439 lines
13 KiB
C
439 lines
13 KiB
C
/*
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* This file is part of the MicroPython project, http://micropython.org/
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*
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* The MIT License (MIT)
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*
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* SPDX-FileCopyrightText: Copyright (c) 2013, 2014 Damien P. George
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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#include "py/mpconfig.h"
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#if MICROPY_FLOAT_IMPL != MICROPY_FLOAT_IMPL_NONE
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#include <assert.h>
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#include <stdlib.h>
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#include <stdint.h>
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#include <math.h>
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#include "py/formatfloat.h"
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/***********************************************************************
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Routine for converting a arbitrary floating
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point number into a string.
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The code in this funcion was inspired from Fred Bayer's pdouble.c.
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Since pdouble.c was released as Public Domain, I'm releasing this
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code as public domain as well.
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The original code can be found in https://github.com/dhylands/format-float
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Dave Hylands
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***********************************************************************/
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#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
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// 1 sign bit, 8 exponent bits, and 23 mantissa bits.
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// exponent values 0 and 255 are reserved, exponent can be 1 to 254.
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// exponent is stored with a bias of 127.
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// The min and max floats are on the order of 1x10^37 and 1x10^-37
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#define FPTYPE float
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#define FPCONST(x) x##F
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#define FPROUND_TO_ONE 0.9999995F
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#define FPDECEXP 32
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#define FPMIN_BUF_SIZE 6 // +9e+99
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#define FLT_SIGN_MASK 0x80000000
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#define FLT_EXP_MASK 0x7F800000
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#define FLT_MAN_MASK 0x007FFFFF
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union floatbits {
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float f;
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uint32_t u;
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};
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static inline int fp_signbit(float x) {
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union floatbits fb = {x};
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return fb.u & FLT_SIGN_MASK;
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}
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#define fp_isnan(x) isnan(x)
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#define fp_isinf(x) isinf(x)
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static inline int fp_iszero(float x) {
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union floatbits fb = {x};
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return fb.u == 0;
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}
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static inline int fp_isless1(float x) {
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union floatbits fb = {x};
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return fb.u < 0x3f800000;
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}
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#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
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#define FPTYPE double
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#define FPCONST(x) x
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#define FPROUND_TO_ONE 0.999999999995
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#define FPDECEXP 256
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#define FPMIN_BUF_SIZE 7 // +9e+199
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#define fp_signbit(x) signbit(x)
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#define fp_isnan(x) isnan(x)
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#define fp_isinf(x) isinf(x)
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#define fp_iszero(x) (x == 0)
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#define fp_isless1(x) (x < 1.0)
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#endif
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static const FPTYPE g_pos_pow[] = {
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#if FPDECEXP > 32
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MICROPY_FLOAT_CONST(1e256), MICROPY_FLOAT_CONST(1e128), MICROPY_FLOAT_CONST(1e64),
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#endif
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MICROPY_FLOAT_CONST(1e32), MICROPY_FLOAT_CONST(1e16), MICROPY_FLOAT_CONST(1e8), MICROPY_FLOAT_CONST(1e4), MICROPY_FLOAT_CONST(1e2), MICROPY_FLOAT_CONST(1e1)
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};
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static const FPTYPE g_neg_pow[] = {
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#if FPDECEXP > 32
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MICROPY_FLOAT_CONST(1e-256), MICROPY_FLOAT_CONST(1e-128), MICROPY_FLOAT_CONST(1e-64),
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#endif
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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)
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};
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int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, char sign) {
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char *s = buf;
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if (buf_size <= FPMIN_BUF_SIZE) {
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// FPMIN_BUF_SIZE is the minimum size needed to store any FP number.
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// If the buffer does not have enough room for this (plus null terminator)
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// then don't try to format the float.
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if (buf_size >= 2) {
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*s++ = '?';
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}
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if (buf_size >= 1) {
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*s = '\0';
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}
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return buf_size >= 2;
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}
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if (fp_signbit(f) && !fp_isnan(f)) {
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*s++ = '-';
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f = -f;
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} else {
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if (sign) {
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*s++ = sign;
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}
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}
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// buf_remaining contains bytes available for digits and exponent.
