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
88 * possible float states
91 NORMAL, /**< normal representation, implicit 1 */
93 SUBNORMAL, /**< denormals, implicit 0 */
95 NAN, /**< Not A Number */
98 /** A descriptor for an IEEE float value. */
100 unsigned char exponent_size; /**< size of exponent in bits */
101 unsigned char mantissa_size; /**< size of mantissa in bits */
102 value_class_t clss; /**< state of this float */
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) \
127 char *fc_##code(const void *a, void *result) { \
128 return _calc((const char*)a, NULL, FC_##code, (char*)result); \
131 #define FC_DEFINE2(code) \
132 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).clss) {
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).clss = 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).clss = 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).clss == SUBNORMAL))
346 _desc(out_val).clss = 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).clss != 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).clss == 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).clss = 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).clss = 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).clss = INF;
414 fc_get_min(_desc(out_val).exponent_size, _desc(out_val).mantissa_size, out_val);
423 * Operations involving NaN's must return NaN
425 #define handle_NAN(a, b, result) \
427 if (_desc(a).clss == NAN) { \
428 if (a != result) memcpy(result, a, calc_buffer_size); \
431 if (_desc(b).clss == NAN) { \
432 if (b != result) memcpy(result, b, calc_buffer_size); \
439 * calculate a + b, where a is the value with the bigger exponent
441 static char* _fadd(const char* a, const char* b, char* result)
449 handle_NAN(a, b, result);
451 /* make sure result has a descriptor */
452 if (result != a && result != b)
453 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
455 /* determine if this is an addition or subtraction */
456 sign = _sign(a) ^ _sign(b);
458 /* produce NaN on inf - inf */
459 if (sign && (_desc(a).clss == INF) && (_desc(b).clss == INF))
460 return fc_get_qnan(_desc(a).exponent_size, _desc(b).mantissa_size, result);
462 temp = alloca(value_size);
463 exp_diff = alloca(value_size);
465 /* get exponent difference */
466 sc_sub(_exp(a), _exp(b), exp_diff);
468 /* initially set sign to be the sign of a, special treatment of subtraction
469 * when exponents are equal is required though.
470 * Also special care about the sign is needed when the mantissas are equal
472 if (sign && sc_val_to_long(exp_diff) == 0) {
473 switch (sc_comp(_mant(a), _mant(b))) {
475 _sign(result) = _sign(a); /* abs(a) is bigger and a is negative */
478 _sign(result) = (rounding_mode == FC_TONEGATIVE);
481 _sign(result) = _sign(b); /* abs(b) is bigger and b is negative */
484 /* can't be reached */
489 _sign(result) = _sign(a);
491 /* sign has been taken care of, check for special cases */
492 if (_desc(a).clss == ZERO) {
493 if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
496 if (_desc(b).clss == ZERO) {
497 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
501 if (_desc(a).clss == INF) {
502 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
505 if (_desc(b).clss == INF) {
506 if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, calc_buffer_size-SIGN_POS-1);
510 /* shift the smaller value to the right to align the radix point */
511 /* subnormals have their radix point shifted to the right,
512 * take care of this first */
513 if ((_desc(b).clss == SUBNORMAL) && (_desc(a).clss != SUBNORMAL))
515 sc_val_from_ulong(1, temp);
516 sc_sub(exp_diff, temp, exp_diff);
519 _shift_right(_mant(b), exp_diff, temp);
520 sticky = sc_had_carry();
524 /* if subtracting a little more than the represented value or adding a little
525 * more than the represented value to a negative value this, in addition to the
526 * still set sticky bit, takes account of the 'little more' */
527 char *temp1 = alloca(calc_buffer_size);
528 sc_val_from_ulong(1, temp1);
529 sc_add(temp, temp1, temp);
533 if (sc_comp(_mant(a), temp) == -1)
534 sc_sub(temp, _mant(a), _mant(result));
