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https://github.com/netwide-assembler/nasm.git
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4da5b8c2dd
Refactor the floating-point formatting code so that the 80-bit format can be supported with common code. This fixes 80-bit denorms as a side effect; the shift value in 80-bit denorms was completely wrong.
744 lines
20 KiB
C
744 lines
20 KiB
C
/* float.c floating-point constant support for the Netwide Assembler
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*
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* The Netwide Assembler is copyright (C) 1996 Simon Tatham and
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* Julian Hall. All rights reserved. The software is
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* redistributable under the licence given in the file "Licence"
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* distributed in the NASM archive.
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*
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* initial version 13/ix/96 by Simon Tatham
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*/
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#include "compiler.h"
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#include <ctype.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <inttypes.h>
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#include "nasm.h"
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#include "float.h"
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/*
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* -----------------
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* local variables
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* -----------------
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*/
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static efunc error;
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static bool daz = false; /* denormals as zero */
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static enum float_round rc = FLOAT_RC_NEAR; /* rounding control */
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/*
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* -----------
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* constants
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* -----------
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*/
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/* 112 bits + 64 bits for accuracy + 16 bits for rounding */
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#define MANT_WORDS 12
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/* 52 digits fit in 176 bits because 10^53 > 2^176 > 10^52 */
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#define MANT_DIGITS 52
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/* the format and the argument list depend on MANT_WORDS */
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#define MANT_FMT "%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x"
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#define MANT_ARG SOME_ARG(mant, 0)
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#define SOME_ARG(a,i) (a)[(i)+0], (a)[(i)+1], (a)[(i)+2], (a)[(i)+3], \
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(a)[(i)+4], (a)[(i)+5], (a)[(i)+6], (a)[(i)+7], (a)[(i)+8], \
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(a)[(i)+9], (a)[(i)+10], (a)[(i)+11]
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/*
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* ---------------------------------------------------------------------------
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* emit a printf()-like debug message... but only if DEBUG_FLOAT was defined
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* ---------------------------------------------------------------------------
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*/
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#ifdef DEBUG_FLOAT
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#define dprintf(x) printf x
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#else /* */
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#define dprintf(x) do { } while (0)
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#endif /* */
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/*
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* ---------------------------------------------------------------------------
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* multiply
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* ---------------------------------------------------------------------------
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*/
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static int float_multiply(uint16_t * to, uint16_t * from)
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{
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uint32_t temp[MANT_WORDS * 2];
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int32_t i, j;
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/*
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* guaranteed that top bit of 'from' is set -- so we only have
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* to worry about _one_ bit shift to the left
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*/
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dprintf(("%s=" MANT_FMT "\n", "mul1", SOME_ARG(to, 0)));
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dprintf(("%s=" MANT_FMT "\n", "mul2", SOME_ARG(from, 0)));
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memset(temp, 0, sizeof temp);
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for (i = 0; i < MANT_WORDS; i++) {
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for (j = 0; j < MANT_WORDS; j++) {
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uint32_t n;
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n = (uint32_t) to[i] * (uint32_t) from[j];
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temp[i + j] += n >> 16;
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temp[i + j + 1] += n & 0xFFFF;
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}
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}
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for (i = MANT_WORDS * 2; --i;) {
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temp[i - 1] += temp[i] >> 16;
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temp[i] &= 0xFFFF;
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}
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dprintf(("%s=" MANT_FMT "_" MANT_FMT "\n", "temp", SOME_ARG(temp, 0),
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SOME_ARG(temp, MANT_WORDS)));
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if (temp[0] & 0x8000) {
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for (i = 0; i < MANT_WORDS; i++) {
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to[i] = temp[i] & 0xFFFF;
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}
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dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), 0));
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return 0;
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} else {
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for (i = 0; i < MANT_WORDS; i++) {
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to[i] = (temp[i] << 1) + !!(temp[i + 1] & 0x8000);
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}
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dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), -1));
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return -1;
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}
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}
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/*
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* ---------------------------------------------------------------------------
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* convert
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* ---------------------------------------------------------------------------
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*/
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static bool ieee_flconvert(const char *string, uint16_t * mant,
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int32_t * exponent)
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{
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char digits[MANT_DIGITS];
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char *p, *q, *r;
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uint16_t mult[MANT_WORDS], bit;
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uint16_t *m;
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int32_t tenpwr, twopwr;
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int32_t extratwos;
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bool started, seendot, warned;
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p = digits;
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tenpwr = 0;
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started = seendot = warned = false;
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while (*string && *string != 'E' && *string != 'e') {
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if (*string == '.') {
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if (!seendot) {
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seendot = true;
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} else {
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error(ERR_NONFATAL,