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// It is buf_size minus room for the sign and null byte.
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int buf_remaining = buf_size - 1 - (s - buf);
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{
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char uc = fmt & 0x20;
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if (fp_isinf(f)) {
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*s++ = 'I' ^ uc;
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*s++ = 'N' ^ uc;
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*s++ = 'F' ^ uc;
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goto ret;
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} else if (fp_isnan(f)) {
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*s++ = 'N' ^ uc;
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*s++ = 'A' ^ uc;
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*s++ = 'N' ^ uc;
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ret:
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*s = '\0';
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return s - buf;
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}
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}
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if (prec < 0) {
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prec = 6;
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}
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char e_char = 'E' | (fmt & 0x20); // e_char will match case of fmt
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fmt |= 0x20; // Force fmt to be lowercase
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char org_fmt = fmt;
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if (fmt == 'g' && prec == 0) {
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prec = 1;
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}
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int e, e1;
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int dec = 0;
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char e_sign = '\0';
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int num_digits = 0;
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const FPTYPE *pos_pow = g_pos_pow;
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const FPTYPE *neg_pow = g_neg_pow;
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if (fp_iszero(f)) {
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e = 0;
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if (fmt == 'f') {
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// Truncate precision to prevent buffer overflow
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if (prec + 2 > buf_remaining) {
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prec = buf_remaining - 2;
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}
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num_digits = prec + 1;
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} else {
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// Truncate precision to prevent buffer overflow
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if (prec + 6 > buf_remaining) {
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prec = buf_remaining - 6;
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}
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if (fmt == 'e') {
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e_sign = '+';
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}
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}
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} else if (fp_isless1(f)) {
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// We need to figure out what an integer digit will be used
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// in case 'f' is used (or we revert other format to it below).
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// As we just tested number to be <1, this is obviously 0,
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// but we can round it up to 1 below.
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char first_dig = '0';
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if (f >= FPROUND_TO_ONE) {
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first_dig = '1';
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}
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// Build negative exponent
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for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
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if (*neg_pow > f) {
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e += e1;
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f *= *pos_pow;
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}
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}
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char e_sign_char = '-';
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if (fp_isless1(f) && f >= FPROUND_TO_ONE) {
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f = FPCONST(1.0);
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if (e == 0) {
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e_sign_char = '+';
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}
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} else if (fp_isless1(f)) {
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e++;
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f *= FPCONST(10.0);
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}
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// If the user specified 'g' format, and e is <= 4, then we'll switch
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// to the fixed format ('f')
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if (fmt == 'f' || (fmt == 'g' && e <= 4)) {
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fmt = 'f';
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dec = -1;
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*s++ = first_dig;
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if (org_fmt == 'g') {
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prec += (e - 1);
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}
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// truncate precision to prevent buffer overflow
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if (prec + 2 > buf_remaining) {
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prec = buf_remaining - 2;
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}
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num_digits = prec;
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if (num_digits) {
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*s++ = '.';
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while (--e && num_digits) {
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*s++ = '0';
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num_digits--;
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}
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}
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} else {
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// For e & g formats, we'll be printing the exponent, so set the
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// sign.
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e_sign = e_sign_char;
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dec = 0;
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if (prec > (buf_remaining - FPMIN_BUF_SIZE)) {
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prec = buf_remaining - FPMIN_BUF_SIZE;
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if (fmt == 'g') {
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prec++;
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}
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}
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}
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} else {
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// Build positive exponent
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for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
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if (*pos_pow <= f) {
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e += e1;
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f *= *neg_pow;
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}
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}
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// It can be that f was right on the edge of an entry in pos_pow needs to be reduced
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if ((int)f >= 10) {
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e += 1;
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f *= FPCONST(0.1);
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}
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// If the user specified fixed format (fmt == 'f') and e makes the
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// number too big to fit into the available buffer, then we'll
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// switch to the 'e' format.
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if (fmt == 'f') {
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if (e >= buf_remaining) {
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fmt = 'e';
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} else if ((e + prec + 2) > buf_remaining) {
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prec = buf_remaining - e - 2;
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if (prec < 0) {
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// This means no decimal point, so we can add one back
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// for the decimal.
