/* * Copyright (C) 1995-2011 University of Karlsruhe. All right reserved. * * This file is part of libFirm. * * This file may be distributed and/or modified under the terms of the * GNU General Public License version 2 as published by the Free Software * Foundation and appearing in the file LICENSE.GPL included in the * packaging of this file. * * Licensees holding valid libFirm Professional Edition licenses may use * this file in accordance with the libFirm Commercial License. * Agreement provided with the Software. * * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE. */ /** * @file * @brief tarval floating point calculations * @date 2003 * @author Mathias Heil * @version $Id$ */ #include "config.h" #include "fltcalc.h" #include "strcalc.h" #include "error.h" #include /* undef some reused constants defined by math.h */ #ifdef NAN # undef NAN #endif #include #include #include #include #include #include "xmalloc.h" #ifndef HAVE_STRTOLD #define strtold(s, e) strtod(s, e) #endif #ifdef _MSC_VER #include #define isnan(x) _isnan(x) static inline int isinf(double x) { return !_finite(x) && !_isnan(x); } #endif /** The number of extra precision rounding bits */ #define ROUNDING_BITS 2 typedef uint32_t UINT32; #ifdef HAVE_LONG_DOUBLE #ifdef WORDS_BIGENDIAN typedef union { struct { UINT32 high; UINT32 mid; UINT32 low; } val; volatile long double d; } value_t; #else typedef union { struct { UINT32 low; UINT32 mid; UINT32 high; } val; volatile long double d; } value_t; #endif #else #ifdef WORDS_BIGENDIAN typedef union { struct { UINT32 high; UINT32 low; } val; volatile double d; } value_t; #else typedef union { struct { UINT32 low; UINT32 high; } val; volatile double d; } value_t; #endif #endif #define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size) /* our floating point value */ struct fp_value { ieee_descriptor_t desc; char sign; char value[1]; /* exp[value_size] + mant[value_size] */ }; #define _exp(a) &((a)->value[0]) #define _mant(a) &((a)->value[value_size]) #define _save_result(x) memcpy((x), sc_get_buffer(), value_size) #define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res)) #define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res)) #ifdef FLTCALC_DEBUG # define DEBUGPRINTF(x) printf x #else # define DEBUGPRINTF(x) ((void)0) #endif #ifdef FLTCALC_TRACE_CALC # define TRACEPRINTF(x) printf x #else # define TRACEPRINTF(x) ((void)0) #endif /** The immediate precision. */ static unsigned immediate_prec = 0; /** A temporal buffer. */ static fp_value *calc_buffer = NULL; /** Current rounding mode.*/ static fc_rounding_mode_t rounding_mode; static int calc_buffer_size; static int value_size; static int max_precision; /** Exact flag. */ static int fc_exact = 1; #if 0 static void fail_char(const char *str, unsigned int len, int pos) { if (*(str+pos)) printf("ERROR: Unexpected character '%c'\n", *(str + pos)); else printf("ERROR: Unexpected end of string\n"); while (len-- && *str) printf("%c", *str++); printf("\n"); while (pos--) printf(" "); printf("^\n"); /* the front end has to to check constant strings */ exit(-1); } #endif /** pack machine-like */ static void *pack(const fp_value *int_float, void *packed) { char *shift_val; char *temp; fp_value *val_buffer; int pos; temp = (char*) alloca(value_size); shift_val = (char*) alloca(value_size); switch ((value_class_t)int_float->desc.clss) { case NAN: val_buffer = (fp_value*) alloca(calc_buffer_size); fc_get_qnan(&int_float->desc, val_buffer); int_float = val_buffer; break; case INF: val_buffer = (fp_value*) alloca(calc_buffer_size); fc_get_plusinf(&int_float->desc, val_buffer); val_buffer->sign = int_float->sign; int_float = val_buffer; break; default: break; } assert(int_float->desc.explicit_one <= 1); /* pack sign: move it to the left after exponent AND mantissa */ sc_val_from_ulong(int_float->sign, temp); pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one; sc_val_from_ulong(pos, NULL); _shift_left(temp, sc_get_buffer(), packed); /* pack exponent: move it to the left after mantissa */ pos = int_float->desc.mantissa_size + int_float->desc.explicit_one; sc_val_from_ulong(pos, shift_val); _shift_left(_exp(int_float), shift_val, temp); /* combine