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;
134 static void fail_char(const char *str, unsigned int len, int pos)
137 printf("ERROR: Unexpected character '%c'\n", *(str + pos));
139 printf("ERROR: Unexpected end of string\n");
140 while (len-- && *str) printf("%c", *str++); printf("\n");
141 while (pos--) printf(" "); printf("^\n");
142 /* the front end has to to check constant strings */
147 /** pack machine-like */
148 static void *pack(const fp_value *int_float, void *packed)
152 fp_value *val_buffer;
155 temp = (char*) alloca(value_size);
156 shift_val = (char*) alloca(value_size);
158 switch ((value_class_t)int_float->desc.clss) {
160 val_buffer = (fp_value*) alloca(calc_buffer_size);
161 fc_get_qnan(&int_float->desc, val_buffer);
162 int_float = val_buffer;
166 val_buffer = (fp_value*) alloca(calc_buffer_size);
167 fc_get_plusinf(&int_float->desc, val_buffer);
168 val_buffer->sign = int_float->sign;
169 int_float = val_buffer;
175 assert(int_float->desc.explicit_one <= 1);
177 /* pack sign: move it to the left after exponent AND mantissa */
178 sc_val_from_ulong(int_float->sign, temp);
180 pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
181 sc_val_from_ulong(pos, NULL);
182 _shift_left(temp, sc_get_buffer(), packed);
184 /* pack exponent: move it to the left after mantissa */
185 pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
186 sc_val_from_ulong(pos, shift_val);
187 _shift_left(_exp(int_float), shift_val, temp);
189 /* combine sign|exponent */
190 sc_or(temp, packed, packed);
192 /* extract mantissa */
193 /* remove rounding bits */
194 sc_val_from_ulong(ROUNDING_BITS, shift_val);
195 _shift_right(_mant(int_float), shift_val, temp);
197 /* remove leading 1 (or 0 if denormalized) */
198 sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */
199 sc_and(temp, shift_val, temp);
201 /* combine sign|exponent|mantissa */
202 sc_or(temp, packed, packed);
208 * Normalize a fp_value.
210 * @return non-zero if result is exact
212 static int normalize(const fp_value *in_val, fp_value *out_val, int sticky)
216 char lsb, guard, round, round_dir = 0;
217 char *temp = (char*) alloca(value_size);
219 /* save rounding bits at the end */
220 hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
222 if (in_val != out_val) {
223 out_val->sign = in_val->sign;
224 memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc));
227 out_val->desc.clss = NORMAL;
229 /* mantissa all zeros, so zero exponent (because of explicit one) */
230 if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) {
231 sc_val_from_ulong(0, _exp(out_val));
235 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
238 sc_val_from_ulong(-hsb-1, temp);
240 _shift_right(_mant(in_val), temp, _mant(out_val));
242 /* remember if some bits were shifted away */
243 if (sc_had_carry()) {
247 sc_add(_exp(in_val), temp, _exp(out_val));
248 } else if (hsb > -1) {
250 sc_val_from_ulong(hsb+1, temp);
252 _shift_left(_mant(in_val), temp, _mant(out_val));
254 sc_sub(_exp(in_val), temp, _exp(out_val));
257 /* check for exponent underflow */
258 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
259 DEBUGPRINTF(("Exponent underflow!\n"));
260 /* exponent underflow */
261 /* shift the mantissa right to have a zero exponent */
262 sc_val_from_ulong(1, temp);
263 sc_sub(temp, _exp(out_val), NULL);
265 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
266 if (sc_had_carry()) {
270 /* denormalized means exponent of zero */
271 sc_val_from_ulong(0, _exp(out_val));
273 out_val->desc.clss = SUBNORMAL;
276 /* perform rounding by adding a value that clears the guard bit and the round bit
277 * and either causes a carry to round up or not */
278 /* get the last 3 bits of the value */
279 lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
280 guard = (lsb&0x2)>>1;
283 switch (rounding_mode) {
285 /* round to nearest representable value, if in doubt choose the version
287 round_dir = guard && (sticky || round || lsb>>2);
