3 * File name: ir/tv/fltcalc.c
9 * Copyright: (c) 2003 Universität Karlsruhe
10 * Licence: This file protected by GPL - GNU GENERAL PUBLIC LICENSE.
22 #include <math.h> /* need isnan() and isinf() (will be changed)*/
23 /* undef some reused constants defined by math.h */
28 #ifdef HAVE_INTTYPES_H
45 typedef uint32_t UINT32;
47 #ifdef HAVE_LONG_DOUBLE
48 #ifdef WORDS_BIGENDIAN
55 volatile long double d;
64 volatile long double d;
68 #ifdef WORDS_BIGENDIAN
105 #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
107 /* because variable sized structs are impossible, the internal
108 * value is represented as a pseudo-struct char array, addressed
111 * char sign; // 0 for positive, 1 for negative
112 * char exp[value_size];
113 * char mant[value_size];
117 #define _sign(a) (((char*)a)[SIGN_POS])
118 #define _exp(a) (&((char*)a)[EXPONENT_POS])
119 #define _mant(a) (&((char*)a)[MANTISSA_POS])
120 #define _desc(a) (*(descriptor_t *)&((char *)a)[DESCRIPTOR_POS])
122 #define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
123 #define _shift_right(x, y, b) sc_shr((x), (y), value_size*4, 0, (b))
124 #define _shift_left(x, y, b) sc_shl((x), (y), value_size*4, 0, (b))
126 #define FC_DEFINE1(code) char* fc_##code(const void *a, void *result) \
128 return _calc((const char*)a, NULL, FC_##code, (char*)result); \
131 #define FC_DEFINE2(code) char* fc_##code(const void *a, const void *b, void *result) \
133 return _calc((const char*)a, (const char*)b, FC_##code, (char*)result); \
136 #define FUNC_PTR(code) fc_##code
139 # define DEBUGPRINTF(x) printf x
141 # define DEBUGPRINTF(x) ((void)0)
144 #if FLTCALC_TRACE_CALC
145 # define TRACEPRINTF(x) printf x
147 # define TRACEPRINTF(x) ((void)0)
150 static char *calc_buffer = NULL;
152 static fc_rounding_mode_t rounding_mode;
154 static int calc_buffer_size;
155 static int value_size;
157 static int EXPONENT_POS;
158 static int MANTISSA_POS;
159 static int DESCRIPTOR_POS;
161 static int max_precision;
166 static void _fail_char(const char *str, unsigned int len, int pos)
169 printf("ERROR: Unexpected character '%c'\n", *(str + pos));
171 printf("ERROR: Unexpected end of string\n");
172 while (len-- && *str) printf("%c", *str++); printf("\n");
173 while (pos--) printf(" "); printf("^\n");
174 /* the front end has to to check constant strings */
179 /* pack machine-like */
180 static char* _pack(const char *int_float, char *packed)
186 temp = alloca(value_size);
187 shift_val = alloca(value_size);
189 switch (_desc(int_float).class) {
191 val_buffer = alloca(calc_buffer_size);
192 fc_get_qnan(_desc(int_float).exponent_size, _desc(int_float).mantissa_size, val_buffer);
193 int_float = val_buffer;
197 val_buffer = alloca(calc_buffer_size);
198 fc_get_plusinf(_desc(int_float).exponent_size, _desc(int_float).mantissa_size, val_buffer);
199 _sign(val_buffer) = _sign(int_float);
200 int_float = val_buffer;
207 sc_val_from_ulong(_sign(int_float), temp);
209 sc_val_from_ulong(_desc(int_float).exponent_size + _desc(int_float).mantissa_size, NULL);
210 _shift_left(temp, sc_get_buffer(), packed);
212 /* extract exponent */
213 sc_val_from_ulong(_desc(int_float).mantissa_size, shift_val);
215 _shift_left(_exp(int_float), shift_val, temp);
217 sc_or(temp, packed, packed);
219 /* extract mantissa */
220 /* remove 2 rounding bits */
221 sc_val_from_ulong(2, shift_val);
222 _shift_right(_mant(int_float), shift_val, temp);
224 /* remove leading 1 (or 0 if denormalized) */
225 sc_max_from_bits(_desc(int_float).mantissa_size, 0, shift_val); /* all mantissa bits are 1's */
226 sc_and(temp, shift_val, temp);
229 sc_or(temp, packed, packed);
234 char* _normalize(const char *in_val, char *out_val, int sticky)
237 char lsb, guard, round, round_dir = 0;
240 temp = alloca(value_size);
242 /* +2: save two rounding bits at the end */
243 hsb = 2 + _desc(in_val).mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
245 if (in_val != out_val)
247 _sign(out_val) = _sign(in_val);
248 memcpy(&_desc(out_val), &_desc(in_val), sizeof(descriptor_t));
251 _desc(out_val).class = NORMAL;
253 /* mantissa all zeros, so zero exponent (because of explicit one)*/
254 if (hsb == 2 + _desc(in_val).mantissa_size)
256 sc_val_from_ulong(0, _exp(out_val));
260 /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */
264 sc_val_from_ulong(-hsb-1, temp);
