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micropython/py/formatfloat.c

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/*
* This file is part of the MicroPython project, http://micropython.org/
*
* The MIT License (MIT)
*
* Copyright (c) 2013, 2014 Damien P. George
*
* 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.
*/
#include "py/mpconfig.h"
#include "py/misc.h"
#if MICROPY_FLOAT_IMPL != MICROPY_FLOAT_IMPL_NONE
#include <assert.h>
#include <stdlib.h>
#include <stdint.h>
#include <math.h>
#include "py/formatfloat.h"
/***********************************************************************
Routine for converting a arbitrary floating
point number into a string.
The code in this funcion 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 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
#define FPTYPE float
#define FPCONST(x) x##F
#define FPROUND_TO_ONE 0.9999995F
#define FPDECEXP 32
#define FPMIN_BUF_SIZE 6 // +9e+99
#define FLT_SIGN_MASK 0x80000000
#define FLT_EXP_MASK 0x7F800000
#define FLT_MAN_MASK 0x007FFFFF
union floatbits {
float f;
uint32_t u;
};
static inline int fp_signbit(float x) {
union floatbits fb = {x};
return fb.u & FLT_SIGN_MASK;
}
#define fp_isnan(x) isnan(x)
#define fp_isinf(x) isinf(x)
static inline int fp_iszero(float x) {
union floatbits fb = {x};
return fb.u == 0;
}
static inline int fp_isless1(float x) {
union floatbits fb = {x};
return fb.u < 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_ge_eps(FPTYPE x, FPTYPE y) {
mp_float_union_t fb_y = {y};
// Back off 2 eps.
// This is valid for almost all values, but in practice
// it's only used when y = 1eX for X>=0.
fb_y.i -= 2;
return x >= fb_y.f;
}
static const FPTYPE g_pos_pow[] = {
#if FPDECEXP > 32
MICROPY_FLOAT_CONST(1e256), MICROPY_FLOAT_CONST(1e128), MICROPY_FLOAT_CONST(1e64),
#endif
MICROPY_FLOAT_CONST(1e32), MICROPY_FLOAT_CONST(1e16), MICROPY_FLOAT_CONST(1e8), MICROPY_FLOAT_CONST(1e4), MICROPY_FLOAT_CONST(1e2), MICROPY_FLOAT_CONST(1e1)
};
static const FPTYPE g_neg_pow[] = {
#if FPDECEXP > 32
MICROPY_FLOAT_CONST(1e-256), MICROPY_FLOAT_CONST(1e-128), MICROPY_FLOAT_CONST(1e-64),
#endif
MICROPY_FLOAT_CONST(1e-32), MICROPY_FLOAT_CONST(1e-16), MICROPY_FLOAT_CONST(1e-8), MICROPY_FLOAT_CONST(1e-4), MICROPY_FLOAT_CONST(1e-2), MICROPY_FLOAT_CONST(1e-1)
};
int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, char sign) {
char *s = buf;
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 (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;
}
}
// 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, e1;
int dec = 0;
char e_sign = '\0';
int num_digits = 0;
const FPTYPE *pos_pow = g_pos_pow;
const FPTYPE *neg_pow = g_neg_pow;
int signed_e = 0;
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_mod = f;
// Build negative exponent
for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
if (*neg_pow > f_mod) {
e += e1;
f_mod *= *pos_pow;
}
}
char e_sign_char = '-';
if (fp_isless1(f_mod) && f_mod >= FPROUND_TO_ONE) {
f_mod = FPCONST(1.0);
if (e == 0) {
e_sign_char = '+';
}
} else if (fp_isless1(f_mod)) {
e++;
f_mod *= FPCONST(10.0);
}
// 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;
++num_digits;
} else {
// For e & g formats, we'll be printing the exponent, so set the
// sign.
e_sign = e_sign_char;
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 innaccuracies 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.
FPTYPE u_base = FPCONST(1.0);
for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++) {
FPTYPE next_u = u_base * *pos_pow;
// fp_ge_eps performs "f >= (next_u - 2eps)" so that if, for
// numerical reasons, f is very close to a power of ten but
// not strictly equal, we still treat it as that power of 10.
// The comparison was failing for maybe 10% of 1eX values, but
// although rounding fixed many of them, there were still some
// rendering as 9.99999998e(X-1).
if (fp_ge_eps(f, next_u)) {
u_base = next_u;
e += e1;
}
}
// 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;
}
if (signed_e < 0) {
// The algorithm below treats numbers smaller than 1 by scaling them
// repeatedly by 10 to bring the new digit to the top. Our input number
// was smaller than 1, so scale it up to be 1 <= f < 10.
FPTYPE u_base = FPCONST(1.0);
const FPTYPE *pow_u = g_pos_pow;
for (int m = FPDECEXP; m; m >>= 1, pow_u++) {
if (m & e) {
u_base *= *pow_u;
}
}
f *= u_base;
}
int d = 0;
int num_digits_left = num_digits;
for (int digit_index = signed_e; num_digits_left >= 0; --digit_index) {
FPTYPE u_base = FPCONST(1.0);
if (digit_index > 0) {
// Generate 10^digit_index for positive digit_index.
const FPTYPE *pow_u = g_pos_pow;
int target_index = digit_index;
for (int m = FPDECEXP; m; m >>= 1, pow_u++) {
if (m & target_index) {
u_base *= *pow_u;
}
}
}
for (d = 0; d < 9; ++d) {
// This is essentially "if (f < u_base)", but with 2eps margin
// so that if f is just a tiny bit smaller, we treat it as
// equal (and accept the additional digit value).
if (!fp_ge_eps(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_left > 0) {
// Emit this number (the leading digit).
*s++ = '0' + d;
if (dec == 0 && prec > 0) {
*s++ = '.';
}
}
--dec;
--num_digits_left;
if (digit_index <= 0) {
// Once we get below 1.0, we scale up f instead of calculting
// 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 = '+';
}
} else {
e++;
}
} 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) {
s++;
}
}
char *ss = s;
while (ss > rs) {
*ss = ss[-1];
ss--;
}
*rs = '1';
}
}
// 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
while (s[-1] == '0') {
s--;
}
if (s[-1] == '.') {
s--;
}
}
// Append the exponent
if (e_sign) {
*s++ = e_char;
*s++ = e_sign;
if (FPMIN_BUF_SIZE == 7 && 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);
return s - buf;
}
#endif // MICROPY_FLOAT_IMPL != MICROPY_FLOAT_IMPL_NONE
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