290 /* if positive: round to one if the exact value is bigger, else to zero */
291 round_dir = (!out_val->sign && (guard || round || sticky));
294 /* if negative: round to one if the exact value is bigger, else to zero */
295 round_dir = (out_val->sign && (guard || round || sticky));
298 /* always round to 0 (chopping mode) */
302 DEBUGPRINTF(("Rounding (s%d, l%d, g%d, r%d, s%d) %s\n", out_val->sign, lsb>>2, guard, round, sticky, (round_dir)?"up":"down"));
304 if (round_dir == 1) {
305 guard = (round^guard)<<1;
306 lsb = !(round || guard)<<2 | guard | round;
308 lsb = -((guard<<1) | round);
311 /* add the rounded value */
313 sc_val_from_long(lsb, temp);
314 sc_add(_mant(out_val), temp, _mant(out_val));
318 /* could have rounded down to zero */
319 if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL))
320 out_val->desc.clss = ZERO;
322 /* check for rounding overflow */
323 hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
324 if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) {
325 sc_val_from_ulong(1, temp);
326 _shift_right(_mant(out_val), temp, _mant(out_val));
327 if (exact && sc_had_carry())
329 sc_add(_exp(out_val), temp, _exp(out_val));
330 } else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) {
331 /* overflow caused the mantissa to be normal again,
332 * so adapt the exponent accordingly */
333 sc_val_from_ulong(1, temp);
334 sc_add(_exp(out_val), temp, _exp(out_val));
336 out_val->desc.clss = NORMAL;
338 /* no further rounding is needed, because rounding overflow means
339 * the carry of the original rounding was propagated all the way
340 * up to the bit left of the radix point. This implies the bits
341 * to the right are all zeros (rounding is +1) */
343 /* check for exponent overflow */
344 sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp);
345 if (sc_comp(_exp(out_val), temp) != -1) {
346 DEBUGPRINTF(("Exponent overflow!\n"));
347 /* exponent overflow, reaction depends on rounding method:
349 * mode | sign of value | result
350 *--------------------------------------------------------------
351 * TO_NEAREST | + | +inf
353 *--------------------------------------------------------------
354 * TO_POSITIVE | + | +inf
355 * | - | smallest representable value
356 *--------------------------------------------------------------
357 * TO_NEAGTIVE | + | largest representable value
359 *--------------------------------------------------------------
360 * TO_ZERO | + | largest representable value
361 * | - | smallest representable value
362 *--------------------------------------------------------------*/
363 if (out_val->sign == 0) {
364 /* value is positive */
365 switch (rounding_mode) {
368 out_val->desc.clss = INF;
373 fc_get_max(&out_val->desc, out_val);
376 /* value is negative */
377 switch (rounding_mode) {
380 out_val->desc.clss = INF;
385 fc_get_min(&out_val->desc, out_val);
393 * Operations involving NaN's must return NaN.
394 * They are NOT exact.
396 #define handle_NAN(a, b, result) \
398 if (a->desc.clss == NAN) { \
399 if (a != result) memcpy(result, a, calc_buffer_size); \
403 if (b->desc.clss == NAN) { \
404 if (b != result) memcpy(result, b, calc_buffer_size); \
412 * calculate a + b, where a is the value with the bigger exponent
414 static void _fadd(const fp_value *a, const fp_value *b, fp_value *result)
424 handle_NAN(a, b, result);
426 /* make sure result has a descriptor */
427 if (result != a && result != b)
428 result->desc = a->desc;
430 /* determine if this is an addition or subtraction */
431 sign = a->sign ^ b->sign;
433 /* produce NaN on inf - inf */
434 if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) {
436 fc_get_qnan(&a->desc, result);
440 temp = (char*) alloca(value_size);
441 exp_diff = (char*) alloca(value_size);
443 /* get exponent difference */
444 sc_sub(_exp(a), _exp(b), exp_diff);
446 /* initially set sign to be the sign of a, special treatment of subtraction
447 * when exponents are equal is required though.
