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
34 /* undef some reused constants defined by math.h */
48 #define strtold(s, e) strtod(s, e)
53 #define isnan(x) _isnan(x)
54 static inline int isinf(double x)
56 return !_finite(x) && !_isnan(x);
60 /** The number of extra precision rounding bits */
61 #define ROUNDING_BITS 2
63 typedef uint32_t UINT32;
67 #ifdef WORDS_BIGENDIAN
72 #ifdef HAVE_LONG_DOUBLE
75 #ifdef WORDS_BIGENDIAN
81 #ifdef HAVE_LONG_DOUBLE
82 volatile long double d;
88 #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
90 /* our floating point value */
92 ieee_descriptor_t desc;
94 char value[1]; /* exp[value_size] + mant[value_size] */
97 #define _exp(a) &((a)->value[0])
98 #define _mant(a) &((a)->value[value_size])
100 #define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
101 #define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res))
102 #define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res))
106 # define DEBUGPRINTF(x) printf x
108 # define DEBUGPRINTF(x) ((void)0)
111 #ifdef FLTCALC_TRACE_CALC
112 # define TRACEPRINTF(x) printf x
114 # define TRACEPRINTF(x) ((void)0)
117 /** The immediate precision. */
118 static unsigned immediate_prec = 0;
120 /** A temporal buffer. */
121 static fp_value *calc_buffer = NULL;
123 /** Current rounding mode.*/
124 static fc_rounding_mode_t rounding_mode;
126 static int calc_buffer_size;
127 static int value_size;
128 static int max_precision;
131 static int fc_exact = 1;
133 /** pack machine-like */
134 static void *pack(const fp_value *int_float, void *packed)
138 fp_value *val_buffer;
141 temp = (char*) alloca(value_size);
142 shift_val = (char*) alloca(value_size);
144 switch ((value_class_t)int_float->desc.clss) {
146 val_buffer = (fp_value*) alloca(calc_buffer_size);
147 fc_get_qnan(&int_float->desc, val_buffer);
148 int_float = val_buffer;
152 val_buffer = (fp_value*) alloca(calc_buffer_size);
153 fc_get_plusinf(&int_float->desc, val_buffer);
154 val_buffer->sign = int_float->sign;
155 int_float = val_buffer;
161 assert(int_float->desc.explicit_one <= 1);
163 /* pack sign: move it to the left after exponent AND mantissa */
164 sc_val_from_ulong(int_float->sign, temp);
166 pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
167 sc_val_from_ulong(pos, NULL);
168 _shift_left(temp, sc_get_buffer(), packed);
170 /* pack exponent: move it to the left after mantissa */
171 pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
172 sc_val_from_ulong(pos, shift_val);
173 _shift_left(_exp(int_float), shift_val, temp);
175 /* combine sign|exponent */
176 sc_or(temp, packed, packed);
178 /* extract mantissa */
179 /* remove rounding bits */
180 sc_val_from_ulong(ROUNDING_BITS, shift_val);
181 _shift_right(_mant(int_float), shift_val, temp);
183 /* remove leading 1 (or 0 if denormalized) */
184 sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */
185 sc_and(temp, shift_val, temp);
187 /* combine sign|exponent|mantissa */
188 sc_or(temp, packed, packed);
194 * Normalize a fp_value.