536 sc_sub(_mant(a), temp, _mant(result));
538 sc_add(_mant(a), temp, _mant(result));
541 /* _normalize expects a 'normal' radix point, adding two subnormals
542 * results in a subnormal radix point -> shifting before normalizing */
543 if ((_desc(a).clss == SUBNORMAL) && (_desc(b).clss == SUBNORMAL))
545 sc_val_from_ulong(1, NULL);
546 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
549 /* resulting exponent is the bigger one */
550 memmove(_exp(result), _exp(a), value_size);
552 return _normalize(result, result, sticky);
558 static char* _fmul(const char* a, const char* b, char* result)
562 handle_NAN(a, b, result);
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).clss == ZERO) {
573 if (_desc(b).clss == 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).clss == ZERO) {
580 if (_desc(a).clss == 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).clss == INF) {
588 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
591 if (_desc(b).clss == 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).clss == SUBNORMAL) ^ (_desc(b).clss == 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());
626 static char* _fdiv(const char* a, const char* b, char* result)
628 char *temp, *dividend;
630 handle_NAN(a, b, result);
632 temp = alloca(value_size);
633 dividend = alloca(value_size);
635 if (result != a && result != b)
636 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
638 _sign(result) = _sign(a) ^ _sign(b);
640 /* produce nan on 0/0 and inf/inf */
641 if (_desc(a).clss == ZERO) {
642 if (_desc(b).clss == ZERO)
644 fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
647 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
651 if (_desc(b).clss == INF) {
652 if (_desc(a).clss == INF)
654 fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
657 sc_val_from_ulong(0, NULL);
658 _save_result(_exp(result));
659 _save_result(_mant(result));
660 _desc(result).clss = ZERO;
665 if (_desc(a).clss == INF) {
667 if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, calc_buffer_size-1);
670 if (_desc(b).clss == ZERO) {
671 /* division by zero */
673 fc_get_minusinf(_desc(a).exponent_size, _desc(a).mantissa_size, result);
675 fc_get_plusinf(_desc(a).exponent_size, _desc(a).mantissa_size, result);
679 /* exp = exp(a) - exp(b) + excess - 1*/
680 sc_sub(_exp(a), _exp(b), _exp(result));
681 sc_val_from_ulong((1 << _desc(a).exponent_size)/2-2, temp);
682 sc_add(_exp(result), temp, _exp(result));
684 /* mixed normal, subnormal values introduce an error of 1, correct it */
685 if ((_desc(a).clss == SUBNORMAL) ^ (_desc(b).clss == SUBNORMAL))
687 sc_val_from_ulong(1, temp);
688 sc_add(_exp(result), temp, _exp(result));
691 /* mant(res) = mant(a) / 1/2mant(b) */
692 /* to gain more bits of precision in the result the dividend could be
693 * shifted left, as this operation does not loose bits. This would not
694 * fit into the integer precision, but due to the rounding bits (which
695 * are always zero because the values are all normalized) the divisor
696 * can be shifted right instead to achieve the same result */
697 sc_val_from_ulong(2 + _desc(result).mantissa_size, temp);
699 _shift_left(_mant(a), temp, dividend);
702 char *divisor = alloca(calc_buffer_size);
703 sc_val_from_ulong(1, divisor);
704 _shift_right(_mant(b), divisor, divisor);
705 sc_div(dividend, divisor, _mant(result));
708 return _normalize(result, result, sc_had_carry());
711 static void _power_of_ten(int exp, descriptor_t *desc, char *result)
719 /* set new descriptor (else result is supposed to already have one) */
721 memcpy(&_desc(result), desc, sizeof(descriptor_t));
723 build = alloca(value_size);
724 temp = alloca(value_size);
726 sc_val_from_ulong((1 << _desc(result).exponent_size)/2-1, _exp(result));
730 /* temp is value of ten now */
731 sc_val_from_ulong(10, NULL);
734 for (exp--; exp > 0; exp--) {
736 sc_mul(build, temp, NULL);
740 /* temp is amount of left shift needed to put the value left of the radix point */
741 sc_val_from_ulong(_desc(result).mantissa_size + 2, temp);
743 _shift_left(build, temp, _mant(result));
745 _normalize(result, result, 0);
750 * Truncate the fractional part away.