448 * Also special care about the sign is needed when the mantissas are equal
450 if (sign && sc_val_to_long(exp_diff) == 0) {
451 switch (sc_comp(_mant(a), _mant(b))) {
453 res_sign = a->sign; /* abs(a) is bigger and a is negative */
456 res_sign = (rounding_mode == FC_TONEGATIVE);
459 res_sign = b->sign; /* abs(b) is bigger and b is negative */
462 /* can't be reached */
469 result->sign = res_sign;
471 /* sign has been taken care of, check for special cases */
472 if (a->desc.clss == ZERO || b->desc.clss == INF) {
474 memcpy(result, b, calc_buffer_size);
475 fc_exact = b->desc.clss == NORMAL;
476 result->sign = res_sign;
479 if (b->desc.clss == ZERO || a->desc.clss == INF) {
481 memcpy(result, a, calc_buffer_size);
482 fc_exact = a->desc.clss == NORMAL;
483 result->sign = res_sign;
487 /* shift the smaller value to the right to align the radix point */
488 /* subnormals have their radix point shifted to the right,
489 * take care of this first */
490 if ((b->desc.clss == SUBNORMAL) && (a->desc.clss != SUBNORMAL)) {
491 sc_val_from_ulong(1, temp);
492 sc_sub(exp_diff, temp, exp_diff);
495 _shift_right(_mant(b), exp_diff, temp);
496 sticky = sc_had_carry();
499 if (sticky && sign) {
500 /* if subtracting a little more than the represented value or adding a little
501 * more than the represented value to a negative value this, in addition to the
502 * still set sticky bit, takes account of the 'little more' */
503 char *temp1 = (char*) alloca(calc_buffer_size);
504 sc_val_from_ulong(1, temp1);
505 sc_add(temp, temp1, temp);
509 if (sc_comp(_mant(a), temp) == -1)
510 sc_sub(temp, _mant(a), _mant(result));
512 sc_sub(_mant(a), temp, _mant(result));
514 sc_add(_mant(a), temp, _mant(result));
517 /* _normalize expects a 'normal' radix point, adding two subnormals
518 * results in a subnormal radix point -> shifting before normalizing */
519 if ((a->desc.clss == SUBNORMAL) && (b->desc.clss == SUBNORMAL)) {
520 sc_val_from_ulong(1, NULL);
521 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
524 /* resulting exponent is the bigger one */
525 memmove(_exp(result), _exp(a), value_size);
527 fc_exact &= normalize(result, result, sticky);
533 static void _fmul(const fp_value *a, const fp_value *b, fp_value *result)
541 handle_NAN(a, b, result);
543 temp = (char*) alloca(value_size);
545 if (result != a && result != b)
546 result->desc = a->desc;
548 result->sign = res_sign = a->sign ^ b->sign;
550 /* produce NaN on 0 * inf */
551 if (a->desc.clss == ZERO) {
552 if (b->desc.clss == INF) {
553 fc_get_qnan(&a->desc, result);
557 memcpy(result, a, calc_buffer_size);
558 result->sign = res_sign;
562 if (b->desc.clss == ZERO) {
563 if (a->desc.clss == INF) {
564 fc_get_qnan(&a->desc, result);
568 memcpy(result, b, calc_buffer_size);
569 result->sign = res_sign;
574 if (a->desc.clss == INF) {
577 memcpy(result, a, calc_buffer_size);
578 result->sign = res_sign;
581 if (b->desc.clss == INF) {
584 memcpy(result, b, calc_buffer_size);
585 result->sign = res_sign;
589 /* exp = exp(a) + exp(b) - excess */
590 sc_add(_exp(a), _exp(b), _exp(result));
592 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
593 sc_sub(_exp(result), temp, _exp(result));
595 /* mixed normal, subnormal values introduce an error of 1, correct it */
596 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
597 sc_val_from_ulong(1, temp);
598 sc_add(_exp(result), temp, _exp(result));
601 sc_mul(_mant(a), _mant(b), _mant(result));
603 /* realign result: after a multiplication the digits right of the radix
604 * point are the sum of the factors' digits after the radix point. As all
605 * values are normalized they both have the same amount of these digits,
606 * which has to be restored by proper shifting
607 * because of the rounding bits */
608 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
610 _shift_right(_mant(result), temp, _mant(result));
611 sticky = sc_had_carry();
614 fc_exact &= normalize(result, result, sticky);
620 static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result)
623 char *temp, *dividend;
628 handle_NAN(a, b, result);
630 temp = (char*) alloca(value_size);
631 dividend = (char*) alloca(value_size);
633 if (result != a && result != b)
634 result->desc = a->desc;
636 result->sign = res_sign = a->sign ^ b->sign;
638 /* produce NAN on 0/0 and inf/inf */
639 if (a->desc.clss == ZERO) {
640 if (b->desc.clss == ZERO) {
642 fc_get_qnan(&a->desc, result);
647 memcpy(result, a, calc_buffer_size);
648 result->sign = res_sign;
653 if (b->desc.clss == INF) {
655 if (a->desc.clss == INF) {
657 fc_get_qnan(&a->desc, result);
660 sc_val_from_ulong(0, NULL);
661 _save_result(_exp(result));
662 _save_result(_mant(result));
663 result->desc.clss = ZERO;
668 if (a->desc.clss == INF) {
672 memcpy(result, a, calc_buffer_size);
673 result->sign = res_sign;
676 if (b->desc.clss == ZERO) {
678 /* division by zero */
