2 * Copyright (C) 1995-2011 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
44 * portability stuff (why do we even care about the msvc people with their C89?)
48 static long double string_to_long_double(const char *str)
50 #if __STDC_VERSION__ >= 199901L || _POSIX_C_SOURCE >= 200112L
51 return strtold(str, NULL);
53 return strtod(str, NULL);
57 static bool my_isnan(long double val)
59 #if __STDC_VERSION__ >= 199901L
62 /* hopefully the compiler does not optimize aggressively (=incorrect) */
67 static bool my_isinf(long double val)
69 #if __STDC_VERSION__ >= 199901L
72 /* hopefully the compiler does not optimize aggressively (=incorrect) */
73 return my_isnan(val-val) && !my_isnan(val);
77 /** The number of extra precision rounding bits */
78 #define ROUNDING_BITS 2
82 #ifdef WORDS_BIGENDIAN
88 #ifdef WORDS_BIGENDIAN
95 #ifdef WORDS_BIGENDIAN
100 #ifdef WORDS_BIGENDIAN
106 volatile long double d;
109 #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
111 /* our floating point value */
113 ieee_descriptor_t desc;
115 char value[1]; /* exp[value_size] + mant[value_size] */
118 #define _exp(a) &((a)->value[0])
119 #define _mant(a) &((a)->value[value_size])
121 #define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
122 #define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res))
123 #define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res))
127 # define DEBUGPRINTF(x) printf x
129 # define DEBUGPRINTF(x) ((void)0)
132 #ifdef FLTCALC_TRACE_CALC
133 # define TRACEPRINTF(x) printf x
135 # define TRACEPRINTF(x) ((void)0)
138 /** The immediate precision. */
139 static unsigned immediate_prec = 0;
141 /** A temporal buffer. */
142 static fp_value *calc_buffer = NULL;
144 /** Current rounding mode.*/
145 static fc_rounding_mode_t rounding_mode;
147 static int calc_buffer_size;
148 static int value_size;
149 static int max_precision;
152 static int fc_exact = 1;
154 /** pack machine-like */
155 static void *pack(const fp_value *int_float, void *packed)
159 fp_value *val_buffer;
162 temp = (char*) alloca(value_size);
163 shift_val = (char*) alloca(value_size);
165 switch ((value_class_t)int_float->desc.clss) {
167 val_buffer = (fp_value*) alloca(calc_buffer_size);
168 fc_get_qnan(&int_float->desc, val_buffer);
169 int_float = val_buffer;
173 val_buffer = (fp_value*) alloca(calc_buffer_size);
174 fc_get_plusinf(&int_float->desc, val_buffer);
175 val_buffer->sign = int_float->sign;
176 int_float = val_buffer;
182 assert(int_float->desc.explicit_one <= 1);
184 /* pack sign: move it to the left after exponent AND mantissa */
185 sc_val_from_ulong(int_float->sign, temp);
187 pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
188 sc_val_from_ulong(pos, NULL);
189 _shift_left(temp, sc_get_buffer(), packed);
191 /* pack exponent: move it to the left after mantissa */
192 pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
193 sc_val_from_ulong(pos, shift_val);
194 _shift_left(_exp(int_float), shift_val, temp);
196 /* combine sign|exponent */
197 sc_or(temp, packed, packed);
199 /* extract mantissa */
200 /* remove rounding bits */
201 sc_val_from_ulong(ROUNDING_BITS, shift_val);
202 _shift_right(_mant(int_float), shift_val, temp);
204 /* remove leading 1 (or 0 if denormalized) */
205 sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */
206 sc_and(temp, shift_val, temp);
208 /* combine sign|exponent|mantissa */
209 sc_or(temp, packed, packed);
215 * Normalize a fp_value.