196 * @return non-zero if result is exact
198 static int normalize(const fp_value *in_val, fp_value *out_val, int sticky)
202 char lsb, guard, round, round_dir = 0;
203 char *temp = (char*) alloca(value_size);
205 /* save rounding bits at the end */
206 hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
208 if (in_val != out_val) {
209 out_val->sign = in_val->sign;
210 memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc));
213 out_val->desc.clss = NORMAL;
215 /* mantissa all zeros, so zero exponent (because of explicit one) */
216 if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) {
217 sc_val_from_ulong(0, _exp(out_val));
221 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
224 sc_val_from_ulong(-hsb-1, temp);
226 _shift_right(_mant(in_val), temp, _mant(out_val));
228 /* remember if some bits were shifted away */
229 if (sc_had_carry()) {
233 sc_add(_exp(in_val), temp, _exp(out_val));
234 } else if (hsb > -1) {
236 sc_val_from_ulong(hsb+1, temp);
238 _shift_left(_mant(in_val), temp, _mant(out_val));
240 sc_sub(_exp(in_val), temp, _exp(out_val));
243 /* check for exponent underflow */
244 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
245 DEBUGPRINTF(("Exponent underflow!\n"));
246 /* exponent underflow */
247 /* shift the mantissa right to have a zero exponent */
248 sc_val_from_ulong(1, temp);
249 sc_sub(temp, _exp(out_val), NULL);
251 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
252 if (sc_had_carry()) {
256 /* denormalized means exponent of zero */
257 sc_val_from_ulong(0, _exp(out_val));
259 out_val->desc.clss = SUBNORMAL;
262 /* perform rounding by adding a value that clears the guard bit and the round bit
263 * and either causes a carry to round up or not */
264 /* get the last 3 bits of the value */
265 lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
266 guard = (lsb&0x2)>>1;
269 switch (rounding_mode) {
271 /* round to nearest representable value, if in doubt choose the version
273 round_dir = guard && (sticky || round || lsb>>2);
276 /* if positive: round to one if the exact value is bigger, else to zero */
277 round_dir = (!out_val->sign && (guard || round || sticky));
280 /* if negative: round to one if the exact value is bigger, else to zero */
281 round_dir = (out_val->sign && (guard || round || sticky));
284 /* always round to 0 (chopping mode) */
288 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"));
290 if (round_dir == 1) {
291 guard = (round^guard)<<1;
292 lsb = !(round || guard)<<2 | guard | round;
294 lsb = -((guard<<1) | round);
297 /* add the rounded value */
299 sc_val_from_long(lsb, temp);
300 sc_add(_mant(out_val), temp, _mant(out_val));
304 /* could have rounded down to zero */
305 if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL))
306 out_val->desc.clss = ZERO;
308 /* check for rounding overflow */
309 hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
310 if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) {
311 sc_val_from_ulong(1, temp);
312 _shift_right(_mant(out_val), temp, _mant(out_val));
313 if (exact && sc_had_carry())
315 sc_add(_exp(out_val), temp, _exp(out_val));
316 } else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) {
317 /* overflow caused the mantissa to be normal again,
318 * so adapt the exponent accordingly */
319 sc_val_from_ulong(1, temp);
320 sc_add(_exp(out_val), temp, _exp(out_val));
322 out_val->desc.clss = NORMAL;
324 /* no further rounding is needed, because rounding overflow means
325 * the carry of the original rounding was propagated all the way
326 * up to the bit left of the radix point. This implies the bits
327 * to the right are all zeros (rounding is +1) */
329 /* check for exponent overflow */
330 sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp);
331 if (sc_comp(_exp(out_val), temp) != -1) {
332 DEBUGPRINTF(("Exponent overflow!\n"));
333 /* exponent overflow, reaction depends on rounding method:
335 * mode | sign of value | result
336 *--------------------------------------------------------------
337 * TO_NEAREST | + | +inf
339 *--------------------------------------------------------------
340 * TO_POSITIVE | + | +inf
341 * | - | smallest representable value
342 *--------------------------------------------------------------
343 * TO_NEAGTIVE | + | largest representable value
345 *--------------------------------------------------------------
346 * TO_ZERO | + | largest representable value
347 * | - | smallest representable value
348 *--------------------------------------------------------------*/
349 if (out_val->sign == 0) {
350 /* value is positive */
351 switch (rounding_mode) {
354 out_val->desc.clss = INF;
359 fc_get_max(&out_val->desc, out_val);
362 /* value is negative */
363 switch (rounding_mode) {
366 out_val->desc.clss = INF;
371 fc_get_min(&out_val->desc, out_val);
379 * Operations involving NaN's must return NaN.
380 * They are NOT exact.