752 * This does not clip to any integer rang.
754 static char* _trunc(const char *a, char *result)
757 * When exponent == 0 all bits left of the radix point
758 * are the integral part of the value. For 15bit exp_size
759 * this would require a left shift of max. 16383 bits which
761 * But it is enough to ensure that no bit right of the radix
762 * point remains set. This restricts the interesting
763 * exponents to the interval [0, mant_size-1].
764 * Outside this interval the truncated value is either 0 or
765 * it does not have fractional parts.
768 int exp_bias, exp_val;
771 temp = alloca(value_size);
774 memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));
776 exp_bias = (1<<_desc(a).exponent_size)/2-1;
777 exp_val = sc_val_to_long(_exp(a)) - exp_bias;
780 sc_val_from_ulong(0, NULL);
781 _save_result(_exp(result));
782 _save_result(_mant(result));
783 _desc(result).clss = ZERO;
788 if (exp_val > _desc(a).mantissa_size) {
790 memcpy(result, a, calc_buffer_size);
795 /* set up a proper mask to delete all bits right of the
796 * radix point if the mantissa had been shifted until exp == 0 */
797 sc_max_from_bits(1 + exp_val, 0, temp);
798 sc_val_from_long(_desc(a).mantissa_size - exp_val + 2, NULL);
799 _shift_left(temp, sc_get_buffer(), temp);
801 /* and the mask and return the result */
802 sc_and(_mant(a), temp, _mant(result));
804 if (a != result) memcpy(_exp(result), _exp(a), value_size);
810 * This does value sanity checking(or should do it), sets up any prerequisites,
811 * calls the proper internal functions, clears up and returns
814 char* _calc(const char *a, const char *b, int opcode, char *result)
817 #ifdef FLTCALC_TRACE_CALC
820 buffer = alloca(100);
823 if (result == NULL) result = calc_buffer;
825 TRACEPRINTF(("%s ", fc_print(a, buffer, 100, FC_PACKED)));
829 /* make the value with the bigger exponent the first one */
830 TRACEPRINTF(("+ %s ", fc_print(b, buffer, 100, FC_PACKED)));
831 if (sc_comp(_exp(a), _exp(b)) == -1)
837 TRACEPRINTF(("- %s ", fc_print(b, buffer, 100, FC_PACKED)));
838 temp = alloca(calc_buffer_size);
839 memcpy(temp, b, calc_buffer_size);
840 _sign(temp) = !_sign(b);
841 if (sc_comp(_exp(a), _exp(temp)) == -1)
842 _fadd(temp, a, result);
844 _fadd(a, temp, result);
847 TRACEPRINTF(("* %s ", fc_print(b, buffer, 100, FC_PACKED)));
851 TRACEPRINTF(("/ %s ", fc_print(b, buffer, 100, FC_PACKED)));
855 TRACEPRINTF(("negated "));
856 if (a != result) memcpy(result, a, calc_buffer_size);
857 _sign(result) = !_sign(a);
860 TRACEPRINTF(("truncated to integer "));
864 TRACEPRINTF(("rounded to integer "));
869 TRACEPRINTF(("= %s\n", fc_print(result, buffer, 100, FC_PACKED)));
874 * functions defined in fltcalc.h
876 const void *fc_get_buffer(void)
881 int fc_get_buffer_length(void)
883 return calc_buffer_size;
886 char* fc_val_from_str(const char *str, unsigned int len, char exp_size, char mant_size, char *result)
899 int exp_int, hsb, state;
904 char *mant_str, *exp_val, *power_val;
906 if (result == NULL) result = calc_buffer;
908 exp_val = alloca(value_size);
909 power_val = alloca(calc_buffer_size);
910 mant_str = alloca((len)?(len):(strlen(str)));
912 _desc(result).exponent_size = exp_size;
913 _desc(result).mantissa_size = mant_size;
914 _desc(result).clss = NORMAL;
921 while (len == 0 || str-old_str < len)
938 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
