define fp_isinf(x) isinf(x)
static inline int fp_iszero(float x) {
mp_float_union_t fb = {x};
return fb.i == 0;
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
static inline int fp_isless1(mp_float_t x) {
return x < 1.0;
}
static inline int fp_isless1(float x) {
mp_float_union_t fb = {x};
static inline int fp_iszero(mp_float_t x) {
return x == 0.0;
}
#if MICROPY_FLOAT_FORMAT_IMPL != MICROPY_FLOAT_FORMAT_IMPL_APPROX
static inline int fp_equal(mp_float_t x, mp_float_t y) {
return x == y;
}
#else
static inline mp_float_t fp_diff(mp_float_t x, mp_float_t y) {
return x - y;
}
#endif
#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
// The functions below are roughly equivalent to the ones above,
// but they are optimized to reduce code footprint by skipping
// handling for special values such as nan, inf, +/-0.0
// for ports where FP support is done in software.
//
// They also take into account lost bits of REPR_C as needed.
static inline int fp_isless1(mp_float_t x) {
mp_float_union_t fb = { x };
return fb.i < 0x3f800000;
}
#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
#define FPTYPE double
#define FPCONST(x) x
#define FPROUND_TO_ONE 0.999999999995
#define FPDECEXP 256
#define FPMIN_BUF_SIZE 7 // +9e+199
#define fp_signbit(x) signbit(x)
#define fp_isnan(x) isnan(x)
#define fp_isinf(x) isinf(x)
#define fp_iszero(x) (x == 0)
#define fp_isless1(x) (x < 1.0)
#endif // MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT/DOUBLE
static inline int fp_expval(FPTYPE x) {
mp_float_union_t fb = {x};
return (int)((fb.i >> MP_FLOAT_FRAC_BITS) & (~(0xFFFFFFFF << MP_FLOAT_EXP_BITS))) - MP_FLOAT_EXP_OFFSET;
static inline int fp_iszero(mp_float_t x) {
mp_float_union_t x_check = { x };
return !x_check.i; // this is valid for REPR_C as well
}
int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, char sign) {
#if MICROPY_FLOAT_FORMAT_IMPL != MICROPY_FLOAT_FORMAT_IMPL_APPROX
static inline int fp_equal(mp_float_t x, mp_float_t y) {
mp_float_union_t x_check = { x };
mp_float_union_t y_check = { y };
#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C
return (x_check.i & ~3) == (y_check.i & ~3);
#else
return x_check.i == y_check.i;
#endif
}
#else
static inline mp_float_t fp_diff(mp_float_t x, mp_float_t y) {
#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C
mp_float_union_t x_check = { x };
mp_float_union_t y_check = { y };
x_check.i &= ~3;
y_check.i &= ~3;
return x_check.f - y_check.f;
#else
return x - y;
#endif
}
#endif
char *s = buf;
#endif
if (buf_size <= FPMIN_BUF_SIZE) {
// FPMIN_BUF_SIZE is the minimum size needed to store any FP number.
// If the buffer does not have enough room for this (plus null terminator)
// then don't try to format the float.
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
#define FPMIN_BUF_SIZE 6 // +9e+99
#define MAX_MANTISSA_DIGITS (9)
#define SAFE_MANTISSA_DIGITS (6)
#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
#define FPMIN_BUF_SIZE 7 // +9e+199
#define MAX_MANTISSA_DIGITS (19)
#define SAFE_MANTISSA_DIGITS (16)
#endif
if (buf_size >= 2) {
*s++ = '?';
}
if (buf_size >= 1) {
*s = '\0';
}
return buf_size >= 2;
}
if (fp_signbit(f) && !fp_isnan(f)) {
*s++ = '-';
f = -f;
} else {
if (sign) {
*s++ = sign;
}
}
// Internal formatting flags
#define FMT_MODE_E 0x01 // render using scientific notation (%e)
#define FMT_MODE_G 0x02 // render using general format (%g)
#define FMT_MODE_F 0x04 // render using using expanded fixed-point format (%f)
#define FMT_E_CASE 0x20 // don't change this value (used for case conversion!)
// buf_remaining contains bytes available for digits and exponent.
// It is buf_size minus room for the sign and null byte.
int buf_remaining = buf_size - 1 - (s - buf);
{
char uc = fmt & 0x20;
if (fp_isinf(f)) {
*s++ = 'I' ^ uc;
*s++ = 'N' ^ uc;
*s++ = 'F' ^ uc;
goto ret;
} else if (fp_isnan(f)) {
*s++ = 'N' ^ uc;
*s++ = 'A' ^ uc;
*s++ = 'N' ^ uc;
ret:
*s = '\0';
return s - buf;
}
}
if (prec < 0) {
prec = 6;
}
char e_char = 'E' | (fmt & 0x20); // e_char will match case of fmt
fmt |= 0x20; // Force fmt to be lowercase
char org_fmt = fmt;
if (fmt == 'g' && prec == 0) {
prec = 1;
}
int e;
int dec = 0;
char e_sign = '\0';
int num_digits = 0;
int signed_e = 0;
// Approximate power of 10 exponent from binary exponent.
// abs(e_guess) is lower bound on abs(power of 10 exponent).
int e_guess = (int)(fp_expval(f) * FPCONST(0.3010299956639812)); // 1/log2(10).
if (fp_iszero(f)) {
e = 0;
if (fmt == 'f') {
// Truncate precision to prevent buffer overflow
if (prec + 2 > buf_remaining) {
prec = buf_remaining - 2;
}
num_digits = prec + 1;
} else {
// Truncate precision to prevent buffer overflow
if (prec + 6 > buf_remaining) {
prec = buf_remaining - 6;
}
if (fmt == 'e') {
e_sign = '+';
}
}
} else if (fp_isless1(f)) {
FPTYPE f_entry = f; // Save f in case we go to 'f' format.
// Build negative exponent
e = -e_guess;
FPTYPE u_base = MICROPY_FLOAT_C_FUN(pow)(10, -e);
while (u_base > f) {
++e;
u_base = MICROPY_FLOAT_C_FUN(pow)(10, -e);
}
// Normalize out the inferred unit. Use divide because
// pow(10, e) * pow(10, -e) is slightly < 1 for some e in float32
// (e.g. print("%.12f" % ((1e13) * (1e-13))))
f /= u_base;
// If the user specified 'g' format, and e is <= 4, then we'll switch
// to the fixed format ('f')
if (fmt == 'f' || (fmt == 'g' && e <= 4)) {
fmt = 'f';
dec = 0;
if (org_fmt == 'g') {
prec += (e - 1);
}
// truncate precision to prevent buffer overflow
if (prec + 2 > buf_remaining) {
prec = buf_remaining - 2;
}
num_digits = prec;
signed_e = 0;
f = f_entry;
++num_digits;
