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+/*
+ * This file is part of the MicroPython project, http://micropython.org/
+ *
+ * The MIT License (MIT)
+ *
+ * SPDX-FileCopyrightText: 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"
+#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
+
+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;
+
+ 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)) {
+ // We need to figure out what an integer digit will be used
+ // in case 'f' is used (or we revert other format to it below).
+ // As we just tested number to be <1, this is obviously 0,
+ // but we can round it up to 1 below.
+ char first_dig = '0';
+ if (f >= FPROUND_TO_ONE) {
+ first_dig = '1';
+ }
+
+ // Build negative exponent
+ for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
+ if (*neg_pow > f) {
+ e += e1;
+ f *= *pos_pow;
+ }
+ }
+ char e_sign_char = '-';
+ if (fp_isless1(f) && f >= FPROUND_TO_ONE) {
+ f = FPCONST(1.0);
+ if (e == 0) {
+ e_sign_char = '+';
+ }
+ } else if (fp_isless1(f)) {
+ e++;
+ f *= 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 = -1;
+ *s++ = first_dig;
+
+ 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;
+ if (num_digits) {
+ *s++ = '.';
+ while (--e && num_digits) {
+ *s++ = '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++;
+ }
+ }
+ }
+ } else {
+ // Build positive exponent
+ for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
+ if (*pos_pow <= f) {
+ e += e1;
+ f *= *neg_pow;
+ }
+ }
+
+ // It can be that f was right on the edge of an entry in pos_pow needs to be reduced
+ if ((int)f >= 10) {
+ e += 1;
+ f *= FPCONST(0.1);
+ }
+
+ // 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 = '+';
+ }
+ }
+ if (prec < 0) {
+ // This can happen when the prec is trimmed to prevent buffer overflow
+ prec = 0;
+ }
+
+ // We now have num.f as a floating point number between >= 1 and < 10
+ // (or equal to zero), and e contains the absolute value of the power of
+ // 10 exponent. and (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;
+ }
+
+ // Print the digits of the mantissa
+ for (int i = 0; i < num_digits; ++i, --dec) {
+ int32_t d = (int32_t)f;
+ if (d < 0) {
+ *s++ = '0';
+ } else {
+ *s++ = '0' + d;
+ }
+ if (dec == 0 && prec > 0) {
+ *s++ = '.';
+ }
+ f -= (FPTYPE)d;
+ f *= FPCONST(10.0);
+ }
+
+ // Round
+ // If we print non-exponential format (i.e. 'f'), but a digit we're going
+ // to round by (e) is too far away, then there's nothing to round.
+ if ((org_fmt != 'f' || e <= num_digits) && f >= FPCONST(5.0)) {
+ 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'
+ 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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