266 _shift_right(_mant(in_val), temp, _mant(out_val));
268 /* remember if some bits were shifted away */
269 if (!sticky) sticky = sc_had_carry();
271 sc_add(_exp(in_val), temp, _exp(out_val));
276 sc_val_from_ulong(hsb+1, temp);
278 _shift_left(_mant(in_val), temp, _mant(out_val));
280 sc_sub(_exp(in_val), temp, _exp(out_val));
283 /* check for exponent underflow */
284 if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
285 DEBUGPRINTF(("Exponent underflow!\n"));
286 /* exponent underflow */
287 /* shift the mantissa right to have a zero exponent */
288 sc_val_from_ulong(1, temp);
289 sc_sub(temp, _exp(out_val), NULL);
291 _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
292 if (!sticky) sticky = sc_had_carry();
293 /* denormalized means exponent of zero */
294 sc_val_from_ulong(0, _exp(out_val));
296 _desc(out_val).class = SUBNORMAL;
299 /* perform rounding by adding a value that clears the guard bit and the round bit
300 * and either causes a carry to round up or not */
301 /* get the last 3 bits of the value */
302 lsb = sc_sub_bits(_mant(out_val), _desc(out_val).mantissa_size + 2, 0) & 0x7;
303 guard = (lsb&0x2)>>1;
306 switch (rounding_mode)
309 /* round to nearest representable value, if in doubt choose the version
311 round_dir = guard && (sticky || round || lsb>>2);
314 /* if positive: round to one if the exact value is bigger, else to zero */
315 round_dir = (!_sign(out_val) && (guard || round || sticky));
318 /* if negative: round to one if the exact value is bigger, else to zero */
319 round_dir = (_sign(out_val) && (guard || round || sticky));
322 /* always round to 0 (chopping mode) */
326 DEBUGPRINTF(("Rounding (s%d, l%d, g%d, r%d, s%d) %s\n", _sign(out_val), lsb>>2, guard, round, sticky, (round_dir)?"up":"down"));
330 guard = (round^guard)<<1;
331 lsb = !(round || guard)<<2 | guard | round;
335 lsb = -((guard<<1) | round);
338 /* add the rounded value */
340 sc_val_from_long(lsb, temp);
341 sc_add(_mant(out_val), temp, _mant(out_val));
344 /* could have rounded down to zero */
345 if (sc_is_zero(_mant(out_val)) && (_desc(out_val).class == SUBNORMAL))
346 _desc(out_val).class = ZERO;
348 /* check for rounding overflow */
349 hsb = 2 + _desc(out_val).mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
350 if ((_desc(out_val).class != SUBNORMAL) && (hsb < -1))
352 sc_val_from_ulong(1, temp);
353 _shift_right(_mant(out_val), temp, _mant(out_val));
355 sc_add(_exp(out_val), temp, _exp(out_val));
357 else if ((_desc(out_val).class == SUBNORMAL) && (hsb == -1))
359 /* overflow caused the mantissa to be normal again,
360 * so adapt the exponent accordingly */
361 sc_val_from_ulong(1, temp);
362 sc_add(_exp(out_val), temp, _exp(out_val));
364 _desc(out_val).class = NORMAL;
366 /* no further rounding is needed, because rounding overflow means
367 * the carry of the original rounding was propagated all the way
368 * up to the bit left of the radix point. This implies the bits
369 * to the right are all zeros (rounding is +1) */
371 /* check for exponent overflow */
372 sc_val_from_ulong((1 << _desc(out_val).exponent_size) - 1, temp);
373 if (sc_comp(_exp(out_val), temp) != -1) {
374 DEBUGPRINTF(("Exponent overflow!\n"));
375 /* exponent overflow, reaction depends on rounding method:
377 * mode | sign of value | result
378 *--------------------------------------------------------------
379 * TO_NEAREST | + | +inf
381 *--------------------------------------------------------------
382 * TO_POSITIVE | + | +inf
383 * | - | smallest representable value
384 *--------------------------------------------------------------
385 * TO_NEAGTIVE | + | largest representable value
387 *--------------------------------------------------------------
388 * TO_ZERO | + | largest representable value
389 * | - | smallest representable value
390 *--------------------------------------------------------------*/
391 if (_sign(out_val) == 0)
393 /* value is positive */
394 switch (rounding_mode) {
397 _desc(out_val).class = INF;
402 fc_get_max(_desc(out_val).exponent_size, _desc(out_val).mantissa_size, out_val);
405 /* value is negative */
406 switch (rounding_mode) {
409 _desc(out_val).class = INF;
414 fc_get_min(_desc(out_val).exponent_size, _desc(out_val).mantissa_size, out_val);
423 * calculate a + b, where a is the value with the bigger exponent
425 static char* _add(const char* a, const char* b, char* result)