} else {
// For e & g formats, we'll be printing the exponent, so set the
// sign.
e_sign = '-';
dec = 0;
if (prec > (buf_remaining - FPMIN_BUF_SIZE)) {
prec = buf_remaining - FPMIN_BUF_SIZE;
if (fmt == 'g') {
prec++;
}
}
signed_e = -e;
}
} else {
// Build positive exponent.
// We don't modify f at this point to avoid inaccuracies from
// scaling it. Instead, we find the product of powers of 10
// that is not greater than it, and use that to start the
// mantissa.
e = e_guess;
FPTYPE next_u = MICROPY_FLOAT_C_FUN(pow)(10, e + 1);
while (f >= next_u) {
++e;
next_u = MICROPY_FLOAT_C_FUN(pow)(10, e + 1);
}
// If the user specified fixed format (fmt == 'f') and e makes the
// number too big to fit into the available buffer, then we'll
// switch to the 'e' format.
if (fmt == 'f') {
if (e >= buf_remaining) {
fmt = 'e';
} else if ((e + prec + 2) > buf_remaining) {
prec = buf_remaining - e - 2;
if (prec < 0) {
// This means no decimal point, so we can add one back
// for the decimal.
prec++;
}
}
}
if (fmt == 'e' && prec > (buf_remaining - FPMIN_BUF_SIZE)) {
prec = buf_remaining - FPMIN_BUF_SIZE;
}
if (fmt == 'g') {
// Truncate precision to prevent buffer overflow
if (prec + (FPMIN_BUF_SIZE - 1) > buf_remaining) {
prec = buf_remaining - (FPMIN_BUF_SIZE - 1);
}
}
// If the user specified 'g' format, and e is < prec, then we'll switch
// to the fixed format.
if (fmt == 'g' && e < prec) {
fmt = 'f';
prec -= (e + 1);
}
if (fmt == 'f') {
dec = e;
num_digits = prec + e + 1;
} else {
e_sign = '+';
}
signed_e = e;
}
if (prec < 0) {
// This can happen when the prec is trimmed to prevent buffer overflow
prec = 0;
}
// At this point e contains the absolute value of the power of 10 exponent.
// (dec + 1) == the number of dgits before the decimal.
// For e, prec is # digits after the decimal
// For f, prec is # digits after the decimal
// For g, prec is the max number of significant digits
//
// For e & g there will be a single digit before the decimal
// for f there will be e digits before the decimal
if (fmt == 'e') {
num_digits = prec + 1;
} else if (fmt == 'g') {
if (prec == 0) {
prec = 1;
}
num_digits = prec;
}
int d = 0;
for (int digit_index = signed_e; num_digits >= 0; --digit_index) {
FPTYPE u_base = FPCONST(1.0);
if (digit_index > 0) {
// Generate 10^digit_index for positive digit_index.
u_base = MICROPY_FLOAT_C_FUN(pow)(10, digit_index);
}
for (d = 0; d < 9; ++d) {
if (f < u_base) {
break;
}
f -= u_base;
}
// We calculate one more digit than we display, to use in rounding
// below. So only emit the digit if it's one that we display.
if (num_digits > 0) {
// Emit this number (the leading digit).
*s++ = '0' + d;
if (dec == 0 && prec > 0) {
static char *mp_prepend_zeros(char *s, int cnt) {
*s++ = '0';
*s++ = '.';
while (cnt > 0) {
*s++ = '0';
cnt--;
}
}
--dec;
--num_digits;
if (digit_index <= 0) {
// Once we get below 1.0, we scale up f instead of calculating
// negative powers of 10 in u_base. This provides better
// renditions of exact decimals like 1/16 etc.
f *= FPCONST(10.0);
}
}
// Rounding. If the next digit to print is >= 5, round up.
if (d >= 5) {
char *rs = s;
rs--;
while (1) {
if (*rs == '.') {
rs--;
continue;
}
if (*rs < '0' || *rs > '9') {
// + or -
rs++; // So we sit on the digit to the right of the sign
break;
}
if (*rs < '9') {
(*rs)++;
break;
}
*rs = '0';
if (rs == buf) {
break;
}
rs--;
}
if (*rs == '0') {
// We need to insert a 1
if (rs[1] == '.' && fmt != 'f') {
// We're going to round 9.99 to 10.00
// Move the decimal point
rs[0] = '.';
rs[1] = '0';
if (e_sign == '-') {
e--;
if (e == 0) {
e_sign = '+';
}
return s;
}
// Helper to convert a decimal mantissa (provided as an mp_large_float_uint_t) to string
static int mp_format_mantissa(mp_large_float_uint_t mantissa, mp_large_float_uint_t mantissa_cap, char *buf, char *s,
int num_digits, int max_exp_zeros, int trailing_zeros, int dec, int e, int fmt_flags) {
DEBUG_PRINTF("mantissa=" MP_FFUINT_FMT " exp=%d (cap=" MP_FFUINT_FMT "):\n", mantissa, e, mantissa_cap);
if (mantissa) {
// If rounding/searching created an extra digit or removed too many, fix mantissa first
if (mantissa >= mantissa_cap) {
if (fmt_flags & FMT_MODE_F) {
assert(e >= 0);
num_digits++;
dec++;
} else {
mantissa /= 10;
e++;
}
}
}
// When 'g' format is used, replace small exponents by explicit zeros
if ((fmt_flags & FMT_MODE_G) && e != 0) {
if (e >= 0) {
// If 0 < e < max_exp_zeros, expand positive exponent into trailing zeros
if (e < max_exp_zeros) {
dec += e;
if (dec >= num_digits) {
trailing_zeros = dec - (num_digits - 1);
}
e = 0;
}
} else {
// Need at extra digit at the end to make room for the leading '1'
// but if we're at the buffer size limit, just drop the final digit.
if ((size_t)(s + 1 - buf) < buf_size) {
// If -4 <= e < 0, expand negative exponent without losing significant digits
if (e >= -4) {
int cnt = 0;
while (e < 0 && !(mantissa % 10)) {
mantissa /= 10;
cnt++;
e++;
}
num_digits -= cnt;
s = mp_prepend_zeros(s, cnt - e - 1);
dec = 255;
e = 0;
}
}
}
// Convert the integer mantissa to string
for (int digit = num_digits - 1; digit >= 0; digit--) {
int digit_ofs = (digit > dec ? digit + 1 : digit);
s[digit_ofs] = '0' + (int)(mantissa % 10);
mantissa /= 10;
}
int dot = (dec >= 255);
if (dec + 1 < num_digits) {
dot = 1;
s++;
s[dec] = '.';
}
}
char *ss = s;
while (ss > rs) {
*ss = ss[-1];
ss--;
}
*rs = '1';
}
}
s += num_digits;
#if DEBUG_FLOAT_FORMATTING
*s = 0;
DEBUG_PRINTF(" = %s exp=%d num_digits=%d zeros=%d dec=%d\n", buf, e, num_digits, trailing_zeros, dec);
#endif