382 #define handle_NAN(a, b, result) \
384 if (a->desc.clss == NAN) { \
385 if (a != result) memcpy(result, a, calc_buffer_size); \
389 if (b->desc.clss == NAN) { \
390 if (b != result) memcpy(result, b, calc_buffer_size); \
398 * calculate a + b, where a is the value with the bigger exponent
400 static void _fadd(const fp_value *a, const fp_value *b, fp_value *result)
410 handle_NAN(a, b, result);
412 /* make sure result has a descriptor */
413 if (result != a && result != b)
414 result->desc = a->desc;
416 /* determine if this is an addition or subtraction */
417 sign = a->sign ^ b->sign;
419 /* produce NaN on inf - inf */
420 if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) {
422 fc_get_qnan(&a->desc, result);
426 temp = (char*) alloca(value_size);
427 exp_diff = (char*) alloca(value_size);
429 /* get exponent difference */
430 sc_sub(_exp(a), _exp(b), exp_diff);
432 /* initially set sign to be the sign of a, special treatment of subtraction
433 * when exponents are equal is required though.
434 * Also special care about the sign is needed when the mantissas are equal
436 if (sign && sc_val_to_long(exp_diff) == 0) {
437 switch (sc_comp(_mant(a), _mant(b))) {
439 res_sign = a->sign; /* abs(a) is bigger and a is negative */
442 res_sign = (rounding_mode == FC_TONEGATIVE);
445 res_sign = b->sign; /* abs(b) is bigger and b is negative */
448 /* can't be reached */
455 result->sign = res_sign;
457 /* sign has been taken care of, check for special cases */
458 if (a->desc.clss == ZERO || b->desc.clss == INF) {
460 memcpy(result, b, calc_buffer_size);
461 fc_exact = b->desc.clss == NORMAL;
462 result->sign = res_sign;
465 if (b->desc.clss == ZERO || a->desc.clss == INF) {
467 memcpy(result, a, calc_buffer_size);
468 fc_exact = a->desc.clss == NORMAL;
469 result->sign = res_sign;
473 /* shift the smaller value to the right to align the radix point */
474 /* subnormals have their radix point shifted to the right,
475 * take care of this first */
476 if ((b->desc.clss == SUBNORMAL) && (a->desc.clss != SUBNORMAL)) {
477 sc_val_from_ulong(1, temp);
478 sc_sub(exp_diff, temp, exp_diff);
481 _shift_right(_mant(b), exp_diff, temp);
482 sticky = sc_had_carry();
485 if (sticky && sign) {
486 /* if subtracting a little more than the represented value or adding a little
487 * more than the represented value to a negative value this, in addition to the
488 * still set sticky bit, takes account of the 'little more' */
489 char *temp1 = (char*) alloca(calc_buffer_size);
490 sc_val_from_ulong(1, temp1);
491 sc_add(temp, temp1, temp);
495 if (sc_comp(_mant(a), temp) == -1)
496 sc_sub(temp, _mant(a), _mant(result));
498 sc_sub(_mant(a), temp, _mant(result));
500 sc_add(_mant(a), temp, _mant(result));
503 /* _normalize expects a 'normal' radix point, adding two subnormals
504 * results in a subnormal radix point -> shifting before normalizing */
505 if ((a->desc.clss == SUBNORMAL) && (b->desc.clss == SUBNORMAL)) {
506 sc_val_from_ulong(1, NULL);
507 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
510 /* resulting exponent is the bigger one */
511 memmove(_exp(result), _exp(a), value_size);
513 fc_exact &= normalize(result, result, sticky);
519 static void _fmul(const fp_value *a, const fp_value *b, fp_value *result)
527 handle_NAN(a, b, result);
529 temp = (char*) alloca(value_size);
531 if (result != a && result != b)
532 result->desc = a->desc;
534 result->sign = res_sign = a->sign ^ b->sign;
536 /* produce NaN on 0 * inf */
537 if (a->desc.clss == ZERO) {
538 if (b->desc.clss == INF) {
539 fc_get_qnan(&a->desc, result);
543 memcpy(result, a, calc_buffer_size);
544 result->sign = res_sign;
548 if (b->desc.clss == ZERO) {
549 if (a->desc.clss == INF) {
550 fc_get_qnan(&a->desc, result);
554 memcpy(result, b, calc_buffer_size);
555 result->sign = res_sign;
560 if (a->desc.clss == INF) {
563 memcpy(result, a, calc_buffer_size);
564 result->sign = res_sign;