217 * @return non-zero if result is exact
219 static int normalize(const fp_value *in_val, fp_value *out_val, int sticky)
223 char lsb, guard, round, round_dir = 0;
224 char *temp = (char*) alloca(value_size);
226 /* save rounding bits at the end */
227 hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
229 if (in_val != out_val) {
230 out_val->sign = in_val->sign;
231 out_val->desc = in_val->desc;
234 out_val->desc.clss = FC_NORMAL;
236 /* mantissa all zeros, so zero exponent (because of explicit one) */
237 if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) {
238 sc_val_from_ulong(0, _exp(out_val));
242 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
245 sc_val_from_ulong(-hsb-1, temp);
247 _shift_right(_mant(in_val), temp, _mant(out_val));
249 /* remember if some bits were shifted away */
250 if (sc_had_carry()) {
254 sc_add(_exp(in_val), temp, _exp(out_val));
255 } else if (hsb > -1) {
257 sc_val_from_ulong(hsb+1, temp);
259 _shift_left(_mant(in_val), temp, _mant(out_val));
261 sc_sub(_exp(in_val), temp, _exp(out_val));
264 /* check for exponent underflow */
265 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
266 DEBUGPRINTF(("Exponent underflow!\n"));
267 /* exponent underflow */
268 /* shift the mantissa right to have a zero exponent */
269 sc_val_from_ulong(1, temp);
270 sc_sub(temp, _exp(out_val), NULL);
272 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
273 if (sc_had_carry()) {
277 /* denormalized means exponent of zero */
278 sc_val_from_ulong(0, _exp(out_val));
280 out_val->desc.clss = FC_SUBNORMAL;
283 /* perform rounding by adding a value that clears the guard bit and the round bit
284 * and either causes a carry to round up or not */
285 /* get the last 3 bits of the value */
286 lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
287 guard = (lsb&0x2)>>1;
290 switch (rounding_mode) {
292 /* round to nearest representable value, if in doubt choose the version
294 round_dir = guard && (sticky || round || lsb>>2);
297 /* if positive: round to one if the exact value is bigger, else to zero */
298 round_dir = (!out_val->sign && (guard || round || sticky));
301 /* if negative: round to one if the exact value is bigger, else to zero */
302 round_dir = (out_val->sign && (guard || round || sticky));
305 /* always round to 0 (chopping mode) */
309 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"));
311 if (round_dir == 1) {
312 guard = (round^guard)<<1;
313 lsb = !(round || guard)<<2 | guard | round;
315 lsb = -((guard<<1) | round);
318 /* add the rounded value */
320 sc_val_from_long(lsb, temp);
321 sc_add(_mant(out_val), temp, _mant(out_val));
325 /* could have rounded down to zero */
326 if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == FC_SUBNORMAL))
327 out_val->desc.clss = FC_ZERO;
329 /* check for rounding overflow */
330 hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
331 if ((out_val->desc.clss != FC_SUBNORMAL) && (hsb < -1)) {
332 sc_val_from_ulong(1, temp);
333 _shift_right(_mant(out_val), temp, _mant(out_val));
334 if (exact && sc_had_carry())
336 sc_add(_exp(out_val), temp, _exp(out_val));
337 } else if ((out_val->desc.clss == FC_SUBNORMAL) && (hsb == -1)) {
338 /* overflow caused the mantissa to be normal again,
339 * so adapt the exponent accordingly */
340 sc_val_from_ulong(1, temp);
341 sc_add(_exp(out_val), temp, _exp(out_val));
343 out_val->desc.clss = FC_NORMAL;
345 /* no further rounding is needed, because rounding overflow means
346 * the carry of the original rounding was propagated all the way
347 * up to the bit left of the radix point. This implies the bits
348 * to the right are all zeros (rounding is +1) */
350 /* check for exponent overflow */
351 sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp);
352 if (sc_comp(_exp(out_val), temp) != -1) {
353 DEBUGPRINTF(("Exponent overflow!\n"));
354 /* exponent overflow, reaction depends on rounding method:
356 * mode | sign of value | result
357 *--------------------------------------------------------------
358 * TO_NEAREST | + | +inf
360 *--------------------------------------------------------------
361 * TO_POSITIVE | + | +inf
362 * | - | smallest representable value
363 *--------------------------------------------------------------
364 * TO_NEAGTIVE | + | largest representable value
366 *--------------------------------------------------------------
367 * TO_ZERO | + | largest representable value
368 * | - | smallest representable value
369 *--------------------------------------------------------------*/
370 if (out_val->sign == 0) {
371 /* value is positive */
372 switch (rounding_mode) {
375 out_val->desc.clss = FC_INF;
380 fc_get_max(&out_val->desc, out_val);
383 /* value is negative */
384 switch (rounding_mode) {
387 out_val->desc.clss = FC_INF;
392 fc_get_min(&out_val->desc, out_val);
400 * Operations involving NaN's must return NaN.
401 * They are NOT exact.
403 #define handle_NAN(a, b, result) \
405 if (a->desc.clss == FC_NAN) { \
406 if (a != result) memcpy(result, a, calc_buffer_size); \
410 if (b->desc.clss == FC_NAN) { \
411 if (b != result) memcpy(result, b, calc_buffer_size); \
419 * calculate a + b, where a is the value with the bigger exponent
421 static void _fadd(const fp_value *a, const fp_value *b, fp_value *result)
431 handle_NAN(a, b, result);
433 /* make sure result has a descriptor */
434 if (result != a && result != b)
435 result->desc = a->desc;
437 /* determine if this is an addition or subtraction */
438 sign = a->sign ^ b->sign;
440 /* produce NaN on inf - inf */
441 if (sign && (a->desc.clss == FC_INF) && (b->desc.clss == FC_INF)) {
443 fc_get_qnan(&a->desc, result);
447 temp = (char*) alloca(value_size);
448 exp_diff = (char*) alloca(value_size);
450 /* get exponent difference */
451 sc_sub(_exp(a), _exp(b), exp_diff);
453 /* initially set sign to be the sign of a, special treatment of subtraction
454 * when exponents are equal is required though.