433 if (_desc(a).class == NAN) {
434 if (a != result) memcpy(result, a, calc_buffer_size);
437 if (_desc(b).class == NAN) {
438 if (b != result) memcpy(result, b, calc_buffer_size);
442 /* make sure result has a descriptor */
443 if (result != a && result != b)
444 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
446 /* determine if this is an addition or subtraction */
447 sign = _sign(a) ^ _sign(b);
449 /* produce NaN on inf - inf */
450 if (sign && (_desc(a).class == INF) && (_desc(b).class == INF))
451 return fc_get_qnan(_desc(a).exponent_size, _desc(b).mantissa_size, result);
453 temp = alloca(value_size);
454 exp_diff = alloca(value_size);
456 /* get exponent difference */
457 sc_sub(_exp(a), _exp(b), exp_diff);
459 /* initially set sign to be the sign of a, special treatment of subtraction
460 * when exponents are equal is required though.
461 * Also special care about the sign is needed when the mantissas are equal
463 if (sign && sc_val_to_long(exp_diff) == 0) {
464 switch (sc_comp(_mant(a), _mant(b))) {
466 if (_sign(a)) _sign(result) = 1; /* abs(a) is bigger and a is negative */
467 else _sign(result) = 0;
470 if (rounding_mode == FC_TONEGATIVE)
476 if (_sign(b)) _sign(result) = 1; /* abs(b) is bigger and b is negative */
477 else _sign(result) = 0;
480 /* can't be reached */
484 _sign(result) = _sign(a);
487 /* sign has been taken care of, check for special cases */
488 if (_desc(a).class == ZERO) {
489 if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
492 if (_desc(b).class == ZERO) {
493 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
497 if (_desc(a).class == INF) {
498 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
501 if (_desc(b).class == INF) {
502 if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
506 /* shift the smaller value to the right to align the radix point */
507 /* subnormals have their radix point shifted to the right,
508 * take care of this first */
509 if ((_desc(b).class == SUBNORMAL) && (_desc(a).class != SUBNORMAL))
511 sc_val_from_ulong(1, temp);
512 sc_sub(exp_diff, temp, exp_diff);
515 _shift_right(_mant(b), exp_diff, temp);
516 sticky = sc_had_carry();
520 /* if subtracting a little more than the represented value or adding a little
521 * more than the represented value to a negative value this, in addition to the
522 * still set sticky bit, takes account of the 'little more' */
523 char *temp1 = alloca(calc_buffer_size);
524 sc_val_from_ulong(1, temp1);
525 sc_add(temp, temp1, temp);
529 if (sc_comp(_mant(a), temp) == -1)
530 sc_sub(temp, _mant(a), _mant(result));
532 sc_sub(_mant(a), temp, _mant(result));
534 sc_add(_mant(a), temp, _mant(result));
537 /* _normalize expects a 'normal' radix point, adding two subnormals
538 * results in a subnormal radix point -> shifting before normalizing */
539 if ((_desc(a).class == SUBNORMAL) && (_desc(b).class == SUBNORMAL))
541 sc_val_from_ulong(1, NULL);
542 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
545 /* resulting exponent is the bigger one */
546 memmove(_exp(result), _exp(a), value_size);
548 return _normalize(result, result, sticky);
551 static char* _mul(const char* a, const char* b, char* result)
555 if (_desc(a).class == NAN) {
556 if (a != result) memcpy(result, a, calc_buffer_size);
559 if (_desc(b).class == NAN) {
560 if (b != result) memcpy(result, b, calc_buffer_size);
564 temp = alloca(value_size);
566 if (result != a && result != b)
567 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
569 _sign(result) = _sign(a) ^ _sign(b);
571 /* produce NaN on 0 * inf */
572 if (_desc(a).class == ZERO) {
573 if (_desc(b).class == INF)
574 fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
576 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
579 if (_desc(b).class == ZERO) {
580 if (_desc(a).class == INF)
581 fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
583 if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, calc_buffer_size-1);
587 if (_desc(a).class == INF) {
588 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
591 if (_desc(b).class == INF) {
592 if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, calc_buffer_size-1);
596 /* exp = exp(a) + exp(b) - excess */
597 sc_add(_exp(a), _exp(b), _exp(result));
599 sc_val_from_ulong((1<<_desc(a).exponent_size)/2-1, temp);