680 fc_get_minusinf(&a->desc, result);
682 fc_get_plusinf(&a->desc, result);
686 /* exp = exp(a) - exp(b) + excess - 1*/
687 sc_sub(_exp(a), _exp(b), _exp(result));
688 sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp);
689 sc_add(_exp(result), temp, _exp(result));
691 /* mixed normal, subnormal values introduce an error of 1, correct it */
692 if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
693 sc_val_from_ulong(1, temp);
694 sc_add(_exp(result), temp, _exp(result));
697 /* mant(res) = mant(a) / 1/2mant(b) */
698 /* to gain more bits of precision in the result the dividend could be
699 * shifted left, as this operation does not loose bits. This would not
700 * fit into the integer precision, but due to the rounding bits (which
701 * are always zero because the values are all normalized) the divisor
702 * can be shifted right instead to achieve the same result */
703 sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
705 _shift_left(_mant(a), temp, dividend);
708 char *divisor = (char*) alloca(calc_buffer_size);
709 sc_val_from_ulong(1, divisor);
710 _shift_right(_mant(b), divisor, divisor);
711 sc_div(dividend, divisor, _mant(result));
712 sticky = sc_had_carry();
716 fc_exact &= normalize(result, result, sticky);
720 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result)
728 /* set new descriptor (else result is supposed to already have one) */
730 result->desc = *desc;
732 build = alloca(value_size);
733 temp = alloca(value_size);
735 sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
738 /* temp is value of ten now */
739 sc_val_from_ulong(10, NULL);
742 for (exp--; exp > 0; exp--) {
744 sc_mul(build, temp, NULL);
748 /* temp is amount of left shift needed to put the value left of the radix point */
749 sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
751 _shift_left(build, temp, _mant(result));
753 _normalize(result, result, 0);
759 * Truncate the fractional part away.
761 * This does not clip to any integer range.
763 static void _trunc(const fp_value *a, fp_value *result)
766 * When exponent == 0 all bits left of the radix point
767 * are the integral part of the value. For 15bit exp_size
768 * this would require a left shift of max. 16383 bits which
770 * But it is enough to ensure that no bit right of the radix
771 * point remains set. This restricts the interesting
772 * exponents to the interval [0, mant_size-1].
773 * Outside this interval the truncated value is either 0 or
774 * it does not have fractional parts.
777 int exp_bias, exp_val;
780 /* fixme: can be exact */
783 temp = (char*) alloca(value_size);
786 result->desc = a->desc;
788 exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
789 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
792 sc_val_from_ulong(0, NULL);
793 _save_result(_exp(result));
794 _save_result(_mant(result));
795 result->desc.clss = ZERO;
800 if (exp_val > a->desc.mantissa_size) {
802 memcpy(result, a, calc_buffer_size);
807 /* set up a proper mask to delete all bits right of the
808 * radix point if the mantissa had been shifted until exp == 0 */
809 sc_max_from_bits(1 + exp_val, 0, temp);
810 sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL);
811 _shift_left(temp, sc_get_buffer(), temp);
813 /* and the mask and return the result */
814 sc_and(_mant(a), temp, _mant(result));
817 memcpy(_exp(result), _exp(a), value_size);
818 result->sign = a->sign;
823 * functions defined in fltcalc.h
825 const void *fc_get_buffer(void)
830 int fc_get_buffer_length(void)
832 return calc_buffer_size;
835 void *fc_val_from_str(const char *str, size_t len, const ieee_descriptor_t *desc, void *result)
839 /* XXX excuse of an implementation to make things work */
841 fp_value *tmp = (fp_value*) alloca(calc_buffer_size);
842 ieee_descriptor_t tmp_desc;
844 buffer = (char*) alloca(len+1);
845 memcpy(buffer, str, len);
847 val = strtold(buffer, NULL);
849 DEBUGPRINTF(("val_from_str(%s)\n", str));
850 tmp_desc.exponent_size = 15;
851 tmp_desc.mantissa_size = 63;
852 tmp_desc.explicit_one = 1;
853 tmp_desc.clss = NORMAL;
854 fc_val_from_ieee754(val, &tmp_desc, tmp);
856 return fc_cast(tmp, desc, (fp_value*) result);
859 fp_value *fc_val_from_ieee754(LLDBL l, const ieee_descriptor_t *desc, fp_value *result)
862 int bias_res, bias_val, mant_val;
865 UINT32 exponent, mantissa0, mantissa1;
868 bias_res = ((1 << (desc->exponent_size - 1)) - 1);
870 #ifdef HAVE_LONG_DOUBLE
873 sign = (srcval.val.high & 0x00008000) != 0;
874 exponent = (srcval.val.high & 0x00007FFF) ;
875 mantissa0 = srcval.val.mid;
876 mantissa1 = srcval.val.low;
877 #else /* no long double */
880 sign = (srcval.val.high & 0x80000000) != 0;
881 exponent = (srcval.val.high & 0x7FF00000) >> 20;
882 mantissa0 = srcval.val.high & 0x000FFFFF;
883 mantissa1 = srcval.val.low;
886 #ifdef HAVE_LONG_DOUBLE