945 state = RIGHT_OF_DOT;
956 _fail_char(old_str, len, str - old_str);
962 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
963 mant_str[pos++] = *(str++);
967 state = RIGHT_OF_DOT;
978 mant_str[pos] = '\0';
982 _fail_char(old_str, len, str - old_str);
988 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
989 mant_str[pos++] = *(str++);
1000 mant_str[pos] = '\0';
1004 _fail_char(old_str, len, str - old_str);
1014 if (*(str-1) != 'e' && *(str-1) != 'E') _fail_char(old_str, len, str - old_str);
1018 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
1019 mant_str[pos] = '\0';
1026 _fail_char(old_str, len, str - old_str);
1032 case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
1037 case '\0': goto done;
1040 _fail_char(old_str, len, str - old_str);
1043 } /* switch(state) */
1046 sc_val_from_str(mant_str, strlen(mant_str), _mant(result));
1048 /* shift to put value left of radix point */
1049 sc_val_from_ulong(mant_size + 2, exp_val);
1051 _shift_left(_mant(result), exp_val, _mant(result));
1053 sc_val_from_ulong((1 << exp_size)/2-1, _exp(result));
1055 _normalize(result, result, 0);
1057 if (state == EXPONENT) {
1058 exp_int -= atoi(str-pos);
1061 _power_of_ten(exp_int, &_desc(result), power_val);
1063 _fdiv(result, power_val, result);
1068 /* XXX excuse of an implementation to make things work */
1070 #ifdef HAVE_LONG_DOUBLE
1071 val = strtold(str, NULL);
1073 val = strtod(str, NULL);
1076 DEBUGPRINTF(("val_from_str(%s)\n", str));
1077 return fc_val_from_float(val, exp_size, mant_size, result);
1081 char* fc_val_from_float(LLDBL l, char exp_size, char mant_size, char* result)
1084 int bias_res, bias_val, mant_val;
1086 UINT32 sign, exponent, mantissa0, mantissa1;
1089 bias_res = ((1<<exp_size)/2-1);
1091 #ifdef HAVE_LONG_DOUBLE
1094 sign = (srcval.val.high & 0x00008000) != 0;
1095 exponent = (srcval.val.high & 0x00007FFF) ;
1096 mantissa0 = srcval.val.mid;
1097 mantissa1 = srcval.val.low;
1098 #else /* no long double */
1101 sign = (srcval.val.high & 0x80000000) != 0;
1102 exponent = (srcval.val.high & 0x7FF00000) >> 20;
1103 mantissa0 = srcval.val.high & 0x000FFFFF;
1104 mantissa1 = srcval.val.low;
1107 #ifdef HAVE_LONG_DOUBLE
1108 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)); */
1109 DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1111 TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low));
1112 DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
1115 if (result == NULL) result = calc_buffer;
1116 temp = alloca(value_size);
1118 _desc(result).exponent_size = exp_size;
1119 _desc(result).mantissa_size = mant_size;
1122 _sign(result) = sign;
1124 /* sign and flag suffice to identify nan or inf, no exponent/mantissa
1125 * encoding is needed. the function can return immediately in these cases */
1127 _desc(result).clss = NAN;
1128 TRACEPRINTF(("val_from_float resulted in NAN\n"));
1131 else if (isinf(l)) {
1132 _desc(result).clss = INF;
1133 TRACEPRINTF(("val_from_float resulted in %sINF\n", (_sign(result)==1)?"-":""));
1137 /* build exponent, because input and output exponent and mantissa sizes may differ
1138 * this looks more complicated than it is: unbiased input exponent + output bias,
1139 * minus the mantissa difference which is added again later when the output float
1140 * becomes normalized */
