1 /* float.c floating-point constant support for the Netwide Assembler
3 * The Netwide Assembler is copyright (C) 1996 Simon Tatham and
4 * Julian Hall. All rights reserved. The software is
5 * redistributable under the licence given in the file "Licence"
6 * distributed in the NASM archive.
8 * initial version 13/ix/96 by Simon Tatham
28 static bool daz
= false; /* denormals as zero */
29 static enum float_round rc
= FLOAT_RC_NEAR
; /* rounding control */
37 /* 112 bits + 64 bits for accuracy + 16 bits for rounding */
40 /* 52 digits fit in 176 bits because 10^53 > 2^176 > 10^52 */
41 #define MANT_DIGITS 52
43 /* the format and the argument list depend on MANT_WORDS */
44 #define MANT_FMT "%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x"
45 #define MANT_ARG SOME_ARG(mant, 0)
47 #define SOME_ARG(a,i) (a)[(i)+0], (a)[(i)+1], (a)[(i)+2], (a)[(i)+3], \
48 (a)[(i)+4], (a)[(i)+5], (a)[(i)+6], (a)[(i)+7], (a)[(i)+8], \
49 (a)[(i)+9], (a)[(i)+10], (a)[(i)+11]
52 * ---------------------------------------------------------------------------
53 * emit a printf()-like debug message... but only if DEBUG_FLOAT was defined
54 * ---------------------------------------------------------------------------
58 #define dprintf(x) printf x
60 #define dprintf(x) do { } while (0)
64 * ---------------------------------------------------------------------------
66 * ---------------------------------------------------------------------------
68 static int float_multiply(uint16_t * to
, uint16_t * from
)
70 uint32_t temp
[MANT_WORDS
* 2];
74 * guaranteed that top bit of 'from' is set -- so we only have
75 * to worry about _one_ bit shift to the left
77 dprintf(("%s=" MANT_FMT
"\n", "mul1", SOME_ARG(to
, 0)));
78 dprintf(("%s=" MANT_FMT
"\n", "mul2", SOME_ARG(from
, 0)));
80 memset(temp
, 0, sizeof temp
);
82 for (i
= 0; i
< MANT_WORDS
; i
++) {
83 for (j
= 0; j
< MANT_WORDS
; j
++) {
85 n
= (uint32_t) to
[i
] * (uint32_t) from
[j
];
86 temp
[i
+ j
] += n
>> 16;
87 temp
[i
+ j
+ 1] += n
& 0xFFFF;
91 for (i
= MANT_WORDS
* 2; --i
;) {
92 temp
[i
- 1] += temp
[i
] >> 16;
96 dprintf(("%s=" MANT_FMT
"_" MANT_FMT
"\n", "temp", SOME_ARG(temp
, 0),
97 SOME_ARG(temp
, MANT_WORDS
)));
99 if (temp
[0] & 0x8000) {
100 for (i
= 0; i
< MANT_WORDS
; i
++) {
101 to
[i
] = temp
[i
] & 0xFFFF;
103 dprintf(("%s=" MANT_FMT
" (%i)\n", "prod", SOME_ARG(to
, 0), 0));
106 for (i
= 0; i
< MANT_WORDS
; i
++) {
107 to
[i
] = (temp
[i
] << 1) + !!(temp
[i
+ 1] & 0x8000);
109 dprintf(("%s=" MANT_FMT
" (%i)\n", "prod", SOME_ARG(to
, 0), -1));
115 * ---------------------------------------------------------------------------
117 * ---------------------------------------------------------------------------
119 static bool ieee_flconvert(const char *string
, uint16_t * mant
,
122 char digits
[MANT_DIGITS
];
124 uint16_t mult
[MANT_WORDS
], bit
;
126 int32_t tenpwr
, twopwr
;
128 bool started
, seendot
, warned
;
131 started
= seendot
= warned
= false;
132 while (*string
&& *string
!= 'E' && *string
!= 'e') {
133 if (*string
== '.') {
138 "too many periods in floating-point constant");
141 } else if (*string
>= '0' && *string
<= '9') {
142 if (*string
== '0' && !started
) {
148 if (p
< digits
+ sizeof(digits
)) {
149 *p
++ = *string
- '0';
153 "floating-point constant significand contains "
154 "more than %i digits", MANT_DIGITS
);
162 } else if (*string
== '_') {
167 "invalid character in floating-point constant %s: '%c'",
168 "significand", *string
);
176 string
++; /* eat the E */
177 if (*string
== '+') {
179 } else if (*string
== '-') {
184 if (*string
>= '0' && *string
<= '9') {
185 i
= (i
* 10) + (*string
- '0');
188 * To ensure that underflows and overflows are
189 * handled properly we must avoid wraparounds of
190 * the signed integer value that is used to hold
191 * the exponent. Therefore we cap the exponent at
192 * +/-5000, which is slightly more/less than
193 * what's required for normal and denormal numbers
194 * in single, double, and extended precision, but
195 * sufficient to avoid signed integer wraparound.