600 sc_sub(_exp(result), temp, _exp(result));
602 /* mixed normal, subnormal values introduce an error of 1, correct it */
603 if ((_desc(a).class == SUBNORMAL) ^ (_desc(b).class == SUBNORMAL))
605 sc_val_from_ulong(1, temp);
606 sc_add(_exp(result), temp, _exp(result));
609 sc_mul(_mant(a), _mant(b), _mant(result));
611 /* realign result: after a multiplication the digits right of the radix
612 * point are the sum of the factors' digits after the radix point. As all
613 * values are normalized they both have the same amount of these digits,
614 * which has to be restored by proper shifting
615 * +2 because of the two rounding bits */
616 sc_val_from_ulong(2 + _desc(result).mantissa_size, temp);
618 _shift_right(_mant(result), temp, _mant(result));
620 return _normalize(result, result, sc_had_carry());
623 static char* _div(const char* a, const char* b, char* result)
625 char *temp, *dividend;
627 if (_desc(a).class == NAN) {
628 if (a != result) memcpy(result, a, calc_buffer_size);
631 if (_desc(b).class == NAN) {
632 if (b != result) memcpy(result, b, calc_buffer_size);
636 temp = alloca(value_size);
637 dividend = alloca(value_size);
639 if (result != a && result != b)
640 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
642 _sign(result) = _sign(a) ^ _sign(b);
644 /* produce nan on 0/0 and inf/inf */
645 if (_desc(a).class == ZERO) {
646 if (_desc(b).class == ZERO)
648 fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
651 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
655 if (_desc(b).class == INF) {
656 if (_desc(a).class == INF)
658 fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
661 sc_val_from_ulong(0, NULL);
662 _save_result(_exp(result));
663 _save_result(_mant(result));
664 _desc(result).class = ZERO;
669 if (_desc(a).class == INF) {
671 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
674 if (_desc(b).class == ZERO) {
675 /* division by zero */
677 fc_get_minusinf(_desc(a).exponent_size, _desc(a).mantissa_size, result);
679 fc_get_plusinf(_desc(a).exponent_size, _desc(a).mantissa_size, result);
683 /* exp = exp(a) - exp(b) + excess - 1*/
684 sc_sub(_exp(a), _exp(b), _exp(result));
685 sc_val_from_ulong((1 << _desc(a).exponent_size)/2-2, temp);
686 sc_add(_exp(result), temp, _exp(result));
688 /* mixed normal, subnormal values introduce an error of 1, correct it */
689 if ((_desc(a).class == SUBNORMAL) ^ (_desc(b).class == SUBNORMAL))
691 sc_val_from_ulong(1, temp);
692 sc_add(_exp(result), temp, _exp(result));
695 /* mant(res) = mant(a) / 1/2mant(b) */
696 /* to gain more bits of precision in the result the dividend could be
697 * shifted left, as this operation does not loose bits. This would not
698 * fit into the integer precision, but due to the rounding bits (which
699 * are always zero because the values are all normalized) the divisor
700 * can be shifted right instead to achieve the same result */
701 sc_val_from_ulong(2 + _desc(result).mantissa_size, temp);
703 _shift_left(_mant(a), temp, dividend);
706 char *divisor = alloca(calc_buffer_size);
707 sc_val_from_ulong(1, divisor);
708 _shift_right(_mant(b), divisor, divisor);
709 sc_div(dividend, divisor, _mant(result));
712 return _normalize(result, result, sc_had_carry());
715 void _power_of_ten(int exp, descriptor_t *desc, char *result)
723 /* set new descriptor (else result is supposed to already have one) */
725 memcpy(&_desc(result), desc, sizeof(descriptor_t));
727 build = alloca(value_size);
728 temp = alloca(value_size);
730 sc_val_from_ulong((1 << _desc(result).exponent_size)/2-1, _exp(result));
734 /* temp is value of ten now */
735 sc_val_from_ulong(10, NULL);
738 for (exp--; exp > 0; exp--) {
740 sc_mul(build, temp, NULL);
744 /* temp is amount of left shift needed to put the value left of the radix point */
745 sc_val_from_ulong(_desc(result).mantissa_size + 2, temp);
747 _shift_left(build, temp, _mant(result));
749 _normalize(result, result, 0);
753 static char* _trunc(const char *a, char *result)
755 /* when exponent == 0 all bits left of the radix point
756 * are the integral part of the value. For 15bit exp_size
757 * this would require a left shift of max. 16383 bits which
759 * But it is enough to ensure that no bit right of the radix
760 * point remains set. This restricts the interesting
761 * exponents to the interval [0, mant_size-1].