// verify that we did not overrun the input buffer so far
assert((size_t)(s + 1 - buf) <= buf_size);
if (org_fmt == 'g' && prec > 0) {
// Remove trailing zeros and a trailing decimal point
// Append or remove trailing zeros, as required by format
if (trailing_zeros) {
dec -= num_digits - 1;
while (trailing_zeros--) {
if (!dec--) {
*s++ = '.';
dot = 1;
}
*s++ = '0';
}
}
if (fmt_flags & FMT_MODE_G) {
// 'g' format requires to remove trailing zeros after decimal point
if (dot) {
while (s[-1] == '0') {
s--;
}
@ -403,22 +246,324 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
s--;
}
}
// Append the exponent
if (e_sign) {
*s++ = e_char;
*s++ = e_sign;
if (FPMIN_BUF_SIZE == 7 && e >= 100) {
}
// Append the exponent if needed
if (((e != 0) || (fmt_flags & FMT_MODE_E)) && !(fmt_flags & FMT_MODE_F)) {
*s++ = 'E' | (fmt_flags & FMT_E_CASE);
if (e >= 0) {
*s++ = '+';
} else {
*s++ = '-';
e = -e;
}
if (e >= 100) {
*s++ = '0' + (e / 100);
}
*s++ = '0' + ((e / 10) % 10);
*s++ = '0' + (e % 10);
}
*s = '\0';
// verify that we did not overrun the input buffer
assert((size_t)(s + 1 - buf) <= buf_size);
DEBUG_PRINTF(" ===> %s\n", buf);
return s - buf;
}
// minimal value expected for buf_size, to avoid checking everywhere for overflow
#define MIN_BUF_SIZE (MAX_MANTISSA_DIGITS + 10)
int mp_format_float(mp_float_t f_entry, char *buf_entry, size_t buf_size, char fmt, int prec, char sign) {
assert(buf_size >= MIN_BUF_SIZE);
// Handle sign
mp_float_t f = f_entry;
char *buf = buf_entry;
if (signbit(f_entry) && !isnan(f_entry)) {
f = -f;
sign = '-';
}
if (sign) {
*buf++ = sign;
buf_size--;
}
// Handle inf/nan
char uc = fmt & 0x20;
{
char *s = buf;
if (isinf(f)) {
*s++ = 'I' ^ uc;
*s++ = 'N' ^ uc;
*s++ = 'F' ^ uc;
goto ret;
} else if (isnan(f)) {
*s++ = 'N' ^ uc;
*s++ = 'A' ^ uc;
*s++ = 'N' ^ uc;
ret:
*s = '\0';
return s - buf_entry;
}
}
// Decode format character
int fmt_flags = (unsigned char)uc; // setup FMT_E_CASE, clear all other bits
char lofmt = (char)(fmt | 0x20); // fmt in lowercase
if (lofmt == 'f') {
fmt_flags |= FMT_MODE_F;
} else if (lofmt == 'g') {
fmt_flags |= FMT_MODE_G;
} else {
fmt_flags |= FMT_MODE_E;
}
// When precision is unspecified, default to 6
if (prec < 0) {
prec = 6;
}
// Use high precision for `repr`, but switch to exponent mode
// after 16 digits in any case to match CPython behaviour
int max_exp_zeros = (prec < (int)buf_size - 3 ? prec : (int)buf_size - 3);
if (prec == MP_FLOAT_REPR_PREC) {
prec = MAX_MANTISSA_DIGITS;
max_exp_zeros = 16;
}
// Precompute the exact decimal exponent of f, such that
// abs(e) is lower bound on abs(power of 10 exponent).
int e = 0;
if (!fp_iszero(f)) {
// Approximate power of 10 exponent from binary exponent.
e = (int)(fp_expval(f) * MICROPY_FLOAT_CONST(0.3010299956639812)); // 1/log2(10).
int positive_exp = !fp_isless1(f);
mp_float_t u_base = (mp_float_t)mp_decimal_exp((mp_large_float_t)1.0, e + positive_exp);
while ((f >= u_base) == positive_exp) {
e += (positive_exp ? 1 : -1);
u_base = (mp_float_t)mp_decimal_exp((mp_large_float_t)1.0, e + positive_exp);
}
}
// For 'e' format, prec is # digits after the decimal
// For 'f' format, prec is # digits after the decimal
// For 'g' format, prec is the max number of significant digits
//
// For 'e' & 'g' format, there will be a single digit before the decimal
// For 'f' format, zeros must be expanded instead of using an exponent.
// Make sure there is enough room in the buffer for them, or switch to format 'g'.
if ((fmt_flags & FMT_MODE_F) && e > 0) {
int req_size = e + prec + 2;
if (req_size > (int)buf_size) {
fmt_flags ^= FMT_MODE_F;
fmt_flags |= FMT_MODE_G;
prec++;
}
}
// To work independently of the format, we precompute:
// - the max number of significant digits to produce
// - the number of leading zeros to prepend (mode f only)
// - the number of trailing zeros to append
int max_digits = prec;
int lead_zeros = 0;
int trail_zeros = 0;
if (fmt_flags & FMT_MODE_F) {
if (max_digits > (int)buf_size - 3) {
// cannot satisfy requested number of decimals given buf_size, sorry
max_digits = (int)buf_size - 3;
}
if (e < 0) {
if (max_digits > 2 && e < -2) {
// Insert explicit leading zeros
lead_zeros = (-e < max_digits ? -e : max_digits) - 2;
max_digits -= lead_zeros;
} else {
max_digits++;
}
} else {
max_digits += e + 1;
}
} else {
if (!(fmt_flags & FMT_MODE_G) || max_digits == 0) {
max_digits++;
}
}
if (max_digits > MAX_MANTISSA_DIGITS) {
// use trailing zeros to avoid overflowing the mantissa
trail_zeros = max_digits - MAX_MANTISSA_DIGITS;
max_digits = MAX_MANTISSA_DIGITS;
}
int overhead = (fmt_flags & FMT_MODE_F ? 3 : FPMIN_BUF_SIZE + 1);
if (trail_zeros > (int)buf_size - max_digits - overhead) {
// cannot satisfy requested number of decimals given buf_size, sorry
trail_zeros = (int)buf_size - max_digits - overhead;
}
// When the caller asks for more precision than available for sure,
// Look for a shorter (rounded) representation first, and only dig
// into more digits if there is no short representation.
int num_digits = (SAFE_MANTISSA_DIGITS < max_digits ? SAFE_MANTISSA_DIGITS : max_digits);
try_again:
;
char *s = buf;
int extra_zeros = trail_zeros + (max_digits - num_digits);
int decexp;
int dec = 0;
if (fp_iszero(f)) {
// no need for scaling 0.0
decexp = 0;
} else if (fmt_flags & FMT_MODE_F) {
decexp = num_digits - 1;
if (e < 0) {
// Negative exponent: we keep a single leading zero in the mantissa,
// as using more would waste precious digits needed for accuracy.
if (lead_zeros > 0) {
// We are using leading zeros
s = mp_prepend_zeros(s, lead_zeros);