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"too many periods in floating-point constant");
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return false;
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}
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} else if (*string >= '0' && *string <= '9') {
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if (*string == '0' && !started) {
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if (seendot) {
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tenpwr--;
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}
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} else {
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started = true;
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if (p < digits + sizeof(digits)) {
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*p++ = *string - '0';
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} else {
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if (!warned) {
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error(ERR_WARNING,
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"floating-point constant significand contains "
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"more than %i digits", MANT_DIGITS);
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warned = true;
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}
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}
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if (!seendot) {
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tenpwr++;
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}
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}
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} else if (*string == '_') {
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/* do nothing */
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} else {
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error(ERR_NONFATAL,
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"invalid character in floating-point constant %s: '%c'",
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"significand", *string);
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return false;
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}
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string++;
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}
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if (*string) {
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int32_t i = 0;
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bool neg = false;
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string++; /* eat the E */
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if (*string == '+') {
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string++;
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} else if (*string == '-') {
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neg = true;
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string++;
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}
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while (*string) {
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if (*string >= '0' && *string <= '9') {
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i = (i * 10) + (*string - '0');
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/*
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* To ensure that underflows and overflows are
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* handled properly we must avoid wraparounds of
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* the signed integer value that is used to hold
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* the exponent. Therefore we cap the exponent at
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* +/-5000, which is slightly more/less than
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* what's required for normal and denormal numbers
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* in single, double, and extended precision, but
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* sufficient to avoid signed integer wraparound.
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*/
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if (i > 5000) {
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break;
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}
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} else if (*string == '_') {
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/* do nothing */
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} else {
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error(ERR_NONFATAL,
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"invalid character in floating-point constant %s: '%c'",
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"exponent", *string);
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return false;
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}
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string++;
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}
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if (neg) {
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i = 0 - i;
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}
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tenpwr += i;
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}
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/*
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* At this point, the memory interval [digits,p) contains a
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* series of decimal digits zzzzzzz, such that our number X
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* satisfies X = 0.zzzzzzz * 10^tenpwr.
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*/
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q = digits;
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dprintf(("X = 0."));
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while (q < p) {
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dprintf(("%c", *q + '0'));
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q++;
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}
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dprintf((" * 10^%i\n", tenpwr));
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/*
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* Now convert [digits,p) to our internal representation.
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*/
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bit = 0x8000;
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for (m = mant; m < mant + MANT_WORDS; m++) {
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*m = 0;
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}
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m = mant;
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q = digits;
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started = false;
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twopwr = 0;
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while (m < mant + MANT_WORDS) {
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uint16_t carry = 0;
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while (p > q && !p[-1]) {
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p--;
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}
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if (p <= q) {
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break;
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}
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for (r = p; r-- > q;) {
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int32_t i;
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i = 2 * *r + carry;
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if (i >= 10) {
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carry = 1;
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i -= 10;
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} else {
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carry = 0;
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}
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*r = i;
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}
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if (carry) {
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*m |= bit;
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started = true;
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}
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if (started) {
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if (bit == 1) {
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bit = 0x8000;
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m++;
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} else {
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bit >>= 1;
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}
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} else {
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twopwr--;
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}
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}
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twopwr += tenpwr;
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/*
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* At this point, the 'mant' array contains the first frac-
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* tional places of a base-2^16 real number which when mul-
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* tiplied by 2^twopwr and 5^tenpwr gives X.