sign|exponent */ sc_or(temp, packed, packed); /* extract mantissa */ /* remove rounding bits */ sc_val_from_ulong(ROUNDING_BITS, shift_val); _shift_right(_mant(int_float), shift_val, temp); /* remove leading 1 (or 0 if denormalized) */ sc_max_from_bits(pos, 0, shift_val); /* all mantissa bits are 1's */ sc_and(temp, shift_val, temp); /* combine sign|exponent|mantissa */ sc_or(temp, packed, packed); return packed; } /** * Normalize a fp_value. * * @return non-zero if result is exact */ static int normalize(const fp_value *in_val, fp_value *out_val, int sticky) { int exact = 1; int hsb; char lsb, guard, round, round_dir = 0; char *temp = (char*) alloca(value_size); /* save rounding bits at the end */ hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1; if (in_val != out_val) { out_val->sign = in_val->sign; memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc)); } out_val->desc.clss = NORMAL; /* mantissa all zeros, so zero exponent (because of explicit one) */ if (hsb == ROUNDING_BITS + in_val->desc.mantissa_size) { sc_val_from_ulong(0, _exp(out_val)); hsb = -1; } /* shift the first 1 into the left of the radix point (i.e. hsb == -1) */ if (hsb < -1) { /* shift right */ sc_val_from_ulong(-hsb-1, temp); _shift_right(_mant(in_val), temp, _mant(out_val)); /* remember if some bits were shifted away */ if (sc_had_carry()) { exact = 0; sticky = 1; } sc_add(_exp(in_val), temp, _exp(out_val)); } else if (hsb > -1) { /* shift left */ sc_val_from_ulong(hsb+1, temp); _shift_left(_mant(in_val), temp, _mant(out_val)); sc_sub(_exp(in_val), temp, _exp(out_val)); } /* check for exponent underflow */ if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) { DEBUGPRINTF(("Exponent underflow!\n")); /* exponent underflow */ /* shift the mantissa right to have a zero exponent */ sc_val_from_ulong(1, temp); sc_sub(temp, _exp(out_val), NULL); _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val)); if (sc_had_carry()) { exact = 0; sticky = 1; } /* denormalized means exponent of zero */ sc_val_from_ulong(0, _exp(out_val)); out_val->desc.clss = SUBNORMAL; } /* perform rounding by adding a value that clears the guard bit and the round bit * and either causes a carry to round up or not */ /* get the last 3 bits of the value */ lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7; guard = (lsb&0x2)>>1; round = lsb&0x1; switch (rounding_mode) { case FC_TONEAREST: /* round to nearest representable value, if in doubt choose the version * with lsb == 0 */ round_dir = guard && (sticky || round || lsb>>2); break; case FC_TOPOSITIVE: /* if positive: round to one if the exact value is bigger, else to zero */ round_dir = (!out_val->sign && (guard || round || sticky)); break; case FC_TONEGATIVE: /* if negative: round to one if the exact value is bigger, else to zero */ round_dir = (out_val->sign && (guard || round || sticky)); break; case FC_TOZERO: /* always round to 0 (chopping mode) */ round_dir = 0; break; } 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")); if (round_dir == 1) { guard = (round^guard)<<1; lsb = !(round || guard)<<2 | guard | round; } else { lsb = -((guard<<1) | round); } /* add the rounded value */ if (lsb != 0) { sc_val_from_long(lsb, temp); sc_add(_mant(out_val), temp, _mant(out_val)); exact = 0; } /* could have rounded down to zero */ if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL)) out_val->desc.clss = ZERO; /* check for rounding overflow */ hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1; if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) { sc_val_from_ulong(1, temp); _shift_right(_mant(out_val), temp, _mant(out_val)); if (exact && sc_had_carry()) exact = 0; sc_add(_exp(out_val), temp, _exp(out_val)); } else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) { /* overflow caused the mantissa to be normal again, * so adapt the exponent accordingly */ sc_val_from_ulong(1, temp); sc_add(_exp(out_val), temp, _exp(out_val)); out_val->desc.clss = NORMAL; } /* no further rounding is needed, because rounding overflow means * the carry of the original rounding was propagated all the way * up to the bit left of the radix point. This implies the bits * to the right are all zeros (rounding is +1) */ /* check for exponent overflow */ sc_val_from_ulong((1 << out_val->desc.exponent_size) - 1, temp); if (sc_comp(_exp(out_val), temp) != -1) { DEBUGPRINTF(("Exponent overflow!