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 license given in the file "LICENSE"
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 /* "A limb is like a digit but bigger */
38 typedef uint32_t fp_limb
;
39 typedef uint64_t fp_2limb
;
42 #define LIMB_BYTES (LIMB_BITS/8)
43 #define LIMB_TOP_BIT ((fp_limb)1 << (LIMB_BITS-1))
44 #define LIMB_MASK ((fp_limb)(~0))
45 #define LIMB_ALL_BYTES ((fp_limb)0x01010101)
46 #define LIMB_BYTE(x) ((x)*LIMB_ALL_BYTES)
48 /* 112 bits + 64 bits for accuracy + 16 bits for rounding */
51 /* 52 digits fit in 176 bits because 10^53 > 2^176 > 10^52 */
52 #define MANT_DIGITS 52
54 /* the format and the argument list depend on MANT_LIMBS */
55 #define MANT_FMT "%08x_%08x_%08x_%08x_%08x_%08x"
56 #define MANT_ARG SOME_ARG(mant, 0)
58 #define SOME_ARG(a,i) (a)[(i)+0], (a)[(i)+1], (a)[(i)+2], (a)[(i)+3], \
59 (a)[(i)+4], (a)[(i)+5]
62 * ---------------------------------------------------------------------------
63 * emit a printf()-like debug message... but only if DEBUG_FLOAT was defined
64 * ---------------------------------------------------------------------------
68 #define dprintf(x) printf x
70 #define dprintf(x) do { } while (0)
74 * ---------------------------------------------------------------------------
76 * ---------------------------------------------------------------------------
78 static int float_multiply(fp_limb
*to
, fp_limb
*from
)
80 fp_2limb temp
[MANT_LIMBS
* 2];
84 * guaranteed that top bit of 'from' is set -- so we only have
85 * to worry about _one_ bit shift to the left
87 dprintf(("%s=" MANT_FMT
"\n", "mul1", SOME_ARG(to
, 0)));
88 dprintf(("%s=" MANT_FMT
"\n", "mul2", SOME_ARG(from
, 0)));
90 memset(temp
, 0, sizeof temp
);
92 for (i
= 0; i
< MANT_LIMBS
; i
++) {
93 for (j
= 0; j
< MANT_LIMBS
; j
++) {
95 n
= (fp_2limb
) to
[i
] * (fp_2limb
) from
[j
];
96 temp
[i
+ j
] += n
>> LIMB_BITS
;
97 temp
[i
+ j
+ 1] += (fp_limb
)n
;
101 for (i
= MANT_LIMBS
* 2; --i
;) {
102 temp
[i
- 1] += temp
[i
] >> LIMB_BITS
;
103 temp
[i
] &= LIMB_MASK
;
106 dprintf(("%s=" MANT_FMT
"_" MANT_FMT
"\n", "temp", SOME_ARG(temp
, 0),
107 SOME_ARG(temp
, MANT_LIMBS
)));
109 if (temp
[0] & LIMB_TOP_BIT
) {
110 for (i
= 0; i
< MANT_LIMBS
; i
++) {
111 to
[i
] = temp
[i
] & LIMB_MASK
;
113 dprintf(("%s=" MANT_FMT
" (%i)\n", "prod", SOME_ARG(to
, 0), 0));
116 for (i
= 0; i
< MANT_LIMBS
; i
++) {
117 to
[i
] = (temp
[i
] << 1) + !!(temp
[i
+ 1] & LIMB_TOP_BIT
);
119 dprintf(("%s=" MANT_FMT
" (%i)\n", "prod", SOME_ARG(to
, 0), -1));
125 * ---------------------------------------------------------------------------
126 * read an exponent; returns INT32_MAX on error
127 * ---------------------------------------------------------------------------
129 static int32_t read_exponent(const char *string
, int32_t max
)
134 if (*string
== '+') {
136 } else if (*string
== '-') {
141 if (*string
>= '0' && *string
<= '9') {
142 i
= (i
* 10) + (*string
- '0');
145 * To ensure that underflows and overflows are
146 * handled properly we must avoid wraparounds of
147 * the signed integer value that is used to hold
148 * the exponent. Therefore we cap the exponent at
149 * +/-5000, which is slightly more/less than
150 * what's required for normal and denormal numbers
151 * in single, double, and extended precision, but
152 * sufficient to avoid signed integer wraparound.