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*/
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dprintf(("X = " MANT_FMT " * 2^%i * 5^%i\n", MANT_ARG, twopwr,
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tenpwr));
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/*
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* Now multiply 'mant' by 5^tenpwr.
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*/
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if (tenpwr < 0) { /* mult = 5^-1 = 0.2 */
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for (m = mult; m < mult + MANT_WORDS - 1; m++) {
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*m = 0xCCCC;
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}
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mult[MANT_WORDS - 1] = 0xCCCD;
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extratwos = -2;
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tenpwr = -tenpwr;
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/*
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* If tenpwr was 1000...000b, then it becomes 1000...000b. See
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* the "ANSI C" comment below for more details on that case.
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*
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* Because we already truncated tenpwr to +5000...-5000 inside
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* the exponent parsing code, this shouldn't happen though.
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*/
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} else if (tenpwr > 0) { /* mult = 5^+1 = 5.0 */
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mult[0] = 0xA000;
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for (m = mult + 1; m < mult + MANT_WORDS; m++) {
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*m = 0;
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}
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extratwos = 3;
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} else {
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extratwos = 0;
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}
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while (tenpwr) {
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dprintf(("loop=" MANT_FMT " * 2^%i * 5^%i (%i)\n", MANT_ARG,
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twopwr, tenpwr, extratwos));
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if (tenpwr & 1) {
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dprintf(("mant*mult\n"));
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twopwr += extratwos + float_multiply(mant, mult);
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}
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dprintf(("mult*mult\n"));
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extratwos = extratwos * 2 + float_multiply(mult, mult);
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tenpwr >>= 1;
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/*
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* In ANSI C, the result of right-shifting a signed integer is
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* considered implementation-specific. To ensure that the loop
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* terminates even if tenpwr was 1000...000b to begin with, we
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* manually clear the MSB, in case a 1 was shifted in.
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*
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* Because we already truncated tenpwr to +5000...-5000 inside
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* the exponent parsing code, this shouldn't matter; neverthe-
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* less it is the right thing to do here.
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*/
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tenpwr &= (uint32_t) - 1 >> 1;
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}
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/*
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* At this point, the 'mant' array contains the first frac-
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* tional places of a base-2^16 real number in [0.5,1) that
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* when multiplied by 2^twopwr gives X. Or it contains zero
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* of course. We are done.
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*/
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*exponent = twopwr;
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return true;
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}
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/*
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* ---------------------------------------------------------------------------
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* round a mantissa off after i words
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* ---------------------------------------------------------------------------
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*/
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#define ROUND_COLLECT_BITS \
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for (j = i; j < MANT_WORDS; j++) { \
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m = m | mant[j]; \
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}
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#define ROUND_ABS_DOWN \
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for (j = i; j < MANT_WORDS; j++) { \
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mant[j] = 0x0000; \
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}
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#define ROUND_ABS_UP \
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do { \
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++mant[--i]; \
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mant[i] &= 0xFFFF; \
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} while (i > 0 && !mant[i]); \
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return (!i && !mant[i]);
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static bool ieee_round(int sign, uint16_t * mant, int32_t i)
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{
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uint16_t m = 0;
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int32_t j;
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if ((sign == 0x0000) || (sign == 0x8000)) {
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if (rc == FLOAT_RC_NEAR) {
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if (mant[i] & 0x8000) {
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mant[i] &= 0x7FFF;
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ROUND_COLLECT_BITS;
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mant[i] |= 0x8000;
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if (m) {
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ROUND_ABS_UP;
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} else {
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if (mant[i - 1] & 1) {
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ROUND_ABS_UP;
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} else {
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ROUND_ABS_DOWN;
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}
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}
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} else {
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ROUND_ABS_DOWN;
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}
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} else if (((sign == 0x0000) && (rc == FLOAT_RC_DOWN))
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|| ((sign == 0x8000) && (rc == FLOAT_RC_UP))) {
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ROUND_COLLECT_BITS;
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if (m) {
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ROUND_ABS_DOWN;
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}
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} else if (((sign == 0x0000) && (rc == FLOAT_RC_UP))
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|| ((sign == 0x8000) && (rc == FLOAT_RC_DOWN))) {
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ROUND_COLLECT_BITS;
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if (m) {
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ROUND_ABS_UP;
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}
