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 */
49 #define isnan(x) _isnan(x)
50 static inline int isinf(double x)
52 return !_finite(x) && !_isnan(x);
54 #define strtold(s, e) strtod(s, e)
56 #define HAVE_LONG_DOUBLE
59 /** The number of extra precision rounding bits */
60 #define ROUNDING_BITS 2
62 typedef uint32_t UINT32;
66 #ifdef WORDS_BIGENDIAN
71 #ifdef HAVE_LONG_DOUBLE
74 #ifdef WORDS_BIGENDIAN
80 #ifdef HAVE_LONG_DOUBLE
81 volatile long double d;
87 #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
89 /* our floating point value */
91 ieee_descriptor_t desc;
93 char value[1]; /* exp[value_size] + mant[value_size] */
96 #define _exp(a) &((a)->value[0])
97 #define _mant(a) &((a)->value[value_size])
99 #define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
100 #define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res))
101 #define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res))
105 # define DEBUGPRINTF(x) printf x
107 # define DEBUGPRINTF(x) ((void)0)
110 #ifdef FLTCALC_TRACE_CALC
111 # define TRACEPRINTF(x) printf x
113 # define TRACEPRINTF(x) ((void)0)
116 /** The immediate precision. */
117 static unsigned immediate_prec = 0;
119 /** A temporal buffer. */
120 static fp_value *calc_buffer = NULL;
122 /** Current rounding mode.*/
123 static fc_rounding_mode_t rounding_mode;
125 static int calc_buffer_size;
126 static int value_size;
127 static int max_precision;
130 static int fc_exact = 1;
132 /** pack machine-like */
133 static void *pack(const fp_value *int_float, void *packed)
137 fp_value *val_buffer;
140 temp = (char*) alloca(value_size);
141 shift_val = (char*) alloca(value_size);
143 switch ((value_class_t)int_float->desc.clss) {
145 val_buffer = (fp_value*) alloca(calc_buffer_size);
146 fc_get_qnan(&int_float->desc, val_buffer);
147 int_float = val_buffer;
151 val_buffer = (fp_value*) alloca(calc_buffer_size);
152 fc_get_plusinf(&int_float->desc, val_buffer);
153 val_buffer->sign = int_float->sign;
154 int_float = val_buffer;
160 assert(int_float->desc.explicit_one <= 1);
162 /* pack sign: move it to the left after exponent AND mantissa */
163 sc_val_from_ulong(int_float->sign, temp);
165 pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
166 sc_val_from_ulong(pos, NULL);
167 _shift_left(temp, sc_get_buffer(), packed);
169 /* pack exponent: move it to the left after mantissa */
170 pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
171 sc_val_from_ulong(pos, shift_val);
172 _shift_left(_exp(int_float), shift_val, temp);
174 /* combine sign|exponent */
175 sc_or(temp, packed, packed);
177 /* extract mantissa */
178 /* remove rounding bits */
179 sc_val_from_ulong(ROUNDING_BITS, shift_val);
180 _shift_right(_mant(int_float), shift_val, temp);
182 /* remove leading 1 (or 0 if denormalized) */
183 sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */
184 sc_and(temp, shift_val, temp);
186 /* combine sign|exponent|mantissa */
187 sc_or(temp, packed, packed);
193 * Normalize a fp_value.