156 } else if (*string
== '_') {
159 error(ERR_NONFATAL
|ERR_PASS1
,
160 "invalid character in floating-point constant %s: '%c'",
161 "exponent", *string
);
171 * ---------------------------------------------------------------------------
173 * ---------------------------------------------------------------------------
175 static bool ieee_flconvert(const char *string
, fp_limb
*mant
,
178 char digits
[MANT_DIGITS
];
180 fp_limb mult
[MANT_LIMBS
], bit
;
182 int32_t tenpwr
, twopwr
;
184 bool started
, seendot
, warned
;
189 started
= seendot
= false;
191 while (*string
&& *string
!= 'E' && *string
!= 'e') {
192 if (*string
== '.') {
196 error(ERR_NONFATAL
|ERR_PASS1
,
197 "too many periods in floating-point constant");
200 } else if (*string
>= '0' && *string
<= '9') {
201 if (*string
== '0' && !started
) {
207 if (p
< digits
+ sizeof(digits
)) {
208 *p
++ = *string
- '0';
211 error(ERR_WARNING
|ERR_WARN_FL_TOOLONG
|ERR_PASS1
,
212 "floating-point constant significand contains "
213 "more than %i digits", MANT_DIGITS
);
221 } else if (*string
== '_') {
224 error(ERR_NONFATAL
|ERR_PASS1
,
225 "invalid character in floating-point constant %s: '%c'",
226 "significand", *string
);
235 string
++; /* eat the E */
236 e
= read_exponent(string
, 5000);
243 * At this point, the memory interval [digits,p) contains a
244 * series of decimal digits zzzzzzz, such that our number X
245 * satisfies X = 0.zzzzzzz * 10^tenpwr.
250 dprintf(("%c", *q
+ '0'));
253 dprintf((" * 10^%i\n", tenpwr
));
256 * Now convert [digits,p) to our internal representation.
259 for (m
= mant
; m
< mant
+ MANT_LIMBS
; m
++) {
266 while (m
< mant
+ MANT_LIMBS
) {
268 while (p
> q
&& !p
[-1]) {
274 for (r
= p
; r
-- > q
;) {
303 * At this point, the 'mant' array contains the first frac-
304 * tional places of a base-2^16 real number which when mul-
305 * tiplied by 2^twopwr and 5^tenpwr gives X.
307 dprintf(("X = " MANT_FMT
" * 2^%i * 5^%i\n", MANT_ARG
, twopwr
,
311 * Now multiply 'mant' by 5^tenpwr.
313 if (tenpwr
< 0) { /* mult = 5^-1 = 0.2 */
314 for (m
= mult
; m
< mult
+ MANT_LIMBS
- 1; m
++) {
315 *m
= LIMB_BYTE(0xcc);
317 mult
[MANT_LIMBS
- 1] = LIMB_BYTE(0xcc)+1;
322 * If tenpwr was 1000...000b, then it becomes 1000...000b. See
323 * the "ANSI C" comment below for more details on that case.
325 * Because we already truncated tenpwr to +5000...-5000 inside
326 * the exponent parsing code, this shouldn't happen though.
328 } else if (tenpwr
> 0) { /* mult = 5^+1 = 5.0 */
329 mult
[0] = (fp_limb
)5 << (LIMB_BITS
-3); /* 0xA000... */
330 for (m
= mult
+ 1; m
< mult
+ MANT_LIMBS
; m
++) {
338 dprintf(("loop=" MANT_FMT
" * 2^%i * 5^%i (%i)\n", MANT_ARG
,
339 twopwr
, tenpwr
, extratwos
));
341 dprintf(("mant*mult\n"));
342 twopwr
+= extratwos
+ float_multiply(mant
, mult
);
344 dprintf(("mult*mult\n"));
345 extratwos
= extratwos
* 2 + float_multiply(mult
, mult
);
349 * In ANSI C, the result of right-shifting a signed integer is
350 * considered implementation-specific. To ensure that the loop
351 * terminates even if tenpwr was 1000...000b to begin with, we
352 * manually clear the MSB, in case a 1 was shifted in.
354 * Because we already truncated tenpwr to +5000...-5000 inside
355 * the exponent parsing code, this shouldn't matter; neverthe-
356 * less it is the right thing to do here.
