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 /* undef some reused constants defined by math.h */
46 /** The number of extra precision rounding bits */
47 #define ROUNDING_BITS 2
49 typedef uint32_t UINT32;
51 #ifdef HAVE_LONG_DOUBLE
52 #ifdef WORDS_BIGENDIAN
59 volatile long double d;
68 volatile long double d;
72 #ifdef WORDS_BIGENDIAN
91 #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
93 /* our floating point value */
95 ieee_descriptor_t desc;
97 char value[1]; /* exp[value_size] + mant[value_size] */
100 #define _exp(a) &((a)->value[0])
101 #define _mant(a) &((a)->value[value_size])
103 #define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
104 #define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res))
105 #define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res))
109 # define DEBUGPRINTF(x) printf x
111 # define DEBUGPRINTF(x) ((void)0)
114 #ifdef FLTCALC_TRACE_CALC
115 # define TRACEPRINTF(x) printf x
117 # define TRACEPRINTF(x) ((void)0)
120 /** The immediate precision. */
121 static unsigned immediate_prec = 0;
123 /** A temporal buffer. */
124 static fp_value *calc_buffer = NULL;
126 /** Current rounding mode.*/
127 static fc_rounding_mode_t rounding_mode;
129 static int calc_buffer_size;
130 static int value_size;
131 static int max_precision;
134 static int fc_exact = 1;
137 static void fail_char(const char *str, unsigned int len, int pos) {
139 printf("ERROR: Unexpected character '%c'\n", *(str + pos));
141 printf("ERROR: Unexpected end of string\n");
142 while (len-- && *str) printf("%c", *str++); printf("\n");
143 while (pos--) printf(" "); printf("^\n");
144 /* the front end has to to check constant strings */
149 /** pack machine-like */
150 static void *pack(const fp_value *int_float, void *packed) {
153 fp_value *val_buffer;
156 temp = alloca(value_size);
157 shift_val = alloca(value_size);
159 switch ((value_class_t)int_float->desc.clss) {
161 val_buffer = alloca(calc_buffer_size);
162 fc_get_qnan(&int_float->desc, val_buffer);
163 int_float = val_buffer;
167 val_buffer = alloca(calc_buffer_size);
168 fc_get_plusinf(&int_float->desc, val_buffer);
169 val_buffer->sign = int_float->sign;
170 int_float = val_buffer;
176 assert(int_float->desc.explicit_one <= 1);
178 /* pack sign: move it to the left after exponent AND mantissa */
179 sc_val_from_ulong(int_float->sign, temp);
181 pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
182 sc_val_from_ulong(pos, NULL);
183 _shift_left(temp, sc_get_buffer(), packed);
185 /* pack exponent: move it to the left after mantissa */
186 pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
187 sc_val_from_ulong(pos, shift_val);
188 _shift_left(_exp(int_float), shift_val, temp);
190 /* combine sign|exponent */
191 sc_or(temp, packed, packed);
193 /* extract mantissa */
194 /* remove rounding bits */
195 sc_val_from_ulong(ROUNDING_BITS, shift_val);
196 _shift_right(_mant(int_float), shift_val, temp);
198 /* remove leading 1 (or 0 if denormalized) */
199 sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */
200 sc_and(temp, shift_val, temp);
202 /* combine sign|exponent|mantissa */
203 sc_or(temp, packed, packed);
209 * Normalize a fp_value.