762 * Outside this interval the truncated value is either 0 or
763 * it is are already truncated */
765 int exp_bias, exp_val;
768 temp = alloca(value_size);
771 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
773 exp_bias = (1<<_desc(a).exponent_size)/2-1;
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 _desc(result).class = ZERO;
785 if (exp_val > _desc(a).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(_desc(a).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));
801 if (a != result) memcpy(_exp(result), _exp(a), value_size);
807 * This does value sanity checking(or should do it), sets up any prerequisites,
808 * calls the proper internal functions, clears up and returns
811 char* _calc(const char *a, const char *b, int opcode, char *result)
814 #ifdef FLTCALC_TRACE_CALC
817 buffer = alloca(100);
820 if (result == NULL) result = calc_buffer;
822 TRACEPRINTF(("%s ", fc_print(a, buffer, 100, FC_PACKED)));
826 /* make the value with the bigger exponent the first one */
827 TRACEPRINTF(("+ %s ", fc_print(b, buffer, 100, FC_PACKED)));
828 if (sc_comp(_exp(a), _exp(b)) == -1)
834 TRACEPRINTF(("- %s ", fc_print(b, buffer, 100, FC_PACKED)));
835 temp = alloca(calc_buffer_size);
836 memcpy(temp, b, calc_buffer_size);
837 _sign(temp) = !_sign(b);
838 if (sc_comp(_exp(a), _exp(temp)) == -1)
839 _add(temp, a, result);
841 _add(a, temp, result);
844 TRACEPRINTF(("* %s ", fc_print(b, buffer, 100, FC_PACKED)));
848 TRACEPRINTF(("/ %s ", fc_print(b, buffer, 100, FC_PACKED)));
852 TRACEPRINTF(("negated "));
853 if (a != result) memcpy(result, a, calc_buffer_size);
854 _sign(result) = !_sign(a);
863 TRACEPRINTF(("= %s\n", fc_print(result, buffer, 100, FC_PACKED)));
868 * functions defined in fltcalc.h
870 const void *fc_get_buffer(void)
875 const int fc_get_buffer_length(void)
877 return calc_buffer_size;
880 char* fc_val_from_str(const char *str, unsigned int len, char exp_size, char mant_size, char *result)
893 int exp_int, hsb, state;
898 char *mant_str, *exp_val, *power_val;
900 if (result == NULL) result = calc_buffer;
902 exp_val = alloca(value_size);
903 power_val = alloca(calc_buffer_size);
904 mant_str = alloca((len)?(len):(strlen(str)));
906 _desc(result).exponent_size = exp_size;
907 _desc(result).mantissa_size = mant_size;
908 _desc(result).class = NORMAL;
915 while (len == 0 || str-old_str < len)
932 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
939 state = RIGHT_OF_DOT;
950 _fail_char(old_str, len, str - old_str);
956 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
957 mant_str[pos++] = *(str++);
961 state = RIGHT_OF_DOT;
972 mant_str[pos] = '\0';
976 _fail_char(old_str, len, str - old_str);
982 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
983 mant_str[pos++] = *(str++);
994 mant_str[pos] = '\0';
998 _fail_char(old_str, len, str - old_str);
1008 if (*(str-1) != 'e' && *(str-1) != 'E') _fail_char(old_str, len, str - old_str);
1012 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
1013 mant_str[pos] = '\0';
1020 _fail_char(old_str, len, str - old_str);
1026 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
1031 case '\0': goto done;
1034 _fail_char(old_str, len, str - old_str);
1037 } /* switch(state) */
1040 sc_val_from_str(mant_str, strlen(mant_str), _mant(result));
1042 /* shift to put value left of radix point */
1043 sc_val_from_ulong(mant_size + 2, exp_val);
1045 _shift_left(_mant(result), exp_val, _mant(result));
1047 sc_val_from_ulong((1 << exp_size)/2-1, _exp(result));
1049 _normalize(result, result, 0);
1051 if (state == EXPONENT) {
1052 exp_int -= atoi(str-pos);
1055 _power_of_ten(exp_int, &_desc(result), power_val);
1057 _div(result, power_val, result);
1062 /* XXX excuse of an implementation to make things work */
1064 #ifdef HAVE_LONG_DOUBLE
1065 val = strtold(str, NULL);
1067 val = strtod(str, NULL);
1070 DEBUGPRINTF(("val_from_str(%s)\n", str));
1071 return fc_val_from_float(val, exp_size, mant_size, result);
1075 char* fc_val_from_float(LLDBL l, char exp_size, char mant_size, char* result)
1078 int bias_res, bias_val, mant_val;
1080 UINT32 sign, exponent, mantissa0, mantissa1;
1083 bias_res = ((1<<exp_size)/2-1);
1085 #ifdef HAVE_LONG_DOUBLE
1088 sign = (srcval.val.high & 0x00008000) != 0;
1089 exponent = (srcval.val.high & 0x00007FFF) ;
1090 mantissa0 = srcval.val.mid;
1091 mantissa1 = srcval.val.low;
1092 #else /* no long double */
1095 sign = (srcval.val.high & 0x80000000) != 0;
1096 exponent = (srcval.val.high & 0x7FF00000) >> 20;
1097 mantissa0 = srcval.val.high & 0x000FFFFF;