195 * @return non-zero if result is exact
197 static int normalize(const fp_value *in_val, fp_value *out_val, int sticky)
201 char lsb, guard, round, round_dir = 0;
202 char *temp = (char*) alloca(value_size);
204 /* save rounding bits at the end */
205 hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
207 if (in_val != out_val) {
208 out_val->sign = in_val->sign;
209 memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc));
212 out_val->desc.clss = NORMAL;
214 /* mantissa all zeros, so zero exponent (because of explicit one) */
215 if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) {
216 sc_val_from_ulong(0, _exp(out_val));
220 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
223 sc_val_from_ulong(-hsb-1, temp);
225 _shift_right(_mant(in_val), temp, _mant(out_val));
227 /* remember if some bits were shifted away */
228 if (sc_had_carry()) {
232 sc_add(_exp(in_val), temp, _exp(out_val));
233 } else if (hsb > -1) {
235 sc_val_from_ulong(hsb+1, temp);
237 _shift_left(_mant(in_val), temp, _mant(out_val));
239 sc_sub(_exp(in_val), temp, _exp(out_val));
242 /* check for exponent underflow */
243 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
244 DEBUGPRINTF(("Exponent underflow!\n"));
245 /* exponent underflow */
246 /* shift the mantissa right to have a zero exponent */
247 sc_val_from_ulong(1, temp);
248 sc_sub(temp, _exp(out_val), NULL);
250 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
251 if (sc_had_carry()) {
255 /* denormalized means exponent of zero */
256 sc_val_from_ulong(0, _exp(out_val));
258 out_val->desc.clss = SUBNORMAL;
261 /* perform rounding by adding a value that clears the guard bit and the round bit
262 * and either causes a carry to round up or not */
263 /* get the last 3 bits of the value */
264 lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
265 guard = (lsb&0x2)>>1;
268 switch (rounding_mode) {
270 /* round to nearest representable value, if in doubt choose the version
272 round_dir = guard && (sticky || round || lsb>>2);
275 /* if positive: round to one if the exact value is bigger, else to zero */
276 round_dir = (!out_val->sign && (guard || round || sticky));
279 /* if negative: round to one if the exact value is bigger, else to zero */
280 round_dir = (out_val->sign && (guard || round || sticky));
283 /* always round to 0 (chopping mode) */
287 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"));
289 if (round_dir == 1) {
290 guard = (round^guard)<<1;
291 lsb = !(round || guard)<<2 | guard | round;
293 lsb = -((guard<<1) | round);
296 /* add the rounded value */
298 sc_val_from_long(lsb, temp);
299 sc_add(_mant(out_val), temp, _mant(out_val));
303 /* could have rounded down to zero */
304 if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL))
305 out_val->desc.clss = ZERO;
307 /* check for rounding overflow */
308 hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
309 if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) {
310 sc_val_from_ulong(1, temp);
311 _shift_right(_mant(out_val), temp, _mant(out_val));
312 if (exact && sc_had_carry())
314 sc_add(_exp(out_val), temp, _exp(out_val));
315 } else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) {
316 /* overflow caused the mantissa to be normal again,
317 * so adapt the exponent accordingly */
318 sc_val_from_ulong(1, temp);
319 sc_add(_exp(out_val), temp, _exp(out_val));
321 out_val->desc.clss = NORMAL;
323 /* no further rounding is needed, because rounding overflow means
324 * the carry of the original rounding was propagated all the way
325 * up to the bit left of the radix point. This implies the bits
326 * to the right are all zeros (rounding is +1) */
328 /* check for exponent overflow */
329 sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp);
330 if (sc_comp(_exp(out_val), temp) != -1) {
331 DEBUGPRINTF(("Exponent overflow!\n"));
332 /* exponent overflow, reaction depends on rounding method:
334 * mode | sign of value | result
335 *--------------------------------------------------------------
336 * TO_NEAREST | + | +inf
338 *--------------------------------------------------------------
339 * TO_POSITIVE | + | +inf
340 * | - | smallest representable value
341 *--------------------------------------------------------------
342 * TO_NEAGTIVE | + | largest representable value
344 *--------------------------------------------------------------
345 * TO_ZERO | + | largest representable value
346 * | - | smallest representable value
347 *--------------------------------------------------------------*/
348 if (out_val->sign == 0) {
349 /* value is positive */
350 switch (rounding_mode) {
353 out_val->desc.clss = INF;
358 fc_get_max(&out_val->desc, out_val);
361 /* value is negative */
362 switch (rounding_mode) {
365 out_val->desc.clss = INF;
370 fc_get_min(&out_val->desc, out_val);
378 * Operations involving NaN's must return NaN.
379 * They are NOT exact.
381 #define handle_NAN(a, b, result) \
383 if (a->desc.clss == NAN) { \
384 if (a != result) memcpy(result, a, calc_buffer_size); \
388 if (b->desc.clss == NAN) { \
389 if (b != result) memcpy(result, b, calc_buffer_size); \
397 * calculate a + b, where a is the value with the bigger exponent
399 static void _fadd(const fp_value *a, const fp_value *b, fp_value *result)
409 handle_NAN(a, b, result);
411 /* make sure result has a descriptor */
412 if (result != a && result != b)
413 result->desc = a->desc;
415 /* determine if this is an addition or subtraction */
416 sign = a->sign ^ b->sign;
418 /* produce NaN on inf - inf */
419 if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) {
421 fc_get_qnan(&a->desc, result);
425 temp = (char*) alloca(value_size);
426 exp_diff = (char*) alloca(value_size);
428 /* get exponent difference */
429 sc_sub(_exp(a), _exp(b), exp_diff);
431 /* initially set sign to be the sign of a, special treatment of subtraction
432 * when exponents are equal is required though.