455 * Also special care about the sign is needed when the mantissas are equal
457 if (sign && sc_val_to_long(exp_diff) == 0) {
458 switch (sc_comp(_mant(a), _mant(b))) {
460 res_sign = a->sign; /* abs(a) is bigger and a is negative */
463 res_sign = (rounding_mode == FC_TONEGATIVE);
466 res_sign = b->sign; /* abs(b) is bigger and b is negative */
469 /* can't be reached */
476 result->sign = res_sign;
478 /* sign has been taken care of, check for special cases */
479 if (a->desc.clss == FC_ZERO || b->desc.clss == FC_INF) {
481 memcpy(result, b, calc_buffer_size);
482 fc_exact = b->desc.clss == FC_NORMAL;
483 result->sign = res_sign;
486 if (b->desc.clss == FC_ZERO || a->desc.clss == FC_INF) {
488 memcpy(result, a, calc_buffer_size);
489 fc_exact = a->desc.clss == FC_NORMAL;
490 result->sign = res_sign;
494 /* shift the smaller value to the right to align the radix point */
495 /* subnormals have their radix point shifted to the right,
496 * take care of this first */
497 if ((b->desc.clss == FC_SUBNORMAL) && (a->desc.clss != FC_SUBNORMAL)) {
498 sc_val_from_ulong(1, temp);
499 sc_sub(exp_diff, temp, exp_diff);
502 _shift_right(_mant(b), exp_diff, temp);
503 sticky = sc_had_carry();
506 if (sticky && sign) {
507 /* if subtracting a little more than the represented value or adding a little
508 * more than the represented value to a negative value this, in addition to the
509 * still set sticky bit, takes account of the 'little more' */
510 char *temp1 = (char*) alloca(calc_buffer_size);
511 sc_val_from_ulong(1, temp1);
512 sc_add(temp, temp1, temp);
516 if (sc_comp(_mant(a), temp) == -1)
517 sc_sub(temp, _mant(a), _mant(result));
519 sc_sub(_mant(a), temp, _mant(result));
521 sc_add(_mant(a), temp, _mant(result));
524 /* _normalize expects a 'normal' radix point, adding two subnormals
525 * results in a subnormal radix point -> shifting before normalizing */
526 if ((a->desc.clss == FC_SUBNORMAL) && (b->desc.clss == FC_SUBNORMAL)) {
527 sc_val_from_ulong(1, NULL);
528 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
531 /* resulting exponent is the bigger one */
532 memmove(_exp(result), _exp(a), value_size);
534 fc_exact &= normalize(result, result, sticky);
540 static void _fmul(const fp_value *a, const fp_value *b, fp_value *result)
548 handle_NAN(a, b, result);
550 temp = (char*) alloca(value_size);
552 if (result != a && result != b)
553 result->desc = a->desc;
555 result->sign = res_sign = a->sign ^ b->sign;
557 /* produce NaN on 0 * inf */
558 if (a->desc.clss == FC_ZERO) {
559 if (b->desc.clss == FC_INF) {
560 fc_get_qnan(&a->desc, result);
564 memcpy(result, a, calc_buffer_size);
565 result->sign = res_sign;
569 if (b->desc.clss == FC_ZERO) {
570 if (a->desc.clss == FC_INF) {
571 fc_get_qnan(&a->desc, result);
575 memcpy(result, b, calc_buffer_size);
576 result->sign = res_sign;
581 if (a->desc.clss == FC_INF) {
584 memcpy(result, a, calc_buffer_size);
585 result->sign = res_sign;
588 if (b->desc.clss == FC_INF) {
591 memcpy(result, b, calc_buffer_size);
592 result->sign = res_sign;
596 /* exp = exp(a) + exp(b) - excess */
597 sc_add(_exp(a), _exp(b), _exp(result));
599 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
600 sc_sub(_exp(result), temp, _exp(result));
602 /* mixed normal, subnormal values introduce an error of 1, correct it */
603 if ((a->desc.clss == FC_SUBNORMAL) ^ (b->desc.clss == FC_SUBNORMAL)) {
604 sc_val_from_ulong(1, temp);
605 sc_add(_exp(result), temp, _exp(result));
608 sc_mul(_mant(a), _mant(b), _mant(result));
610 /* realign result: after a multiplication the digits right of the radix
611 * point are the sum of the factors' digits after the radix point. As all
612 * values are normalized they both have the same amount of these digits,