decexp += lead_zeros + 1;
dec = 255; // no decimal dot
} else {
// Small negative exponent, work directly on the mantissa
dec = 0;
}
} else {
// Positive exponent: we will add trailing zeros separately
decexp -= e;
dec = e;
}
} else {
decexp = num_digits - e - 1;
}
DEBUG_PRINTF("input=%.19g e=%d fmt=%c max_d=%d num_d=%d decexp=%d dec=%d l0=%d r0=%d\n",
(double)f, e, lofmt, max_digits, num_digits, decexp, dec, lead_zeros, extra_zeros);
// At this point,
// - buf points to beginning of output buffer for the unsigned representation
// - num_digits == the number of mantissa digits to add
// - (dec + 1) == the number of digits to print before adding a decimal point
// - decexp == the power of 10 exponent to apply to f to get the decimal mantissa
// - e == the power of 10 exponent to append ('e' or 'g' format)
mp_large_float_uint_t mantissa_cap = 10;
for (int n = 1; n < num_digits; n++) {
mantissa_cap *= 10;
}
// Build the decimal mantissa into a large uint
mp_large_float_uint_t mantissa = 1;
if (sizeof(mp_large_float_t) == sizeof(mp_float_t) && num_digits > SAFE_MANTISSA_DIGITS && decexp > 1) {
// if we don't have large floats, use integer multiply to produce the last digits
if (num_digits > SAFE_MANTISSA_DIGITS + 1 && decexp > 2) {
mantissa = 100;
decexp -= 2;
} else {
mantissa = 10;
decexp -= 1;
}
}
mp_large_float_t mantissa_f = mp_decimal_exp((mp_large_float_t)f, decexp);
mantissa *= (mp_large_float_uint_t)(mantissa_f + (mp_large_float_t)0.5);
DEBUG_PRINTF("input=%.19g fmt=%c num_digits=%d dec=%d mantissa=" MP_FFUINT_FMT " r0=%d\n", (double)f, lofmt, num_digits, dec, mantissa, extra_zeros);
// Finally convert the decimal mantissa to a floating-point string, according to formatting rules
int reprlen = mp_format_mantissa(mantissa, mantissa_cap, buf, s, num_digits, max_exp_zeros, extra_zeros, dec, e, fmt_flags);
assert(reprlen + 1 <= (int)buf_size);
#if MICROPY_FLOAT_FORMAT_IMPL != MICROPY_FLOAT_FORMAT_IMPL_APPROX
if (num_digits < max_digits) {
// The initial precision might not be sufficient for an exact representation
// for all numbers. If the result is not exact, restart using next precision.
// parse the resulting number and compare against the original
mp_float_t check;
DEBUG_PRINTF("input=%.19g, compare to float('%s')\n", (double)f, buf);
mp_parse_float_internal(buf, reprlen, &check);
if (!fp_equal(check, f)) {
num_digits++;
DEBUG_PRINTF("Not perfect, retry using more digits (%d)\n", num_digits);
goto try_again;
}
}
#else
// The initial decimal mantissa might not have been be completely accurate due
// to the previous loating point operations. The best way to verify this is to
// parse the resulting number and compare against the original
mp_float_t check;
DEBUG_PRINTF("input=%.19g, compare to float('%s')\n", (double)f, buf);
mp_parse_float_internal(buf, reprlen, &check);
mp_float_t diff = fp_diff(check, f);
mp_float_t best_diff = diff;
mp_large_float_uint_t best_mantissa = mantissa;
if (fp_iszero(diff)) {
// we have a perfect match
DEBUG_PRINTF(MP_FFUINT_FMT ": perfect match (direct)\n", mantissa);
} else {
// In order to get the best possible representation, we will perform a
// dichotomic search for a reversible representation.
// This will also provide optimal rounding on the fly.
unsigned err_range = 1;
if (num_digits > SAFE_MANTISSA_DIGITS) {
err_range <<= 3 * (num_digits - SAFE_MANTISSA_DIGITS);
}
int maxruns = 3 + 3 * (MAX_MANTISSA_DIGITS - SAFE_MANTISSA_DIGITS);
while (maxruns-- > 0) {
// update mantissa according to dichotomic search
if (signbit(diff)) {
mantissa += err_range;
} else {
// mantissa is expected to always have more significant digits than err_range
assert(mantissa >= err_range);
mantissa -= err_range;
}
// retry conversion
reprlen = mp_format_mantissa(mantissa, mantissa_cap, buf, s, num_digits, max_exp_zeros, extra_zeros, dec, e, fmt_flags);
assert(reprlen + 1 <= (int)buf_size);
DEBUG_PRINTF("input=%.19g, compare to float('%s')\n", (double)f, buf);
mp_parse_float_internal(buf, reprlen, &check);
DEBUG_PRINTF("check=%.19g num_digits=%d e=%d mantissa=" MP_FFUINT_FMT "\n", (double)check, num_digits, e, mantissa);
diff = fp_diff(check, f);
if (fp_iszero(diff)) {
// we have a perfect match
DEBUG_PRINTF(MP_FFUINT_FMT ": perfect match\n", mantissa);
break;
}
// keep track of our best estimate
mp_float_t delta = MICROPY_FLOAT_C_FUN(fabs)(diff) - MICROPY_FLOAT_C_FUN(fabs)(best_diff);
if (signbit(delta) || (fp_iszero(delta) && !(mantissa % 10u))) {
best_diff = diff;
best_mantissa = mantissa;
}
// string repr is not perfect: continue a dichotomic improvement
DEBUG_PRINTF(MP_FFUINT_FMT ": %.19g, err_range=%d\n", mantissa, (double)check, err_range);
if (err_range > 1) {
err_range >>= 1;
} else {
// We have tried all possible mantissa, without finding a reversible repr.
// Check if we have an alternate precision to try.
if (num_digits < max_digits) {
num_digits++;
DEBUG_PRINTF("Failed to find a perfect match, try with more digits (%d)\n", num_digits);
goto try_again;
}
// Otherwise, keep the closest one, which is either the first one or the last one.
if (mantissa == best_mantissa) {
// Last guess is the best one
DEBUG_PRINTF(MP_FFUINT_FMT ": last guess was the best one\n", mantissa);
} else {
// We had a better guess earlier
DEBUG_PRINTF(MP_FFUINT_FMT ": use best guess\n", mantissa);
reprlen = mp_format_mantissa(best_mantissa, mantissa_cap, buf, s, num_digits, max_exp_zeros, extra_zeros, dec, e, fmt_flags);
}
break;
}
}
}
#endif
return buf + reprlen - buf_entry;
}
#endif // MICROPY_FLOAT_IMPL != MICROPY_FLOAT_IMPL_NONE