433 * Also special care about the sign is needed when the mantissas are equal
435 if (sign && sc_val_to_long(exp_diff) == 0) {
436 switch (sc_comp(_mant(a), _mant(b))) {
438 res_sign = a->sign; /* abs(a) is bigger and a is negative */
441 res_sign = (rounding_mode == FC_TONEGATIVE);
444 res_sign = b->sign; /* abs(b) is bigger and b is negative */
447 /* can't be reached */
454 result->sign = res_sign;
456 /* sign has been taken care of, check for special cases */
457 if (a->desc.clss == ZERO || b->desc.clss == INF) {
459 memcpy(result, b, calc_buffer_size);
460 fc_exact = b->desc.clss == NORMAL;
461 result->sign = res_sign;
464 if (b->desc.clss == ZERO || a->desc.clss == INF) {
466 memcpy(result, a, calc_buffer_size);
467 fc_exact = a->desc.clss == NORMAL;
468 result->sign = res_sign;
472 /* shift the smaller value to the right to align the radix point */
473 /* subnormals have their radix point shifted to the right,
474 * take care of this first */
475 if ((b->desc.clss == SUBNORMAL) && (a->desc.clss != SUBNORMAL)) {
476 sc_val_from_ulong(1, temp);
477 sc_sub(exp_diff, temp, exp_diff);
480 _shift_right(_mant(b), exp_diff, temp);
481 sticky = sc_had_carry();
484 if (sticky && sign) {
485 /* if subtracting a little more than the represented value or adding a little
486 * more than the represented value to a negative value this, in addition to the
487 * still set sticky bit, takes account of the 'little more' */
488 char *temp1 = (char*) alloca(calc_buffer_size);
489 sc_val_from_ulong(1, temp1);
490 sc_add(temp, temp1, temp);
494 if (sc_comp(_mant(a), temp) == -1)
495 sc_sub(temp, _mant(a), _mant(result));
497 sc_sub(_mant(a), temp, _mant(result));
499 sc_add(_mant(a), temp, _mant(result));
502 /* _normalize expects a 'normal' radix point, adding two subnormals
503 * results in a subnormal radix point -> shifting before normalizing */
504 if ((a->desc.clss == SUBNORMAL) && (b->desc.clss == SUBNORMAL)) {
505 sc_val_from_ulong(1, NULL);
506 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
509 /* resulting exponent is the bigger one */
510 memmove(_exp(result), _exp(a), value_size);
512 fc_exact &= normalize(result, result, sticky);
518 static void _fmul(const fp_value *a, const fp_value *b, fp_value *result)
526 handle_NAN(a, b, result);
528 temp = (char*) alloca(value_size);
530 if (result != a && result != b)
531 result->desc = a->desc;
533 result->sign = res_sign = a->sign ^ b->sign;
535 /* produce NaN on 0 * inf */
536 if (a->desc.clss == ZERO) {
537 if (b->desc.clss == INF) {
538 fc_get_qnan(&a->desc, result);
542 memcpy(result, a, calc_buffer_size);
543 result->sign = res_sign;
547 if (b->desc.clss == ZERO) {
548 if (a->desc.clss == INF) {
549 fc_get_qnan(&a->desc, result);
553 memcpy(result, b, calc_buffer_size);
554 result->sign = res_sign;
559 if (a->desc.clss == INF) {
562 memcpy(result, a, calc_buffer_size);
563 result->sign = res_sign;
566 if (b->desc.clss == INF) {
569 memcpy(result, b, calc_buffer_size);
570 result->sign = res_sign;
574 /* exp = exp(a) + exp(b) - excess */
575 sc_add(_exp(a), _exp(b), _exp(result));
577 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
578 sc_sub(_exp(result), temp, _exp(result));
580 /* mixed normal, subnormal values introduce an error of 1, correct it */
581 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
582 sc_val_from_ulong(1, temp);
583 sc_add(_exp(result), temp, _exp(result));
586 sc_mul(_mant(a), _mant(b), _mant(result));
588 /* realign result: after a multiplication the digits right of the radix
589 * point are the sum of the factors' digits after the radix point. As all
590 * values are normalized they both have the same amount of these digits,