567 if (b->desc.clss == INF) {
570 memcpy(result, b, calc_buffer_size);
571 result->sign = res_sign;
575 /* exp = exp(a) + exp(b) - excess */
576 sc_add(_exp(a), _exp(b), _exp(result));
578 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
579 sc_sub(_exp(result), temp, _exp(result));
581 /* mixed normal, subnormal values introduce an error of 1, correct it */
582 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
583 sc_val_from_ulong(1, temp);
584 sc_add(_exp(result), temp, _exp(result));
587 sc_mul(_mant(a), _mant(b), _mant(result));
589 /* realign result: after a multiplication the digits right of the radix
590 * point are the sum of the factors' digits after the radix point. As all
591 * values are normalized they both have the same amount of these digits,
592 * which has to be restored by proper shifting
593 * because of the rounding bits */
594 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
596 _shift_right(_mant(result), temp, _mant(result));
597 sticky = sc_had_carry();
600 fc_exact &= normalize(result, result, sticky);
606 static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result)
609 char *temp, *dividend;
614 handle_NAN(a, b, result);
616 temp = (char*) alloca(value_size);
617 dividend = (char*) alloca(value_size);
619 if (result != a && result != b)
620 result->desc = a->desc;
622 result->sign = res_sign = a->sign ^ b->sign;
624 /* produce NAN on 0/0 and inf/inf */
625 if (a->desc.clss == ZERO) {
626 if (b->desc.clss == ZERO) {
628 fc_get_qnan(&a->desc, result);
633 memcpy(result, a, calc_buffer_size);
634 result->sign = res_sign;
639 if (b->desc.clss == INF) {
641 if (a->desc.clss == INF) {
643 fc_get_qnan(&a->desc, result);
646 sc_val_from_ulong(0, NULL);
647 _save_result(_exp(result));
648 _save_result(_mant(result));
649 result->desc.clss = ZERO;
654 if (a->desc.clss == INF) {
658 memcpy(result, a, calc_buffer_size);
659 result->sign = res_sign;
662 if (b->desc.clss == ZERO) {
664 /* division by zero */
666 fc_get_minusinf(&a->desc, result);
668 fc_get_plusinf(&a->desc, result);
672 /* exp = exp(a) - exp(b) + excess - 1*/
673 sc_sub(_exp(a), _exp(b), _exp(result));
674 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp);
675 sc_add(_exp(result), temp, _exp(result));
677 /* mixed normal, subnormal values introduce an error of 1, correct it */
678 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
679 sc_val_from_ulong(1, temp);
680 sc_add(_exp(result), temp, _exp(result));
683 /* mant(res) = mant(a) / 1/2mant(b) */
684 /* to gain more bits of precision in the result the dividend could be
685 * shifted left, as this operation does not loose bits. This would not
686 * fit into the integer precision, but due to the rounding bits (which
687 * are always zero because the values are all normalized) the divisor
688 * can be shifted right instead to achieve the same result */
689 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
691 _shift_left(_mant(a), temp, dividend);
694 char *divisor = (char*) alloca(calc_buffer_size);
695 sc_val_from_ulong(1, divisor);
696 _shift_right(_mant(b), divisor, divisor);
697 sc_div(dividend, divisor, _mant(result));
698 sticky = sc_had_carry();
702 fc_exact &= normalize(result, result, sticky);
706 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result)
714 /* set new descriptor (else result is supposed to already have one) */
716 result->desc = *desc;
718 build = alloca(value_size);
719 temp = alloca(value_size);
721 sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
724 /* temp is value of ten now */
725 sc_val_from_ulong(10, NULL);
728 for (exp--; exp > 0; exp--) {
730 sc_mul(build, temp, NULL);
734 /* temp is amount of left shift needed to put the value left of the radix point */
735 sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
737 _shift_left(build, temp, _mant(result));
739 _normalize(result, result, 0);
745 * Truncate the fractional part away.