211 * @return non-zero if result is exact
213 static int normalize(const fp_value *in_val, fp_value *out_val, int sticky) {
216 char lsb, guard, round, round_dir = 0;
217 char *temp = alloca(value_size);
219 /* save rounding bits at the end */
220 hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
222 if (in_val != out_val) {
223 out_val->sign = in_val->sign;
224 memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc));
227 out_val->desc.clss = NORMAL;
229 /* mantissa all zeros, so zero exponent (because of explicit one) */
230 if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) {
231 sc_val_from_ulong(0, _exp(out_val));
235 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
238 sc_val_from_ulong(-hsb-1, temp);
240 _shift_right(_mant(in_val), temp, _mant(out_val));
242 /* remember if some bits were shifted away */
243 if (sc_had_carry()) {
247 sc_add(_exp(in_val), temp, _exp(out_val));
248 } else if (hsb > -1) {
250 sc_val_from_ulong(hsb+1, temp);
252 _shift_left(_mant(in_val), temp, _mant(out_val));
254 sc_sub(_exp(in_val), temp, _exp(out_val));
257 /* check for exponent underflow */
258 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
259 DEBUGPRINTF(("Exponent underflow!\n"));
260 /* exponent underflow */
261 /* shift the mantissa right to have a zero exponent */
262 sc_val_from_ulong(1, temp);
263 sc_sub(temp, _exp(out_val), NULL);
265 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
266 if (sc_had_carry()) {
270 /* denormalized means exponent of zero */
271 sc_val_from_ulong(0, _exp(out_val));
273 out_val->desc.clss = SUBNORMAL;
276 /* perform rounding by adding a value that clears the guard bit and the round bit
277 * and either causes a carry to round up or not */
278 /* get the last 3 bits of the value */
279 lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
280 guard = (lsb&0x2)>>1;
283 switch (rounding_mode) {
285 /* round to nearest representable value, if in doubt choose the version
287 round_dir = guard && (sticky || round || lsb>>2);
290 /* if positive: round to one if the exact value is bigger, else to zero */
291 round_dir = (!out_val->sign && (guard || round || sticky));
294 /* if negative: round to one if the exact value is bigger, else to zero */
295 round_dir = (out_val->sign && (guard || round || sticky));
298 /* always round to 0 (chopping mode) */
302 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"));
304 if (round_dir == 1) {
305 guard = (round^guard)<<1;
306 lsb = !(round || guard)<<2 | guard | round;
308 lsb = -((guard<<1) | round);
311 /* add the rounded value */
313 sc_val_from_long(lsb, temp);
314 sc_add(_mant(out_val), temp, _mant(out_val));
318 /* could have rounded down to zero */
319 if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL))
320 out_val->desc.clss = ZERO;
322 /* check for rounding overflow */
323 hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
324 if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) {
325 sc_val_from_ulong(1, temp);
326 _shift_right(_mant(out_val), temp, _mant(out_val));
327 if (exact && sc_had_carry())
329 sc_add(_exp(out_val), temp, _exp(out_val));
330 } else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) {
331 /* overflow caused the mantissa to be normal again,
332 * so adapt the exponent accordingly */
333 sc_val_from_ulong(1, temp);
334 sc_add(_exp(out_val), temp, _exp(out_val));
336 out_val->desc.clss = NORMAL;
338 /* no further rounding is needed, because rounding overflow means
339 * the carry of the original rounding was propagated all the way
340 * up to the bit left of the radix point. This implies the bits
341 * to the right are all zeros (rounding is +1) */
343 /* check for exponent overflow */
344 sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp);
345 if (sc_comp(_exp(out_val), temp) != -1) {
346 DEBUGPRINTF(("Exponent overflow!\n"));
347 /* exponent overflow, reaction depends on rounding method:
349 * mode | sign of value | result
350 *--------------------------------------------------------------
351 * TO_NEAREST | + | +inf
353 *--------------------------------------------------------------
354 * TO_POSITIVE | + | +inf
355 * | - | smallest representable value
356 *--------------------------------------------------------------
357 * TO_NEAGTIVE | + | largest representable value
359 *--------------------------------------------------------------
360 * TO_ZERO | + | largest representable value
361 * | - | smallest representable value
362 *--------------------------------------------------------------*/
363 if (out_val->sign == 0) {
364 /* value is positive */
365 switch (rounding_mode) {
368 out_val->desc.clss = INF;
373 fc_get_max(&out_val->desc, out_val);
376 /* value is negative */
377 switch (rounding_mode) {
380 out_val->desc.clss = INF;
385 fc_get_min(&out_val->desc, out_val);
393 * Operations involving NaN's must return NaN.
394 * They are NOT exact.
396 #define handle_NAN(a, b, result) \
398 if (a->desc.clss == NAN) { \
399 if (a != result) memcpy(result, a, calc_buffer_size); \
403 if (b->desc.clss == NAN) { \
404 if (b != result) memcpy(result, b, calc_buffer_size); \
412 * calculate a + b, where a is the value with the bigger exponent
414 static void _fadd(const fp_value *a, const fp_value *b, fp_value *result) {
423 handle_NAN(a, b, result);
425 /* make sure result has a descriptor */
426 if (result != a && result != b)
427 result->desc = a->desc;
429 /* determine if this is an addition or subtraction */
430 sign = a->sign ^ b->sign;
432 /* produce NaN on inf - inf */
433 if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) {
435 fc_get_qnan(&a->desc, result);
439 temp = alloca(value_size);
440 exp_diff = alloca(value_size);
442 /* get exponent difference */
443 sc_sub(_exp(a), _exp(b), exp_diff);
445 /* initially set sign to be the sign of a, special treatment of subtraction
446 * when exponents are equal is required though.
