2 * Copyright (C) 1995-2008 University of Karlsruhe. All right reserved.
4 * This file is part of libFirm.
6 * This file may be distributed and/or modified under the terms of the
7 * GNU General Public License version 2 as published by the Free Software
8 * Foundation and appearing in the file LICENSE.GPL included in the
9 * packaging of this file.
11 * Licensees holding valid libFirm Professional Edition licenses may use
12 * this file in accordance with the libFirm Commercial License.
13 * Agreement provided with the Software.
15 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
16 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * @brief tarval floating point calculations
24 * @author Mathias Heil
33 #include <math.h> /* need isnan() and isinf() (will be changed)*/
34 /* undef some reused constants defined by math.h */
39 #ifdef HAVE_INTTYPES_H
40 # include <inttypes.h>
49 /** The number of extra precision rounding bits */
50 #define ROUNDING_BITS 2
52 typedef uint32_t UINT32;
54 #ifdef HAVE_LONG_DOUBLE
55 #ifdef WORDS_BIGENDIAN
62 volatile long double d;
71 volatile long double d;
75 #ifdef WORDS_BIGENDIAN
94 #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
96 /* our floating point value */
98 ieee_descriptor_t desc;
100 char value[1]; /* exp[value_size] + mant[value_size] */
103 #define _exp(a) &((a)->value[0])
104 #define _mant(a) &((a)->value[value_size])
106 #define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
107 #define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res))
108 #define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res))
112 # define DEBUGPRINTF(x) printf x
114 # define DEBUGPRINTF(x) ((void)0)
117 #ifdef FLTCALC_TRACE_CALC
118 # define TRACEPRINTF(x) printf x
120 # define TRACEPRINTF(x) ((void)0)
123 /** The immediate precision. */
124 static unsigned immediate_prec = 0;
126 /** A temporal buffer. */
127 static fp_value *calc_buffer = NULL;
129 /** Current rounding mode.*/
130 static fc_rounding_mode_t rounding_mode;
132 static int calc_buffer_size;
133 static int value_size;
134 static int max_precision;
137 static int fc_exact = 1;
140 static void fail_char(const char *str, unsigned int len, int pos) {
142 printf("ERROR: Unexpected character '%c'\n", *(str + pos));
144 printf("ERROR: Unexpected end of string\n");
145 while (len-- && *str) printf("%c", *str++); printf("\n");
146 while (pos--) printf(" "); printf("^\n");
147 /* the front end has to to check constant strings */
152 /** pack machine-like */
153 static void *pack(const fp_value *int_float, void *packed) {
156 fp_value *val_buffer;
159 temp = alloca(value_size);
160 shift_val = alloca(value_size);
162 switch ((value_class_t)int_float->desc.clss) {
164 val_buffer = alloca(calc_buffer_size);
165 fc_get_qnan(&int_float->desc, val_buffer);
166 int_float = val_buffer;
170 val_buffer = alloca(calc_buffer_size);
171 fc_get_plusinf(&int_float->desc, val_buffer);
172 val_buffer->sign = int_float->sign;
173 int_float = val_buffer;
179 assert(int_float->desc.explicit_one <= 1);
181 /* pack sign: move it to the left after exponent AND mantissa */
182 sc_val_from_ulong(int_float->sign, temp);
184 pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
185 sc_val_from_ulong(pos, NULL);
186 _shift_left(temp, sc_get_buffer(), packed);
188 /* pack exponent: move it to the left after mantissa */
189 pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
190 sc_val_from_ulong(pos, shift_val);
191 _shift_left(_exp(int_float), shift_val, temp);
193 /* combine sign|exponent */
194 sc_or(temp, packed, packed);
196 /* extract mantissa */
197 /* remove rounding bits */
198 sc_val_from_ulong(ROUNDING_BITS, shift_val);
199 _shift_right(_mant(int_float), shift_val, temp);
201 /* remove leading 1 (or 0 if denormalized) */
202 sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */
203 sc_and(temp, shift_val, temp);
205 /* combine sign|exponent|mantissa */
206 sc_or(temp, packed, packed);
212 * Normalize a fp_value.