887 TRACEPRINTF(("val_from_float(%.8X%.8X%.8X)\n", ((int*)&l)[2], ((int*)&l)[1], ((int*)&l)[0]));/* srcval.val.high, srcval.val.mid, srcval.val.low)); */
888 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
890 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
891 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
894 if (result == NULL) result = calc_buffer;
895 temp = (char*) alloca(value_size);
897 /* CLEAR the buffer, else some bits might be uninitialized */
898 memset(result, 0, fc_get_buffer_length());
900 result->desc.exponent_size = desc->exponent_size;
901 result->desc.mantissa_size = desc->mantissa_size;
902 result->desc.explicit_one = desc->explicit_one;
907 /* sign and flag suffice to identify NaN or inf, no exponent/mantissa
908 * encoding is needed. the function can return immediately in these cases */
910 result->desc.clss = NAN;
911 TRACEPRINTF(("val_from_float resulted in NAN\n"));
913 } else if (isinf(l)) {
914 result->desc.clss = INF;
915 TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
919 /* build exponent, because input and output exponent and mantissa sizes may differ
920 * this looks more complicated than it is: unbiased input exponent + output bias,
921 * minus the mantissa difference which is added again later when the output float
922 * becomes normalized */
923 sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
925 /* build mantissa representation */
927 /* insert the hidden bit */
928 sc_val_from_ulong(1, temp);
929 sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
930 _shift_left(temp, sc_get_buffer(), NULL);
933 sc_val_from_ulong(0, NULL);
936 _save_result(_mant(result));
938 /* bits from the upper word */
939 sc_val_from_ulong(mantissa0, temp);
940 sc_val_from_ulong(34, NULL);
941 _shift_left(temp, sc_get_buffer(), temp);
942 sc_or(_mant(result), temp, _mant(result));
944 /* bits from the lower word */
945 sc_val_from_ulong(mantissa1, temp);
946 sc_val_from_ulong(ROUNDING_BITS, NULL);
947 _shift_left(temp, sc_get_buffer(), temp);
948 sc_or(_mant(result), temp, _mant(result));
950 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
951 * origin one to the left */
953 sc_val_from_ulong(1, NULL);
954 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
957 normalize(result, result, 0);
959 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
964 LLDBL fc_val_to_ieee754(const fp_value *val)
967 fp_value *temp = NULL;
977 ieee_descriptor_t desc;
978 unsigned mantissa_size;
980 #ifdef HAVE_LONG_DOUBLE
981 desc.exponent_size = 15;
982 desc.mantissa_size = 63;
983 desc.explicit_one = 1;
986 desc.exponent_size = 11;
987 desc.mantissa_size = 52;
988 desc.explicit_one = 0;
991 mantissa_size = desc.mantissa_size + desc.explicit_one;
993 temp = (fp_value*) alloca(calc_buffer_size);
994 value = fc_cast(val, &desc, temp);
998 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
999 * lead to wrong results */
1000 exponent = sc_val_to_long(_exp(value)) ;
1002 sc_val_from_ulong(ROUNDING_BITS, NULL);
1003 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
1008 for (byte_offset = 0; byte_offset < 4; byte_offset++)
1009 mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
1011 for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
1012 mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
1014 #ifdef HAVE_LONG_DOUBLE
1015 buildval.val.high = sign << 15;
1016 buildval.val.high |= exponent;
1017 buildval.val.mid = mantissa0;
1018 buildval.val.low = mantissa1;
1019 #else /* no long double */
1020 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1021 buildval.val.high = sign << 31;
1022 buildval.val.high |= exponent << 20;
1023 buildval.val.high |= mantissa0;
1024 buildval.val.low = mantissa1;
1027 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1031 fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result)
1034 int exp_offset, val_bias, res_bias;
1036 if (result == NULL) result = calc_buffer;
1037 temp = (char*) alloca(value_size);
1039 if (value->desc.exponent_size == desc->exponent_size &&
1040 value->desc.mantissa_size == desc->mantissa_size &&
1041 value->desc.explicit_one == desc->explicit_one) {
1042 if (value != result)
1043 memcpy(result, value, calc_buffer_size);
1047 if (value->desc.clss == NAN) {
1048 if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
1049 return fc_get_qnan(desc, result);
1051 return fc_get_snan(desc, result);
1053 else if (value->desc.clss == INF) {
1054 if (value->sign == 0)
1055 return fc_get_plusinf(desc, result);
1057 return fc_get_minusinf(desc, result);
1060 /* set the descriptor of the new value */
1061 result->desc.exponent_size = desc->exponent_size;
1062 result->desc.mantissa_size = desc->mantissa_size;
1063 result->desc.explicit_one = desc->explicit_one;
1064 result->desc.clss = value->desc.clss;
1066 result->sign = value->sign;
1068 /* when the mantissa sizes differ normalizing has to shift to align it.