613 * which has to be restored by proper shifting
614 * because of the rounding bits */
615 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
617 _shift_right(_mant(result), temp, _mant(result));
618 sticky = sc_had_carry();
621 fc_exact &= normalize(result, result, sticky);
627 static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result)
630 char *temp, *dividend;
635 handle_NAN(a, b, result);
637 temp = (char*) alloca(value_size);
638 dividend = (char*) alloca(value_size);
640 if (result != a && result != b)
641 result->desc = a->desc;
643 result->sign = res_sign = a->sign ^ b->sign;
645 /* produce FC_NAN on 0/0 and inf/inf */
646 if (a->desc.clss == FC_ZERO) {
647 if (b->desc.clss == FC_ZERO) {
649 fc_get_qnan(&a->desc, result);
654 memcpy(result, a, calc_buffer_size);
655 result->sign = res_sign;
660 if (b->desc.clss == FC_INF) {
662 if (a->desc.clss == FC_INF) {
664 fc_get_qnan(&a->desc, result);
667 sc_val_from_ulong(0, NULL);
668 _save_result(_exp(result));
669 _save_result(_mant(result));
670 result->desc.clss = FC_ZERO;
675 if (a->desc.clss == FC_INF) {
679 memcpy(result, a, calc_buffer_size);
680 result->sign = res_sign;
683 if (b->desc.clss == FC_ZERO) {
685 /* division by zero */
687 fc_get_minusinf(&a->desc, result);
689 fc_get_plusinf(&a->desc, result);
693 /* exp = exp(a) - exp(b) + excess - 1*/
694 sc_sub(_exp(a), _exp(b), _exp(result));
695 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp);
696 sc_add(_exp(result), temp, _exp(result));
698 /* mixed normal, subnormal values introduce an error of 1, correct it */
699 if ((a->desc.clss == FC_SUBNORMAL) ^ (b->desc.clss == FC_SUBNORMAL)) {
700 sc_val_from_ulong(1, temp);
701 sc_add(_exp(result), temp, _exp(result));
704 /* mant(res) = mant(a) / 1/2mant(b) */
705 /* to gain more bits of precision in the result the dividend could be
706 * shifted left, as this operation does not loose bits. This would not
707 * fit into the integer precision, but due to the rounding bits (which
708 * are always zero because the values are all normalized) the divisor
709 * can be shifted right instead to achieve the same result */
710 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
712 _shift_left(_mant(a), temp, dividend);
715 char *divisor = (char*) alloca(calc_buffer_size);
716 sc_val_from_ulong(1, divisor);
717 _shift_right(_mant(b), divisor, divisor);
718 sc_div(dividend, divisor, _mant(result));
719 sticky = sc_had_carry();
723 fc_exact &= normalize(result, result, sticky);
727 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result)
735 /* set new descriptor (else result is supposed to already have one) */
737 result->desc = *desc;
739 build = alloca(value_size);
740 temp = alloca(value_size);
742 sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
745 /* temp is value of ten now */
746 sc_val_from_ulong(10, NULL);
749 for (exp--; exp > 0; exp--) {
751 sc_mul(build, temp, NULL);
755 /* temp is amount of left shift needed to put the value left of the radix point */
756 sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
758 _shift_left(build, temp, _mant(result));
760 _normalize(result, result, 0);
766 * Truncate the fractional part away.
768 * This does not clip to any integer range.
770 static void _trunc(const fp_value *a, fp_value *result)
773 * When exponent == 0 all bits left of the radix point
774 * are the integral part of the value. For 15bit exp_size
775 * this would require a left shift of max. 16383 bits which
777 * But it is enough to ensure that no bit right of the radix
778 * point remains set. This restricts the interesting
779 * exponents to the interval [0, mant_size-1].
780 * Outside this interval the truncated value is either 0 or
781 * it does not have fractional parts.