214 * @return non-zero if result is exact
216 static int normalize(const fp_value *in_val, fp_value *out_val, int sticky) {
219 char lsb, guard, round, round_dir = 0;
220 char *temp = alloca(value_size);
222 /* save rounding bits at the end */
223 hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
225 if (in_val != out_val) {
226 out_val->sign = in_val->sign;
227 memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc));
230 out_val->desc.clss = NORMAL;
232 /* mantissa all zeros, so zero exponent (because of explicit one) */
233 if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) {
234 sc_val_from_ulong(0, _exp(out_val));
238 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
241 sc_val_from_ulong(-hsb-1, temp);
243 _shift_right(_mant(in_val), temp, _mant(out_val));
245 /* remember if some bits were shifted away */
246 if (sc_had_carry()) {
250 sc_add(_exp(in_val), temp, _exp(out_val));
251 } else if (hsb > -1) {
253 sc_val_from_ulong(hsb+1, temp);
255 _shift_left(_mant(in_val), temp, _mant(out_val));
257 sc_sub(_exp(in_val), temp, _exp(out_val));
260 /* check for exponent underflow */
261 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
262 DEBUGPRINTF(("Exponent underflow!\n"));
263 /* exponent underflow */
264 /* shift the mantissa right to have a zero exponent */
265 sc_val_from_ulong(1, temp);
266 sc_sub(temp, _exp(out_val), NULL);
268 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
269 if (sc_had_carry()) {
273 /* denormalized means exponent of zero */
274 sc_val_from_ulong(0, _exp(out_val));
276 out_val->desc.clss = SUBNORMAL;
279 /* perform rounding by adding a value that clears the guard bit and the round bit
280 * and either causes a carry to round up or not */
281 /* get the last 3 bits of the value */
282 lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
283 guard = (lsb&0x2)>>1;
286 switch (rounding_mode) {
288 /* round to nearest representable value, if in doubt choose the version
290 round_dir = guard && (sticky || round || lsb>>2);
293 /* if positive: round to one if the exact value is bigger, else to zero */
294 round_dir = (!out_val->sign && (guard || round || sticky));
297 /* if negative: round to one if the exact value is bigger, else to zero */
298 round_dir = (out_val->sign && (guard || round || sticky));
301 /* always round to 0 (chopping mode) */
305 DEBUGPRINTF(("Rounding (s%d, l%d, g%d, r%d, s%d) %s\n", out_val->sign, lsb>>2, guard, round, sticky, (round_dir)?"up":"down"));
307 if (round_dir == 1) {
308 guard = (round^guard)<<1;
309 lsb = !(round || guard)<<2 | guard | round;
311 lsb = -((guard<<1) | round);
314 /* add the rounded value */
316 sc_val_from_long(lsb, temp);
317 sc_add(_mant(out_val), temp, _mant(out_val));
321 /* could have rounded down to zero */
322 if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL))
323 out_val->desc.clss = ZERO;
325 /* check for rounding overflow */
326 hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
327 if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) {
328 sc_val_from_ulong(1, temp);
329 _shift_right(_mant(out_val), temp, _mant(out_val));
330 if (exact && sc_had_carry())
332 sc_add(_exp(out_val), temp, _exp(out_val));
333 } else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) {
334 /* overflow caused the mantissa to be normal again,
335 * so adapt the exponent accordingly */
336 sc_val_from_ulong(1, temp);
337 sc_add(_exp(out_val), temp, _exp(out_val));
339 out_val->desc.clss = NORMAL;
341 /* no further rounding is needed, because rounding overflow means
342 * the carry of the original rounding was propagated all the way
343 * up to the bit left of the radix point. This implies the bits
344 * to the right are all zeros (rounding is +1) */
346 /* check for exponent overflow */
347 sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp);
348 if (sc_comp(_exp(out_val), temp) != -1) {
349 DEBUGPRINTF(("Exponent overflow!\n"));
350 /* exponent overflow, reaction depends on rounding method:
352 * mode | sign of value | result
353 *--------------------------------------------------------------
354 * TO_NEAREST | + | +inf
356 *--------------------------------------------------------------
357 * TO_POSITIVE | + | +inf
358 * | - | smallest representable value
359 *--------------------------------------------------------------
360 * TO_NEAGTIVE | + | largest representable value
362 *--------------------------------------------------------------
363 * TO_ZERO | + | largest representable value
364 * | - | smallest representable value
365 *--------------------------------------------------------------*/
366 if (out_val->sign == 0) {
367 /* value is positive */
368 switch (rounding_mode) {
371 out_val->desc.clss = INF;
376 fc_get_max(&out_val->desc, out_val);
379 /* value is negative */
380 switch (rounding_mode) {
383 out_val->desc.clss = INF;
388 fc_get_min(&out_val->desc, out_val);
396 * Operations involving NaN's must return NaN.
397 * They are NOT exact.
399 #define handle_NAN(a, b, result) \
401 if (a->desc.clss == NAN) { \
402 if (a != result) memcpy(result, a, calc_buffer_size); \
406 if (b->desc.clss == NAN) { \
407 if (b != result) memcpy(result, b, calc_buffer_size); \
415 * calculate a + b, where a is the value with the bigger exponent
417 static void _fadd(const fp_value *a, const fp_value *b, fp_value *result) {
426 handle_NAN(a, b, result);
428 /* make sure result has a descriptor */
429 if (result != a && result != b)
430 result->desc = a->desc;
432 /* determine if this is an addition or subtraction */
433 sign = a->sign ^ b->sign;
435 /* produce NaN on inf - inf */
436 if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) {
438 fc_get_qnan(&a->desc, result);
442 temp = alloca(value_size);
443 exp_diff = alloca(value_size);
445 /* get exponent difference */
446 sc_sub(_exp(a), _exp(b), exp_diff);
448 /* initially set sign to be the sign of a, special treatment of subtraction
449 * when exponents are equal is required though.