447 * Also special care about the sign is needed when the mantissas are equal
449 if (sign && sc_val_to_long(exp_diff) == 0) {
450 switch (sc_comp(_mant(a), _mant(b))) {
452 res_sign = a->sign; /* abs(a) is bigger and a is negative */
455 res_sign = (rounding_mode == FC_TONEGATIVE);
458 res_sign = b->sign; /* abs(b) is bigger and b is negative */
461 /* can't be reached */
468 result->sign = res_sign;
470 /* sign has been taken care of, check for special cases */
471 if (a->desc.clss == ZERO || b->desc.clss == INF) {
473 memcpy(result, b, calc_buffer_size);
474 fc_exact = b->desc.clss == NORMAL;
475 result->sign = res_sign;
478 if (b->desc.clss == ZERO || a->desc.clss == INF) {
480 memcpy(result, a, calc_buffer_size);
481 fc_exact = a->desc.clss == NORMAL;
482 result->sign = res_sign;
486 /* shift the smaller value to the right to align the radix point */
487 /* subnormals have their radix point shifted to the right,
488 * take care of this first */
489 if ((b->desc.clss == SUBNORMAL) && (a->desc.clss != SUBNORMAL)) {
490 sc_val_from_ulong(1, temp);
491 sc_sub(exp_diff, temp, exp_diff);
494 _shift_right(_mant(b), exp_diff, temp);
495 sticky = sc_had_carry();
498 if (sticky && sign) {
499 /* if subtracting a little more than the represented value or adding a little
500 * more than the represented value to a negative value this, in addition to the
501 * still set sticky bit, takes account of the 'little more' */
502 char *temp1 = alloca(calc_buffer_size);
503 sc_val_from_ulong(1, temp1);
504 sc_add(temp, temp1, temp);
508 if (sc_comp(_mant(a), temp) == -1)
509 sc_sub(temp, _mant(a), _mant(result));
511 sc_sub(_mant(a), temp, _mant(result));
513 sc_add(_mant(a), temp, _mant(result));
516 /* _normalize expects a 'normal' radix point, adding two subnormals
517 * results in a subnormal radix point -> shifting before normalizing */
518 if ((a->desc.clss == SUBNORMAL) && (b->desc.clss == SUBNORMAL)) {
519 sc_val_from_ulong(1, NULL);
520 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
523 /* resulting exponent is the bigger one */
524 memmove(_exp(result), _exp(a), value_size);
526 fc_exact &= normalize(result, result, sticky);
532 static void _fmul(const fp_value *a, const fp_value *b, fp_value *result) {
539 handle_NAN(a, b, result);
541 temp = alloca(value_size);
543 if (result != a && result != b)
544 result->desc = a->desc;
546 result->sign = res_sign = a->sign ^ b->sign;
548 /* produce NaN on 0 * inf */
549 if (a->desc.clss == ZERO) {
550 if (b->desc.clss == INF) {
551 fc_get_qnan(&a->desc, result);
555 memcpy(result, a, calc_buffer_size);
556 result->sign = res_sign;
560 if (b->desc.clss == ZERO) {
561 if (a->desc.clss == INF) {
562 fc_get_qnan(&a->desc, result);
566 memcpy(result, b, calc_buffer_size);
567 result->sign = res_sign;
572 if (a->desc.clss == INF) {
575 memcpy(result, a, calc_buffer_size);
576 result->sign = res_sign;
579 if (b->desc.clss == INF) {
582 memcpy(result, b, calc_buffer_size);
583 result->sign = res_sign;
587 /* exp = exp(a) + exp(b) - excess */
588 sc_add(_exp(a), _exp(b), _exp(result));
590 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
591 sc_sub(_exp(result), temp, _exp(result));
593 /* mixed normal, subnormal values introduce an error of 1, correct it */
594 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
595 sc_val_from_ulong(1, temp);
596 sc_add(_exp(result), temp, _exp(result));
599 sc_mul(_mant(a), _mant(b), _mant(result));
601 /* realign result: after a multiplication the digits right of the radix
602 * point are the sum of the factors' digits after the radix point. As all
603 * values are normalized they both have the same amount of these digits,