784 int exp_bias, exp_val;
787 /* fixme: can be exact */
790 temp = (char*) alloca(value_size);
793 result->desc = a->desc;
795 exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
796 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
799 sc_val_from_ulong(0, NULL);
800 _save_result(_exp(result));
801 _save_result(_mant(result));
802 result->desc.clss = FC_ZERO;
807 if (exp_val > (long)a->desc.mantissa_size) {
809 memcpy(result, a, calc_buffer_size);
814 /* set up a proper mask to delete all bits right of the
815 * radix point if the mantissa had been shifted until exp == 0 */
816 sc_max_from_bits(1 + exp_val, 0, temp);
817 sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL);
818 _shift_left(temp, sc_get_buffer(), temp);
820 /* and the mask and return the result */
821 sc_and(_mant(a), temp, _mant(result));
824 memcpy(_exp(result), _exp(a), value_size);
825 result->sign = a->sign;
830 * functions defined in fltcalc.h
832 const void *fc_get_buffer(void)
837 int fc_get_buffer_length(void)
839 return calc_buffer_size;
842 void *fc_val_from_str(const char *str, size_t len, const ieee_descriptor_t *desc, void *result)
846 /* XXX excuse of an implementation to make things work */
848 fp_value *tmp = (fp_value*) alloca(calc_buffer_size);
849 ieee_descriptor_t tmp_desc;
851 buffer = (char*) alloca(len+1);
852 memcpy(buffer, str, len);
854 val = string_to_long_double(buffer);
856 DEBUGPRINTF(("val_from_str(%s)\n", str));
857 tmp_desc.exponent_size = 15;
858 tmp_desc.mantissa_size = 63;
859 tmp_desc.explicit_one = 1;
860 tmp_desc.clss = FC_NORMAL;
861 fc_val_from_ieee754(val, &tmp_desc, tmp);
863 return fc_cast(tmp, desc, (fp_value*) result);
866 fp_value *fc_val_from_ieee754(long double l, const ieee_descriptor_t *desc, fp_value *result)
869 int bias_res, bias_val, mant_val;
872 uint32_t exponent, mantissa0, mantissa1;
873 size_t long_double_size = sizeof(long double);
876 bias_res = ((1 << (desc->exponent_size - 1)) - 1);
878 if (long_double_size == 8) {
881 sign = (srcval.val_ld8.high & 0x80000000) != 0;
882 exponent = (srcval.val_ld8.high & 0x7FF00000) >> 20;
883 mantissa0 = srcval.val_ld8.high & 0x000FFFFF;
884 mantissa1 = srcval.val_ld8.low;
886 /* we assume an x86-like 80bit representation of the value... */
887 assert(sizeof(long double)==12 || sizeof(long double)==16);
890 sign = (srcval.val_ld12.high & 0x00008000) != 0;
891 exponent = (srcval.val_ld12.high & 0x00007FFF) ;
892 mantissa0 = srcval.val_ld12.mid;
893 mantissa1 = srcval.val_ld12.low;
896 if (result == NULL) result = calc_buffer;
897 temp = (char*) alloca(value_size);
899 /* CLEAR the buffer, else some bits might be uninitialized */
900 memset(result, 0, fc_get_buffer_length());
902 result->desc.exponent_size = desc->exponent_size;
903 result->desc.mantissa_size = desc->mantissa_size;
904 result->desc.explicit_one = desc->explicit_one;
909 /* sign and flag suffice to identify NaN or inf, no exponent/mantissa
910 * encoding is needed. the function can return immediately in these cases */
912 result->desc.clss = FC_NAN;
913 TRACEPRINTF(("val_from_float resulted in NAN\n"));
915 } else if (my_isinf(l)) {
916 result->desc.clss = FC_INF;
917 TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
921 /* build exponent, because input and output exponent and mantissa sizes may differ
922 * this looks more complicated than it is: unbiased input exponent + output bias,
923 * minus the mantissa difference which is added again later when the output float
924 * becomes normalized */
925 sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
927 /* build mantissa representation */
929 /* insert the hidden bit */
930 sc_val_from_ulong(1, temp);
931 sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
932 _shift_left(temp, sc_get_buffer(), NULL);
935 sc_val_from_ulong(0, NULL);
938 _save_result(_mant(result));
940 /* bits from the upper word */
941 sc_val_from_ulong(mantissa0, temp);
942 sc_val_from_ulong(34, NULL);
943 _shift_left(temp, sc_get_buffer(), temp);
944 sc_or(_mant(result), temp, _mant(result));
946 /* bits from the lower word */
947 sc_val_from_ulong(mantissa1, temp);
948 sc_val_from_ulong(ROUNDING_BITS, NULL);
949 _shift_left(temp, sc_get_buffer(), temp);
950 sc_or(_mant(result), temp, _mant(result));
952 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
953 * origin one to the left */
955 sc_val_from_ulong(1, NULL);
956 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
959 normalize(result, result, 0);
961 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
966 long double fc_val_to_ieee754(const fp_value *val)
969 fp_value *temp = NULL;
971 unsigned byte_offset;
979 ieee_descriptor_t desc;
980 unsigned mantissa_size;
982 size_t long_double_size = sizeof(long double);
984 if (long_double_size == 8) {
985 desc.exponent_size = 11;
986 desc.mantissa_size = 52;