\n")); /* exponent overflow, reaction depends on rounding method: * * mode | sign of value | result *-------------------------------------------------------------- * TO_NEAREST | + | +inf * | - | -inf *-------------------------------------------------------------- * TO_POSITIVE | + | +inf * | - | smallest representable value *-------------------------------------------------------------- * TO_NEAGTIVE | + | largest representable value * | - | -inf *-------------------------------------------------------------- * TO_ZERO | + | largest representable value * | - | smallest representable value *--------------------------------------------------------------*/ if (out_val->sign == 0) { /* value is positive */ switch (rounding_mode) { case FC_TONEAREST: case FC_TOPOSITIVE: out_val->desc.clss = INF; break; case FC_TONEGATIVE: case FC_TOZERO: fc_get_max(&out_val->desc, out_val); } } else { /* value is negative */ switch (rounding_mode) { case FC_TONEAREST: case FC_TONEGATIVE: out_val->desc.clss = INF; break; case FC_TOPOSITIVE: case FC_TOZERO: fc_get_min(&out_val->desc, out_val); } } } return exact; } /** * Operations involving NaN's must return NaN. * They are NOT exact. */ #define handle_NAN(a, b, result) \ do { \ if (a->desc.clss == NAN) { \ if (a != result) memcpy(result, a, calc_buffer_size); \ fc_exact = 0; \ return; \ } \ if (b->desc.clss == NAN) { \ if (b != result) memcpy(result, b, calc_buffer_size); \ fc_exact = 0; \ return; \ } \ }while (0) /** * calculate a + b, where a is the value with the bigger exponent */ static void _fadd(const fp_value *a, const fp_value *b, fp_value *result) { char *temp; char *exp_diff; char sign, res_sign; char sticky; fc_exact = 1; handle_NAN(a, b, result); /* make sure result has a descriptor */ if (result != a && result != b) result->desc = a->desc; /* determine if this is an addition or subtraction */ sign = a->sign ^ b->sign; /* produce NaN on inf - inf */ if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) { fc_exact = 0; fc_get_qnan(&a->desc, result); return; } temp = (char*) alloca(value_size); exp_diff = (char*) alloca(value_size); /* get exponent difference */ sc_sub(_exp(a), _exp(b), exp_diff); /* initially set sign to be the sign of a, special treatment of subtraction * when exponents are equal is required though. * Also special care about the sign is needed when the mantissas are equal * (+/- 0 ?) */ if (sign && sc_val_to_long(exp_diff) == 0) { switch (sc_comp(_mant(a), _mant(b))) { case 1: /* a > b */ res_sign = a->sign; /* abs(a) is bigger and a is negative */ break; case 0: /* a == b */ res_sign = (rounding_mode == FC_TONEGATIVE); break; case -1: /* a < b */ res_sign = b->sign; /* abs(b) is bigger and b is negative */ break; default: /* can't be reached */ res_sign = 0; break; } } else res_sign = a->sign; result->sign = res_sign; /* sign has been taken care of, check for special cases */ if (a->desc.clss == ZERO || b->desc.clss == INF) { if (b != result) memcpy(result, b, calc_buffer_size); fc_exact = b->desc.clss == NORMAL; result->sign = res_sign; return; } if (b->desc.clss == ZERO || a->desc.clss == INF) { if (a != result) memcpy(result, a, calc_buffer_size); fc_exact = a->desc.clss == NORMAL; result->sign = res_sign; return; } /* shift the smaller value to the right to align the radix point */ /* subnormals have their radix point shifted to the right, * take care of this first */ if ((b->desc.clss == SUBNORMAL) && (a->desc.clss != SUBNORMAL)) { sc_val_from_ulong(1, temp); sc_sub(exp_diff, temp, exp_diff); } _shift_right(_mant(b), exp_diff, temp); sticky = sc_had_carry(); fc_exact &= !sticky; if (sticky && sign) { /* if subtracting a little more than the represented value or adding a little * more than the represented value to a negative value this, in addition to the * still set sticky bit, takes account of the 'little more' */ char *temp1 = (char*) alloca(calc_buffer_size); sc_val_from_ulong(1, temp1); sc_add(temp, temp1, temp); } if (sign) { if (sc_comp(_mant(a), temp) == -1) sc_sub(temp, _mant(a), _mant(result)); else sc_sub(_mant(a), temp, _mant(result)); } else { sc_add(_mant(a), temp, _mant(result)); } /* _normalize expects a 'normal' radix point, adding two subnormals * results in a subnormal radix point -> shifting before normalizing */ if ((a->desc.clss == SUBNORMAL) && (b->desc.clss == SUBNORMAL)) { sc_val_from_ulong(1, NULL); _shift_left(_mant(result), sc_get_buffer(), _mant(result)); } /* resulting exponent is the bigger one */ memmove(_exp(result), _exp(a), value_size); fc_exact &= normalize(result, result, sticky); } /** * calculate a * b */ static void _fmul(const fp_value *a, const fp_value *b, fp_value *result) { int sticky; char *temp; char res_sign; fc_exact = 1; handle_NAN(a, b, result); temp = (char*) alloca(value_size); if (result != a && result != b) result->desc = a->desc; result->sign = res_sign = a->sign ^ b->sign; /* produce NaN on 0 * inf */ if (a->desc.clss == ZERO) { if (b->desc.clss == INF) { fc_get_qnan(&a->desc, result); fc_exact = 0; } else { if (a != result) memcpy(result, a, calc_buffer_size); result->sign = res_sign; } return; } if (b->desc.clss == ZERO) { if (a->desc.clss == INF) { fc_get_qnan(&a->desc, result); fc_exact = 0; } else { if (b != result) memcpy(result, b, calc_buffer_size); result->sign = res_sign; } return; } if (a->desc.clss == INF) { fc_exact = 0; if (a != result) memcpy(result, a, calc_buffer_size); result->sign = res_sign; return; } if (b->desc.clss == INF) { fc_exact = 0; if (b != result) memcpy(result, b, calc_buffer_size); result->sign = res_sign; return; } /* exp = exp(a) + exp(b) - excess */ sc_add(_exp(a), _exp(b), _exp(result)); sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp); sc_sub(_exp(result), temp, _exp(result)); /* mixed normal, subnormal values introduce an error of 1, correct it */ if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) { sc_val_from_ulong(1, temp); sc_add(_exp(result), temp, _exp(result)); } sc_mul(_mant(a), _mant(b), _mant(result)); /* realign result: after a multiplication the digits right of the radix * point are the sum of the factors' digits after the radix point. As all * values are normalized they both have the same amount of these digits, * which has to be restored by proper shifting * because of the rounding bits */ sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp); _shift_right(_mant(result), temp, _mant(result)); sticky = sc_had_carry(); fc_exact &= !sticky; fc_exact &= normalize(result, result, sticky); } /** * calculate a / b */ static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result) { int sticky; char *temp, *dividend; char res_sign; fc_exact = 1; handle_NAN(a, b, result); temp = (char*) alloca(value_size); dividend = (char*) alloca(value_size); if (result != a && result != b) result->desc = a->desc; result->sign = res_sign = a->sign ^ b->sign; /* produce NAN on 0/0 and inf/inf */ if (a->desc.clss == ZERO) { if (b->desc.clss == ZERO) { /* 0/0 -> NaN */ fc_get_qnan(&a->desc, result); fc_exact = 0; } else { /* 0/x -> a */ if (a != result) memcpy(result, a, calc_buffer_size); result->sign = res_sign; } return; } if (b->desc.clss == INF) { fc_exact = 0; if (a->desc.clss == INF) { /* inf/inf -> NaN */ fc_get_qnan(&a->desc, result); } else { /* x/inf -> 0 */ sc_val_from_ulong(0, NULL); _save_result(_exp(result)); _save_result(_mant(result)); result->desc.clss = ZERO; } return; } if (a->desc.clss == INF) { fc_exact = 0; /* inf/x -> inf */ if (a != result) memcpy(result, a, calc_buffer_size); result->sign = res_sign; return; } if (b->desc.clss == ZERO) { fc_exact = 0; /* division by zero */ if (result->sign) fc_get_minusinf(&a->desc, result); else fc_get_plusinf(&a->desc, result); return; } /* exp = exp(a) - exp(b) + excess - 1*/ sc_sub(_exp(a), _exp(b), _exp(result)); sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 2, temp); sc_add(_exp(result), temp, _exp(result)); /* mixed normal, subnormal values introduce an error of 1, correct it */ if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) { sc_val_from_ulong(1, temp); sc_add(_exp(result), temp, _exp(result)); } /* mant(res) = mant(a) / 1/2mant(b) */ /* to gain more bits of precision in the result the