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prec++;
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}
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}
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}
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if (fmt == 'e' && prec > (buf_remaining - FPMIN_BUF_SIZE)) {
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prec = buf_remaining - FPMIN_BUF_SIZE;
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}
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if (fmt == 'g') {
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// Truncate precision to prevent buffer overflow
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if (prec + (FPMIN_BUF_SIZE - 1) > buf_remaining) {
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prec = buf_remaining - (FPMIN_BUF_SIZE - 1);
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}
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}
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// If the user specified 'g' format, and e is < prec, then we'll switch
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// to the fixed format.
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if (fmt == 'g' && e < prec) {
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fmt = 'f';
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prec -= (e + 1);
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}
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if (fmt == 'f') {
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dec = e;
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num_digits = prec + e + 1;
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} else {
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e_sign = '+';
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}
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}
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if (prec < 0) {
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// This can happen when the prec is trimmed to prevent buffer overflow
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prec = 0;
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}
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// We now have num.f as a floating point number between >= 1 and < 10
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// (or equal to zero), and e contains the absolute value of the power of
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// 10 exponent. and (dec + 1) == the number of dgits before the decimal.
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// For e, prec is # digits after the decimal
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// For f, prec is # digits after the decimal
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// For g, prec is the max number of significant digits
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//
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// For e & g there will be a single digit before the decimal
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// for f there will be e digits before the decimal
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if (fmt == 'e') {
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num_digits = prec + 1;
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} else if (fmt == 'g') {
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if (prec == 0) {
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prec = 1;
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}
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num_digits = prec;
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}
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// Print the digits of the mantissa
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for (int i = 0; i < num_digits; ++i, --dec) {
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int32_t d = (int32_t)f;
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if (d < 0) {
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*s++ = '0';
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} else {
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*s++ = '0' + d;
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}
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if (dec == 0 && prec > 0) {
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*s++ = '.';
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}
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f -= (FPTYPE)d;
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f *= FPCONST(10.0);
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}
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// Round
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// If we print non-exponential format (i.e. 'f'), but a digit we're going
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// to round by (e) is too far away, then there's nothing to round.
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if ((org_fmt != 'f' || e <= num_digits) && f >= FPCONST(5.0)) {
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char *rs = s;
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rs--;
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while (1) {
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if (*rs == '.') {
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rs--;
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continue;
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}
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if (*rs < '0' || *rs > '9') {
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// + or -
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rs++; // So we sit on the digit to the right of the sign
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break;
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}
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if (*rs < '9') {
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(*rs)++;
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break;
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}
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*rs = '0';
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if (rs == buf) {
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break;
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}
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rs--;
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}
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if (*rs == '0') {
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// We need to insert a 1
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if (rs[1] == '.' && fmt != 'f') {
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// We're going to round 9.99 to 10.00
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// Move the decimal point
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rs[0] = '.';
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rs[1] = '0';
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if (e_sign == '-') {
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e--;
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if (e == 0) {
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e_sign = '+';
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}
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} else {
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e++;
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}
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} else {
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// Need at extra digit at the end to make room for the leading '1'
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s++;
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}
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char *ss = s;
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while (ss > rs) {
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*ss = ss[-1];
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ss--;
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}
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*rs = '1';
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}
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}
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// verify that we did not overrun the input buffer so far
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assert((size_t)(s + 1 - buf) <= buf_size);
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if (org_fmt == 'g' && prec > 0) {
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// Remove trailing zeros and a trailing decimal point
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while (s[-1] == '0') {
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s--;
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}
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if (s[-1] == '.') {
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s--;
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}
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}
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// Append the exponent
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if (e_sign) {
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*s++ = e_char;
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*s++ = e_sign;
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if (FPMIN_BUF_SIZE == 7 && e >= 100) {
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*s++ = '0' + (e / 100);
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}
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*s++ = '0' + ((e / 10) % 10);
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*s++ = '0' + (e % 10);
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}
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*s = '\0';
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// verify that we did not overrun the input buffer
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assert((size_t)(s + 1 - buf) <= buf_size);
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return s - buf;
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}
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#endif // MICROPY_FLOAT_IMPL != MICROPY_FLOAT_IMPL_NONE
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