987 desc.explicit_one = 0;
988 desc.clss = FC_NORMAL;
990 desc.exponent_size = 15;
991 desc.mantissa_size = 63;
992 desc.explicit_one = 1;
993 desc.clss = FC_NORMAL;
995 mantissa_size = desc.mantissa_size + desc.explicit_one;
997 temp = (fp_value*) alloca(calc_buffer_size);
998 value = fc_cast(val, &desc, temp);
1002 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
1003 * lead to wrong results */
1004 exponent = sc_val_to_long(_exp(value)) ;
1006 sc_val_from_ulong(ROUNDING_BITS, NULL);
1007 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
1012 for (byte_offset = 0; byte_offset < 4; byte_offset++)
1013 mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
1015 for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
1016 mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
1018 if (long_double_size == 8) {
1019 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1020 buildval.val_ld8.high = sign << 31;
1021 buildval.val_ld8.high |= exponent << 20;
1022 buildval.val_ld8.high |= mantissa0;
1023 buildval.val_ld8.low = mantissa1;
1025 buildval.val_ld12.high = sign << 15;
1026 buildval.val_ld12.high |= exponent;
1027 buildval.val_ld12.mid = mantissa0;
1028 buildval.val_ld12.low = mantissa1;
1031 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1035 fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result)
1038 int exp_offset, val_bias, res_bias;
1040 if (result == NULL) result = calc_buffer;
1041 temp = (char*) alloca(value_size);
1043 if (value->desc.exponent_size == desc->exponent_size &&
1044 value->desc.mantissa_size == desc->mantissa_size &&
1045 value->desc.explicit_one == desc->explicit_one) {
1046 if (value != result)
1047 memcpy(result, value, calc_buffer_size);
1051 if (value->desc.clss == FC_NAN) {
1052 if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
1053 return fc_get_qnan(desc, result);
1055 return fc_get_snan(desc, result);
1057 else if (value->desc.clss == FC_INF) {
1058 if (value->sign == 0)
1059 return fc_get_plusinf(desc, result);
1061 return fc_get_minusinf(desc, result);
1064 /* set the descriptor of the new value */
1065 result->desc.exponent_size = desc->exponent_size;
1066 result->desc.mantissa_size = desc->mantissa_size;
1067 result->desc.explicit_one = desc->explicit_one;
1068 result->desc.clss = value->desc.clss;
1070 result->sign = value->sign;
1072 /* when the mantissa sizes differ normalizing has to shift to align it.
1073 * this would change the exponent, which is unwanted. So calculate this
1074 * offset and add it */
1075 val_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1076 res_bias = (1 << (desc->exponent_size - 1)) - 1;
1078 exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
1079 sc_val_from_long(exp_offset, temp);
1080 sc_add(_exp(value), temp, _exp(result));
1082 /* _normalize expects normalized radix point */
1083 if (value->desc.clss == FC_SUBNORMAL) {
1084 sc_val_from_ulong(1, NULL);
1085 _shift_left(_mant(value), sc_get_buffer(), _mant(result));
1086 } else if (value != result) {
1087 memcpy(_mant(result), _mant(value), value_size);
1089 memmove(_mant(result), _mant(value), value_size);
1092 normalize(result, result, 0);
1093 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1097 fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result)
1099 if (result == NULL) result = calc_buffer;
1101 result->desc.exponent_size = desc->exponent_size;
1102 result->desc.mantissa_size = desc->mantissa_size;
1103 result->desc.explicit_one = desc->explicit_one;
1104 result->desc.clss = FC_NORMAL;
1108 sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
1110 sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
1111 sc_val_from_ulong(ROUNDING_BITS, NULL);
1112 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1117 fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result)
1119 if (result == NULL) result = calc_buffer;
1121 fc_get_max(desc, result);
1127 fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result)
1129 if (result == NULL) result = calc_buffer;
1131 result->desc.exponent_size = desc->exponent_size;
1132 result->desc.mantissa_size = desc->mantissa_size;
1133 result->desc.explicit_one = desc->explicit_one;
1134 result->desc.clss = FC_NAN;
1138 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1140 /* signaling NaN has non-zero mantissa with msb not set */
1141 sc_val_from_ulong(1, _mant(result));
1146 fp_value *fc_get_qnan(const ieee_descriptor_t *desc, fp_value *result)
1148 if (result == NULL) result = calc_buffer;
1150 result->desc.exponent_size = desc->exponent_size;
1151 result->desc.mantissa_size = desc->mantissa_size;
1152 result->desc.explicit_one = desc->explicit_one;
1153 result->desc.clss = FC_NAN;
1157 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1159 /* quiet NaN has the msb of the mantissa set, so shift one there */