1069 * this would change the exponent, which is unwanted. So calculate this
1070 * offset and add it */
1071 val_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1072 res_bias = (1 << (desc->exponent_size - 1)) - 1;
1074 exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
1075 sc_val_from_long(exp_offset, temp);
1076 sc_add(_exp(value), temp, _exp(result));
1078 /* _normalize expects normalized radix point */
1079 if (value->desc.clss == SUBNORMAL) {
1080 sc_val_from_ulong(1, NULL);
1081 _shift_left(_mant(value), sc_get_buffer(), _mant(result));
1082 } else if (value != result) {
1083 memcpy(_mant(result), _mant(value), value_size);
1085 memmove(_mant(result), _mant(value), value_size);
1088 normalize(result, result, 0);
1089 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1093 fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result)
1095 if (result == NULL) result = calc_buffer;
1097 result->desc.exponent_size = desc->exponent_size;
1098 result->desc.mantissa_size = desc->mantissa_size;
1099 result->desc.explicit_one = desc->explicit_one;
1100 result->desc.clss = NORMAL;
1104 sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
1106 sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
1107 sc_val_from_ulong(ROUNDING_BITS, NULL);
1108 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1113 fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result)
1115 if (result == NULL) result = calc_buffer;
1117 fc_get_max(desc, result);
1123 fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result)
1125 if (result == NULL) result = calc_buffer;
1127 result->desc.exponent_size = desc->exponent_size;
1128 result->desc.mantissa_size = desc->mantissa_size;
1129 result->desc.explicit_one = desc->explicit_one;
1130 result->desc.clss = NAN;
1134 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1136 /* signaling NaN has non-zero mantissa with msb not set */
1137 sc_val_from_ulong(1, _mant(result));
1142 fp_value *fc_get_qnan(const ieee_descriptor_t *desc, fp_value *result)
1144 if (result == NULL) result = calc_buffer;
1146 result->desc.exponent_size = desc->exponent_size;
1147 result->desc.mantissa_size = desc->mantissa_size;
1148 result->desc.explicit_one = desc->explicit_one;
1149 result->desc.clss = NAN;
1153 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1155 /* quiet NaN has the msb of the mantissa set, so shift one there */
1156 sc_val_from_ulong(1, _mant(result));
1157 /* mantissa_size >+< 1 because of two extra rounding bits */
1158 sc_val_from_ulong(desc->mantissa_size + 1, NULL);
1159 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1164 fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result)
1168 if (result == NULL) result = calc_buffer;
1170 result->desc.exponent_size = desc->exponent_size;
1171 result->desc.mantissa_size = desc->mantissa_size;
1172 result->desc.explicit_one = desc->explicit_one;
1173 result->desc.clss = INF;
1177 sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result));
1179 mant = _mant(result);
1180 sc_val_from_ulong(0, mant);
1181 if (desc->explicit_one) {
1182 sc_set_bit_at(mant, result->desc.mantissa_size + ROUNDING_BITS);
1188 fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result)
1190 if (result == NULL) result = calc_buffer;
1192 fc_get_plusinf(desc, result);
1198 int fc_comp(const fp_value *val_a, const fp_value *val_b)
1203 * shortcut: if both values are identical, they are either
1204 * Unordered if NaN or equal
1207 return val_a->desc.clss == NAN ? 2 : 0;
1209 /* unordered if one is a NaN */
1210 if (val_a->desc.clss == NAN || val_b->desc.clss == NAN)
1213 /* zero is equal independent of sign */
1214 if ((val_a->desc.clss == ZERO) && (val_b->desc.clss == ZERO))
1217 /* different signs make compare easy */
1218 if (val_a->sign != val_b->sign)
1219 return (val_a->sign == 0) ? (1) : (-1);
1221 mul = val_a->sign ? -1 : 1;
1223 /* both infinity means equality */
1224 if ((val_a->desc.clss == INF) && (val_b->desc.clss == INF))
1227 /* infinity is bigger than the rest */
1228 if (val_a->desc.clss == INF)