1
py/formatfloat.h
View file

@ -29,6 +29,7 @@
#include "py/mpconfig.h"
#if MICROPY_PY_BUILTINS_FLOAT
#define MP_FLOAT_REPR_PREC (99) // magic `prec` value for optimal `repr` behaviour
int mp_format_float(mp_float_t f, char *buf, size_t bufSize, char fmt, int prec, char sign);
#endif

19
py/misc.h
View file

@ -277,6 +277,25 @@ typedef union _mp_float_union_t {
mp_float_uint_t i;
} mp_float_union_t;
#if MICROPY_FLOAT_FORMAT_IMPL == MICROPY_FLOAT_FORMAT_IMPL_EXACT
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
// Exact float conversion requires using internally a bigger sort of floating point
typedef double mp_large_float_t;
#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
typedef long double mp_large_float_t;
#endif
// Always use a 64 bit mantissa for formatting and parsing
typedef uint64_t mp_large_float_uint_t;
#else // MICROPY_FLOAT_FORMAT_IMPL != MICROPY_FLOAT_FORMAT_IMPL_EXACT
// No bigger floating points
typedef mp_float_t mp_large_float_t;
typedef mp_float_uint_t mp_large_float_uint_t;
#endif
#endif // MICROPY_PY_BUILTINS_FLOAT
/** ROM string compression *************/

21
py/mpconfig.h
View file

@ -861,6 +861,27 @@ typedef double mp_float_t;
#define MICROPY_PY_BUILTINS_COMPLEX (MICROPY_PY_BUILTINS_FLOAT)
#endif
// Float to string conversion implementations
//
// Note that the EXACT method is only available if the compiler supports
// floating points larger than mp_float_t:
// - with MICROPY_FLOAT_IMPL_FLOAT, the compiler needs to support `double`
// - with MICROPY_FLOAT_IMPL_DOUBLE, the compiler needs to support `long double`
//
#define MICROPY_FLOAT_FORMAT_IMPL_BASIC (0) // smallest code, but inexact
#define MICROPY_FLOAT_FORMAT_IMPL_APPROX (1) // slightly bigger, almost perfect
#define MICROPY_FLOAT_FORMAT_IMPL_EXACT (2) // bigger code, and 100% exact repr
#ifndef MICROPY_FLOAT_FORMAT_IMPL
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
#define MICROPY_FLOAT_FORMAT_IMPL (MICROPY_FLOAT_FORMAT_IMPL_APPROX)
#elif defined(__SIZEOF_LONG_DOUBLE__) && __SIZEOF_LONG_DOUBLE__ > __SIZEOF_DOUBLE__
#define MICROPY_FLOAT_FORMAT_IMPL (MICROPY_FLOAT_FORMAT_IMPL_EXACT)
#else
#define MICROPY_FLOAT_FORMAT_IMPL (MICROPY_FLOAT_FORMAT_IMPL_APPROX)
#endif
#endif
// Whether to use the native _Float16 for 16-bit float support
#ifndef MICROPY_FLOAT_USE_NATIVE_FLT16
#ifdef __FLT16_MAX__