591 * which has to be restored by proper shifting
592 * because of the rounding bits */
593 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
595 _shift_right(_mant(result), temp, _mant(result));
596 sticky = sc_had_carry();
599 fc_exact &= normalize(result, result, sticky);
605 static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result)
608 char *temp, *dividend;
613 handle_NAN(a, b, result);
615 temp = (char*) alloca(value_size);
616 dividend = (char*) alloca(value_size);
618 if (result != a && result != b)
619 result->desc = a->desc;
621 result->sign = res_sign = a->sign ^ b->sign;
623 /* produce NAN on 0/0 and inf/inf */
624 if (a->desc.clss == ZERO) {
625 if (b->desc.clss == ZERO) {
627 fc_get_qnan(&a->desc, result);
632 memcpy(result, a, calc_buffer_size);
633 result->sign = res_sign;
638 if (b->desc.clss == INF) {
640 if (a->desc.clss == INF) {
642 fc_get_qnan(&a->desc, result);
645 sc_val_from_ulong(0, NULL);
646 _save_result(_exp(result));
647 _save_result(_mant(result));
648 result->desc.clss = ZERO;
653 if (a->desc.clss == INF) {
657 memcpy(result, a, calc_buffer_size);
658 result->sign = res_sign;
661 if (b->desc.clss == ZERO) {
663 /* division by zero */
665 fc_get_minusinf(&a->desc, result);
667 fc_get_plusinf(&a->desc, result);
671 /* exp = exp(a) - exp(b) + excess - 1*/
672 sc_sub(_exp(a), _exp(b), _exp(result));
673 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp);
674 sc_add(_exp(result), temp, _exp(result));
676 /* mixed normal, subnormal values introduce an error of 1, correct it */
677 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
678 sc_val_from_ulong(1, temp);
679 sc_add(_exp(result), temp, _exp(result));
682 /* mant(res) = mant(a) / 1/2mant(b) */
683 /* to gain more bits of precision in the result the dividend could be
684 * shifted left, as this operation does not loose bits. This would not
685 * fit into the integer precision, but due to the rounding bits (which
686 * are always zero because the values are all normalized) the divisor
687 * can be shifted right instead to achieve the same result */
688 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
690 _shift_left(_mant(a), temp, dividend);
693 char *divisor = (char*) alloca(calc_buffer_size);
694 sc_val_from_ulong(1, divisor);
695 _shift_right(_mant(b), divisor, divisor);
696 sc_div(dividend, divisor, _mant(result));
697 sticky = sc_had_carry();
701 fc_exact &= normalize(result, result, sticky);
705 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result)
713 /* set new descriptor (else result is supposed to already have one) */
715 result->desc = *desc;
717 build = alloca(value_size);
718 temp = alloca(value_size);
720 sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
723 /* temp is value of ten now */
724 sc_val_from_ulong(10, NULL);
727 for (exp--; exp > 0; exp--) {
729 sc_mul(build, temp, NULL);
733 /* temp is amount of left shift needed to put the value left of the radix point */
734 sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
736 _shift_left(build, temp, _mant(result));
738 _normalize(result, result, 0);
744 * Truncate the fractional part away.
746 * This does not clip to any integer range.
748 static void _trunc(const fp_value *a, fp_value *result)
751 * When exponent == 0 all bits left of the radix point
752 * are the integral part of the value. For 15bit exp_size
753 * this would require a left shift of max. 16383 bits which
755 * But it is enough to ensure that no bit right of the radix
756 * point remains set. This restricts the interesting
757 * exponents to the interval [0, mant_size-1].
758 * Outside this interval the truncated value is either 0 or
759 * it does not have fractional parts.