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} else if (rc == FLOAT_RC_ZERO) {
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ROUND_ABS_DOWN;
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} else {
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error(ERR_PANIC, "float_round() can't handle rc=%i", rc);
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}
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} else {
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error(ERR_PANIC, "float_round() can't handle sign=%i", sign);
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}
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return false;
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}
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static int hexval(char c)
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{
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if (c >= '0' && c <= '9')
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return c - '0';
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else if (c >= 'a' && c <= 'f')
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return c - 'a' + 10;
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else
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return c - 'A' + 10;
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}
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static bool ieee_flconvert_hex(const char *string, uint16_t * mant,
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int32_t * exponent)
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{
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static const int log2tbl[16] =
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{ -1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 };
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uint16_t mult[MANT_WORDS + 1], *mp;
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int ms;
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int32_t twopwr;
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int seendot, seendigit;
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unsigned char c;
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twopwr = 0;
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seendot = seendigit = 0;
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ms = 0;
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mp = NULL;
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memset(mult, 0, sizeof mult);
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while ((c = *string++) != '\0') {
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if (c == '.') {
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if (!seendot)
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seendot = true;
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else {
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error(ERR_NONFATAL,
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"too many periods in floating-point constant");
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return false;
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}
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} else if (isxdigit(c)) {
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int v = hexval(c);
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if (!seendigit && v) {
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int l = log2tbl[v];
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seendigit = 1;
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mp = mult;
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ms = 15 - l;
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twopwr = seendot ? twopwr - 4 + l : l - 3;
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}
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if (seendigit) {
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if (ms <= 0) {
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*mp |= v >> -ms;
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mp++;
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if (mp > &mult[MANT_WORDS])
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mp = &mult[MANT_WORDS]; /* Guard slot */
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ms += 16;
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}
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*mp |= v << ms;
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ms -= 4;
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if (!seendot)
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twopwr += 4;
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} else {
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if (seendot)
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twopwr -= 4;
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}
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} else if (c == 'p' || c == 'P') {
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twopwr += atoi(string);
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break;
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} else {
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error(ERR_NONFATAL,
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"floating-point constant: `%c' is invalid character", c);
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return false;
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}
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}
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if (!seendigit) {
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memset(mant, 0, 2 * MANT_WORDS); /* Zero */
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*exponent = 0;
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} else {
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memcpy(mant, mult, 2 * MANT_WORDS);
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*exponent = twopwr;
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}
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return true;
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}
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/*
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* Shift a mantissa to the right by i bits.
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*/
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static void ieee_shr(uint16_t * mant, int i)
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{
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uint16_t n, m;
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int j = 0;
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int sr, sl, offs;
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sr = i%16; sl = 16-sr;
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offs = i/16;
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if (sr == 0) {
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if (offs)
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for (j = MANT_WORDS-1; j >= offs; j--)
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mant[j] = mant[j-offs];
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} else {
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n = mant[MANT_WORDS-1-offs] >> sr;
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for (j = MANT_WORDS-1; j > offs; j--) {
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m = mant[j-offs-1];
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mant[j] = (m << sl) | n;
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n = m >> sr;
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}
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mant[j--] = n;
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}
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while (j >= 0)
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mant[j--] = 0;
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}
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#if defined(__i386__) || defined(__x86_64__)
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#define put(a,b) (*(uint16_t *)(a) = (b))
|
|
#else
|
|
#define put(a,b) (((a)[0] = (b)), ((a)[1] = (b) >> 8))
|
|
#endif
|
|
|
|
/* Set a bit, using *bigendian* bit numbering (0 = MSB) */
|
|
static void set_bit(uint16_t *mant, int bit)
|
|
{
|
|
mant[bit >> 4] |= 1 << (~bit & 15);
|
|
}
|
|
|
|
/* Test a single bit */
|
|
static int test_bit(uint16_t *mant, int bit)
|
|
{
|
|
return (mant[bit >> 4] >> (~bit & 15)) & 1;
|
|
}
|
|
|
|
/* Produce standard IEEE formats, with implicit or explicit integer
|
|
bit; this makes the following assumptions:
|
|
|
|
- the sign bit is the MSB, followed by the exponent,
|
|
followed by the integer bit if present.