604 * which has to be restored by proper shifting
605 * because of the rounding bits */
606 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
608 _shift_right(_mant(result), temp, _mant(result));
609 sticky = sc_had_carry();
612 fc_exact &= normalize(result, result, sticky);
618 static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result) {
620 char *temp, *dividend;
625 handle_NAN(a, b, result);
627 temp = alloca(value_size);
628 dividend = alloca(value_size);
630 if (result != a && result != b)
631 result->desc = a->desc;
633 result->sign = res_sign = a->sign ^ b->sign;
635 /* produce NAN on 0/0 and inf/inf */
636 if (a->desc.clss == ZERO) {
637 if (b->desc.clss == ZERO) {
639 fc_get_qnan(&a->desc, result);
644 memcpy(result, a, calc_buffer_size);
645 result->sign = res_sign;
650 if (b->desc.clss == INF) {
652 if (a->desc.clss == INF) {
654 fc_get_qnan(&a->desc, result);
657 sc_val_from_ulong(0, NULL);
658 _save_result(_exp(result));
659 _save_result(_mant(result));
660 result->desc.clss = ZERO;
665 if (a->desc.clss == INF) {
669 memcpy(result, a, calc_buffer_size);
670 result->sign = res_sign;
673 if (b->desc.clss == ZERO) {
675 /* division by zero */
677 fc_get_minusinf(&a->desc, result);
679 fc_get_plusinf(&a->desc, result);
683 /* exp = exp(a) - exp(b) + excess - 1*/
684 sc_sub(_exp(a), _exp(b), _exp(result));
685 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp);
686 sc_add(_exp(result), temp, _exp(result));
688 /* mixed normal, subnormal values introduce an error of 1, correct it */
689 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
690 sc_val_from_ulong(1, temp);
691 sc_add(_exp(result), temp, _exp(result));
694 /* mant(res) = mant(a) / 1/2mant(b) */
695 /* to gain more bits of precision in the result the dividend could be
696 * shifted left, as this operation does not loose bits. This would not
697 * fit into the integer precision, but due to the rounding bits (which
698 * are always zero because the values are all normalized) the divisor
699 * can be shifted right instead to achieve the same result */
700 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
702 _shift_left(_mant(a), temp, dividend);
705 char *divisor = alloca(calc_buffer_size);
706 sc_val_from_ulong(1, divisor);
707 _shift_right(_mant(b), divisor, divisor);
708 sc_div(dividend, divisor, _mant(result));
709 sticky = sc_had_carry();
713 fc_exact &= normalize(result, result, sticky);
717 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result) {
724 /* set new descriptor (else result is supposed to already have one) */
726 result->desc = *desc;
728 build = alloca(value_size);
729 temp = alloca(value_size);
731 sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
734 /* temp is value of ten now */
735 sc_val_from_ulong(10, NULL);
738 for (exp--; exp > 0; exp--) {
740 sc_mul(build, temp, NULL);
744 /* temp is amount of left shift needed to put the value left of the radix point */
745 sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
747 _shift_left(build, temp, _mant(result));
749 _normalize(result, result, 0);
755 * Truncate the fractional part away.
757 * This does not clip to any integer range.
759 static void _trunc(const fp_value *a, fp_value *result) {
761 * When exponent == 0 all bits left of the radix point
762 * are the integral part of the value. For 15bit exp_size
763 * this would require a left shift of max. 16383 bits which
765 * But it is enough to ensure that no bit right of the radix
766 * point remains set. This restricts the interesting
767 * exponents to the interval [0, mant_size-1].
768 * Outside this interval the truncated value is either 0 or
769 * it does not have fractional parts.