450 * Also special care about the sign is needed when the mantissas are equal
452 if (sign && sc_val_to_long(exp_diff) == 0) {
453 switch (sc_comp(_mant(a), _mant(b))) {
455 res_sign = a->sign; /* abs(a) is bigger and a is negative */
458 res_sign = (rounding_mode == FC_TONEGATIVE);
461 res_sign = b->sign; /* abs(b) is bigger and b is negative */
464 /* can't be reached */
471 result->sign = res_sign;
473 /* sign has been taken care of, check for special cases */
474 if (a->desc.clss == ZERO || b->desc.clss == INF) {
476 memcpy(result, b, calc_buffer_size);
477 fc_exact = b->desc.clss == NORMAL;
478 result->sign = res_sign;
481 if (b->desc.clss == ZERO || a->desc.clss == INF) {
483 memcpy(result, a, calc_buffer_size);
484 fc_exact = a->desc.clss == NORMAL;
485 result->sign = res_sign;
489 /* shift the smaller value to the right to align the radix point */
490 /* subnormals have their radix point shifted to the right,
491 * take care of this first */
492 if ((b->desc.clss == SUBNORMAL) && (a->desc.clss != SUBNORMAL)) {
493 sc_val_from_ulong(1, temp);
494 sc_sub(exp_diff, temp, exp_diff);
497 _shift_right(_mant(b), exp_diff, temp);
498 sticky = sc_had_carry();
501 if (sticky && sign) {
502 /* if subtracting a little more than the represented value or adding a little
503 * more than the represented value to a negative value this, in addition to the
504 * still set sticky bit, takes account of the 'little more' */
505 char *temp1 = alloca(calc_buffer_size);
506 sc_val_from_ulong(1, temp1);
507 sc_add(temp, temp1, temp);
511 if (sc_comp(_mant(a), temp) == -1)
512 sc_sub(temp, _mant(a), _mant(result));
514 sc_sub(_mant(a), temp, _mant(result));
516 sc_add(_mant(a), temp, _mant(result));
519 /* _normalize expects a 'normal' radix point, adding two subnormals
520 * results in a subnormal radix point -> shifting before normalizing */
521 if ((a->desc.clss == SUBNORMAL) && (b->desc.clss == SUBNORMAL)) {
522 sc_val_from_ulong(1, NULL);
523 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
526 /* resulting exponent is the bigger one */
527 memmove(_exp(result), _exp(a), value_size);
529 fc_exact &= normalize(result, result, sticky);
535 static void _fmul(const fp_value *a, const fp_value *b, fp_value *result) {
542 handle_NAN(a, b, result);
544 temp = alloca(value_size);
546 if (result != a && result != b)
547 result->desc = a->desc;
549 result->sign = res_sign = a->sign ^ b->sign;
551 /* produce NaN on 0 * inf */
552 if (a->desc.clss == ZERO) {
553 if (b->desc.clss == INF) {
554 fc_get_qnan(&a->desc, result);
558 memcpy(result, a, calc_buffer_size);
559 result->sign = res_sign;
563 if (b->desc.clss == ZERO) {
564 if (a->desc.clss == INF) {
565 fc_get_qnan(&a->desc, result);
569 memcpy(result, b, calc_buffer_size);
570 result->sign = res_sign;
575 if (a->desc.clss == INF) {
578 memcpy(result, a, calc_buffer_size);
579 result->sign = res_sign;
582 if (b->desc.clss == INF) {
585 memcpy(result, b, calc_buffer_size);
586 result->sign = res_sign;
590 /* exp = exp(a) + exp(b) - excess */
591 sc_add(_exp(a), _exp(b), _exp(result));
593 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
594 sc_sub(_exp(result), temp, _exp(result));
596 /* mixed normal, subnormal values introduce an error of 1, correct it */
597 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
598 sc_val_from_ulong(1, temp);
599 sc_add(_exp(result), temp, _exp(result));
602 sc_mul(_mant(a), _mant(b), _mant(result));
604 /* realign result: after a multiplication the digits right of the radix
605 * point are the sum of the factors' digits after the radix point. As all
606 * values are normalized they both have the same amount of these digits,
607 * which has to be restored by proper shifting
608 * because of the rounding bits */
609 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
611 _shift_right(_mant(result), temp, _mant(result));
612 sticky = sc_had_carry();
615 fc_exact &= normalize(result, result, sticky);
621 static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result) {
623 char *temp, *dividend;
628 handle_NAN(a, b, result);
630 temp = alloca(value_size);
631 dividend = alloca(value_size);
633 if (result != a && result != b)
634 result->desc = a->desc;
636 result->sign = res_sign = a->sign ^ b->sign;
638 /* produce NAN on 0/0 and inf/inf */
639 if (a->desc.clss == ZERO) {
640 if (b->desc.clss == ZERO) {
642 fc_get_qnan(&a->desc, result);
647 memcpy(result, a, calc_buffer_size);
648 result->sign = res_sign;
653 if (b->desc.clss == INF) {
655 if (a->desc.clss == INF) {
657 fc_get_qnan(&a->desc, result);
660 sc_val_from_ulong(0, NULL);
661 _save_result(_exp(result));
662 _save_result(_mant(result));
663 result->desc.clss = ZERO;
668 if (a->desc.clss == INF) {
672 memcpy(result, a, calc_buffer_size);
673 result->sign = res_sign;