762 int exp_bias, exp_val;
765 /* fixme: can be exact */
768 temp = (char*) alloca(value_size);
771 result->desc = a->desc;
773 exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
774 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
777 sc_val_from_ulong(0, NULL);
778 _save_result(_exp(result));
779 _save_result(_mant(result));
780 result->desc.clss = ZERO;
785 if (exp_val > a->desc.mantissa_size) {
787 memcpy(result, a, calc_buffer_size);
792 /* set up a proper mask to delete all bits right of the
793 * radix point if the mantissa had been shifted until exp == 0 */
794 sc_max_from_bits(1 + exp_val, 0, temp);
795 sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL);
796 _shift_left(temp, sc_get_buffer(), temp);
798 /* and the mask and return the result */
799 sc_and(_mant(a), temp, _mant(result));
802 memcpy(_exp(result), _exp(a), value_size);
803 result->sign = a->sign;
808 * functions defined in fltcalc.h
810 const void *fc_get_buffer(void)
815 int fc_get_buffer_length(void)
817 return calc_buffer_size;
820 void *fc_val_from_str(const char *str, size_t len, const ieee_descriptor_t *desc, void *result)
824 /* XXX excuse of an implementation to make things work */
826 fp_value *tmp = (fp_value*) alloca(calc_buffer_size);
827 ieee_descriptor_t tmp_desc;
829 buffer = (char*) alloca(len+1);
830 memcpy(buffer, str, len);
832 val = strtold(buffer, NULL);
834 DEBUGPRINTF(("val_from_str(%s)\n", str));
835 tmp_desc.exponent_size = 15;
836 tmp_desc.mantissa_size = 63;
837 tmp_desc.explicit_one = 1;
838 tmp_desc.clss = NORMAL;
839 fc_val_from_ieee754(val, &tmp_desc, tmp);
841 return fc_cast(tmp, desc, (fp_value*) result);
844 fp_value *fc_val_from_ieee754(LLDBL l, const ieee_descriptor_t *desc, fp_value *result)
847 int bias_res, bias_val, mant_val;
850 UINT32 exponent, mantissa0, mantissa1;
853 bias_res = ((1 << (desc->exponent_size - 1)) - 1);
855 #ifdef HAVE_LONG_DOUBLE
858 sign = (srcval.val.high & 0x00008000) != 0;
859 exponent = (srcval.val.high & 0x00007FFF) ;
860 mantissa0 = srcval.val.mid;
861 mantissa1 = srcval.val.low;
862 #else /* no long double */
865 sign = (srcval.val.high & 0x80000000) != 0;
866 exponent = (srcval.val.high & 0x7FF00000) >> 20;
867 mantissa0 = srcval.val.high & 0x000FFFFF;
868 mantissa1 = srcval.val.low;
871 #ifdef HAVE_LONG_DOUBLE
872 TRACEPRINTF(("val_from_float(%.8X%.8X%.8X)\n", srcval.val.high & 0xFFFF, srcval.val.mid, srcval.val.low));
873 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
875 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
876 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
879 if (result == NULL) result = calc_buffer;
880 temp = (char*) alloca(value_size);
882 /* CLEAR the buffer, else some bits might be uninitialized */
883 memset(result, 0, fc_get_buffer_length());
885 result->desc.exponent_size = desc->exponent_size;
886 result->desc.mantissa_size = desc->mantissa_size;
887 result->desc.explicit_one = desc->explicit_one;
892 /* sign and flag suffice to identify NaN or inf, no exponent/mantissa
893 * encoding is needed. the function can return immediately in these cases */
895 result->desc.clss = NAN;
896 TRACEPRINTF(("val_from_float resulted in NAN\n"));
898 } else if (isinf(l)) {
899 result->desc.clss = INF;
900 TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
904 /* build exponent, because input and output exponent and mantissa sizes may differ
905 * this looks more complicated than it is: unbiased input exponent + output bias,
906 * minus the mantissa difference which is added again later when the output float
907 * becomes normalized */
908 sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
910 /* build mantissa representation */
912 /* insert the hidden bit */
913 sc_val_from_ulong(1, temp);
914 sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
915 _shift_left(temp, sc_get_buffer(), NULL);
918 sc_val_from_ulong(0, NULL);
921 _save_result(_mant(result));
923 /* bits from the upper word */
924 sc_val_from_ulong(mantissa0, temp);
925 sc_val_from_ulong(34, NULL);
926 _shift_left(temp, sc_get_buffer(), temp);
927 sc_or(_mant(result), temp, _mant(result));
929 /* bits from the lower word */
930 sc_val_from_ulong(mantissa1, temp);
931 sc_val_from_ulong(ROUNDING_BITS, NULL);
932 _shift_left(temp, sc_get_buffer(), temp);
933 sc_or(_mant(result), temp, _mant(result));
935 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
936 * origin one to the left */
938 sc_val_from_ulong(1, NULL);
939 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
942 normalize(result, result, 0);
944 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
949 LLDBL fc_val_to_ieee754(const fp_value *val)
952 fp_value *temp = NULL;
962 ieee_descriptor_t desc;
963 unsigned mantissa_size;
965 #ifdef HAVE_LONG_DOUBLE
966 desc.exponent_size = 15;
967 desc.mantissa_size = 63;