772 int exp_bias, exp_val;
775 /* fixme: can be exact */
778 temp = alloca(value_size);
781 result->desc = a->desc;
783 exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
784 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
787 sc_val_from_ulong(0, NULL);
788 _save_result(_exp(result));
789 _save_result(_mant(result));
790 result->desc.clss = ZERO;
795 if (exp_val > a->desc.mantissa_size) {
797 memcpy(result, a, calc_buffer_size);
802 /* set up a proper mask to delete all bits right of the
803 * radix point if the mantissa had been shifted until exp == 0 */
804 sc_max_from_bits(1 + exp_val, 0, temp);
805 sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL);
806 _shift_left(temp, sc_get_buffer(), temp);
808 /* and the mask and return the result */
809 sc_and(_mant(a), temp, _mant(result));
812 memcpy(_exp(result), _exp(a), value_size);
813 result->sign = a->sign;
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 #if defined(HAVE_LONG_DOUBLE) && !defined(__CYGWIN__)
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;
1041 UINT32 exponent, mantissa0, mantissa1;
1044 bias_res = ((1 << (desc->exponent_size - 1)) - 1);
1046 #ifdef HAVE_LONG_DOUBLE
1049 sign = (srcval.val.high & 0x00008000) != 0;
1050 exponent = (srcval.val.high & 0x00007FFF) ;
1051 mantissa0 = srcval.val.mid;
1052 mantissa1 = srcval.val.low;
1053 #else /* no long double */
1056 sign = (srcval.val.high & 0x80000000) != 0;
1057 exponent = (srcval.val.high & 0x7FF00000) >> 20;
1058 mantissa0 = srcval.val.high & 0x000FFFFF;
1059 mantissa1 = srcval.val.low;
1062 #ifdef HAVE_LONG_DOUBLE
1063 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)); */
1064 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1066 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
1067 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1070 if (result == NULL) result = calc_buffer;
1071 temp = alloca(value_size);
1073 /* CLEAR the buffer, else some bits might be uninitialized */
1074 memset(result, 0, fc_get_buffer_length());
1076 result->desc.exponent_size = desc->exponent_size;
1077 result->desc.mantissa_size = desc->mantissa_size;
1078 result->desc.explicit_one = desc->explicit_one;
1081 result->sign = sign;
1083 /* sign and flag suffice to identify NaN or inf, no exponent/mantissa
1084 * encoding is needed. the function can return immediately in these cases */
1086 result->desc.clss = NAN;
1087 TRACEPRINTF(("val_from_float resulted in NAN\n"));
1090 else if (isinf(l)) {
1091 result->desc.clss = INF;
1092 TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
1096 /* build exponent, because input and output exponent and mantissa sizes may differ
1097 * this looks more complicated than it is: unbiased input exponent + output bias,
1098 * minus the mantissa difference which is added again later when the output float
1099 * becomes normalized */
1100 sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
1102 /* build mantissa representation */
1103 if (exponent != 0) {
1104 /* insert the hidden bit */
1105 sc_val_from_ulong(1, temp);
1106 sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
1107 _shift_left(temp, sc_get_buffer(), NULL);
1110 sc_val_from_ulong(0, NULL);
1113 _save_result(_mant(result));
1115 /* bits from the upper word */
1116 sc_val_from_ulong(mantissa0, temp);
1117 sc_val_from_ulong(34, NULL);
1118 _shift_left(temp, sc_get_buffer(), temp);
1119 sc_or(_mant(result), temp, _mant(result));
1121 /* bits from the lower word */
1122 sc_val_from_ulong(mantissa1, temp);
1123 sc_val_from_ulong(ROUNDING_BITS, NULL);
1124 _shift_left(temp, sc_get_buffer(), temp);
1125 sc_or(_mant(result), temp, _mant(result));
1127 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
1128 * origin one to the left */
1129 if (exponent == 0) {
1130 sc_val_from_ulong(1, NULL);
1131 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1134 normalize(result, result, 0);
1136 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
1141 LLDBL fc_val_to_ieee754(const fp_value *val) {
1143 fp_value *temp = NULL;
1153 ieee_descriptor_t desc;
1154 unsigned mantissa_size;
1156 #ifdef HAVE_LONG_DOUBLE
1157 desc.exponent_size = 15;
1158 desc.mantissa_size = 63;
1159 desc.explicit_one = 1;
1162 desc.exponent_size = 11;
1163 desc.mantissa_size = 52;
1164 desc.explicit_one = 0;
1167 mantissa_size = desc.mantissa_size + desc.explicit_one;
1169 temp = alloca(calc_buffer_size);
1170 value = fc_cast(val, &desc, temp);
1174 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
1175 * lead to wrong results */
1176 exponent = sc_val_to_long(_exp(value)) ;
1178 sc_val_from_ulong(ROUNDING_BITS, NULL);
1179 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
1184 for (byte_offset = 0; byte_offset < 4; byte_offset++)
1185 mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
1187 for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
1188 mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
1190 #ifdef HAVE_LONG_DOUBLE
1191 buildval.val.high = sign << 15;
1192 buildval.val.high |= exponent;
1193 buildval.val.mid = mantissa0;
1194 buildval.val.low = mantissa1;
1195 #else /* no long double */
1196 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1197 buildval.val.high = sign << 31;
1198 buildval.val.high |= exponent << 20;
1199 buildval.val.high |= mantissa0;
1200 buildval.val.low = mantissa1;
1203 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1207 fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result) {
1209 int exp_offset, val_bias, res_bias;
1211 if (result == NULL) result = calc_buffer;
1212 temp = alloca(value_size);
1214 if (value->desc.exponent_size == desc->exponent_size &&
1215 value->desc.mantissa_size == desc->mantissa_size &&
1216 value->desc.explicit_one == desc->explicit_one) {
1217 if (value != result)
1218 memcpy(result, value, calc_buffer_size);
1222 if (value->desc.clss == NAN) {
1223 if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
1224 return fc_get_qnan(desc, result);
1226 return fc_get_snan(desc, result);
1228 else if(value->desc.clss == INF) {
1229 if (value->sign == 0)
1230 return fc_get_plusinf(desc, result);
1232 return fc_get_minusinf(desc, result);
1235 /* set the descriptor of the new value */
1236 result->desc.exponent_size = desc->exponent_size;
1237 result->desc.mantissa_size = desc->mantissa_size;
1238 result->desc.explicit_one = desc->explicit_one;
1239 result->desc.clss = value->desc.clss;
1241 result->sign = value->sign;
1243 /* when the mantissa sizes differ normalizing has to shift to align it.