676 if (b->desc.clss == ZERO) {
678 /* division by zero */
680 fc_get_minusinf(&a->desc, result);
682 fc_get_plusinf(&a->desc, result);
686 /* exp = exp(a) - exp(b) + excess - 1*/
687 sc_sub(_exp(a), _exp(b), _exp(result));
688 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp);
689 sc_add(_exp(result), temp, _exp(result));
691 /* mixed normal, subnormal values introduce an error of 1, correct it */
692 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
693 sc_val_from_ulong(1, temp);
694 sc_add(_exp(result), temp, _exp(result));
697 /* mant(res) = mant(a) / 1/2mant(b) */
698 /* to gain more bits of precision in the result the dividend could be
699 * shifted left, as this operation does not loose bits. This would not
700 * fit into the integer precision, but due to the rounding bits (which
701 * are always zero because the values are all normalized) the divisor
702 * can be shifted right instead to achieve the same result */
703 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
705 _shift_left(_mant(a), temp, dividend);
708 char *divisor = alloca(calc_buffer_size);
709 sc_val_from_ulong(1, divisor);
710 _shift_right(_mant(b), divisor, divisor);
711 sc_div(dividend, divisor, _mant(result));
712 sticky = sc_had_carry();
716 fc_exact &= normalize(result, result, sticky);
720 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result) {
727 /* set new descriptor (else result is supposed to already have one) */
729 result->desc = *desc;
731 build = alloca(value_size);
732 temp = alloca(value_size);
734 sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
737 /* temp is value of ten now */
738 sc_val_from_ulong(10, NULL);
741 for (exp--; exp > 0; exp--) {
743 sc_mul(build, temp, NULL);
747 /* temp is amount of left shift needed to put the value left of the radix point */
748 sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
750 _shift_left(build, temp, _mant(result));
752 _normalize(result, result, 0);
758 * Truncate the fractional part away.
760 * This does not clip to any integer range.
762 static void _trunc(const fp_value *a, fp_value *result) {
764 * When exponent == 0 all bits left of the radix point
765 * are the integral part of the value. For 15bit exp_size
766 * this would require a left shift of max. 16383 bits which
768 * But it is enough to ensure that no bit right of the radix
769 * point remains set. This restricts the interesting
770 * exponents to the interval [0, mant_size-1].
771 * Outside this interval the truncated value is either 0 or
772 * it does not have fractional parts.
775 int exp_bias, exp_val;
778 /* fixme: can be exact */
781 temp = alloca(value_size);
784 result->desc = a->desc;
786 exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
787 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
790 sc_val_from_ulong(0, NULL);
791 _save_result(_exp(result));
792 _save_result(_mant(result));
793 result->desc.clss = ZERO;
798 if (exp_val > a->desc.mantissa_size) {
800 memcpy(result, a, calc_buffer_size);
805 /* set up a proper mask to delete all bits right of the
806 * radix point if the mantissa had been shifted until exp == 0 */
807 sc_max_from_bits(1 + exp_val, 0, temp);
808 sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL);
809 _shift_left(temp, sc_get_buffer(), temp);
811 /* and the mask and return the result */
812 sc_and(_mant(a), temp, _mant(result));
814 if (a != result) memcpy(_exp(result), _exp(a), value_size);
818 * functions defined in fltcalc.h
820 const void *fc_get_buffer(void) {
824 int fc_get_buffer_length(void) {
825 return calc_buffer_size;
828 void *fc_val_from_str(const char *str, unsigned int len, const ieee_descriptor_t *desc, void *result) {
840 int exp_int, hsb, state;
845 char *mant_str, *exp_val, *power_val;
848 if (result == NULL) result = calc_buffer;
850 exp_val = alloca(value_size);
851 power_val = alloca(calc_buffer_size);
852 mant_str = alloca((len)?(len):(strlen(str)));
854 result->desc.exponent_size = desc->exponent_size;
855 result->desc.mantissa_size = desc->mantissa_size;
856 result->desc.explicit_one = desc->explicit_one;
857 result->desc.clss = NORMAL;
864 while (len == 0 || str-old_str < len) {
880 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
887 state = RIGHT_OF_DOT;
898 fail_char(old_str, len, str - old_str);
904 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
905 mant_str[pos++] = *(str++);
909 state = RIGHT_OF_DOT;
920 mant_str[pos] = '\0';
924 fail_char(old_str, len, str - old_str);
930 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
931 mant_str[pos++] = *(str++);
942 mant_str[pos] = '\0';
946 fail_char(old_str, len, str - old_str);
956 if (*(str-1) != 'e' && *(str-1) != 'E') fail_char(old_str, len, str - old_str);
960 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
961 mant_str[pos] = '\0';