1098 mantissa1 = srcval.val.low;
1101 #ifdef HAVE_LONG_DOUBLE
1102 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)); */
1103 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1105 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
1106 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1109 if (result == NULL) result = calc_buffer;
1110 temp = alloca(value_size);
1112 _desc(result).exponent_size = exp_size;
1113 _desc(result).mantissa_size = mant_size;
1116 _sign(result) = sign;
1118 /* sign and flag suffice to identify nan or inf, no exponent/mantissa
1119 * encoding is needed. the function can return immediately in these cases */
1121 _desc(result).class = NAN;
1122 TRACEPRINTF(("val_from_float resulted in NAN\n"));
1125 else if (isinf(l)) {
1126 _desc(result).class = INF;
1127 TRACEPRINTF(("val_from_float resulted in %sINF\n", (_sign(result)==1)?"-":""));
1131 /* build exponent, because input and output exponent and mantissa sizes may differ
1132 * this looks more complicated than it is: unbiased input exponent + output bias,
1133 * minus the mantissa difference which is added again later when the output float
1134 * becomes normalized */
1135 #ifdef HAVE_EXPLICIT_ONE
1136 sc_val_from_long((exponent-bias_val+bias_res)-(mant_val-mant_size-1), _exp(result));
1138 sc_val_from_long((exponent-bias_val+bias_res)-(mant_val-mant_size), _exp(result));
1141 /* build mantissa representation */
1142 #ifndef HAVE_EXPLICIT_ONE
1145 /* insert the hidden bit */
1146 sc_val_from_ulong(1, temp);
1147 sc_val_from_ulong(mant_val + 2, NULL);
1148 _shift_left(temp, sc_get_buffer(), NULL);
1153 sc_val_from_ulong(0, NULL);
1156 _save_result(_mant(result));
1158 /* bits from the upper word */
1159 sc_val_from_ulong(mantissa0, temp);
1160 sc_val_from_ulong(34, NULL);
1161 _shift_left(temp, sc_get_buffer(), temp);
1162 sc_or(_mant(result), temp, _mant(result));
1164 /* bits from the lower word */
1165 sc_val_from_ulong(mantissa1, temp);
1166 sc_val_from_ulong(2, NULL);
1167 _shift_left(temp, sc_get_buffer(), temp);
1168 sc_or(_mant(result), temp, _mant(result));
1170 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
1171 * origin one to the left */
1174 sc_val_from_ulong(1, NULL);
1175 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1178 _normalize(result, result, 0);
1180 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
1185 LLDBL fc_val_to_float(const void *val)
1199 #ifdef HAVE_LONG_DOUBLE
1200 char result_exponent = 15;
1201 char result_mantissa = 64;
1203 char result_exponent = 11;
1204 char result_mantissa = 52;
1207 temp = alloca(calc_buffer_size);
1208 #ifdef HAVE_EXPLICIT_ONE
1209 value = fc_cast(val, result_exponent, result_mantissa-1, temp);
1211 value = fc_cast(val, result_exponent, result_mantissa, temp);
1214 sign = _sign(value);
1216 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
1217 * lead to wrong results */
1218 exponent = sc_val_to_long(_exp(value)) ;
1220 sc_val_from_ulong(2, NULL);
1221 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
1226 for (byte_offset = 0; byte_offset < 4; byte_offset++)
1227 mantissa1 |= sc_sub_bits(_mant(value), result_mantissa, byte_offset) << (byte_offset<<3);
1229 for (; (byte_offset<<3) < result_mantissa; byte_offset++)
1230 mantissa0 |= sc_sub_bits(_mant(value), result_mantissa, byte_offset) << ((byte_offset-4)<<3);
1232 #ifdef HAVE_LONG_DOUBLE
1233 buildval.val.high = sign << 15;
1234 buildval.val.high |= exponent;
1235 buildval.val.mid = mantissa0;
1236 buildval.val.low = mantissa1;
1237 #else /* no long double */
1238 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1239 buildval.val.high = sign << 31;
1240 buildval.val.high |= exponent << 20;
1241 buildval.val.high |= mantissa0;
1242 buildval.val.low = mantissa1;
1245 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1249 char* fc_cast(const void *val, char exp_size, char mant_size, char *result)
1251 const char *value = (const char*) val;
1253 int exp_offset, val_bias, res_bias;
1255 if (result == NULL) result = calc_buffer;
1256 temp = alloca(value_size);
1258 if (_desc(value).exponent_size == exp_size && _desc(value).mantissa_size == mant_size)
1260 if (value != result) memcpy(result, value, calc_buffer_size);
1264 /* set the descriptor of the new value */
1265 _desc(result).exponent_size = exp_size;
1266 _desc(result).mantissa_size = mant_size;
1267 _desc(result).class = _desc(value).class;
1269 _sign(result) = _sign(value);
1271 /* when the mantissa sizes differ normalizing has to shift to align it.