1141 #ifdef HAVE_EXPLICIT_ONE
1142 sc_val_from_long((exponent-bias_val+bias_res)-(mant_val-mant_size-1), _exp(result));
1144 sc_val_from_long((exponent-bias_val+bias_res)-(mant_val-mant_size), _exp(result));
1147 /* build mantissa representation */
1148 #ifndef HAVE_EXPLICIT_ONE
1151 /* insert the hidden bit */
1152 sc_val_from_ulong(1, temp);
1153 sc_val_from_ulong(mant_val + 2, NULL);
1154 _shift_left(temp, sc_get_buffer(), NULL);
1159 sc_val_from_ulong(0, NULL);
1162 _save_result(_mant(result));
1164 /* bits from the upper word */
1165 sc_val_from_ulong(mantissa0, temp);
1166 sc_val_from_ulong(34, NULL);
1167 _shift_left(temp, sc_get_buffer(), temp);
1168 sc_or(_mant(result), temp, _mant(result));
1170 /* bits from the lower word */
1171 sc_val_from_ulong(mantissa1, temp);
1172 sc_val_from_ulong(2, NULL);
1173 _shift_left(temp, sc_get_buffer(), temp);
1174 sc_or(_mant(result), temp, _mant(result));
1176 /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
1177 * origin one to the left */
1180 sc_val_from_ulong(1, NULL);
1181 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1184 _normalize(result, result, 0);
1186 TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
1191 LLDBL fc_val_to_float(const void *val)
1205 #ifdef HAVE_LONG_DOUBLE
1206 char result_exponent = 15;
1207 char result_mantissa = 64;
1209 char result_exponent = 11;
1210 char result_mantissa = 52;
1213 temp = alloca(calc_buffer_size);
1214 #ifdef HAVE_EXPLICIT_ONE
1215 value = fc_cast(val, result_exponent, result_mantissa-1, temp);
1217 value = fc_cast(val, result_exponent, result_mantissa, temp);
1220 sign = _sign(value);
1222 /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not
1223 * lead to wrong results */
1224 exponent = sc_val_to_long(_exp(value)) ;
1226 sc_val_from_ulong(2, NULL);
1227 _shift_right(_mant(value), sc_get_buffer(), _mant(value));
1232 for (byte_offset = 0; byte_offset < 4; byte_offset++)
1233 mantissa1 |= sc_sub_bits(_mant(value), result_mantissa, byte_offset) << (byte_offset<<3);
1235 for (; (byte_offset<<3) < result_mantissa; byte_offset++)
1236 mantissa0 |= sc_sub_bits(_mant(value), result_mantissa, byte_offset) << ((byte_offset-4)<<3);
1238 #ifdef HAVE_LONG_DOUBLE
1239 buildval.val.high = sign << 15;
1240 buildval.val.high |= exponent;
1241 buildval.val.mid = mantissa0;
1242 buildval.val.low = mantissa1;
1243 #else /* no long double */
1244 mantissa0 &= 0x000FFFFF; /* get rid of garbage */
1245 buildval.val.high = sign << 31;
1246 buildval.val.high |= exponent << 20;
1247 buildval.val.high |= mantissa0;
1248 buildval.val.low = mantissa1;
1251 TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
1255 char* fc_cast(const void *val, char exp_size, char mant_size, char *result)
1257 const char *value = (const char*) val;
1259 int exp_offset, val_bias, res_bias;
1261 if (result == NULL) result = calc_buffer;
1262 temp = alloca(value_size);
1264 if (_desc(value).exponent_size == exp_size && _desc(value).mantissa_size == mant_size)
1266 if (value != result) memcpy(result, value, calc_buffer_size);
1270 /* set the descriptor of the new value */
1271 _desc(result).exponent_size = exp_size;
1272 _desc(result).mantissa_size = mant_size;
1273 _desc(result).clss = _desc(value).clss;
1275 _sign(result) = _sign(value);
1277 /* when the mantissa sizes differ normalizing has to shift to align it.