968 fail_char(old_str, len, str - old_str);
974 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
979 case '\0': goto done;
982 fail_char(old_str, len, str - old_str);
985 } /* switch(state) */
988 sc_val_from_str(mant_str, strlen(mant_str), _mant(result));
990 /* shift to put value left of radix point */
991 sc_val_from_ulong(mant_size + ROUNDING_BITS, exp_val);
993 _shift_left(_mant(result), exp_val, _mant(result));
995 sc_val_from_ulong((1 << (exp_size - 1)) - 1, _exp(result));
997 _normalize(result, result, 0);
999 if (state == EXPONENT) {
1000 exp_int -= atoi(str-pos);
1003 _power_of_ten(exp_int, &result->desc, power_val);
1005 _fdiv(result, power_val, result);
1009 /* XXX excuse of an implementation to make things work */
1011 fp_value *tmp = alloca(calc_buffer_size);
1012 ieee_descriptor_t tmp_desc;
1015 #ifdef HAVE_LONG_DOUBLE
1016 val = strtold(str, NULL);
1017 DEBUGPRINTF(("val_from_str(%s)\n", str));
1018 tmp_desc.exponent_size = 15;
1019 tmp_desc.mantissa_size = 63;
1020 tmp_desc.explicit_one = 1;
1021 tmp_desc.clss = NORMAL;
1022 fc_val_from_ieee754(val, &tmp_desc, tmp);
1024 val = strtod(str, NULL);
1025 DEBUGPRINTF(("val_from_str(%s)\n", str));
1026 tmp_desc.exponent_size = 11;
1027 tmp_desc.mantissa_size = 52;
1028 tmp_desc.explicit_one = 0;
1029 tmp_desc.clss = NORMAL;
1030 fc_val_from_ieee754(val, &tmp_desc, tmp);
1031 #endif /* HAVE_LONG_DOUBLE */
1032 return fc_cast(tmp, desc, result);
1036 fp_value *fc_val_from_ieee754(LLDBL l, const ieee_descriptor_t *desc, fp_value *result) {
1038 int bias_res, bias_val, mant_val;
1040 UINT32 sign, exponent, mantissa0, mantissa1;
1043 bias_res = ((1 << (desc->exponent_size - 1)) - 1);
1045 #ifdef HAVE_LONG_DOUBLE
1048 sign = (srcval.val.high & 0x00008000) != 0;
1049 exponent = (srcval.val.high & 0x00007FFF) ;
1050 mantissa0 = srcval.val.mid;
1051 mantissa1 = srcval.val.low;
1052 #else /* no long double */
1055 sign = (srcval.val.high & 0x80000000) != 0;
1056 exponent = (srcval.val.high & 0x7FF00000) >> 20;
1057 mantissa0 = srcval.val.high & 0x000FFFFF;
1058 mantissa1 = srcval.val.low;
1061 #ifdef HAVE_LONG_DOUBLE
1062 TRACEPRINTF(("val_from_float(%.8X%.8X%.8X)\n", ((int*)&l)[2], ((int*)&l)[1], ((int*)&l)[0]));/* srcval.val.high, srcval.val.mid, srcval.val.low)); */
1063 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1065 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
1066 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1069 if (result == NULL) result = calc_buffer;
1070 temp = alloca(value_size);
1072 /* CLEAR the buffer, else some bits might be uninitialized */
1073 memset(result, 0, fc_get_buffer_length());
1075 result->desc.exponent_size = desc->exponent_size;
1076 result->desc.mantissa_size = desc->mantissa_size;
1077 result->desc.explicit_one = desc->explicit_one;
1080 result->sign = sign;
1082 /* sign and flag suffice to identify NaN or inf, no exponent/mantissa
1083 * encoding is needed. the function can return immediately in these cases */
1085 result->desc.clss = NAN;
1086 TRACEPRINTF(("val_from_float resulted in NAN\n"));
1089 else if (isinf(l)) {
1090 result->desc.clss = INF;
1091 TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
1095 /* build exponent, because input and output exponent and mantissa sizes may differ
1096 * this looks more complicated than it is: unbiased input exponent + output bias,
1097 * minus the mantissa difference which is added again later when the output float
1098 * becomes normalized */
1099 sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
1101 /* build mantissa representation */
1102 if (exponent != 0) {
1103 /* insert the hidden bit */
1104 sc_val_from_ulong(1, temp);
1105 sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
1106 _shift_left(temp, sc_get_buffer(), NULL);
1109 sc_val_from_ulong(0, NULL);
1112 _save_result(_mant(result));
1114 /* bits from the upper word */
1115 sc_val_from_ulong(mantissa0, temp);
1116 sc_val_from_ulong(34, NULL);
1117 _shift_left(temp, sc_get_buffer(), temp);
1118 sc_or(_mant(result), temp, _mant(result));
1120 /* bits from the lower word */
1121 sc_val_from_ulong(mantissa1, temp);
1122 sc_val_from_ulong(ROUNDING_BITS, NULL);
1123 _shift_left(temp, sc_get_buffer(), temp);
1124 sc_or(_mant(result), temp, _mant(result));
1126 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
1127 * origin one to the left */
1128 if (exponent == 0) {
1129 sc_val_from_ulong(1, NULL);
1130 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1133 normalize(result, result, 0);
1135 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
1140 LLDBL fc_val_to_ieee754(const fp_value *val) {
1142 fp_value *temp = NULL;
1152 ieee_descriptor_t desc;
1153 unsigned mantissa_size;
1155 #ifdef HAVE_LONG_DOUBLE
1156 desc.exponent_size = 15;
1157 desc.mantissa_size = 63;