358 tenpwr
&= (uint32_t) - 1 >> 1;
362 * At this point, the 'mant' array contains the first frac-
363 * tional places of a base-2^16 real number in [0.5,1) that
364 * when multiplied by 2^twopwr gives X. Or it contains zero
365 * of course. We are done.
372 * ---------------------------------------------------------------------------
373 * operations of specific bits
374 * ---------------------------------------------------------------------------
377 /* Set a bit, using *bigendian* bit numbering (0 = MSB) */
378 static void set_bit(fp_limb
*mant
, int bit
)
380 mant
[bit
/LIMB_BITS
] |= LIMB_TOP_BIT
>> (bit
& (LIMB_BITS
-1));
383 /* Test a single bit */
384 static int test_bit(const fp_limb
*mant
, int bit
)
386 return (mant
[bit
/LIMB_BITS
] >> (~bit
& (LIMB_BITS
-1))) & 1;
389 /* Report if the mantissa value is all zero */
390 static bool is_zero(const fp_limb
*mant
)
394 for (i
= 0; i
< MANT_LIMBS
; i
++)
402 * ---------------------------------------------------------------------------
403 * round a mantissa off after i words
404 * ---------------------------------------------------------------------------
407 #define ROUND_COLLECT_BITS \
409 m = mant[i] & (2*bit-1); \
410 for (j = i+1; j < MANT_LIMBS; j++) \
414 #define ROUND_ABS_DOWN \
416 mant[i] &= ~(bit-1); \
417 for (j = i+1; j < MANT_LIMBS; j++) \
422 #define ROUND_ABS_UP \
424 mant[i] = (mant[i] & ~(bit-1)) + bit; \
425 for (j = i+1; j < MANT_LIMBS; j++) \
427 while (i > 0 && !mant[i]) \
432 static bool ieee_round(bool minus
, fp_limb
*mant
, int bits
)
436 int i
= bits
/ LIMB_BITS
;
437 int p
= bits
% LIMB_BITS
;
438 fp_limb bit
= LIMB_TOP_BIT
>> p
;
440 if (rc
== FLOAT_RC_NEAR
) {
448 if (test_bit(mant
, bits
-1)) {
457 } else if (rc
== FLOAT_RC_ZERO
||
458 rc
== (minus
? FLOAT_RC_UP
: FLOAT_RC_DOWN
)) {
461 /* rc == (minus ? FLOAT_RC_DOWN : FLOAT_RC_UP) */
462 /* Round toward +/- infinity */
473 /* Returns a value >= 16 if not a valid hex digit */
474 static unsigned int hexval(char c
)
476 unsigned int v
= (unsigned char) c
;
478 if (v
>= '0' && v
<= '9')
481 return (v
|0x20) - 'a' + 10;
484 /* Handle floating-point numbers with radix 2^bits and binary exponent */
485 static bool ieee_flconvert_bin(const char *string
, int bits
,
486 fp_limb
*mant
, int32_t *exponent
)
488 static const int log2tbl
[16] =
489 { -1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 };
490 fp_limb mult
[MANT_LIMBS
+ 1], *mp
;
493 bool seendot
, seendigit
;
495 const int radix
= 1 << bits
;
499 seendot
= seendigit
= false;
503 memset(mult
, 0, sizeof mult
);
505 while ((c
= *string
++) != '\0') {
510 error(ERR_NONFATAL
|ERR_PASS1
,
511 "too many periods in floating-point constant");
514 } else if ((v
= hexval(c
)) < (unsigned int)radix
) {
515 if (!seendigit
&& v
) {
520 ms
= (LIMB_BITS
-1)-l
;
522 twopwr
= seendot
? twopwr
-bits
+l
: l
+1-bits
;
529 if (mp
> &mult
[MANT_LIMBS
])
530 mp
= &mult
[MANT_LIMBS
]; /* Guard slot */
542 } else if (c
== 'p' || c
== 'P') {
544 e
= read_exponent(string
, 20000);
549 } else if (c
== '_') {
552 error(ERR_NONFATAL
|ERR_PASS1
,
553 "floating-point constant: `%c' is invalid character", c
);
559 memset(mant
, 0, MANT_LIMBS
*sizeof(fp_limb
)); /* Zero */
562 memcpy(mant
, mult
, MANT_LIMBS
*sizeof(fp_limb
));
570 * Shift a mantissa to the right by i bits.