968 desc.explicit_one = 1;
971 desc.exponent_size = 11;
972 desc.mantissa_size = 52;
973 desc.explicit_one = 0;
976 mantissa_size = desc.mantissa_size + desc.explicit_one;
978 temp = (fp_value*) alloca(calc_buffer_size);
979 value = fc_cast(val, &desc, temp);
983 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
984 * lead to wrong results */
985 exponent = sc_val_to_long(_exp(value)) ;
987 sc_val_from_ulong(ROUNDING_BITS, NULL);
988 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
993 for (byte_offset = 0; byte_offset < 4; byte_offset++)
994 mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
996 for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
997 mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
999 #ifdef HAVE_LONG_DOUBLE
1000 buildval.val.high = sign << 15;
1001 buildval.val.high |= exponent;
1002 buildval.val.mid = mantissa0;
1003 buildval.val.low = mantissa1;
1004 #else /* no long double */
1005 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1006 buildval.val.high = sign << 31;
1007 buildval.val.high |= exponent << 20;
1008 buildval.val.high |= mantissa0;
1009 buildval.val.low = mantissa1;
1012 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1016 fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result)
1019 int exp_offset, val_bias, res_bias;
1021 if (result == NULL) result = calc_buffer;
1022 temp = (char*) alloca(value_size);
1024 if (value->desc.exponent_size == desc->exponent_size &&
1025 value->desc.mantissa_size == desc->mantissa_size &&
1026 value->desc.explicit_one == desc->explicit_one) {
1027 if (value != result)
1028 memcpy(result, value, calc_buffer_size);
1032 if (value->desc.clss == NAN) {
1033 if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
1034 return fc_get_qnan(desc, result);
1036 return fc_get_snan(desc, result);
1038 else if (value->desc.clss == INF) {
1039 if (value->sign == 0)
1040 return fc_get_plusinf(desc, result);
1042 return fc_get_minusinf(desc, result);
1045 /* set the descriptor of the new value */
1046 result->desc.exponent_size = desc->exponent_size;
1047 result->desc.mantissa_size = desc->mantissa_size;
1048 result->desc.explicit_one = desc->explicit_one;
1049 result->desc.clss = value->desc.clss;
1051 result->sign = value->sign;
1053 /* when the mantissa sizes differ normalizing has to shift to align it.
1054 * this would change the exponent, which is unwanted. So calculate this
1055 * offset and add it */
1056 val_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1057 res_bias = (1 << (desc->exponent_size - 1)) - 1;
1059 exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
1060 sc_val_from_long(exp_offset, temp);
1061 sc_add(_exp(value), temp, _exp(result));
1063 /* _normalize expects normalized radix point */
1064 if (value->desc.clss == SUBNORMAL) {
1065 sc_val_from_ulong(1, NULL);
1066 _shift_left(_mant(value), sc_get_buffer(), _mant(result));
1067 } else if (value != result) {
1068 memcpy(_mant(result), _mant(value), value_size);
1070 memmove(_mant(result), _mant(value), value_size);
1073 normalize(result, result, 0);
1074 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1078 fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result)
1080 if (result == NULL) result = calc_buffer;
1082 result->desc.exponent_size = desc->exponent_size;
1083 result->desc.mantissa_size = desc->mantissa_size;
1084 result->desc.explicit_one = desc->explicit_one;
1085 result->desc.clss = NORMAL;
1089 sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
1091 sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
1092 sc_val_from_ulong(ROUNDING_BITS, NULL);
1093 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1098 fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result)
1100 if (result == NULL) result = calc_buffer;
1102 fc_get_max(desc, result);
1108 fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result)
1110 if (result == NULL) result = calc_buffer;
1112 result->desc.exponent_size = desc->exponent_size;
1113 result->desc.mantissa_size = desc->mantissa_size;
1114 result->desc.explicit_one = desc->explicit_one;
1115 result->desc.clss = NAN;
1119 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1121 /* signaling NaN has non-zero mantissa with msb not set */
1122 sc_val_from_ulong(1, _mant(result));
1127 fp_value *fc_get_qnan(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 = NAN;
1138 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1140 /* quiet NaN has the msb of the mantissa set, so shift one there */
1141 sc_val_from_ulong(1, _mant(result));
1142 /* mantissa_size >+< 1 because of two extra rounding bits */
1143 sc_val_from_ulong(desc->mantissa_size + 1, NULL);
1144 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1149 fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result)
1153 if (result == NULL) result = calc_buffer;