1158 desc.explicit_one = 1;
1161 desc.exponent_size = 11;
1162 desc.mantissa_size = 52;
1163 desc.explicit_one = 0;
1166 mantissa_size = desc.mantissa_size + desc.explicit_one;
1168 temp = alloca(calc_buffer_size);
1169 value = fc_cast(val, &desc, temp);
1173 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
1174 * lead to wrong results */
1175 exponent = sc_val_to_long(_exp(value)) ;
1177 sc_val_from_ulong(ROUNDING_BITS, NULL);
1178 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
1183 for (byte_offset = 0; byte_offset < 4; byte_offset++)
1184 mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
1186 for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
1187 mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
1189 #ifdef HAVE_LONG_DOUBLE
1190 buildval.val.high = sign << 15;
1191 buildval.val.high |= exponent;
1192 buildval.val.mid = mantissa0;
1193 buildval.val.low = mantissa1;
1194 #else /* no long double */
1195 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1196 buildval.val.high = sign << 31;
1197 buildval.val.high |= exponent << 20;
1198 buildval.val.high |= mantissa0;
1199 buildval.val.low = mantissa1;
1202 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1206 fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result) {
1208 int exp_offset, val_bias, res_bias;
1210 if (result == NULL) result = calc_buffer;
1211 temp = alloca(value_size);
1213 if (value->desc.exponent_size == desc->exponent_size &&
1214 value->desc.mantissa_size == desc->mantissa_size &&
1215 value->desc.explicit_one == desc->explicit_one) {
1216 if (value != result)
1217 memcpy(result, value, calc_buffer_size);
1221 if (value->desc.clss == NAN) {
1222 if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
1223 return fc_get_qnan(desc, result);
1225 return fc_get_snan(desc, result);
1228 /* set the descriptor of the new value */
1229 result->desc.exponent_size = desc->exponent_size;
1230 result->desc.mantissa_size = desc->mantissa_size;
1231 result->desc.explicit_one = desc->explicit_one;
1232 result->desc.clss = value->desc.clss;
1234 result->sign = value->sign;
1236 /* when the mantissa sizes differ normalizing has to shift to align it.
1237 * this would change the exponent, which is unwanted. So calculate this
1238 * offset and add it */
1239 val_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1240 res_bias = (1 << (desc->exponent_size - 1)) - 1;
1242 exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
1243 sc_val_from_long(exp_offset, temp);
1244 sc_add(_exp(value), temp, _exp(result));
1246 /* _normalize expects normalized radix point */
1247 if (value->desc.clss == SUBNORMAL) {
1248 sc_val_from_ulong(1, NULL);
1249 _shift_left(_mant(value), sc_get_buffer(), _mant(result));
1250 } else if (value != result) {
1251 memcpy(_mant(result), _mant(value), value_size);
1253 memmove(_mant(result), _mant(value), value_size);
1256 normalize(result, result, 0);
1257 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1261 fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result) {
1262 if (result == NULL) result = calc_buffer;
1264 result->desc.exponent_size = desc->exponent_size;
1265 result->desc.mantissa_size = desc->mantissa_size;
1266 result->desc.explicit_one = desc->explicit_one;
1267 result->desc.clss = NORMAL;
1271 sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
1273 sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
1274 sc_val_from_ulong(ROUNDING_BITS, NULL);
1275 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1280 fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result) {
1281 if (result == NULL) result = calc_buffer;
1283 fc_get_max(desc, result);
1289 fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result) {
1290 if (result == NULL) result = calc_buffer;
1292 result->desc.exponent_size = desc->exponent_size;
1293 result->desc.mantissa_size = desc->mantissa_size;
1294 result->desc.explicit_one = desc->explicit_one;
1295 result->desc.clss = NAN;
1299 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1301 /* signaling NaN has non-zero mantissa with msb not set */
1302 sc_val_from_ulong(1, _mant(result));
1307 fp_value *fc_get_qnan(const ieee_descriptor_t *desc, fp_value *result) {
1308 if (result == NULL) result = calc_buffer;
1310 result->desc.exponent_size = desc->exponent_size;
1311 result->desc.mantissa_size = desc->mantissa_size;
1312 result->desc.explicit_one = desc->explicit_one;
1313 result->desc.clss = NAN;
1317 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1319 /* quiet NaN has the msb of the mantissa set, so shift one there */
1320 sc_val_from_ulong(1, _mant(result));
1321 /* mantissa_size >+< 1 because of two extra rounding bits */
1322 sc_val_from_ulong(desc->mantissa_size + 1, NULL);