12
py/mpprint.c
View file

@ -338,7 +338,7 @@ int mp_print_mp_int(const mp_print_t *print, mp_obj_t x, unsigned int base, int
#if MICROPY_PY_BUILTINS_FLOAT
int mp_print_float(const mp_print_t *print, mp_float_t f, char fmt, unsigned int flags, char fill, int width, int prec) {
char buf[32];
char buf[36];
char sign = '\0';
int chrs = 0;
@ -349,11 +349,17 @@ int mp_print_float(const mp_print_t *print, mp_float_t f, char fmt, unsigned int
sign = ' ';
}
int len = mp_format_float(f, buf, sizeof(buf), fmt, prec, sign);
int len = mp_format_float(f, buf, sizeof(buf) - 3, fmt, prec, sign);
char *s = buf;
if ((flags & PF_FLAG_ADD_PERCENT) && (size_t)(len + 1) < sizeof(buf)) {
if ((flags & PF_FLAG_ALWAYS_DECIMAL) && strchr(buf, '.') == NULL && strchr(buf, 'e') == NULL && strchr(buf, 'n') == NULL) {
buf[len++] = '.';
buf[len++] = '0';
buf[len] = '\0';
}
if (flags & PF_FLAG_ADD_PERCENT) {
buf[len++] = '%';
buf[len] = '\0';
}

1
py/mpprint.h
View file

@ -36,6 +36,7 @@
#define PF_FLAG_CENTER_ADJUST (0x020)
#define PF_FLAG_ADD_PERCENT (0x040)
#define PF_FLAG_SHOW_OCTAL_LETTER (0x080)
#define PF_FLAG_ALWAYS_DECIMAL (0x100)
#define PF_FLAG_SEP_POS (9) // must be above all the above PF_FLAGs
#if MICROPY_PY_IO && MICROPY_PY_SYS_STDFILES

31
py/objcomplex.c
View file

@ -45,29 +45,18 @@ typedef struct _mp_obj_complex_t {
static void complex_print(const mp_print_t *print, mp_obj_t o_in, mp_print_kind_t kind) {
(void)kind;
mp_obj_complex_t *o = MP_OBJ_TO_PTR(o_in);
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
char buf[16];
#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C
const int precision = 6;
#else
const int precision = 7;
#endif
#else
char buf[32];
const int precision = 16;
#endif
if (o->real == 0) {
mp_format_float(o->imag, buf, sizeof(buf), 'g', precision, '\0');
mp_printf(print, "%sj", buf);
const char *suffix;
int flags = 0;
if (o->real != 0) {
mp_print_str(print, "(");
mp_print_float(print, o->real, 'g', 0, '\0', -1, MP_FLOAT_REPR_PREC);
flags = PF_FLAG_SHOW_SIGN;
suffix = "j)";
} else {
mp_format_float(o->real, buf, sizeof(buf), 'g', precision, '\0');
mp_printf(print, "(%s", buf);
if (o->imag >= 0 || isnan(o->imag)) {
mp_print_str(print, "+");
}
mp_format_float(o->imag, buf, sizeof(buf), 'g', precision, '\0');
mp_printf(print, "%sj)", buf);
suffix = "j";
}
mp_print_float(print, o->imag, 'g', flags, '\0', -1, MP_FLOAT_REPR_PREC);
mp_print_str(print, suffix);
}
static mp_obj_t complex_make_new(const mp_obj_type_t *type_in, size_t n_args, size_t n_kw, const mp_obj_t *args) {

18
py/objfloat.c
View file

@ -110,23 +110,7 @@ mp_int_t mp_float_hash(mp_float_t src) {
static void float_print(const mp_print_t *print, mp_obj_t o_in, mp_print_kind_t kind) {
(void)kind;
mp_float_t o_val = mp_obj_float_get(o_in);
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
char buf[16];
#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C
const int precision = 6;
#else
const int precision = 7;
#endif
#else
char buf[32];
const int precision = 16;
#endif
mp_format_float(o_val, buf, sizeof(buf), 'g', precision, '\0');
mp_print_str(print, buf);
if (strchr(buf, '.') == NULL && strchr(buf, 'e') == NULL && strchr(buf, 'n') == NULL) {
// Python floats always have decimal point (unless inf or nan)
mp_print_str(print, ".0");
}
mp_print_float(print, o_val, 'g', PF_FLAG_ALWAYS_DECIMAL, '\0', -1, MP_FLOAT_REPR_PREC);
}
static mp_obj_t float_make_new(const mp_obj_type_t *type_in, size_t n_args, size_t n_kw, const mp_obj_t *args) {

50
py/parsenum.c
View file

@ -210,7 +210,7 @@ typedef enum {
} parse_dec_in_t;
// MANTISSA_MAX is used to retain precision while not overflowing mantissa
#define MANTISSA_MAX (sizeof(mp_float_uint_t) == 8 ? 0x1999999999999998ULL : 0x19999998U)
#define MANTISSA_MAX (sizeof(mp_large_float_uint_t) == 8 ? 0x1999999999999998ULL : 0x19999998U)
// MAX_EXACT_POWER_OF_5 is the largest value of x so that 5^x can be stored exactly in a float
#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
@ -220,11 +220,45 @@ typedef enum {
#endif
// Helper to compute `num * (10.0 ** dec_exp)`
mp_float_t mp_decimal_exp(mp_float_t num, int dec_exp) {
if (dec_exp == 0 || num == MICROPY_FLOAT_CONST(0.0)) {
mp_large_float_t mp_decimal_exp(mp_large_float_t num, int dec_exp) {
if (dec_exp == 0 || num == (mp_large_float_t)(0.0)) {
return num;
}
#if MICROPY_FLOAT_FORMAT_IMPL == MICROPY_FLOAT_FORMAT_IMPL_EXACT
// If the assert below fails, it means you have chosen MICROPY_FLOAT_FORMAT_IMPL_EXACT
// manually on a platform where `larger floats` are not supported, which would
// result in inexact conversions. To fix this issue, change your `mpconfigport.h`
// and select MICROPY_FLOAT_FORMAT_IMPL_APPROX instead
assert(sizeof(mp_large_float_t) > sizeof(mp_float_t));
// Perform power using simple multiplications, to avoid
// dependency to higher-precision pow() function
int neg_exp = (dec_exp < 0);
if (neg_exp) {
dec_exp = -dec_exp;
}
mp_large_float_t res = num;
mp_large_float_t expo = (mp_large_float_t)10.0;
while (dec_exp) {
if (dec_exp & 1) {
if (neg_exp) {
res /= expo;
} else {
res *= expo;
}
}
dec_exp >>= 1;
if (dec_exp) {
expo *= expo;
}
}
return res;
#else
// MICROPY_FLOAT_FORMAT_IMPL != MICROPY_FLOAT_FORMAT_IMPL_EXACT
mp_float_union_t res = {num};
// Multiply first by (2.0 ** dec_exp) via the exponent
// - this will ensure that the result of `pow()` is always in mp_float_t range
@ -238,12 +272,14 @@ mp_float_t mp_decimal_exp(mp_float_t num, int dec_exp) {
} else {
res.f *= MICROPY_FLOAT_C_FUN(pow)(5, dec_exp);
}
return (mp_float_t)res.f;
return (mp_large_float_t)res.f;
#endif
}
// Break out inner digit accumulation routine to ease trailing zero deferral.
static mp_float_uint_t accept_digit(mp_float_uint_t p_mantissa, unsigned int dig, int *p_exp_extra, int in) {
static mp_large_float_uint_t accept_digit(mp_large_float_uint_t p_mantissa, unsigned int dig, int *p_exp_extra, int in) {
// Core routine to ingest an additional digit.
if (p_mantissa < MANTISSA_MAX) {
// dec_val won't overflow so keep accumulating
@ -267,7 +303,7 @@ const char *mp_parse_float_internal(const char *str, size_t len, mp_float_t *res
parse_dec_in_t in = PARSE_DEC_IN_INTG;
bool exp_neg = false;
mp_float_uint_t mantissa = 0;
mp_large_float_uint_t mantissa = 0;
int exp_val = 0;
int exp_extra = 0;
int trailing_zeros_intg = 0, trailing_zeros_frac = 0;