1230 if (val_b->desc.clss == INF)
1233 /* check first exponent, that mantissa if equal */
1234 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1240 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1246 int fc_is_zero(const fp_value *a)
1248 return a->desc.clss == ZERO;
1251 int fc_is_negative(const fp_value *a)
1256 int fc_is_inf(const fp_value *a)
1258 return a->desc.clss == INF;
1261 int fc_is_nan(const fp_value *a)
1263 return a->desc.clss == NAN;
1266 int fc_is_subnormal(const fp_value *a)
1268 return a->desc.clss == SUBNORMAL;
1271 char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base)
1276 mul_1 = (char*) alloca(calc_buffer_size);
1280 switch ((value_class_t)val->desc.clss) {
1282 snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+');
1285 snprintf(buf, buflen, "NaN");
1288 snprintf(buf, buflen, "0.0");
1291 flt_val = fc_val_to_ieee754(val);
1292 #ifdef HAVE_LONG_DOUBLE
1293 /* XXX 30 is arbitrary */
1294 snprintf(buf, buflen, "%.30LE", flt_val);
1296 snprintf(buf, buflen, "%.18E", 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 #ifdef HAVE_LONG_DOUBLE
1315 snprintf(buf, buflen, "%LA", flt_val);
1317 snprintf(buf, buflen, "%A", flt_val);
1324 snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0));
1325 buf[buflen - 1] = '\0';
1331 unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs)
1333 /* this is used to cache the packed version of the value */
1334 static char *packed_value = NULL;
1336 if (packed_value == NULL) packed_value = XMALLOCN(char, value_size);
1339 pack(value, packed_value);
1341 return sc_sub_bits(packed_value, num_bits, byte_ofs);
1344 /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */
1345 int fc_zero_mantissa(const fp_value *value)
1347 return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size;
1350 /* Returns the exponent of a value. */
1351 int fc_get_exponent(const fp_value *value)
1353 int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1;
1354 return sc_val_to_long(_exp(value)) - exp_bias;
1357 /* Return non-zero if a given value can be converted lossless into another precision */
1358 int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc)
1363 /* handle some special cases first */
1364 switch (value->desc.clss) {
1373 /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */
1374 exp_bias = (1 << (desc->exponent_size - 1)) - 1;
1375 v = fc_get_exponent(value) + exp_bias;
1376 if (0 < v && v < (1 << desc->exponent_size) - 1) {
1377 /* exponent can be encoded, now check the mantissa */
1378 v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value));
1379 return v <= desc->mantissa_size;
1385 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
1387 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1388 rounding_mode = mode;
1390 return rounding_mode;
1393 fc_rounding_mode_t fc_get_rounding_mode(void)
1395 return rounding_mode;
1398 void init_fltcalc(int precision)
1400 if (calc_buffer == NULL) {
1401 /* does nothing if already init */
1402 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1404 init_strcalc(precision + 2 + ROUNDING_BITS);
1406 /* needs additionally rounding bits, one bit as explicit 1., and one for
1407 * addition overflow */
1408 max_precision = sc_get_precision() - (2 + ROUNDING_BITS);
1409 if (max_precision < precision)
1410 printf("WARNING: not enough precision available, using %d\n", max_precision);
1412 rounding_mode = FC_TONEAREST;
1413 value_size = sc_get_buffer_length();
1414 calc_buffer_size = sizeof(fp_value) + 2*value_size - 1;
1416 calc_buffer = (fp_value*) xmalloc(calc_buffer_size);
1417 memset(calc_buffer, 0, calc_buffer_size);
1418 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer));
1419 #ifdef HAVE_LONG_DOUBLE
1420 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1422 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1424 #ifdef WORDS_BIGENDIAN
1425 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1427 DEBUGPRINTF(("\tWord order is little endian\n\n"));
1432 void finish_fltcalc (void)
1434 free(calc_buffer); calc_buffer = NULL;
1437 #ifdef FLTCALC_TRACE_CALC