1160 sc_val_from_ulong(1, _mant(result));
1161 /* mantissa_size >+< 1 because of two extra rounding bits */
1162 sc_val_from_ulong(desc->mantissa_size + 1, NULL);
1163 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1168 fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result)
1172 if (result == NULL) result = calc_buffer;
1174 result->desc.exponent_size = desc->exponent_size;
1175 result->desc.mantissa_size = desc->mantissa_size;
1176 result->desc.explicit_one = desc->explicit_one;
1177 result->desc.clss = FC_INF;
1181 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1183 mant = _mant(result);
1184 sc_val_from_ulong(0, mant);
1185 if (desc->explicit_one) {
1186 sc_set_bit_at(mant, result->desc.mantissa_size + ROUNDING_BITS);
1192 fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result)
1194 if (result == NULL) result = calc_buffer;
1196 fc_get_plusinf(desc, result);
1202 int fc_comp(const fp_value *val_a, const fp_value *val_b)
1207 * shortcut: if both values are identical, they are either
1208 * Unordered if NaN or equal
1211 return val_a->desc.clss == FC_NAN ? 2 : 0;
1213 /* unordered if one is a NaN */
1214 if (val_a->desc.clss == FC_NAN || val_b->desc.clss == FC_NAN)
1217 /* zero is equal independent of sign */
1218 if ((val_a->desc.clss == FC_ZERO) && (val_b->desc.clss == FC_ZERO))
1221 /* different signs make compare easy */
1222 if (val_a->sign != val_b->sign)
1223 return (val_a->sign == 0) ? (1) : (-1);
1225 mul = val_a->sign ? -1 : 1;
1227 /* both infinity means equality */
1228 if ((val_a->desc.clss == FC_INF) && (val_b->desc.clss == FC_INF))
1231 /* infinity is bigger than the rest */
1232 if (val_a->desc.clss == FC_INF)
1234 if (val_b->desc.clss == FC_INF)
1237 /* check first exponent, that mantissa if equal */
1238 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1244 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1250 int fc_is_zero(const fp_value *a)
1252 return a->desc.clss == FC_ZERO;
1255 int fc_is_negative(const fp_value *a)
1260 int fc_is_inf(const fp_value *a)
1262 return a->desc.clss == FC_INF;
1265 int fc_is_nan(const fp_value *a)
1267 return a->desc.clss == FC_NAN;
1270 int fc_is_subnormal(const fp_value *a)
1272 return a->desc.clss == FC_SUBNORMAL;
1275 char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base)
1278 long double flt_val;
1280 mul_1 = (char*) alloca(calc_buffer_size);
1284 switch ((value_class_t)val->desc.clss) {
1286 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1289 snprintf(buf, buflen, "NaN");
1292 snprintf(buf, buflen, "0.0");
1295 flt_val = fc_val_to_ieee754(val);
1296 /* XXX 30 is arbitrary */
1297 snprintf(buf, buflen, "%.30LE", flt_val);
1302 switch ((value_class_t)val->desc.clss) {
1304 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1307 snprintf(buf, buflen, "NaN");
1310 snprintf(buf, buflen, "0.0");
1313 flt_val = fc_val_to_ieee754(val);
1314 snprintf(buf, buflen, "%LA", flt_val);
1320 snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0));
1321 buf[buflen - 1] = '\0';
1327 unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs)
1329 /* this is used to cache the packed version of the value */
1330 static char *packed_value = NULL;
1332 if (packed_value == NULL) packed_value = XMALLOCN(char, value_size);
1335 pack(value, packed_value);
1337 return sc_sub_bits(packed_value, num_bits, byte_ofs);
1340 /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */
1341 int fc_zero_mantissa(const fp_value *value)
1343 return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size;
1346 /* Returns the exponent of a value. */
1347 int fc_get_exponent(const fp_value *value)
1349 int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1350 return sc_val_to_long(_exp(value)) - exp_bias;
1353 /* Return non-zero if a given value can be converted lossless into another precision */
1354 int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc)
1359 /* handle some special cases first */
1360 switch (value->desc.clss) {
1369 /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */
1370 exp_bias = (1 << (desc->exponent_size - 1)) - 1;
1371 v = fc_get_exponent(value) + exp_bias;
1372 if (0 < v && v < (1 << desc->exponent_size) - 1) {
1373 /* exponent can be encoded, now check the mantissa */
1374 v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value));
1375 return v <= (int)desc->mantissa_size;
1381 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
1383 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1384 rounding_mode = mode;
1386 return rounding_mode;
1389 fc_rounding_mode_t fc_get_rounding_mode(void)
1391 return rounding_mode;
1394 void init_fltcalc(int precision)
1396 if (calc_buffer == NULL) {
1397 /* does nothing if already init */
1398 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1400 init_strcalc(precision + 2 + ROUNDING_BITS);