1272 * this would change the exponent, which is unwanted. So calculate this
1273 * offset and add it */
1274 val_bias = (1<<_desc(value).exponent_size)/2-1;
1275 res_bias = (1<<exp_size)/2-1;
1277 exp_offset = (res_bias - val_bias) - (_desc(value).mantissa_size - mant_size);
1278 sc_val_from_long(exp_offset, temp);
1279 sc_add(_exp(value), temp, _exp(result));
1281 /* _normalize expects normalized radix point */
1282 if (_desc(val).class == SUBNORMAL) {
1283 sc_val_from_ulong(1, NULL);
1284 _shift_left(_mant(val), sc_get_buffer(), _mant(result));
1285 } else if (value != result) {
1286 memcpy(_mant(result), _mant(value), value_size);
1288 memmove(_mant(result), _mant(value), value_size);
1291 _normalize(result, result, 0);
1292 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1296 char* fc_get_max(unsigned int exponent_size, unsigned int mantissa_size, char* result)
1298 if (result == NULL) result = calc_buffer;
1300 _desc(result).exponent_size = exponent_size;
1301 _desc(result).mantissa_size = mantissa_size;
1302 _desc(result).class = NORMAL;
1306 sc_val_from_ulong((1<<exponent_size) - 2, _exp(result));
1308 sc_max_from_bits(mantissa_size + 1, 0, _mant(result));
1309 sc_val_from_ulong(2, NULL);
1310 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1315 char* fc_get_min(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1317 if (result == NULL) result = calc_buffer;
1319 fc_get_max(exponent_size, mantissa_size, result);
1325 char* fc_get_snan(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1327 if (result == NULL) result = calc_buffer;
1329 _desc(result).exponent_size = exponent_size;
1330 _desc(result).mantissa_size = mantissa_size;
1331 _desc(result).class = NAN;
1335 sc_val_from_ulong((1<<exponent_size)-1, _exp(result));
1337 /* signaling NaN has non-zero mantissa with msb not set */
1338 sc_val_from_ulong(1, _mant(result));
1343 char* fc_get_qnan(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1345 if (result == NULL) result = calc_buffer;
1347 _desc(result).exponent_size = exponent_size;
1348 _desc(result).mantissa_size = mantissa_size;
1349 _desc(result).class = NAN;
1353 sc_val_from_ulong((1<<exponent_size)-1, _exp(result));
1355 /* quiet NaN has the msb of the mantissa set, so shift one there */
1356 sc_val_from_ulong(1, _mant(result));
1357 /* mantissa_size >+< 1 because of two extra rounding bits */
1358 sc_val_from_ulong(mantissa_size + 1, NULL);
1359 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1364 char* fc_get_plusinf(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1366 if (result == NULL) result = calc_buffer;
1368 _desc(result).exponent_size = exponent_size;
1369 _desc(result).mantissa_size = mantissa_size;
1370 _desc(result).class = NORMAL;
1374 sc_val_from_ulong((1<<exponent_size)-1, _exp(result));
1376 sc_val_from_ulong(0, _mant(result));
1381 char* fc_get_minusinf(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1383 if (result == NULL) result = calc_buffer;
1385 fc_get_plusinf(exponent_size, mantissa_size, result);
1391 int fc_comp(const void *a, const void *b)
1393 const char *val_a = (const char*)a;
1394 const char *val_b = (const char*)b;
1398 * shortcut: if both values are identical, they are either
1399 * Unordered if NaN or equal
1402 return _desc(val_a).class == NAN ? 2 : 0;
1404 /* unordered if one is a NaN */
1405 if (_desc(val_a).class == NAN || _desc(val_b).class == NAN)
1408 /* zero is equal independent of sign */
1409 if ((_desc(val_a).class == ZERO) && (_desc(val_b).class == ZERO))
1412 /* different signs make compare easy */
1413 if (_sign(val_a) != _sign(val_b))
1414 return (_sign(val_a)==0)?(1):(-1);
1416 mul = _sign(a) ? -1 : 1;
1418 /* both infinity means equality */
1419 if ((_desc(val_a).class == INF) && (_desc(val_b).class == INF))