1323 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1328 fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result) {
1329 if (result == NULL) result = calc_buffer;
1331 result->desc.exponent_size = desc->exponent_size;
1332 result->desc.mantissa_size = desc->mantissa_size;
1333 result->desc.explicit_one = desc->explicit_one;
1334 result->desc.clss = INF;
1338 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1340 sc_val_from_ulong(0, _mant(result));
1345 fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result) {
1346 if (result == NULL) result = calc_buffer;
1348 fc_get_plusinf(desc, result);
1354 int fc_comp(const fp_value *val_a, const fp_value *val_b) {
1358 * shortcut: if both values are identical, they are either
1359 * Unordered if NaN or equal
1362 return val_a->desc.clss == NAN ? 2 : 0;
1364 /* unordered if one is a NaN */
1365 if (val_a->desc.clss == NAN || val_b->desc.clss == NAN)
1368 /* zero is equal independent of sign */
1369 if ((val_a->desc.clss == ZERO) && (val_b->desc.clss == ZERO))
1372 /* different signs make compare easy */
1373 if (val_a->sign != val_b->sign)
1374 return (val_a->sign == 0) ? (1) : (-1);
1376 mul = val_a->sign ? -1 : 1;
1378 /* both infinity means equality */
1379 if ((val_a->desc.clss == INF) && (val_b->desc.clss == INF))
1382 /* infinity is bigger than the rest */
1383 if (val_a->desc.clss == INF)
1385 if (val_b->desc.clss == INF)
1388 /* check first exponent, that mantissa if equal */
1389 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1395 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1401 int fc_is_zero(const fp_value *a) {
1402 return a->desc.clss == ZERO;
1405 int fc_is_negative(const fp_value *a) {
1409 int fc_is_inf(const fp_value *a) {
1410 return a->desc.clss == INF;
1413 int fc_is_nan(const fp_value *a) {
1414 return a->desc.clss == NAN;
1417 int fc_is_subnormal(const fp_value *a) {
1418 return a->desc.clss == SUBNORMAL;
1421 char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base) {
1425 mul_1 = alloca(calc_buffer_size);
1429 switch ((value_class_t)val->desc.clss) {
1431 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1434 snprintf(buf, buflen, "NaN");
1437 snprintf(buf, buflen, "0.0");
1440 flt_val = fc_val_to_ieee754(val);
1441 #ifdef HAVE_LONG_DOUBLE
1442 /* XXX 30 is arbitrary */
1443 snprintf(buf, buflen, "%.30LE", flt_val);
1445 snprintf(buf, buflen, "%.18E", flt_val);
1451 switch ((value_class_t)val->desc.clss) {
1453 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1456 snprintf(buf, buflen, "NAN");
1459 snprintf(buf, buflen, "0.0");
1462 flt_val = fc_val_to_ieee754(val);
1463 #ifdef HAVE_LONG_DOUBLE
1464 snprintf(buf, buflen, "%LA", flt_val);
1466 snprintf(buf, buflen, "%A", flt_val);
1473 snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0));
1474 buf[buflen - 1] = '\0';
1480 unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs) {
1481 /* this is used to cache the packed version of the value */
1482 static char *packed_value = NULL;
1484 if (packed_value == NULL) packed_value = XMALLOCN(char, value_size);
1487 pack(value, packed_value);
1489 return sc_sub_bits(packed_value, num_bits, byte_ofs);
1492 /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */
1493 int fc_zero_mantissa(const fp_value *value) {
1494 return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size;
1497 /* Returns the exponent of a value. */
1498 int fc_get_exponent(const fp_value *value) {
1499 int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1500 return sc_val_to_long(_exp(value)) - exp_bias;
1503 /* Return non-zero if a given value can be converted lossless into another precision */
1504 int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc) {
1508 /* handle some special cases first */
1509 switch (value->desc.clss) {
1518 /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */
1519 exp_bias = (1 << (desc->exponent_size - 1)) - 1;
1520 v = fc_get_exponent(value) + exp_bias;
1521 if (0 < v && v < (1 << desc->exponent_size) - 1) {
1522 /* exponent can be encoded, now check the mantissa */
1523 v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value));
1524 return v < desc->mantissa_size;
1530 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode) {
1531 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1532 rounding_mode = mode;
1534 return rounding_mode;
1537 fc_rounding_mode_t fc_get_rounding_mode(void) {
1538 return rounding_mode;
1541 void init_fltcalc(int precision) {
1542 if (calc_buffer == NULL) {
1543 /* does nothing if already init */
1544 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1546 init_strcalc(precision + 2 + ROUNDING_BITS);
1548 /* needs additionally rounding bits, one bit as explicit 1., and one for
1549 * addition overflow */
1550 max_precision = sc_get_precision() - (2 + ROUNDING_BITS);