1402 /* needs additionally rounding bits, one bit as explicit 1., and one for
1403 * addition overflow */
1404 max_precision = sc_get_precision() - (2 + ROUNDING_BITS);
1405 if (max_precision < precision)
1406 printf("WARNING: not enough precision available, using %d\n", max_precision);
1408 rounding_mode = FC_TONEAREST;
1409 value_size = sc_get_buffer_length();
1410 calc_buffer_size = sizeof(fp_value) + 2*value_size - 1;
1412 calc_buffer = (fp_value*) xmalloc(calc_buffer_size);
1413 memset(calc_buffer, 0, calc_buffer_size);
1414 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer));
1418 void finish_fltcalc (void)
1420 free(calc_buffer); calc_buffer = NULL;
1423 #ifdef FLTCALC_TRACE_CALC
1424 static char buffer[100];
1427 /* definition of interface functions */
1428 fp_value *fc_add(const fp_value *a, const fp_value *b, fp_value *result)
1430 if (result == NULL) result = calc_buffer;
1432 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1433 TRACEPRINTF(("+ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1435 /* make the value with the bigger exponent the first one */
1436 if (sc_comp(_exp(a), _exp(b)) == -1)
1437 _fadd(b, a, result);
1439 _fadd(a, b, result);
1441 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1445 fp_value *fc_sub(const fp_value *a, const fp_value *b, fp_value *result)
1449 if (result == NULL) result = calc_buffer;
1451 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1452 TRACEPRINTF(("- %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1454 temp = (fp_value*) alloca(calc_buffer_size);
1455 memcpy(temp, b, calc_buffer_size);
1456 temp->sign = !b->sign;
1457 if (sc_comp(_exp(a), _exp(temp)) == -1)
1458 _fadd(temp, a, result);
1460 _fadd(a, temp, result);
1462 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1466 fp_value *fc_mul(const fp_value *a, const fp_value *b, fp_value *result)
1468 if (result == NULL) result = calc_buffer;
1470 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1471 TRACEPRINTF(("* %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1473 _fmul(a, b, result);
1475 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1479 fp_value *fc_div(const fp_value *a, const fp_value *b, fp_value *result)
1481 if (result == NULL) result = calc_buffer;
1483 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1484 TRACEPRINTF(("/ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1486 _fdiv(a, b, result);
1488 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1492 fp_value *fc_neg(const fp_value *a, fp_value *result)
1494 if (result == NULL) result = calc_buffer;
1496 TRACEPRINTF(("- %s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1499 memcpy(result, a, calc_buffer_size);
1500 result->sign = !a->sign;
1502 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1506 fp_value *fc_int(const fp_value *a, fp_value *result)
1508 if (result == NULL) result = calc_buffer;
1510 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1511 TRACEPRINTF(("truncated to integer "));
1515 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1519 fp_value *fc_rnd(const fp_value *a, fp_value *result)
1521 if (result == NULL) result = calc_buffer;
1524 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1525 TRACEPRINTF(("rounded to integer "));
1527 panic("fc_rnd() not yet implemented");
1531 * convert a floating point value into an sc value ...
1533 int fc_flt2int(const fp_value *a, void *result, ir_mode *dst_mode)
1535 if (a->desc.clss == FC_NORMAL) {
1536 int exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
1537 int exp_val = sc_val_to_long(_exp(a)) - exp_bias;
1542 if (a->sign && !mode_is_signed(dst_mode)) {
1543 /* FIXME: for now we cannot convert this */
1547 tgt_bits = get_mode_size_bits(dst_mode);
1548 if (mode_is_signed(dst_mode))
1551 assert(exp_val >= 0 && "floating point value not integral before fc_flt2int() call");
1552 mantissa_size = a->desc.mantissa_size + ROUNDING_BITS;
1553 shift = exp_val - mantissa_size;
1555 if (tgt_bits < mantissa_size + 1)
1556 tgt_bits = mantissa_size + 1;
1558 sc_shlI(_mant(a), shift, tgt_bits, 0, result);
1560 sc_shrI(_mant(a), -shift, tgt_bits, 0, result);
1563 /* check for overflow */
1564 highest = sc_get_highest_set_bit(result);
1566 if (mode_is_signed(dst_mode)) {
1567 if (highest == sc_get_lowest_set_bit(result)) {
1568 /* need extra test for MIN_INT */
1569 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1570 /* FIXME: handle overflow */
1574 if (highest >= (int) get_mode_size_bits(dst_mode) - 1) {
1575 /* FIXME: handle overflow */
1580 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1581 /* FIXME: handle overflow */
1587 sc_neg(result, result);
1591 else if (a->desc.clss == FC_ZERO) {
1599 unsigned fc_set_immediate_precision(unsigned bits)
1601 unsigned old = immediate_prec;
1603 immediate_prec = bits;
1607 int fc_is_exact(void)