1438 static char buffer[100];
1441 /* definition of interface functions */
1442 fp_value *fc_add(const fp_value *a, const fp_value *b, fp_value *result)
1444 if (result == NULL) result = calc_buffer;
1446 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1447 TRACEPRINTF(("+ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1449 /* make the value with the bigger exponent the first one */
1450 if (sc_comp(_exp(a), _exp(b)) == -1)
1451 _fadd(b, a, result);
1453 _fadd(a, b, result);
1455 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1459 fp_value *fc_sub(const fp_value *a, const fp_value *b, fp_value *result)
1463 if (result == NULL) result = calc_buffer;
1465 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1466 TRACEPRINTF(("- %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1468 temp = (fp_value*) alloca(calc_buffer_size);
1469 memcpy(temp, b, calc_buffer_size);
1470 temp->sign = !b->sign;
1471 if (sc_comp(_exp(a), _exp(temp)) == -1)
1472 _fadd(temp, a, result);
1474 _fadd(a, temp, result);
1476 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1480 fp_value *fc_mul(const fp_value *a, const fp_value *b, fp_value *result)
1482 if (result == NULL) result = calc_buffer;
1484 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1485 TRACEPRINTF(("* %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1487 _fmul(a, b, result);
1489 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1493 fp_value *fc_div(const fp_value *a, const fp_value *b, fp_value *result)
1495 if (result == NULL) result = calc_buffer;
1497 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1498 TRACEPRINTF(("/ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED)));
1500 _fdiv(a, b, result);
1502 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1506 fp_value *fc_neg(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)));
1513 memcpy(result, a, calc_buffer_size);
1514 result->sign = !a->sign;
1516 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1520 fp_value *fc_int(const fp_value *a, fp_value *result)
1522 if (result == NULL) result = calc_buffer;
1524 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1525 TRACEPRINTF(("truncated to integer "));
1529 TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED)));
1533 fp_value *fc_rnd(const fp_value *a, fp_value *result)
1535 if (result == NULL) result = calc_buffer;
1538 TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED)));
1539 TRACEPRINTF(("rounded to integer "));
1541 panic("fc_rnd() not yet implemented");
1545 * convert a floating point value into an sc value ...
1547 int fc_flt2int(const fp_value *a, void *result, ir_mode *dst_mode)
1549 if (a->desc.clss == NORMAL) {
1550 int exp_bias = (1 << (a->desc.exponent_size - 1)) - 1;
1551 int exp_val = sc_val_to_long(_exp(a)) - exp_bias;
1556 if (a->sign && !mode_is_signed(dst_mode)) {
1557 /* FIXME: for now we cannot convert this */
1561 tgt_bits = get_mode_size_bits(dst_mode);
1562 if (mode_is_signed(dst_mode))
1565 assert(exp_val >= 0 && "floating point value not integral before fc_flt2int() call");
1566 mantissa_size = a->desc.mantissa_size + ROUNDING_BITS;
1567 shift = exp_val - mantissa_size;
1569 if (tgt_bits < mantissa_size + 1)
1570 tgt_bits = mantissa_size + 1;
1572 sc_shlI(_mant(a), shift, tgt_bits, 0, result);
1574 sc_shrI(_mant(a), -shift, tgt_bits, 0, result);
1577 /* check for overflow */
1578 highest = sc_get_highest_set_bit(result);
1580 if (mode_is_signed(dst_mode)) {
1581 if (highest == sc_get_lowest_set_bit(result)) {
1582 /* need extra test for MIN_INT */
1583 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1584 /* FIXME: handle overflow */
1588 if (highest >= (int) get_mode_size_bits(dst_mode) - 1) {
1589 /* FIXME: handle overflow */
1594 if (highest >= (int) get_mode_size_bits(dst_mode)) {
1595 /* FIXME: handle overflow */
1601 sc_neg(result, result);
1605 else if (a->desc.clss == ZERO) {
1613 unsigned fc_set_immediate_precision(unsigned bits)
1615 unsigned old = immediate_prec;
1617 immediate_prec = bits;
1621 int fc_is_exact(void)