1244 * this would change the exponent, which is unwanted. So calculate this
1245 * offset and add it */
1246 val_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1247 res_bias = (1 << (desc->exponent_size - 1)) - 1;
1249 exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
1250 sc_val_from_long(exp_offset, temp);
1251 sc_add(_exp(value), temp, _exp(result));
1253 /* _normalize expects normalized radix point */
1254 if (value->desc.clss == SUBNORMAL) {
1255 sc_val_from_ulong(1, NULL);
1256 _shift_left(_mant(value), sc_get_buffer(), _mant(result));
1257 } else if (value != result) {
1258 memcpy(_mant(result), _mant(value), value_size);
1260 memmove(_mant(result), _mant(value), value_size);
1263 normalize(result, result, 0);
1264 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1268 fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result) {
1269 if (result == NULL) result = calc_buffer;
1271 result->desc.exponent_size = desc->exponent_size;
1272 result->desc.mantissa_size = desc->mantissa_size;
1273 result->desc.explicit_one = desc->explicit_one;
1274 result->desc.clss = NORMAL;
1278 sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
1280 sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
1281 sc_val_from_ulong(ROUNDING_BITS, NULL);
1282 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1287 fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result) {
1288 if (result == NULL) result = calc_buffer;
1290 fc_get_max(desc, result);
1296 fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result) {
1297 if (result == NULL) result = calc_buffer;
1299 result->desc.exponent_size = desc->exponent_size;
1300 result->desc.mantissa_size = desc->mantissa_size;
1301 result->desc.explicit_one = desc->explicit_one;
1302 result->desc.clss = NAN;
1306 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1308 /* signaling NaN has non-zero mantissa with msb not set */
1309 sc_val_from_ulong(1, _mant(result));
1314 fp_value *fc_get_qnan(const ieee_descriptor_t *desc, fp_value *result) {
1315 if (result == NULL) result = calc_buffer;
1317 result->desc.exponent_size = desc->exponent_size;
1318 result->desc.mantissa_size = desc->mantissa_size;
1319 result->desc.explicit_one = desc->explicit_one;
1320 result->desc.clss = NAN;
1324 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1326 /* quiet NaN has the msb of the mantissa set, so shift one there */
1327 sc_val_from_ulong(1, _mant(result));
1328 /* mantissa_size >+< 1 because of two extra rounding bits */
1329 sc_val_from_ulong(desc->mantissa_size + 1, NULL);
1330 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1335 fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result)
1339 if (result == NULL) result = calc_buffer;
1341 result->desc.exponent_size = desc->exponent_size;
1342 result->desc.mantissa_size = desc->mantissa_size;
1343 result->desc.explicit_one = desc->explicit_one;
1344 result->desc.clss = INF;
1348 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1350 mant = _mant(result);
1351 sc_val_from_ulong(0, mant);
1352 if (desc->explicit_one) {
1353 sc_set_bit_at(mant, result->desc.mantissa_size + ROUNDING_BITS);
1359 fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result) {
1360 if (result == NULL) result = calc_buffer;
1362 fc_get_plusinf(desc, result);
1368 int fc_comp(const fp_value *val_a, const fp_value *val_b) {
1372 * shortcut: if both values are identical, they are either
1373 * Unordered if NaN or equal
1376 return val_a->desc.clss == NAN ? 2 : 0;
1378 /* unordered if one is a NaN */
1379 if (val_a->desc.clss == NAN || val_b->desc.clss == NAN)
1382 /* zero is equal independent of sign */
1383 if ((val_a->desc.clss == ZERO) && (val_b->desc.clss == ZERO))
1386 /* different signs make compare easy */
1387 if (val_a->sign != val_b->sign)
1388 return (val_a->sign == 0) ? (1) : (-1);
1390 mul = val_a->sign ? -1 : 1;
1392 /* both infinity means equality */
1393 if ((val_a->desc.clss == INF) && (val_b->desc.clss == INF))
1396 /* infinity is bigger than the rest */
1397 if (val_a->desc.clss == INF)
1399 if (val_b->desc.clss == INF)
1402 /* check first exponent, that mantissa if equal */