1278 * this would change the exponent, which is unwanted. So calculate this
1279 * offset and add it */
1280 val_bias = (1<<_desc(value).exponent_size)/2-1;
1281 res_bias = (1<<exp_size)/2-1;
1283 exp_offset = (res_bias - val_bias) - (_desc(value).mantissa_size - mant_size);
1284 sc_val_from_long(exp_offset, temp);
1285 sc_add(_exp(value), temp, _exp(result));
1287 /* _normalize expects normalized radix point */
1288 if (_desc(val).clss == SUBNORMAL) {
1289 sc_val_from_ulong(1, NULL);
1290 _shift_left(_mant(val), sc_get_buffer(), _mant(result));
1291 } else if (value != result) {
1292 memcpy(_mant(result), _mant(value), value_size);
1294 memmove(_mant(result), _mant(value), value_size);
1297 _normalize(result, result, 0);
1298 TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
1302 char* fc_get_max(unsigned int exponent_size, unsigned int mantissa_size, char* result)
1304 if (result == NULL) result = calc_buffer;
1306 _desc(result).exponent_size = exponent_size;
1307 _desc(result).mantissa_size = mantissa_size;
1308 _desc(result).clss = NORMAL;
1312 sc_val_from_ulong((1<<exponent_size) - 2, _exp(result));
1314 sc_max_from_bits(mantissa_size + 1, 0, _mant(result));
1315 sc_val_from_ulong(2, NULL);
1316 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1321 char* fc_get_min(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1323 if (result == NULL) result = calc_buffer;
1325 fc_get_max(exponent_size, mantissa_size, result);
1331 char* fc_get_snan(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1333 if (result == NULL) result = calc_buffer;
1335 _desc(result).exponent_size = exponent_size;
1336 _desc(result).mantissa_size = mantissa_size;
1337 _desc(result).clss = NAN;
1341 sc_val_from_ulong((1<<exponent_size)-1, _exp(result));
1343 /* signaling NaN has non-zero mantissa with msb not set */
1344 sc_val_from_ulong(1, _mant(result));
1349 char* fc_get_qnan(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1351 if (result == NULL) result = calc_buffer;
1353 _desc(result).exponent_size = exponent_size;
1354 _desc(result).mantissa_size = mantissa_size;
1355 _desc(result).clss = NAN;
1359 sc_val_from_ulong((1<<exponent_size)-1, _exp(result));
1361 /* quiet NaN has the msb of the mantissa set, so shift one there */
1362 sc_val_from_ulong(1, _mant(result));
1363 /* mantissa_size >+< 1 because of two extra rounding bits */
1364 sc_val_from_ulong(mantissa_size + 1, NULL);
1365 _shift_left(_mant(result), sc_get_buffer(), _mant(result));
1370 char* fc_get_plusinf(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1372 if (result == NULL) result = calc_buffer;
1374 _desc(result).exponent_size = exponent_size;
1375 _desc(result).mantissa_size = mantissa_size;
1376 _desc(result).clss = NORMAL;
1380 sc_val_from_ulong((1<<exponent_size)-1, _exp(result));
1382 sc_val_from_ulong(0, _mant(result));
1387 char* fc_get_minusinf(unsigned int exponent_size, unsigned int mantissa_size, char *result)
1389 if (result == NULL) result = calc_buffer;
1391 fc_get_plusinf(exponent_size, mantissa_size, result);
1397 int fc_comp(const void *a, const void *b)
1399 const char *val_a = (const char*)a;
1400 const char *val_b = (const char*)b;
1404 * shortcut: if both values are identical, they are either
1405 * Unordered if NaN or equal
1408 return _desc(val_a).clss == NAN ? 2 : 0;
1410 /* unordered if one is a NaN */
1411 if (_desc(val_a).clss == NAN || _desc(val_b).clss == NAN)
1414 /* zero is equal independent of sign */
1415 if ((_desc(val_a).clss == ZERO) && (_desc(val_b).clss == ZERO))
1418 /* different signs make compare easy */
1419 if (_sign(val_a) != _sign(val_b))
1420 return (_sign(val_a)==0)?(1):(-1);