747 * This does not clip to any integer range.
749 static void _trunc(const fp_value *a, fp_value *result)
752 * When exponent == 0 all bits left of the radix point
753 * are the integral part of the value. For 15bit exp_size
754 * this would require a left shift of max. 16383 bits which
756 * But it is enough to ensure that no bit right of the radix
757 * point remains set. This restricts the interesting
758 * exponents to the interval [0, mant_size-1].
759 * Outside this interval the truncated value is either 0 or
760 * it does not have fractional parts.
763 int exp_bias, exp_val;
766 /* fixme: can be exact */
769 temp = (char*) alloca(value_size);
772 result->desc = a->desc;
774 exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
775 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
778 sc_val_from_ulong(0, NULL);
779 _save_result(_exp(result));
780 _save_result(_mant(result));
781 result->desc.clss = ZERO;
786 if (exp_val > a->desc.mantissa_size) {
788 memcpy(result, a, calc_buffer_size);
793 /* set up a proper mask to delete all bits right of the
794 * radix point if the mantissa had been shifted until exp == 0 */
795 sc_max_from_bits(1 + exp_val, 0, temp);
796 sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL);
797 _shift_left(temp, sc_get_buffer(), temp);
799 /* and the mask and return the result */
800 sc_and(_mant(a), temp, _mant(result));
803 memcpy(_exp(result), _exp(a), value_size);
804 result->sign = a->sign;
809 * functions defined in fltcalc.h
811 const void *fc_get_buffer(void)
816 int fc_get_buffer_length(void)
818 return calc_buffer_size;
821 void *fc_val_from_str(const char *str, size_t len, const ieee_descriptor_t *desc, void *result)
825 /* XXX excuse of an implementation to make things work */
827 fp_value *tmp = (fp_value*) alloca(calc_buffer_size);
828 ieee_descriptor_t tmp_desc;
830 buffer = (char*) alloca(len+1);
831 memcpy(buffer, str, len);
833 val = strtold(buffer, NULL);
835 DEBUGPRINTF(("val_from_str(%s)\n", str));
836 tmp_desc.exponent_size = 15;
837 tmp_desc.mantissa_size = 63;
838 tmp_desc.explicit_one = 1;
839 tmp_desc.clss = NORMAL;
840 fc_val_from_ieee754(val, &tmp_desc, tmp);
842 return fc_cast(tmp, desc, (fp_value*) result);
845 fp_value *fc_val_from_ieee754(LLDBL l, const ieee_descriptor_t *desc, fp_value *result)
848 int bias_res, bias_val, mant_val;
851 UINT32 exponent, mantissa0, mantissa1;
854 bias_res = ((1 << (desc->exponent_size - 1)) - 1);
856 #ifdef HAVE_LONG_DOUBLE
859 sign = (srcval.val.high & 0x00008000) != 0;
860 exponent = (srcval.val.high & 0x00007FFF) ;
861 mantissa0 = srcval.val.mid;
862 mantissa1 = srcval.val.low;
863 #else /* no long double */
866 sign = (srcval.val.high & 0x80000000) != 0;
867 exponent = (srcval.val.high & 0x7FF00000) >> 20;
868 mantissa0 = srcval.val.high & 0x000FFFFF;
869 mantissa1 = srcval.val.low;
872 #ifdef HAVE_LONG_DOUBLE
873 TRACEPRINTF(("val_from_float(%.8X%.8X%.8X)\n", srcval.val.high & 0xFFFF, srcval.val.mid, srcval.val.low));
874 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
876 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
877 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
880 if (result == NULL) result = calc_buffer;
881 temp = (char*) alloca(value_size);
883 /* CLEAR the buffer, else some bits might be uninitialized */
884 memset(result, 0, fc_get_buffer_length());
886 result->desc.exponent_size = desc->exponent_size;
887 result->desc.mantissa_size = desc->mantissa_size;
888 result->desc.explicit_one = desc->explicit_one;
893 /* sign and flag suffice to identify NaN or inf, no exponent/mantissa
894 * encoding is needed. the function can return immediately in these cases */
896 result->desc.clss = NAN;
897 TRACEPRINTF(("val_from_float resulted in NAN\n"));
899 } else if (isinf(l)) {
900 result->desc.clss = INF;
901 TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