1403 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1409 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1415 int fc_is_zero(const fp_value *a) {
1416 return a->desc.clss == ZERO;
1419 int fc_is_negative(const fp_value *a) {
1423 int fc_is_inf(const fp_value *a) {
1424 return a->desc.clss == INF;
1427 int fc_is_nan(const fp_value *a) {
1428 return a->desc.clss == NAN;
1431 int fc_is_subnormal(const fp_value *a) {
1432 return a->desc.clss == SUBNORMAL;
1435 char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base) {
1439 mul_1 = alloca(calc_buffer_size);
1443 switch ((value_class_t)val->desc.clss) {
1445 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1448 snprintf(buf, buflen, "NaN");
1451 snprintf(buf, buflen, "0.0");
1454 flt_val = fc_val_to_ieee754(val);
1455 #ifdef HAVE_LONG_DOUBLE
1456 /* XXX 30 is arbitrary */
1457 snprintf(buf, buflen, "%.30LE", flt_val);
1459 snprintf(buf, buflen, "%.18E", flt_val);
1465 switch ((value_class_t)val->desc.clss) {
1467 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1470 snprintf(buf, buflen, "NAN");
1473 snprintf(buf, buflen, "0.0");
1476 flt_val = fc_val_to_ieee754(val);
1477 #ifdef HAVE_LONG_DOUBLE
1478 snprintf(buf, buflen, "%LA", flt_val);
1480 snprintf(buf, buflen, "%A", flt_val);
1487 snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0));
1488 buf[buflen - 1] = '\0';
1494 unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs) {
1495 /* this is used to cache the packed version of the value */
1496 static char *packed_value = NULL;
1498 if (packed_value == NULL) packed_value = XMALLOCN(char, value_size);
1501 pack(value, packed_value);
1503 return sc_sub_bits(packed_value, num_bits, byte_ofs);
1506 /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */
1507 int fc_zero_mantissa(const fp_value *value) {
1508 return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size;
1511 /* Returns the exponent of a value. */
1512 int fc_get_exponent(const fp_value *value) {
1513 int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1514 return sc_val_to_long(_exp(value)) - exp_bias;
1517 /* Return non-zero if a given value can be converted lossless into another precision */
1518 int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc) {
1522 /* handle some special cases first */
1523 switch (value->desc.clss) {
1532 /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */
1533 exp_bias = (1 << (desc->exponent_size - 1)) - 1;
1534 v = fc_get_exponent(value) + exp_bias;
1535 if (0 < v && v < (1 << desc->exponent_size) - 1) {
1536 /* exponent can be encoded, now check the mantissa */
1537 v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value));
1538 return v <= desc->mantissa_size;
1544 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode) {
1545 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1546 rounding_mode = mode;
1548 return rounding_mode;
1551 fc_rounding_mode_t fc_get_rounding_mode(void) {
1552 return rounding_mode;
1555 void init_fltcalc(int precision) {
1556 if (calc_buffer == NULL) {
1557 /* does nothing if already init */
1558 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1560 init_strcalc(precision + 2 + ROUNDING_BITS);
1562 /* needs additionally rounding bits, one bit as explicit 1., and one for
1563 * addition overflow */
1564 max_precision = sc_get_precision() - (2 + ROUNDING_BITS);
1565 if (max_precision < precision)
1566 printf("WARNING: not enough precision available, using %d\n", max_precision);
1568 rounding_mode = FC_TONEAREST;
1569 value_size = sc_get_buffer_length();
1570 calc_buffer_size = sizeof(fp_value) + 2*value_size - 1;
1572 calc_buffer = xmalloc(calc_buffer_size);
1573 memset(calc_buffer, 0, calc_buffer_size);
1574 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer));
1575 #ifdef HAVE_LONG_DOUBLE
1576 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1578 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1580 #ifdef WORDS_BIGENDIAN
1581 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1583 DEBUGPRINTF(("\tWord order is little endian\n\n"));
1588 void finish_fltcalc (void) {
1589 free(calc_buffer); calc_buffer = NULL;
1592 #ifdef FLTCALC_TRACE_CALC
1593 static char buffer[100];