1422 mul = _sign(a) ? -1 : 1;
1424 /* both infinity means equality */
1425 if ((_desc(val_a).clss == INF) && (_desc(val_b).clss == INF))
1428 /* infinity is bigger than the rest */
1429 if (_desc(val_a).clss == INF)
1431 if (_desc(val_b).clss == INF)
1434 /* check first exponent, that mantissa if equal */
1435 switch (sc_comp(_exp(val_a), _exp(val_b))) {
1441 return sc_comp(_mant(val_a), _mant(val_b)) * mul;
1447 int fc_is_zero(const void *a)
1449 return _desc(a).clss == ZERO;
1452 int fc_is_negative(const void *a)
1457 int fc_is_inf(const void *a)
1459 return _desc(a).clss == INF;
1462 int fc_is_nan(const void *a)
1464 return _desc(a).clss == NAN;
1467 int fc_is_subnormal(const void *a)
1469 return _desc(a).clss == SUBNORMAL;
1472 char *fc_print(const void *a, char *buf, int buflen, unsigned base)
1477 val = (const char*)a;
1479 mul_1 = alloca(calc_buffer_size);
1483 switch (_desc(val).clss) {
1485 if (buflen >= 8+_sign(val)) sprintf(buf, "%sINFINITY", _sign(val)?"-":"");
1486 else snprintf(buf, buflen, "%sINF", _sign(val)?"-":NULL);
1489 snprintf(buf, buflen, "NAN");
1492 snprintf(buf, buflen, "0.0");
1495 /* XXX to be implemented */
1496 #ifdef HAVE_LONG_DOUBLE
1497 /* XXX 30 is arbitrary */
1498 snprintf(buf, buflen, "%.30LE", fc_val_to_float(val));
1500 snprintf(buf, buflen, "%.18E", fc_val_to_float(val));
1506 switch (_desc(val).clss) {
1508 if (buflen >= 8+_sign(val)) sprintf(buf, "%sINFINITY", _sign(val)?"-":"");
1509 else snprintf(buf, buflen, "%sINF", _sign(val)?"-":NULL);
1512 snprintf(buf, buflen, "NAN");
1515 snprintf(buf, buflen, "0.0");
1518 #ifdef HAVE_LONG_DOUBLE
1519 snprintf(buf, buflen, "%LA", fc_val_to_float(val));
1521 snprintf(buf, buflen, "%A", fc_val_to_float(val));
1528 snprintf(buf, buflen, "%s", sc_print(_pack(val, mul_1), value_size*4, SC_HEX));
1534 unsigned char fc_sub_bits(const void *value, unsigned num_bits, unsigned byte_ofs)
1536 /* this is used to cache the packed version of the value */
1537 static char *pack = NULL;
1539 if (pack == NULL) pack = xmalloc(value_size);
1542 _pack((const char*)value, pack);
1544 return sc_sub_bits(pack, num_bits, byte_ofs);
1547 fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
1549 if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
1550 rounding_mode = mode;
1552 return rounding_mode;
1555 fc_rounding_mode_t fc_get_rounding_mode(void)
1557 return rounding_mode;
1560 void init_fltcalc(int precision)
1562 if (calc_buffer == NULL) {
1563 /* does nothing if already init */
1564 if (precision == 0) precision = FC_DEFAULT_PRECISION;
1566 init_strcalc(precision + 4);
1568 /* needs additionally two bits to round, a bit as explicit 1., and one for
1569 * addition overflow */
1570 max_precision = sc_get_precision() - 4;
1571 if (max_precision < precision)
1572 printf("WARING: not enough precision available, using %d\n", max_precision);
1574 rounding_mode = FC_TONEAREST;
1575 value_size = sc_get_buffer_length();
1577 EXPONENT_POS = SIGN_POS + sizeof(char);
1578 MANTISSA_POS = EXPONENT_POS + value_size;
1579 DESCRIPTOR_POS = MANTISSA_POS + value_size;
1580 calc_buffer_size = DESCRIPTOR_POS + sizeof(descriptor_t);
1582 calc_buffer = xmalloc(calc_buffer_size);
1583 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));
1584 #ifdef HAVE_LONG_DOUBLE
1585 DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n"));
1587 DEBUGPRINTF(("\tUsing double (1-11-52) interface\n"));
1589 #ifdef WORDS_BIGENDIAN
1590 DEBUGPRINTF(("\tWord order is big endian\n\n"));
1592 DEBUGPRINTF(("\tWord order is little endian\n\n"));
1597 void finish_fltcalc (void) {
1598 free(calc_buffer); calc_buffer = NULL;
1601 /* definition of interface functions */