200 } else if (*string
== '_') {
205 "invalid character in floating-point constant %s: '%c'",
206 "exponent", *string
);
218 * At this point, the memory interval [digits,p) contains a
219 * series of decimal digits zzzzzzz, such that our number X
220 * satisfies X = 0.zzzzzzz * 10^tenpwr.
225 dprintf(("%c", *q
+ '0'));
228 dprintf((" * 10^%i\n", tenpwr
));
231 * Now convert [digits,p) to our internal representation.
234 for (m
= mant
; m
< mant
+ MANT_WORDS
; m
++) {
241 while (m
< mant
+ MANT_WORDS
) {
243 while (p
> q
&& !p
[-1]) {
249 for (r
= p
; r
-- > q
;) {
278 * At this point, the 'mant' array contains the first frac-
279 * tional places of a base-2^16 real number which when mul-
280 * tiplied by 2^twopwr and 5^tenpwr gives X.
282 dprintf(("X = " MANT_FMT
" * 2^%i * 5^%i\n", MANT_ARG
, twopwr
,
286 * Now multiply 'mant' by 5^tenpwr.
288 if (tenpwr
< 0) { /* mult = 5^-1 = 0.2 */
289 for (m
= mult
; m
< mult
+ MANT_WORDS
- 1; m
++) {
292 mult
[MANT_WORDS
- 1] = 0xCCCD;
297 * If tenpwr was 1000...000b, then it becomes 1000...000b. See
298 * the "ANSI C" comment below for more details on that case.
300 * Because we already truncated tenpwr to +5000...-5000 inside
301 * the exponent parsing code, this shouldn't happen though.
303 } else if (tenpwr
> 0) { /* mult = 5^+1 = 5.0 */
305 for (m
= mult
+ 1; m
< mult
+ MANT_WORDS
; m
++) {
313 dprintf(("loop=" MANT_FMT
" * 2^%i * 5^%i (%i)\n", MANT_ARG
,
314 twopwr
, tenpwr
, extratwos
));
316 dprintf(("mant*mult\n"));
317 twopwr
+= extratwos
+ float_multiply(mant
, mult
);
319 dprintf(("mult*mult\n"));
320 extratwos
= extratwos
* 2 + float_multiply(mult
, mult
);
324 * In ANSI C, the result of right-shifting a signed integer is
325 * considered implementation-specific. To ensure that the loop
326 * terminates even if tenpwr was 1000...000b to begin with, we
327 * manually clear the MSB, in case a 1 was shifted in.
329 * Because we already truncated tenpwr to +5000...-5000 inside
330 * the exponent parsing code, this shouldn't matter; neverthe-
331 * less it is the right thing to do here.
333 tenpwr
&= (uint32_t) - 1 >> 1;
337 * At this point, the 'mant' array contains the first frac-
338 * tional places of a base-2^16 real number in [0.5,1) that
339 * when multiplied by 2^twopwr gives X. Or it contains zero
340 * of course. We are done.