1596 /* definition of interface functions */
1597 fp_value *fc_add(const fp_value *a, const fp_value *b, fp_value *result) {
1598 if (result == NULL) result = calc_buffer;
1600 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1601 TRACEPRINTF(("+ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1603 /* make the value with the bigger exponent the first one */
1604 if (sc_comp(_exp(a), _exp(b)) == -1)
1605 _fadd(b, a, result);
1607 _fadd(a, b, result);
1609 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1613 fp_value *fc_sub(const fp_value *a, const fp_value *b, fp_value *result) {
1616 if (result == NULL) result = calc_buffer;
1618 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1619 TRACEPRINTF(("- %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1621 temp = alloca(calc_buffer_size);
1622 memcpy(temp, b, calc_buffer_size);
1623 temp->sign = !b->sign;
1624 if (sc_comp(_exp(a), _exp(temp)) == -1)
1625 _fadd(temp, a, result);
1627 _fadd(a, temp, result);
1629 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1633 fp_value *fc_mul(const fp_value *a, const fp_value *b, fp_value *result) {
1634 if (result == NULL) result = calc_buffer;
1636 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1637 TRACEPRINTF(("* %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1639 _fmul(a, b, result);
1641 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1645 fp_value *fc_div(const fp_value *a, const fp_value *b, fp_value *result) {
1646 if (result == NULL) result = calc_buffer;
1648 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1649 TRACEPRINTF(("/ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1651 _fdiv(a, b, result);
1653 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1657 fp_value *fc_neg(const fp_value *a, fp_value *result) {
1658 if (result == NULL) result = calc_buffer;
1660 TRACEPRINTF(("- %s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1663 memcpy(result, a, calc_buffer_size);
1664 result->sign = !a->sign;
1666 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1670 fp_value *fc_int(const fp_value *a, fp_value *result) {
1671 if (result == NULL) result = calc_buffer;
1673 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1674 TRACEPRINTF(("truncated to integer "));
1678 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1682 fp_value *fc_rnd(const fp_value *a, fp_value *result) {
1683 if (result == NULL) result = calc_buffer;
1686 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1687 TRACEPRINTF(("rounded to integer "));
1689 assert(!"fc_rnd() not yet implemented");
1691 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1696 * convert a floating point value into an sc value ...
1698 int fc_flt2int(const fp_value *a, void *result, ir_mode *dst_mode)
1700 if (a->desc.clss == NORMAL) {
1701 int exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
1702 int exp_val = sc_val_to_long(_exp(a)) - exp_bias;
1707 if (a->sign && !mode_is_signed(dst_mode)) {
1708 /* FIXME: for now we cannot convert this */
1712 tgt_bits = get_mode_size_bits(dst_mode);
1713 if (mode_is_signed(dst_mode))
1716 assert(exp_val >= 0 && "floating point value not integral before fc_flt2int() call");
1717 mantissa_size = a->desc.mantissa_size + ROUNDING_BITS;
1718 shift = exp_val - mantissa_size;
1720 if (tgt_bits < mantissa_size + 1)
1721 tgt_bits = mantissa_size + 1;
1723 sc_shlI(_mant(a), shift, tgt_bits, 0, result);
1725 sc_shrI(_mant(a), -shift, tgt_bits, 0, result);
1728 /* check for overflow */
1729 highest = sc_get_highest_set_bit(result);
1731 if (mode_is_signed(dst_mode)) {
1732 if (highest == sc_get_lowest_set_bit(result)) {
1733 /* need extra test for MIN_INT */
1734 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1735 /* FIXME: handle overflow */
1739 if (highest >= (int) get_mode_size_bits(dst_mode) - 1) {
1740 /* FIXME: handle overflow */
1745 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1746 /* FIXME: handle overflow */
1752 sc_neg(result, result);
1756 else if (a->desc.clss == ZERO) {
1764 unsigned fc_set_immediate_precision(unsigned bits) {
1765 unsigned old = immediate_prec;
1767 immediate_prec = bits;
1771 int fc_is_exact(void) {