2
py/parsenum.h
View file

@ -35,7 +35,7 @@
mp_obj_t mp_parse_num_integer(const char *restrict str, size_t len, int base, mp_lexer_t *lex);
#if MICROPY_PY_BUILTINS_FLOAT
mp_float_t mp_decimal_exp(mp_float_t num, int dec_exp);
mp_large_float_t mp_decimal_exp(mp_large_float_t num, int dec_exp);
const char *mp_parse_float_internal(const char *str, size_t len, mp_float_t *res);
#endif

17
tests/float/float_format.py
View file

@ -2,14 +2,25 @@
# general rounding
for val in (116, 1111, 1234, 5010, 11111):
print("%.0f" % val)
print("%.1f" % val)
print("%.3f" % val)
print("Test on %d / 1000:" % val)
for fmt in ("%.5e", "%.3e", "%.1e", "%.0e", "%.3f", "%.1f", "%.0f", "%.3g", "%.1g", "%.0g"):
print(fmt, fmt % (val / 1000))
# make sure round-up to the next unit is handled properly
for val in range(4, 9):
divi = 10**val
print("Test on 99994 / (10 ** %d):" % val)
for fmt in ("%.5e", "%.3e", "%.1e", "%.0e", "%.3f", "%.1f", "%.0f", "%.3g", "%.1g", "%.0g"):
print(fmt, fmt % (99994 / divi))
# make sure rounding is done at the correct precision
for prec in range(8):
print(("%%.%df" % prec) % 6e-5)
# make sure trailing zeroes are added properly
for prec in range(8):
print(("%%.%df" % prec) % 1e19)
# check certain cases that had a digit value of 10 render as a ":" character
print("%.2e" % float("9" * 51 + "e-39"))
print("%.2e" % float("9" * 40 + "e-21"))

73
tests/float/float_format_accuracy.py Normal file
View file

@ -0,0 +1,73 @@
# Test accuracy of `repr` conversions.
# This test also increases code coverage for corner cases.
try:
import array, math, random
except ImportError:
print("SKIP")
raise SystemExit
# The largest errors come from seldom used very small numbers, near the
# limit of the representation. So we keep them out of this test to keep
# the max relative error display useful.
if float("1e-100") == 0.0:
# single-precision
float_type = "f"
float_size = 4
# testing range
min_expo = -96 # i.e. not smaller than 1.0e-29
# Expected results (given >=50'000 samples):
# - MICROPY_FLTCONV_IMPL_EXACT: 100% exact conversions
# - MICROPY_FLTCONV_IMPL_APPROX: >=98.53% exact conversions, max relative error <= 1.01e-7
min_success = 0.980 # with only 1200 samples, the success rate is lower
max_rel_err = 1.1e-7
# REPR_C is typically used with FORMAT_IMPL_BASIC, which has a larger error
is_REPR_C = float("1.0000001") == float("1.0")
if is_REPR_C: # REPR_C
min_success = 0.83
max_rel_err = 5.75e-07
else:
# double-precision
float_type = "d"
float_size = 8
# testing range
min_expo = -845 # i.e. not smaller than 1.0e-254
# Expected results (given >=200'000 samples):
# - MICROPY_FLTCONV_IMPL_EXACT: 100% exact conversions
# - MICROPY_FLTCONV_IMPL_APPROX: >=99.83% exact conversions, max relative error <= 2.7e-16
min_success = 0.997 # with only 1200 samples, the success rate is lower
max_rel_err = 2.7e-16
# Deterministic pseudorandom generator. Designed to be uniform
# on mantissa values and exponents, not on the represented number
def pseudo_randfloat():
rnd_buff = bytearray(float_size)
for _ in range(float_size):
rnd_buff[_] = random.getrandbits(8)
return array.array(float_type, rnd_buff)[0]
random.seed(42)
stats = 0
N = 1200
max_err = 0
for _ in range(N):
f = pseudo_randfloat()
while type(f) is not float or math.isinf(f) or math.isnan(f) or math.frexp(f)[1] <= min_expo:
f = pseudo_randfloat()
str_f = repr(f)
f2 = float(str_f)
if f2 == f:
stats += 1
else:
error = abs((f2 - f) / f)
if max_err < error:
max_err = error
print(N, "values converted")
if stats / N >= min_success and max_err <= max_rel_err:
print("float format accuracy OK")
else:
print("FAILED: repr rate=%.3f%% max_err=%.3e" % (100 * stats / N, max_err))