905 /* build exponent, because input and output exponent and mantissa sizes may differ
906 * this looks more complicated than it is: unbiased input exponent + output bias,
907 * minus the mantissa difference which is added again later when the output float
908 * becomes normalized */
909 sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
911 /* build mantissa representation */
913 /* insert the hidden bit */
914 sc_val_from_ulong(1, temp);
915 sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
916 _shift_left(temp, sc_get_buffer(), NULL);
919 sc_val_from_ulong(0, NULL);
922 _save_result(_mant(result));
924 /* bits from the upper word */
925 sc_val_from_ulong(mantissa0, temp);
926 sc_val_from_ulong(34, NULL);
927 _shift_left(temp, sc_get_buffer(), temp);
928 sc_or(_mant(result), temp, _mant(result));
930 /* bits from the lower word */
931 sc_val_from_ulong(mantissa1, temp);
932 sc_val_from_ulong(ROUNDING_BITS, NULL);
933 _shift_left(temp, sc_get_buffer(), temp);
934 sc_or(_mant(result), temp, _mant(result));
936 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
937 * origin one to the left */
939 sc_val_from_ulong(1, NULL);
940 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
943 normalize(result, result, 0);
945 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
950 LLDBL fc_val_to_ieee754(const fp_value *val)
953 fp_value *temp = NULL;
963 ieee_descriptor_t desc;
964 unsigned mantissa_size;
966 #ifdef HAVE_LONG_DOUBLE
967 desc.exponent_size = 15;
968 desc.mantissa_size = 63;
969 desc.explicit_one = 1;
972 desc.exponent_size = 11;
973 desc.mantissa_size = 52;
974 desc.explicit_one = 0;
977 mantissa_size = desc.mantissa_size + desc.explicit_one;
979 temp = (fp_value*) alloca(calc_buffer_size);
980 value = fc_cast(val, &desc, temp);
984 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
985 * lead to wrong results */
986 exponent = sc_val_to_long(_exp(value)) ;
988 sc_val_from_ulong(ROUNDING_BITS, NULL);
989 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
994 for (byte_offset = 0; byte_offset < 4; byte_offset++)
995 mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
997 for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
998 mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
1000 #ifdef HAVE_LONG_DOUBLE
1001 buildval.val.high = sign << 15;
1002 buildval.val.high |= exponent;
1003 buildval.val.mid = mantissa0;
1004 buildval.val.low = mantissa1;
1005 #else /* no long double */
1006 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1007 buildval.val.high = sign << 31;
1008 buildval.val.high |= exponent << 20;
1009 buildval.val.high |= mantissa0;
1010 buildval.val.low = mantissa1;
1013 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1017 fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result)
1020 int exp_offset, val_bias, res_bias;
1022 if (result == NULL) result = calc_buffer;
1023 temp = (char*) alloca(value_size);
1025 if (value->desc.exponent_size == desc->exponent_size &&
1026 value->desc.mantissa_size == desc->mantissa_size &&
1027 value->desc.explicit_one == desc->explicit_one) {
1028 if (value != result)
1029 memcpy(result, value, calc_buffer_size);
1033 if (value->desc.clss == NAN) {
1034 if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
1035 return fc_get_qnan(desc, result);
1037 return fc_get_snan(desc, result);
1039 else if (value->desc.clss == INF) {
1040 if (value->sign == 0)
1041 return fc_get_plusinf(desc, result);
1043 return fc_get_minusinf(desc, result);
1046 /* set the descriptor of the new value */
1047 result->desc.exponent_size = desc->exponent_size;
1048 result->desc.mantissa_size = desc->mantissa_size;
1049 result->desc.explicit_one = desc->explicit_one;
1050 result->desc.clss = value->desc.clss;
1052 result->sign = value->sign;
1054 /* when the mantissa sizes differ normalizing has to shift to align it.