1551 if (max_precision < precision)
1552 printf("WARNING: not enough precision available, using %d\n", max_precision);
1554 rounding_mode = FC_TONEAREST;
1555 value_size = sc_get_buffer_length();
1556 calc_buffer_size = sizeof(fp_value) + 2*value_size - 1;
1558 calc_buffer = xmalloc(calc_buffer_size);
1559 memset(calc_buffer, 0, calc_buffer_size);
1560 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer));
1561 #ifdef HAVE_LONG_DOUBLE
1562 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1564 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1566 #ifdef WORDS_BIGENDIAN
1567 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1569 DEBUGPRINTF(("\tWord order is little endian\n\n"));
1574 void finish_fltcalc (void) {
1575 free(calc_buffer); calc_buffer = NULL;
1578 #ifdef FLTCALC_TRACE_CALC
1579 static char buffer[100];
1582 /* definition of interface functions */
1583 fp_value *fc_add(const fp_value *a, const fp_value *b, fp_value *result) {
1584 if (result == NULL) result = calc_buffer;
1586 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1587 TRACEPRINTF(("+ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1589 /* make the value with the bigger exponent the first one */
1590 if (sc_comp(_exp(a), _exp(b)) == -1)
1591 _fadd(b, a, result);
1593 _fadd(a, b, result);
1595 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1599 fp_value *fc_sub(const fp_value *a, const fp_value *b, fp_value *result) {
1602 if (result == NULL) result = calc_buffer;
1604 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1605 TRACEPRINTF(("- %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1607 temp = alloca(calc_buffer_size);
1608 memcpy(temp, b, calc_buffer_size);
1609 temp->sign = !b->sign;
1610 if (sc_comp(_exp(a), _exp(temp)) == -1)
1611 _fadd(temp, a, result);
1613 _fadd(a, temp, result);
1615 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1619 fp_value *fc_mul(const fp_value *a, const fp_value *b, fp_value *result) {
1620 if (result == NULL) result = calc_buffer;
1622 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1623 TRACEPRINTF(("* %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1625 _fmul(a, b, result);
1627 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1631 fp_value *fc_div(const fp_value *a, const fp_value *b, fp_value *result) {
1632 if (result == NULL) result = calc_buffer;
1634 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1635 TRACEPRINTF(("/ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1637 _fdiv(a, b, result);
1639 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1643 fp_value *fc_neg(const fp_value *a, fp_value *result) {
1644 if (result == NULL) result = calc_buffer;
1646 TRACEPRINTF(("- %s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1649 memcpy(result, a, calc_buffer_size);
1650 result->sign = !a->sign;
1652 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1656 fp_value *fc_int(const fp_value *a, fp_value *result) {
1657 if (result == NULL) result = calc_buffer;
1659 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1660 TRACEPRINTF(("truncated to integer "));
1664 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1668 fp_value *fc_rnd(const fp_value *a, fp_value *result) {
1669 if (result == NULL) result = calc_buffer;
1672 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1673 TRACEPRINTF(("rounded to integer "));
1675 assert(!"fc_rnd() not yet implemented");
1677 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1682 * convert a floating point value into an sc value ...
1684 int fc_flt2int(const fp_value *a, void *result, ir_mode *dst_mode) {
1685 if (a->desc.clss == NORMAL) {
1686 int exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
1687 int exp_val = sc_val_to_long(_exp(a)) - exp_bias;
1690 if (a->sign && !mode_is_signed(dst_mode)) {
1691 /* FIXME: for now we cannot convert this */
1695 assert(exp_val >= 0 && "floating point value not integral before fc_flt2int() call");
1696 shift = exp_val - (a->desc.mantissa_size + ROUNDING_BITS);
1699 sc_shlI(_mant(a), shift, 64, 0, result);
1701 sc_shrI(_mant(a), -shift, 64, 0, result);
1704 /* check for overflow */
1705 highest = sc_get_highest_set_bit(result);
1707 if (mode_is_signed(dst_mode)) {
1708 if (highest == sc_get_lowest_set_bit(result)) {
1709 /* need extra test for MIN_INT */
1710 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1711 /* FIXME: handle overflow */
1715 if (highest >= (int) get_mode_size_bits(dst_mode) - 1) {
1716 /* FIXME: handle overflow */
1721 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1722 /* FIXME: handle overflow */
1728 sc_neg(result, result);
1732 else if (a->desc.clss == ZERO) {
1740 unsigned fc_set_immediate_precision(unsigned bits) {
1741 unsigned old = immediate_prec;
1743 immediate_prec = bits;
1747 int fc_is_exact(void) {