1155 result->desc.exponent_size = desc->exponent_size;
1156 result->desc.mantissa_size = desc->mantissa_size;
1157 result->desc.explicit_one = desc->explicit_one;
1158 result->desc.clss = INF;
1162 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1164 mant = _mant(result);
1165 sc_val_from_ulong(0, mant);
1166 if (desc->explicit_one) {
1167 sc_set_bit_at(mant, result->desc.mantissa_size + ROUNDING_BITS);
1173 fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result)
1175 if (result == NULL) result = calc_buffer;
1177 fc_get_plusinf(desc, result);
1183 int fc_comp(const fp_value *val_a, const fp_value *val_b)
1188 * shortcut: if both values are identical, they are either
1189 * Unordered if NaN or equal
1192 return val_a->desc.clss == NAN ? 2 : 0;
1194 /* unordered if one is a NaN */
1195 if (val_a->desc.clss == NAN || val_b->desc.clss == NAN)
1198 /* zero is equal independent of sign */
1199 if ((val_a->desc.clss == ZERO) && (val_b->desc.clss == ZERO))
1202 /* different signs make compare easy */
1203 if (val_a->sign != val_b->sign)
1204 return (val_a->sign == 0) ? (1) : (-1);
1206 mul = val_a->sign ? -1 : 1;
1208 /* both infinity means equality */
1209 if ((val_a->desc.clss == INF) && (val_b->desc.clss == INF))
1212 /* infinity is bigger than the rest */
1213 if (val_a->desc.clss == INF)
1215 if (val_b->desc.clss == INF)
1218 /* check first exponent, that mantissa if equal */
1219 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1225 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1231 int fc_is_zero(const fp_value *a)
1233 return a->desc.clss == ZERO;
1236 int fc_is_negative(const fp_value *a)
1241 int fc_is_inf(const fp_value *a)
1243 return a->desc.clss == INF;
1246 int fc_is_nan(const fp_value *a)
1248 return a->desc.clss == NAN;
1251 int fc_is_subnormal(const fp_value *a)
1253 return a->desc.clss == SUBNORMAL;
1256 char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base)
1261 mul_1 = (char*) alloca(calc_buffer_size);
1265 switch ((value_class_t)val->desc.clss) {
1267 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1270 snprintf(buf, buflen, "NaN");
1273 snprintf(buf, buflen, "0.0");
1276 flt_val = fc_val_to_ieee754(val);
1277 #ifdef HAVE_LONG_DOUBLE
1278 /* XXX 30 is arbitrary */
1279 snprintf(buf, buflen, "%.30LE", flt_val);
1281 snprintf(buf, buflen, "%.18E", flt_val);
1287 switch ((value_class_t)val->desc.clss) {
1289 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1292 snprintf(buf, buflen, "NAN");
1295 snprintf(buf, buflen, "0.0");
1298 flt_val = fc_val_to_ieee754(val);
1299 #ifdef HAVE_LONG_DOUBLE
1300 snprintf(buf, buflen, "%LA", flt_val);
1302 snprintf(buf, buflen, "%A", flt_val);
1309 snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0));
1310 buf[buflen - 1] = '\0';
1316 unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs)
1318 /* this is used to cache the packed version of the value */
1319 static char *packed_value = NULL;
1321 if (packed_value == NULL) packed_value = XMALLOCN(char, value_size);
1324 pack(value, packed_value);
1326 return sc_sub_bits(packed_value, num_bits, byte_ofs);
1329 /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */
1330 int fc_zero_mantissa(const fp_value *value)
1332 return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size;
1335 /* Returns the exponent of a value. */
1336 int fc_get_exponent(const fp_value *value)
1338 int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1339 return sc_val_to_long(_exp(value)) - exp_bias;
1342 /* Return non-zero if a given value can be converted lossless into another precision */
1343 int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc)
1348 /* handle some special cases first */
1349 switch (value->desc.clss) {
1358 /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */
1359 exp_bias = (1 << (desc->exponent_size - 1)) - 1;
1360 v = fc_get_exponent(value) + exp_bias;
1361 if (0 < v && v < (1 << desc->exponent_size) - 1) {
1362 /* exponent can be encoded, now check the mantissa */
1363 v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value));
1364 return v <= desc->mantissa_size;
1370 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
1372 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1373 rounding_mode = mode;
1375 return rounding_mode;
1378 fc_rounding_mode_t fc_get_rounding_mode(void)
1380 return rounding_mode;
1383 void init_fltcalc(int precision)
1385 if (calc_buffer == NULL) {
1386 /* does nothing if already init */
1387 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1389 init_strcalc(precision + 2 + ROUNDING_BITS);
1391 /* needs additionally rounding bits, one bit as explicit 1., and one for
1392 * addition overflow */
1393 max_precision = sc_get_precision() - (2 + ROUNDING_BITS);
1394 if (max_precision < precision)
1395 printf("WARNING: not enough precision available, using %d\n", max_precision);