1055 * this would change the exponent, which is unwanted. So calculate this
1056 * offset and add it */
1057 val_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1058 res_bias = (1 << (desc->exponent_size - 1)) - 1;
1060 exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
1061 sc_val_from_long(exp_offset, temp);
1062 sc_add(_exp(value), temp, _exp(result));
1064 /* _normalize expects normalized radix point */
1065 if (value->desc.clss == SUBNORMAL) {
1066 sc_val_from_ulong(1, NULL);
1067 _shift_left(_mant(value), sc_get_buffer(), _mant(result));
1068 } else if (value != result) {
1069 memcpy(_mant(result), _mant(value), value_size);
1071 memmove(_mant(result), _mant(value), value_size);
1074 normalize(result, result, 0);
1075 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1079 fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result)
1081 if (result == NULL) result = calc_buffer;
1083 result->desc.exponent_size = desc->exponent_size;
1084 result->desc.mantissa_size = desc->mantissa_size;
1085 result->desc.explicit_one = desc->explicit_one;
1086 result->desc.clss = NORMAL;
1090 sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
1092 sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
1093 sc_val_from_ulong(ROUNDING_BITS, NULL);
1094 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1099 fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result)
1101 if (result == NULL) result = calc_buffer;
1103 fc_get_max(desc, result);
1109 fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result)
1111 if (result == NULL) result = calc_buffer;
1113 result->desc.exponent_size = desc->exponent_size;
1114 result->desc.mantissa_size = desc->mantissa_size;
1115 result->desc.explicit_one = desc->explicit_one;
1116 result->desc.clss = NAN;
1120 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1122 /* signaling NaN has non-zero mantissa with msb not set */
1123 sc_val_from_ulong(1, _mant(result));
1128 fp_value *fc_get_qnan(const ieee_descriptor_t *desc, fp_value *result)
1130 if (result == NULL) result = calc_buffer;
1132 result->desc.exponent_size = desc->exponent_size;
1133 result->desc.mantissa_size = desc->mantissa_size;
1134 result->desc.explicit_one = desc->explicit_one;
1135 result->desc.clss = NAN;
1139 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1141 /* quiet NaN has the msb of the mantissa set, so shift one there */
1142 sc_val_from_ulong(1, _mant(result));
1143 /* mantissa_size >+< 1 because of two extra rounding bits */
1144 sc_val_from_ulong(desc->mantissa_size + 1, NULL);
1145 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1150 fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result)
1154 if (result == NULL) result = calc_buffer;
1156 result->desc.exponent_size = desc->exponent_size;
1157 result->desc.mantissa_size = desc->mantissa_size;
1158 result->desc.explicit_one = desc->explicit_one;
1159 result->desc.clss = INF;
1163 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1165 mant = _mant(result);
1166 sc_val_from_ulong(0, mant);
1167 if (desc->explicit_one) {
1168 sc_set_bit_at(mant, result->desc.mantissa_size + ROUNDING_BITS);
1174 fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result)
1176 if (result == NULL) result = calc_buffer;
1178 fc_get_plusinf(desc, result);
1184 int fc_comp(const fp_value *val_a, const fp_value *val_b)
1189 * shortcut: if both values are identical, they are either
1190 * Unordered if NaN or equal
1193 return val_a->desc.clss == NAN ? 2 : 0;
1195 /* unordered if one is a NaN */
1196 if (val_a->desc.clss == NAN || val_b->desc.clss == NAN)
1199 /* zero is equal independent of sign */
1200 if ((val_a->desc.clss == ZERO) && (val_b->desc.clss == ZERO))
1203 /* different signs make compare easy */
1204 if (val_a->sign != val_b->sign)
1205 return (val_a->sign == 0) ? (1) : (-1);
1207 mul = val_a->sign ? -1 : 1;
1209 /* both infinity means equality */
1210 if ((val_a->desc.clss == INF) && (val_b->desc.clss == INF))
1213 /* infinity is bigger than the rest */
1214 if (val_a->desc.clss == INF)
1216 if (val_b->desc.clss == INF)
1219 /* check first exponent, that mantissa if equal */
1220 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1226 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1232 int fc_is_zero(const fp_value *a)