|
|
- the sign bit plus exponent fit in 16 bits.
|
|
- the exponent bias is 2^(n-1)-1 for an n-bit exponent */
|
|
|
|
struct ieee_format {
|
|
int words;
|
|
int mantissa; /* Fractional bits in the mantissa */
|
|
int explicit; /* Explicit integer */
|
|
int exponent; /* Bits in the exponent */
|
|
};
|
|
|
|
/*
|
|
* The 16- and 128-bit formats are expected to be in IEEE 754r.
|
|
* AMD SSE5 uses the 16-bit format.
|
|
*
|
|
* The 32- and 64-bit formats are the original IEEE 754 formats.
|
|
*
|
|
* The 80-bit format is x87-specific, but widely used.
|
|
*/
|
|
static const struct ieee_format ieee_16 = { 1, 10, 0, 5 };
|
|
static const struct ieee_format ieee_32 = { 2, 23, 0, 8 };
|
|
static const struct ieee_format ieee_64 = { 4, 52, 0, 11 };
|
|
static const struct ieee_format ieee_80 = { 5, 63, 1, 15 };
|
|
static const struct ieee_format ieee_128 = { 8, 112, 0, 15 };
|
|
|
|
/* Types of values we can generate */
|
|
enum floats {
|
|
FL_ZERO,
|
|
FL_DENORMAL,
|
|
FL_NORMAL,
|
|
FL_INFINITY,
|
|
FL_QNAN,
|
|
FL_SNAN
|
|
};
|
|
|
|
static int to_float(const char *str, int sign, uint8_t * result,
|
|
const struct ieee_format *fmt)
|
|
{
|
|
uint16_t mant[MANT_WORDS], *mp;
|
|
int32_t exponent = 0;
|
|
int32_t expmax = 1 << (fmt->exponent - 1);
|
|
uint16_t one_mask = 0x8000 >> ((fmt->exponent+fmt->explicit) % 16);
|
|
int one_pos = (fmt->exponent+fmt->explicit)/16;
|
|
int i;
|
|
int shift;
|
|
enum floats type;
|
|
bool ok;
|
|
|
|
sign = (sign < 0 ? 0x8000 : 0);
|
|
|
|
if (str[0] == '_') {
|
|
/* Special tokens */
|
|
|
|
switch (str[2]) {
|
|
case 'n': /* __nan__ */
|
|
case 'N':
|
|
case 'q': /* __qnan__ */
|
|
case 'Q':
|
|
type = FL_QNAN;
|
|
break;
|
|
case 's': /* __snan__ */
|
|
case 'S':
|
|
type = FL_SNAN;
|
|
break;
|
|
case 'i': /* __infinity__ */
|
|
case 'I':
|
|
type = FL_INFINITY;
|
|
break;
|
|
default:
|
|
error(ERR_NONFATAL,
|
|
"internal error: unknown FP constant token `%s'\n", str);
|
|
type = FL_QNAN;
|
|
break;
|
|
}
|
|
} else {
|
|
if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
|
|
ok = ieee_flconvert_hex(str + 2, mant, &exponent);
|
|
else
|
|
ok = ieee_flconvert(str, mant, &exponent);
|
|
|
|
if (!ok) {
|
|
type = FL_QNAN;
|
|
} else if (mant[0] & 0x8000) {
|
|
/*
|
|
* Non-zero.