1397 rounding_mode = FC_TONEAREST;
1398 value_size = sc_get_buffer_length();
1399 calc_buffer_size = sizeof(fp_value) + 2*value_size - 1;
1401 calc_buffer = (fp_value*) xmalloc(calc_buffer_size);
1402 memset(calc_buffer, 0, calc_buffer_size);
1403 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer));
1404 #ifdef HAVE_LONG_DOUBLE
1405 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1407 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1409 #ifdef WORDS_BIGENDIAN
1410 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1412 DEBUGPRINTF(("\tWord order is little endian\n\n"));
1417 void finish_fltcalc (void)
1419 free(calc_buffer); calc_buffer = NULL;
1422 #ifdef FLTCALC_TRACE_CALC
1423 static char buffer[100];
1426 /* definition of interface functions */
1427 fp_value *fc_add(const fp_value *a, const fp_value *b, fp_value *result)
1429 if (result == NULL) result = calc_buffer;
1431 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1432 TRACEPRINTF(("+ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1434 /* make the value with the bigger exponent the first one */
1435 if (sc_comp(_exp(a), _exp(b)) == -1)
1436 _fadd(b, a, result);
1438 _fadd(a, b, result);
1440 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1444 fp_value *fc_sub(const fp_value *a, const fp_value *b, fp_value *result)
1448 if (result == NULL) result = calc_buffer;
1450 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1451 TRACEPRINTF(("- %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1453 temp = (fp_value*) alloca(calc_buffer_size);
1454 memcpy(temp, b, calc_buffer_size);
1455 temp->sign = !b->sign;
1456 if (sc_comp(_exp(a), _exp(temp)) == -1)
1457 _fadd(temp, a, result);
1459 _fadd(a, temp, result);
1461 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1465 fp_value *fc_mul(const fp_value *a, const fp_value *b, fp_value *result)
1467 if (result == NULL) result = calc_buffer;
1469 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1470 TRACEPRINTF(("* %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1472 _fmul(a, b, result);
1474 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1478 fp_value *fc_div(const fp_value *a, const fp_value *b, fp_value *result)
1480 if (result == NULL) result = calc_buffer;
1482 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1483 TRACEPRINTF(("/ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1485 _fdiv(a, b, result);
1487 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1491 fp_value *fc_neg(const fp_value *a, fp_value *result)
1493 if (result == NULL) result = calc_buffer;
1495 TRACEPRINTF(("- %s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1498 memcpy(result, a, calc_buffer_size);
1499 result->sign = !a->sign;
1501 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1505 fp_value *fc_int(const fp_value *a, fp_value *result)
1507 if (result == NULL) result = calc_buffer;
1509 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1510 TRACEPRINTF(("truncated to integer "));
1514 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1518 fp_value *fc_rnd(const fp_value *a, fp_value *result)
1520 if (result == NULL) result = calc_buffer;
1523 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1524 TRACEPRINTF(("rounded to integer "));
1526 panic("fc_rnd() not yet implemented");
1530 * convert a floating point value into an sc value ...
1532 int fc_flt2int(const fp_value *a, void *result, ir_mode *dst_mode)
1534 if (a->desc.clss == NORMAL) {
1535 int exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
1536 int exp_val = sc_val_to_long(_exp(a)) - exp_bias;
1541 if (a->sign && !mode_is_signed(dst_mode)) {
1542 /* FIXME: for now we cannot convert this */
1546 tgt_bits = get_mode_size_bits(dst_mode);
1547 if (mode_is_signed(dst_mode))
1550 assert(exp_val >= 0 && "floating point value not integral before fc_flt2int() call");
1551 mantissa_size = a->desc.mantissa_size + ROUNDING_BITS;
1552 shift = exp_val - mantissa_size;
1554 if (tgt_bits < mantissa_size + 1)
1555 tgt_bits = mantissa_size + 1;
1557 sc_shlI(_mant(a), shift, tgt_bits, 0, result);
1559 sc_shrI(_mant(a), -shift, tgt_bits, 0, result);
1562 /* check for overflow */
1563 highest = sc_get_highest_set_bit(result);
1565 if (mode_is_signed(dst_mode)) {
1566 if (highest == sc_get_lowest_set_bit(result)) {
1567 /* need extra test for MIN_INT */
1568 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1569 /* FIXME: handle overflow */
1573 if (highest >= (int) get_mode_size_bits(dst_mode) - 1) {
1574 /* FIXME: handle overflow */
1579 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1580 /* FIXME: handle overflow */
1586 sc_neg(result, result);
1590 else if (a->desc.clss == ZERO) {
1598 unsigned fc_set_immediate_precision(unsigned bits)
1600 unsigned old = immediate_prec;
1602 immediate_prec = bits;
1606 int fc_is_exact(void)