1234 return a->desc.clss == ZERO;
1237 int fc_is_negative(const fp_value *a)
1242 int fc_is_inf(const fp_value *a)
1244 return a->desc.clss == INF;
1247 int fc_is_nan(const fp_value *a)
1249 return a->desc.clss == NAN;
1252 int fc_is_subnormal(const fp_value *a)
1254 return a->desc.clss == SUBNORMAL;
1257 char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base)
1262 mul_1 = (char*) alloca(calc_buffer_size);
1266 switch ((value_class_t)val->desc.clss) {
1268 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1271 snprintf(buf, buflen, "NaN");
1274 snprintf(buf, buflen, "0.0");
1277 flt_val = fc_val_to_ieee754(val);
1278 #ifdef HAVE_LONG_DOUBLE
1279 /* XXX 30 is arbitrary */
1280 snprintf(buf, buflen, "%.30LE", flt_val);
1282 snprintf(buf, buflen, "%.18E", flt_val);
1288 switch ((value_class_t)val->desc.clss) {
1290 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1293 snprintf(buf, buflen, "NAN");
1296 snprintf(buf, buflen, "0.0");
1299 flt_val = fc_val_to_ieee754(val);
1300 #ifdef HAVE_LONG_DOUBLE
1301 snprintf(buf, buflen, "%LA", flt_val);
1303 snprintf(buf, buflen, "%A", flt_val);
1310 snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0));
1311 buf[buflen - 1] = '\0';
1317 unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs)
1319 /* this is used to cache the packed version of the value */
1320 static char *packed_value = NULL;
1322 if (packed_value == NULL) packed_value = XMALLOCN(char, value_size);
1325 pack(value, packed_value);
1327 return sc_sub_bits(packed_value, num_bits, byte_ofs);
1330 /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */
1331 int fc_zero_mantissa(const fp_value *value)
1333 return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size;
1336 /* Returns the exponent of a value. */
1337 int fc_get_exponent(const fp_value *value)
1339 int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1340 return sc_val_to_long(_exp(value)) - exp_bias;
1343 /* Return non-zero if a given value can be converted lossless into another precision */
1344 int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc)
1349 /* handle some special cases first */
1350 switch (value->desc.clss) {
1359 /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */
1360 exp_bias = (1 << (desc->exponent_size - 1)) - 1;
1361 v = fc_get_exponent(value) + exp_bias;
1362 if (0 < v && v < (1 << desc->exponent_size) - 1) {
1363 /* exponent can be encoded, now check the mantissa */
1364 v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value));
1365 return v <= desc->mantissa_size;
1371 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
1373 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1374 rounding_mode = mode;
1376 return rounding_mode;
1379 fc_rounding_mode_t fc_get_rounding_mode(void)
1381 return rounding_mode;
1384 void init_fltcalc(int precision)
1386 if (calc_buffer == NULL) {
1387 /* does nothing if already init */
1388 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1390 init_strcalc(precision + 2 + ROUNDING_BITS);
1392 /* needs additionally rounding bits, one bit as explicit 1., and one for
1393 * addition overflow */
1394 max_precision = sc_get_precision() - (2 + ROUNDING_BITS);
1395 if (max_precision < precision)
1396 printf("WARNING: not enough precision available, using %d\n", max_precision);
1398 rounding_mode = FC_TONEAREST;
1399 value_size = sc_get_buffer_length();
1400 calc_buffer_size = sizeof(fp_value) + 2*value_size - 1;
1402 calc_buffer = (fp_value*) xmalloc(calc_buffer_size);
1403 memset(calc_buffer, 0, calc_buffer_size);
1404 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer));
1405 #ifdef HAVE_LONG_DOUBLE
1406 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1408 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1410 #ifdef WORDS_BIGENDIAN
1411 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1413 DEBUGPRINTF(("\tWord order is little endian\n\n"));
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 == 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 == ZERO) {
1599 unsigned fc_set_immediate_precision(unsigned bits)
1601 unsigned old = immediate_prec;
1603 immediate_prec = bits;
1607 int fc_is_exact(void)