|
|
*/
|
|
exponent--;
|
|
if (exponent >= 2 - expmax && exponent <= expmax) {
|
|
type = FL_NORMAL;
|
|
} else if (!daz && exponent < 2 - expmax &&
|
|
exponent >= 2 - expmax - fmt->mantissa) {
|
|
type = FL_DENORMAL;
|
|
} else if (exponent > 0) {
|
|
error(ERR_NONFATAL,
|
|
"overflow in floating-point constant");
|
|
type = FL_INFINITY;
|
|
} else {
|
|
/* underflow */
|
|
type = FL_ZERO;
|
|
}
|
|
} else {
|
|
/* Zero */
|
|
type = FL_ZERO;
|
|
}
|
|
}
|
|
|
|
switch (type) {
|
|
case FL_ZERO:
|
|
memset(mant, 0, sizeof mant);
|
|
break;
|
|
|
|
case FL_DENORMAL:
|
|
{
|
|
shift = -(exponent + expmax - 2 - fmt->exponent)
|
|
+ fmt->explicit;
|
|
ieee_shr(mant, shift);
|
|
if (ieee_round(sign, mant, fmt->words)
|
|
|| (shift > 0 && test_bit(mant, shift-1))) {
|
|
ieee_shr(mant, 1);
|
|
if (!shift) {
|
|
/* XXX: We shifted into the normal range? */
|
|
/* XXX: This is definitely not right... */
|
|
mant[0] |= 0x8000;
|
|
}
|
|
exponent++; /* UNUSED, WTF? */
|
|
}
|
|
break;
|
|
}
|
|
|
|
case FL_NORMAL:
|
|
exponent += expmax - 1;
|
|
ieee_shr(mant, fmt->exponent+fmt->explicit);
|
|
ieee_round(sign, mant, fmt->words);
|
|
/* did we scale up by one? */
|
|
if (test_bit(mant, fmt->exponent+fmt->explicit-1)) {
|
|
ieee_shr(mant, 1);
|
|
exponent++;
|
|
/* XXX: Handle overflow here */
|
|
}
|
|
|
|
if (!fmt->explicit)
|
|
mant[one_pos] &= ~one_mask; /* remove explicit one */
|
|
mant[0] |= exponent << (15 - fmt->exponent);
|
|
break;
|
|
|
|
case FL_INFINITY:
|
|
case FL_QNAN:
|
|
case FL_SNAN:
|
|
memset(mant, 0, sizeof mant);
|
|
mant[0] = ((1 << fmt->exponent)-1) << (15 - fmt->exponent);
|
|
if (fmt->explicit)
|
|
mant[one_pos] |= one_mask;
|
|
if (type == FL_QNAN)
|
|
set_bit(mant, fmt->exponent+fmt->explicit+1);
|
|
else if (type == FL_SNAN)
|
|
set_bit(mant, fmt->exponent+fmt->explicit+fmt->mantissa);
|
|
break;
|
|
}
|
|
|
|
mant[0] |= sign;
|
|
|
|
for (mp = &mant[fmt->words], i = 0; i < fmt->words; i++) {
|
|
uint16_t m = *--mp;
|
|
put(result, m);
|
|
result += 2;
|
|
}
|
|
|
|
return 1; /* success */
|
|
}
|
|
|
|
int float_const(const char *number, int32_t sign, uint8_t * result,
|
|
int bytes, efunc err)
|
|
{
|
|
error = err;
|
|
|
|
switch (bytes) {
|
|
case 2:
|
|
return to_float(number, sign, result, &ieee_16);
|
|
case 4:
|
|
return to_float(number, sign, result, &ieee_32);
|
|
case 8:
|
|
return to_float(number, sign, result, &ieee_64);
|
|
case 10:
|
|
return to_float(number, sign, result, &ieee_80);
|
|
case 16:
|
|
return to_float(number, sign, result, &ieee_128);
|
|
default:
|
|
error(ERR_PANIC, "strange value %d passed to float_const", bytes);
|
|
return 0;
|
|
}
|
|
}
|