572 static void ieee_shr(fp_limb
*mant
, int i
)
578 sr
= i
% LIMB_BITS
; sl
= LIMB_BITS
-sr
;
583 for (j
= MANT_LIMBS
-1; j
>= offs
; j
--)
584 mant
[j
] = mant
[j
-offs
];
586 n
= mant
[MANT_LIMBS
-1-offs
] >> sr
;
587 for (j
= MANT_LIMBS
-1; j
> offs
; j
--) {
589 mant
[j
] = (m
<< sl
) | n
;
598 /* Produce standard IEEE formats, with implicit or explicit integer
599 bit; this makes the following assumptions:
601 - the sign bit is the MSB, followed by the exponent,
602 followed by the integer bit if present.
603 - the sign bit plus exponent fit in 16 bits.
604 - the exponent bias is 2^(n-1)-1 for an n-bit exponent */
608 int mantissa
; /* Fractional bits in the mantissa */
609 int explicit; /* Explicit integer */
610 int exponent
; /* Bits in the exponent */
614 * The 16- and 128-bit formats are expected to be in IEEE 754r.
615 * AMD SSE5 uses the 16-bit format.
617 * The 32- and 64-bit formats are the original IEEE 754 formats.
619 * The 80-bit format is x87-specific, but widely used.
621 * The 8-bit format appears to be the consensus 8-bit floating-point
622 * format. It is apparently used in graphics applications.
624 static const struct ieee_format ieee_8
= { 1, 3, 0, 4 };
625 static const struct ieee_format ieee_16
= { 2, 10, 0, 5 };
626 static const struct ieee_format ieee_32
= { 4, 23, 0, 8 };
627 static const struct ieee_format ieee_64
= { 8, 52, 0, 11 };
628 static const struct ieee_format ieee_80
= { 10, 63, 1, 15 };
629 static const struct ieee_format ieee_128
= { 16, 112, 0, 15 };
631 /* Types of values we can generate */
641 static int to_packed_bcd(const char *str
, const char *p
,
642 int s
, uint8_t *result
,
643 const struct ieee_format
*fmt
)
649 if (fmt
!= &ieee_80
) {
650 error(ERR_NONFATAL
|ERR_PASS1
,
651 "packed BCD requires an 80-bit format");
657 if (c
>= '0' && c
<= '9') {
660 error(ERR_WARNING
|ERR_PASS1
,
661 "packed BCD truncated to 18 digits");
666 *result
++ = tv
+ ((c
-'0') << 4);
670 } else if (c
== '_') {
673 error(ERR_NONFATAL
|ERR_PASS1
,
674 "invalid character `%c' in packed BCD constant", c
);
687 *result
= (s
< 0) ? 0x80 : 0;
689 return 1; /* success */
692 static int to_float(const char *str
, int s
, uint8_t *result
,
693 const struct ieee_format
*fmt
)
695 fp_limb mant
[MANT_LIMBS
];
696 int32_t exponent
= 0;
697 const int32_t expmax
= 1 << (fmt
->exponent
- 1);
698 fp_limb one_mask
= LIMB_TOP_BIT
>>
699 ((fmt
->exponent
+fmt
->explicit) % LIMB_BITS
);
700 const int one_pos
= (fmt
->exponent
+fmt
->explicit)/LIMB_BITS
;
705 const bool minus
= s
< 0;
706 const int bits
= fmt
->bytes
* 8;
711 "internal errror: empty string passed to float_const");
715 strend
= strchr(str
, '\0');
716 if (strend
[-1] == 'P' || strend
[-1] == 'p')
717 return to_packed_bcd(str
, strend
-2, s
, result
, fmt
);
723 case 'n': /* __nan__ */
725 case 'q': /* __qnan__ */
729 case 's': /* __snan__ */
733 case 'i': /* __infinity__ */
738 error(ERR_NONFATAL
|ERR_PASS1
,
739 "internal error: unknown FP constant token `%s'\n", str
);
748 ok
= ieee_flconvert_bin(str
+2, 4, mant
, &exponent
);
752 ok
= ieee_flconvert_bin(str
+2, 3, mant
, &exponent
);
756 ok
= ieee_flconvert_bin(str
+2, 1, mant
, &exponent
);
760 ok
= ieee_flconvert(str
