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424 lines
13 KiB
424 lines
13 KiB
/*
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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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* 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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#include "py/misc.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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static inline int fp_signbit(float x) {
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mp_float_union_t fb = {x};
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return fb.i & 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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mp_float_union_t fb = {x};
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return fb.i == 0;
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}
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static inline int fp_isless1(float x) {
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mp_float_union_t fb = {x};
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return fb.i < 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 // MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT/DOUBLE
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static inline int fp_expval(FPTYPE x) {
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mp_float_union_t fb = {x};
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return (int)((fb.i >> MP_FLOAT_FRAC_BITS) & (~(0xFFFFFFFF << MP_FLOAT_EXP_BITS))) - MP_FLOAT_EXP_OFFSET;
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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;
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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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int signed_e = 0;
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// Approximate power of 10 exponent from binary exponent.
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// abs(e_guess) is lower bound on abs(power of 10 exponent).
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int e_guess = (int)(fp_expval(f) * FPCONST(0.3010299956639812)); // 1/log2(10).
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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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FPTYPE f_entry = f; // Save f in case we go to 'f' format.
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// Build negative exponent
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e = -e_guess;
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FPTYPE u_base = MICROPY_FLOAT_C_FUN(pow)(10, -e);
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while (u_base > f) {
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++e;
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u_base = MICROPY_FLOAT_C_FUN(pow)(10, -e);
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}
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// Normalize out the inferred unit. Use divide because
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// pow(10, e) * pow(10, -e) is slightly < 1 for some e in float32
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// (e.g. print("%.12f" % ((1e13) * (1e-13))))
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f /= u_base;
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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 = 0;
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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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signed_e = 0;
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f = f_entry;
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++num_digits;
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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 = '-';
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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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signed_e = -e;
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}
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} else {
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// Build positive exponent.
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// We don't modify f at this point to avoid innaccuracies from
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// scaling it. Instead, we find the product of powers of 10
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// that is not greater than it, and use that to start the
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// mantissa.
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e = e_guess;
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FPTYPE next_u = MICROPY_FLOAT_C_FUN(pow)(10, e + 1);
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while (f >= next_u) {
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++e;
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next_u = MICROPY_FLOAT_C_FUN(pow)(10, e + 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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signed_e = e;
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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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// At this point e contains the absolute value of the power of 10 exponent.
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// (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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int d = 0;
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for (int digit_index = signed_e; num_digits >= 0; --digit_index) {
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FPTYPE u_base = FPCONST(1.0);
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if (digit_index > 0) {
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// Generate 10^digit_index for positive digit_index.
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u_base = MICROPY_FLOAT_C_FUN(pow)(10, digit_index);
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}
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for (d = 0; d < 9; ++d) {
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if (f < u_base) {
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break;
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}
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f -= u_base;
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}
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// We calculate one more digit than we display, to use in rounding
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// below. So only emit the digit if it's one that we display.
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if (num_digits > 0) {
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// Emit this number (the leading digit).
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*s++ = '0' + d;
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if (dec == 0 && prec > 0) {
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*s++ = '.';
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}
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}
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--dec;
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--num_digits;
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if (digit_index <= 0) {
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// Once we get below 1.0, we scale up f instead of calculating
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// negative powers of 10 in u_base. This provides better
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// renditions of exact decimals like 1/16 etc.
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f *= FPCONST(10.0);
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}
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}
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// Rounding. If the next digit to print is >= 5, round up.
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if (d >= 5) {
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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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// but if we're at the buffer size limit, just drop the final digit.
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if ((size_t)(s + 1 - buf) < buf_size) {
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s++;
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}
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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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