347 * ---------------------------------------------------------------------------
348 * round a mantissa off after i words
349 * ---------------------------------------------------------------------------
352 #define ROUND_COLLECT_BITS \
353 for (j = i; j < MANT_WORDS; j++) { \
357 #define ROUND_ABS_DOWN \
358 for (j = i; j < MANT_WORDS; j++) { \
362 #define ROUND_ABS_UP \
366 } while (i > 0 && !mant[i]); \
367 return (!i && !mant[i]);
369 static bool ieee_round(int sign
, uint16_t * mant
, int32_t i
)
373 if ((sign
== 0x0000) || (sign
== 0x8000)) {
374 if (rc
== FLOAT_RC_NEAR
) {
375 if (mant
[i
] & 0x8000) {
382 if (mant
[i
- 1] & 1) {
391 } else if (((sign
== 0x0000) && (rc
== FLOAT_RC_DOWN
))
392 || ((sign
== 0x8000) && (rc
== FLOAT_RC_UP
))) {
397 } else if (((sign
== 0x0000) && (rc
== FLOAT_RC_UP
))
398 || ((sign
== 0x8000) && (rc
== FLOAT_RC_DOWN
))) {
403 } else if (rc
== FLOAT_RC_ZERO
) {
406 error(ERR_PANIC
, "float_round() can't handle rc=%i", rc
);
409 error(ERR_PANIC
, "float_round() can't handle sign=%i", sign
);
414 static int hexval(char c
)
416 if (c
>= '0' && c
<= '9')
418 else if (c
>= 'a' && c
<= 'f')
424 static bool ieee_flconvert_hex(const char *string
, uint16_t * mant
,
427 static const int log2tbl
[16] =
428 { -1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 };
429 uint16_t mult
[MANT_WORDS
+ 1], *mp
;
432 int seendot
, seendigit
;
436 seendot
= seendigit
= 0;
440 memset(mult
, 0, sizeof mult
);
442 while ((c
= *string
++) != '\0') {
448 "too many periods in floating-point constant");
451 } else if (isxdigit(c
)) {
454 if (!seendigit
&& v
) {
461 twopwr
= seendot
? twopwr
- 4 + l
: l
- 3;
468 if (mp
> &mult
[MANT_WORDS
])
469 mp
= &mult
[MANT_WORDS
]; /* Guard slot */
481 } else if (c
== 'p' || c
== 'P') {
482 twopwr
+= atoi(string
);
486 "floating-point constant: `%c' is invalid character", c
);
492 memset(mant
, 0, 2 * MANT_WORDS
); /* Zero */
495 memcpy(mant
, mult
, 2 * MANT_WORDS
);
503 * Shift a mantissa to the right by i bits.
505 static void ieee_shr(uint16_t * mant
, int i
)
511 sr
= i
%16; sl
= 16-sr
;
516 for (j
= MANT_WORDS
-1; j
>= offs
; j
--)
517 mant
[j
] = mant
[j
-offs
];
519 n
= mant
[MANT_WORDS
-1-offs
] >> sr
;
520 for (j
= MANT_WORDS
-1; j
> offs
; j
--) {
522 mant
[j
] = (m
<< sl
) | n
;
531 #if defined(__i386__) || defined(__x86_64__)
532 #define put(a,b) (*(uint16_t *)(a) = (b))
534 #define put(a,b) (((a)[0] = (b)), ((a)[1] = (b) >> 8))
537 /* Set a bit, using *bigendian* bit numbering (0 = MSB) */
538 static void set_bit(uint16_t *mant
, int bit
)
540 mant
[bit
>> 4] |= 1 << (~bit
& 15);
543 /* Test a single bit */
544 static int test_bit(uint16_t *mant
, int bit
)
546 return (mant
[bit
>> 4] >> (~bit
& 15)) & 1;
549 /* Produce standard IEEE formats, with implicit or explicit integer
550 bit; this makes the following assumptions:
552 - the sign bit is the MSB, followed by the exponent,
553 followed by the integer bit if present.
554 - the sign bit plus exponent fit in 16 bits.
555 - the exponent bias is 2^(n-1)-1 for an n-bit exponent */
559 int mantissa
; /* Fractional bits in the mantissa */
560 int explicit; /* Explicit integer */
561 int exponent
; /* Bits in the exponent */
565 * The 16- and 128-bit formats are expected to be in IEEE 754r.
566 * AMD SSE5 uses the 16-bit format.