1422 /* infinity is bigger than the rest */
1423 if (_desc(val_a).class == INF)
1425 if (_desc(val_b).class == INF)
1428 /* check first exponent, that mantissa if equal */
1429 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1435 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1441 int fc_is_zero(const void *a)
1443 return _desc(a).class == ZERO;
1446 int fc_is_negative(const void *a)
1451 int fc_is_inf(const void *a)
1453 return _desc(a).class == INF;
1456 int fc_is_nan(const void *a)
1458 return _desc(a).class == NAN;
1461 int fc_is_subnormal(const void *a)
1463 return _desc(a).class == SUBNORMAL;
1466 char *fc_print(const void *a, char *buf, int buflen, unsigned base)
1471 val = (const char*)a;
1473 mul_1 = alloca(calc_buffer_size);
1477 switch (_desc(val).class) {
1479 if (buflen >= 8+_sign(val)) sprintf(buf, "%sINFINITY", _sign(val)?"-":"");
1480 else snprintf(buf, buflen, "%sINF", _sign(val)?"-":NULL);
1483 snprintf(buf, buflen, "NAN");
1486 snprintf(buf, buflen, "0.0");
1489 /* XXX to be implemented */
1490 #ifdef HAVE_LONG_DOUBLE
1491 /* XXX 30 is arbitrary */
1492 snprintf(buf, buflen, "%.30LE", fc_val_to_float(val));
1494 snprintf(buf, buflen, "%.18E", fc_val_to_float(val));
1500 switch (_desc(val).class) {
1502 if (buflen >= 8+_sign(val)) sprintf(buf, "%sINFINITY", _sign(val)?"-":"");
1503 else snprintf(buf, buflen, "%sINF", _sign(val)?"-":NULL);
1506 snprintf(buf, buflen, "NAN");
1509 snprintf(buf, buflen, "0.0");
1512 #ifdef HAVE_LONG_DOUBLE
1513 snprintf(buf, buflen, "%LA", fc_val_to_float(val));
1515 snprintf(buf, buflen, "%A", fc_val_to_float(val));
1522 snprintf(buf, buflen, "%s", sc_print(_pack(val, mul_1), value_size*4, SC_HEX));
1528 unsigned char fc_sub_bits(const void *value, unsigned num_bits, unsigned byte_ofs)
1530 /* this is used to cache the packed version of the value */
1531 static char *pack = NULL;
1533 if (pack == NULL) pack = xmalloc(value_size);
1536 _pack((const char*)value, pack);
1538 return sc_sub_bits(pack, num_bits, byte_ofs);
1541 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
1543 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1544 rounding_mode = mode;
1546 return rounding_mode;
1549 fc_rounding_mode_t fc_get_rounding_mode(void)
1551 return rounding_mode;
1554 void init_fltcalc(int precision)
1556 if (calc_buffer == NULL) {
1557 /* does nothing if already init */
1558 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1560 init_strcalc(precision + 4);
1562 /* needs additionally two bits to round, a bit as explicit 1., and one for
1563 * addition overflow */
1564 max_precision = sc_get_precision() - 4;
1565 if (max_precision < precision)
1566 printf("WARING: not enough precision available, using %d\n", max_precision);
1568 rounding_mode = FC_TONEAREST;
1569 value_size = sc_get_buffer_length();
1571 EXPONENT_POS = SIGN_POS + sizeof(char);
1572 MANTISSA_POS = EXPONENT_POS + value_size;
1573 DESCRIPTOR_POS = MANTISSA_POS + value_size;
1574 calc_buffer_size = DESCRIPTOR_POS + sizeof(descriptor_t);
1576 calc_buffer = xmalloc(calc_buffer_size);
1577 DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\n\tSIGN_POS = %d\n\tEXPONENT_POS = %d\n\tMANTISSA_POS = %d\n\tDESCRIPTOR_POS = %d\n\tCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, SIGN_POS, EXPONENT_POS, MANTISSA_POS, DESCRIPTOR_POS, calc_buffer_size, calc_buffer));
1578 #ifdef HAVE_LONG_DOUBLE
1579 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1581 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1583 #ifdef WORDS_BIGENDIAN
1584 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1586 DEBUGPRINTF(("\tWord order is little endian\n\n"));
1591 void finish_fltcalc (void) {
1592 free(calc_buffer); calc_buffer = NULL;
1595 /* definition of interface functions */