+2, mant
, &exponent
);
763 return to_packed_bcd(str
+2, strend
-1, s
, result
, fmt
);
765 /* Leading zero was just a zero? */
766 ok
= ieee_flconvert(str
, mant
, &exponent
);
769 } else if (str
[0] == '$') {
770 ok
= ieee_flconvert_bin(str
+1, 4, mant
, &exponent
);
772 ok
= ieee_flconvert(str
, mant
, &exponent
);
777 } else if (mant
[0] & LIMB_TOP_BIT
) {
782 if (exponent
>= 2 - expmax
&& exponent
<= expmax
) {
784 } else if (exponent
> 0) {
786 error(ERR_WARNING
|ERR_WARN_FL_OVERFLOW
|ERR_PASS1
,
787 "overflow in floating-point constant");
790 /* underflow or denormal; the denormal code handles
803 memset(mant
, 0, sizeof mant
);
808 shift
= -(exponent
+ expmax
- 2 - fmt
->exponent
)
810 ieee_shr(mant
, shift
);
811 ieee_round(minus
, mant
, bits
);
812 if (mant
[one_pos
] & one_mask
) {
813 /* One's position is set, we rounded up into normal range */
816 mant
[one_pos
] &= ~one_mask
; /* remove explicit one */
817 mant
[0] |= exponent
<< (LIMB_BITS
-1 - fmt
->exponent
);
819 if (daz
|| is_zero(mant
)) {
820 /* Flush denormals to zero */
821 error(ERR_WARNING
|ERR_WARN_FL_UNDERFLOW
|ERR_PASS1
,
822 "underflow in floating-point constant");
825 error(ERR_WARNING
|ERR_WARN_FL_DENORM
|ERR_PASS1
,
826 "denormal floating-point constant");
833 exponent
+= expmax
- 1;
834 ieee_shr(mant
, fmt
->exponent
+fmt
->explicit);
835 ieee_round(minus
, mant
, bits
);
836 /* did we scale up by one? */
837 if (test_bit(mant
, fmt
->exponent
+fmt
->explicit-1)) {
840 if (exponent
>= (expmax
<< 1)-1) {
841 error(ERR_WARNING
|ERR_WARN_FL_OVERFLOW
|ERR_PASS1
,
842 "overflow in floating-point constant");
849 mant
[one_pos
] &= ~one_mask
; /* remove explicit one */
850 mant
[0] |= exponent
<< (LIMB_BITS
-1 - fmt
->exponent
);
857 memset(mant
, 0, sizeof mant
);
858 mant
[0] = (((fp_limb
)1 << fmt
->exponent
)-1)
859 << (LIMB_BITS
-1 - fmt
->exponent
);
861 mant
[one_pos
] |= one_mask
;
863 set_bit(mant
, fmt
->exponent
+fmt
->explicit+1);
864 else if (type
== FL_SNAN
)
865 set_bit(mant
, fmt
->exponent
+fmt
->explicit+fmt
->mantissa
);
869 mant
[0] |= minus
? LIMB_TOP_BIT
: 0;
871 for (i
= fmt
->bytes
- 1; i
>= 0; i
--)
872 *result
++ = mant
[i
/LIMB_BYTES
] >> (((LIMB_BYTES
-1)-(i
%LIMB_BYTES
))*8);
874 return 1; /* success */
877 int float_const(const char *number
, int sign
, uint8_t *result
,
878 int bytes
, efunc err
)
884 return to_float(number
, sign
, result
, &ieee_8
);
886 return to_float(number
, sign
, result
, &ieee_16
);
888 return to_float(number
, sign
, result
, &ieee_32
);
890 return to_float(number
, sign
, result
, &ieee_64
);
892 return to_float(number
, sign
, result
, &ieee_80
);
894 return to_float(number
, sign
, result
, &ieee_128
);
896 error(ERR_PANIC
, "strange value %d passed to float_const", bytes
);
901 /* Set floating-point options */
902 int float_option(const char *option
)
904 if (!nasm_stricmp(option
, "daz")) {
907 } else if (!nasm_stricmp(option
, "nodaz")) {
910 } else if (!nasm_stricmp(option
, "near")) {
913 } else if (!nasm_stricmp(option
, "down")) {
916 } else if (!nasm_stricmp(option
, "up")) {
919 } else if (!nasm_stricmp(option
, "zero")) {
922 } else if (!nasm_stricmp(option
, "default")) {
927 return -1; /* Unknown option */