32
tests/float/float_format_ints.py
View file

@ -12,14 +12,42 @@ for b in [13, 123, 457, 23456]:
print(title, "with format", f_fmt, "gives", f_fmt.format(f))
print(title, "with format", g_fmt, "gives", g_fmt.format(f))
# The tests below check border cases involving all mantissa bits.
# In case of REPR_C, where the mantissa is missing two bits, the
# the string representation for such numbers might not always be exactly
# the same but nevertheless be correct, so we must allow a few exceptions.
is_REPR_C = float("1.0000001") == float("1.0")
# 16777215 is 2^24 - 1, the largest integer that can be completely held
# in a float32.
print("{:f}".format(16777215))
val_str = "{:f}".format(16777215)
# When using REPR_C, 16777215.0 is the same as 16777212.0 or 16777214.4
# (depending on the implementation of pow() function, the result may differ)
if is_REPR_C and (val_str == "16777212.000000" or val_str == "16777214.400000"):
val_str = "16777215.000000"
print(val_str)
# 4294967040 = 16777215 * 128 is the largest integer that is exactly
# represented by a float32 and that will also fit within a (signed) int32.
# The upper bound of our integer-handling code is actually double this,
# but that constant might cause trouble on systems using 32 bit ints.
print("{:f}".format(2147483520))
val_str = "{:f}".format(2147483520)
# When using FLOAT_IMPL_FLOAT, 2147483520.0 == 2147483500.0
# Both representations are valid, the second being "simpler"
is_float32 = float("1e300") == float("inf")
if is_float32 and val_str == "2147483500.000000":
val_str = "2147483520.000000"
# When using REPR_C, 2147483520.0 is the same as 2147483200.0
# Both representations are valid, the second being "simpler"
if is_REPR_C and val_str == "2147483200.000000":
val_str = "2147483520.000000"
print(val_str)
# Very large positive integers can be a test for precision and resolution.
# This is a weird way to represent 1e38 (largest power of 10 for float32).
print("{:.6e}".format(float("9" * 30 + "e8")))

2
tests/float/float_struct_e.py
View file

@ -32,7 +32,7 @@ for j in test_values:
for i in (j, -j):
x = struct.pack("<e", i)
v = struct.unpack("<e", x)[0]
print("%.7f %s %.15f %s" % (i, x, v, i == v))
print("%.7f %s %.7f %s" % (i, x, v, i == v))
# In CPython, packing a float that doesn't fit into a half-float raises OverflowError.
# But in MicroPython it does not, but rather stores the value as inf.

43
tests/float/float_struct_e_doubleprec.py Normal file
View file

@ -0,0 +1,43 @@
# Test struct pack/unpack with 'e' typecode.
try:
import struct
except ImportError:
print("SKIP")
raise SystemExit
test_values = (
1e-7,
2e-7,
1e-6,
1e-5,
1e-4,
1e-3,
1e-2,
0.1,
0,
1,
2,
4,
8,
10,
100,
1e3,
1e4,
6e4,
float("inf"),
)
for j in test_values:
for i in (j, -j):
x = struct.pack("<e", i)
v = struct.unpack("<e", x)[0]
print("%.7f %s %.15f %s" % (i, x, v, i == v))
# In CPython, packing a float that doesn't fit into a half-float raises OverflowError.
# But in MicroPython it does not, but rather stores the value as inf.
# This test is here for coverage.
try:
struct.pack("e", 1e15)
except OverflowError:
pass

43
tests/float/float_struct_e_fp30.py Normal file
View file

@ -0,0 +1,43 @@
# Test struct pack/unpack with 'e' typecode.
try:
import struct
except ImportError:
print("SKIP")
raise SystemExit
test_values = (
1e-7,
2e-7,
1e-6,
1e-5,
1e-4,
1e-3,
1e-2,
0.1,
0,
1,
2,
4,
8,
10,
100,
1e3,
1e4,
6e4,
float("inf"),
)
for j in test_values:
for i in (j, -j):
x = struct.pack("<e", i)
v = struct.unpack("<e", x)[0]
print("%.7f %s %.5f %s" % (i, x, v, i == v))
# In CPython, packing a float that doesn't fit into a half-float raises OverflowError.
# But in MicroPython it does not, but rather stores the value as inf.
# This test is here for coverage.
try:
struct.pack("e", 1e15)
except OverflowError:
pass

2
tests/float/string_format_modulo3.py
View file

@ -1,3 +1,3 @@
# uPy and CPython outputs differ for the following
# Test corner cases where MicroPython and CPython outputs used to differ in the past
print("%.1g" % -9.9) # round up 'g' with '-' sign
print("%.2g" % 99.9) # round up

2
tests/float/string_format_modulo3.py.exp
View file

@ -1,2 +0,0 @@
-10
100

4
tests/ports/unix/extra_coverage.py.exp
View file

@ -127,10 +127,6 @@ TypeError: can't convert NoneType to int
TypeError: can't convert NoneType to int
ValueError:
Warning: test
# format float
?
+1e+00
+1e+00
# binary
123
456

3
tests/ports/unix/ffi_float2.py
View file

@ -29,4 +29,5 @@ except OSError:
for fun in (tgammaf,):
for val in (0.5, 1, 1.0, 1.5, 4, 4.0):
print("%.6f" % fun(val))
# limit to 5 decimals in order to pass with REPR_C with FORMAT_IMPL_BASIC
print("%.5f" % fun(val))

12
tests/ports/unix/ffi_float2.py.exp
View file

@ -1,6 +1,6 @@
1.772454
1.000000
1.000000
0.886227
6.000000
6.000000
1.77245
1.00000
1.00000
0.88623
6.00000
6.00000

4
tests/run-tests.py
View file

@ -785,12 +785,16 @@ def run_tests(pyb, tests, args, result_dir, num_threads=1):
skip_tests.add(
"float/float2int_intbig.py"
) # requires fp32, there's float2int_fp30_intbig.py instead
skip_tests.add(
"float/float_struct_e.py"
) # requires fp32, there's float_struct_e_fp30.py instead
skip_tests.add("float/bytes_construct.py") # requires fp32
skip_tests.add("float/bytearray_construct.py") # requires fp32
skip_tests.add("float/float_format_ints_power10.py") # requires fp32
if upy_float_precision < 64:
skip_tests.add("float/float_divmod.py") # tested by float/float_divmod_relaxed.py instead
skip_tests.add("float/float2int_doubleprec_intbig.py")
skip_tests.add("float/float_struct_e_doubleprec.py")
skip_tests.add("float/float_format_ints_doubleprec.py")
skip_tests.add("float/float_parse_doubleprec.py")