568 * The 32- and 64-bit formats are the original IEEE 754 formats.
570 * The 80-bit format is x87-specific, but widely used.
572 static const struct ieee_format ieee_16
= { 1, 10, 0, 5 };
573 static const struct ieee_format ieee_32
= { 2, 23, 0, 8 };
574 static const struct ieee_format ieee_64
= { 4, 52, 0, 11 };
575 static const struct ieee_format ieee_80
= { 5, 63, 1, 15 };
576 static const struct ieee_format ieee_128
= { 8, 112, 0, 15 };
578 /* Types of values we can generate */
588 static int to_float(const char *str
, int sign
, uint8_t * result
,
589 const struct ieee_format
*fmt
)
591 uint16_t mant
[MANT_WORDS
], *mp
;
592 int32_t exponent
= 0;
593 int32_t expmax
= 1 << (fmt
->exponent
- 1);
594 uint16_t one_mask
= 0x8000 >> ((fmt
->exponent
+fmt
->explicit) % 16);
595 int one_pos
= (fmt
->exponent
+fmt
->explicit)/16;
601 sign
= (sign
< 0 ? 0x8000 : 0);
607 case 'n': /* __nan__ */
609 case 'q': /* __qnan__ */
613 case 's': /* __snan__ */
617 case 'i': /* __infinity__ */
623 "internal error: unknown FP constant token `%s'\n", str
);
628 if (str
[0] == '0' && (str
[1] == 'x' || str
[1] == 'X'))
629 ok
= ieee_flconvert_hex(str
+ 2, mant
, &exponent
);
631 ok
= ieee_flconvert(str
, mant
, &exponent
);
635 } else if (mant
[0] & 0x8000) {
640 if (exponent
>= 2 - expmax
&& exponent
<= expmax
) {
642 } else if (!daz
&& exponent
< 2 - expmax
&&
643 exponent
>= 2 - expmax
- fmt
->mantissa
) {
645 } else if (exponent
> 0) {
647 "overflow in floating-point constant");
661 memset(mant
, 0, sizeof mant
);
666 shift
= -(exponent
+ expmax
- 2 - fmt
->exponent
)
668 ieee_shr(mant
, shift
);
669 if (ieee_round(sign
, mant
, fmt
->words
)
670 || (shift
> 0 && test_bit(mant
, shift
-1))) {
673 /* XXX: We shifted into the normal range? */
674 /* XXX: This is definitely not right... */
677 exponent
++; /* UNUSED, WTF? */
683 exponent
+= expmax
- 1;
684 ieee_shr(mant
, fmt
->exponent
+fmt
->explicit);
685 ieee_round(sign
, mant
, fmt
->words
);
686 /* did we scale up by one? */
687 if (test_bit(mant
, fmt
->exponent
+fmt
->explicit-1)) {
690 /* XXX: Handle overflow here */
694 mant
[one_pos
] &= ~one_mask
; /* remove explicit one */
695 mant
[0] |= exponent
<< (15 - fmt
->exponent
);
701 memset(mant
, 0, sizeof mant
);
702 mant
[0] = ((1 << fmt
->exponent
)-1) << (15 - fmt
->exponent
);
704 mant
[one_pos
] |= one_mask
;
706 set_bit(mant
, fmt
->exponent
+fmt
->explicit+1);
707 else if (type
== FL_SNAN
)
708 set_bit(mant
, fmt
->exponent
+fmt
->explicit+fmt
->mantissa
);
714 for (mp
= &mant
[fmt
->words
], i
= 0; i
< fmt
->words
; i
++) {
720 return 1; /* success */
723 int float_const(const char *number
, int32_t sign
, uint8_t * result
,
724 int bytes
, efunc err
)
730 return to_float(number
, sign
, result
, &ieee_16
);
732 return to_float(number
, sign
, result
, &ieee_32
);
734 return to_float(number
, sign
, result
, &ieee_64
);
736 return to_float(number
, sign
, result
, &ieee_80
);
738 return to_float(number
, sign
, result
, &ieee_128
);
740 error(ERR_PANIC
, "strange value %d passed to float_const", bytes
);