dividend could be * shifted left, as this operation does not loose bits. This would not * fit into the integer precision, but due to the rounding bits (which * are always zero because the values are all normalized) the divisor * can be shifted right instead to achieve the same result */ sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp); _shift_left(_mant(a), temp, dividend); { char *divisor = (char*) alloca(calc_buffer_size); sc_val_from_ulong(1, divisor); _shift_right(_mant(b), divisor, divisor); sc_div(dividend, divisor, _mant(result)); sticky = sc_had_carry(); fc_exact &= !sticky; } fc_exact &= normalize(result, result, sticky); } #if 0 static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result) { char *build; char *temp; /* positive sign */ result->sign = 0; /* set new descriptor (else result is supposed to already have one) */ if (desc != NULL) result->desc = *desc; build = alloca(value_size); temp = alloca(value_size); sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result)); if (exp > 0) { /* temp is value of ten now */ sc_val_from_ulong(10, NULL); _save_result(temp); for (exp--; exp > 0; exp--) { _save_result(build); sc_mul(build, temp, NULL); } _save_result(build); /* temp is amount of left shift needed to put the value left of the radix point */ sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp); _shift_left(build, temp, _mant(result)); _normalize(result, result, 0); } } #endif /** * Truncate the fractional part away. * * This does not clip to any integer range. */ static void _trunc(const fp_value *a, fp_value *result) { /* * When exponent == 0 all bits left of the radix point * are the integral part of the value. For 15bit exp_size * this would require a left shift of max. 16383 bits which * is too much. * But it is enough to ensure that no bit right of the radix * point remains set. This restricts the interesting * exponents to the interval [0, mant_size-1]. * Outside this interval the truncated value is either 0 or * it does not have fractional parts. */ int exp_bias, exp_val; char *temp; /* fixme: can be exact */ fc_exact = 0; temp = (char*) alloca(value_size); if (a != result) result->desc = a->desc; exp_bias = (1 << (a->desc.exponent_size - 1)) - 1; exp_val = sc_val_to_long(_exp(a)) - exp_bias; if (exp_val < 0) { sc_val_from_ulong(0, NULL); _save_result(_exp(result)); _save_result(_mant(result)); result->desc.clss = ZERO; return; } if (exp_val > a->desc.mantissa_size) { if (a != result) memcpy(result, a, calc_buffer_size); return; } /* set up a proper mask to delete all bits right of the * radix point if the mantissa had been shifted until exp == 0 */ sc_max_from_bits(1 + exp_val, 0, temp); sc_val_from_long(a->desc.mantissa_size - exp_val + 2, NULL); _shift_left(temp, sc_get_buffer(), temp); /* and the mask and return the result */ sc_and(_mant(a), temp, _mant(result)); if (a != result) { memcpy(_exp(result), _exp(a), value_size); result->sign = a->sign; } } /******** * functions defined in fltcalc.h ********/ const void *fc_get_buffer(void) { return calc_buffer; } int fc_get_buffer_length(void) { return calc_buffer_size; } void *fc_val_from_str(const char *str, size_t len, const ieee_descriptor_t *desc, void *result) { char *buffer; /* XXX excuse of an implementation to make things work */ LLDBL val; fp_value *tmp = (fp_value*) alloca(calc_buffer_size); ieee_descriptor_t tmp_desc; buffer = (char*) alloca(len+1); memcpy(buffer, str, len); buffer[len] = '\0'; val = strtold(buffer, NULL); DEBUGPRINTF(("val_from_str(%s)\n", str)); tmp_desc.exponent_size = 15; tmp_desc.mantissa_size = 63; tmp_desc.explicit_one = 1; tmp_desc.clss = NORMAL; fc_val_from_ieee754(val, &tmp_desc, tmp); return fc_cast(tmp, desc, (fp_value*) result); } fp_value *fc_val_from_ieee754(LLDBL l, const ieee_descriptor_t *desc, fp_value *result) { char *temp; int bias_res, bias_val, mant_val; value_t srcval; char sign; UINT32 exponent, mantissa0, mantissa1; srcval.d = l; bias_res = ((1 << (desc->exponent_size - 1)) - 1); #ifdef HAVE_LONG_DOUBLE mant_val = 63; bias_val = 0x3fff; sign = (srcval.val.high & 0x00008000) != 0; exponent = (srcval.val.high & 0x00007FFF) ; mantissa0 = srcval.val.mid; mantissa1 = srcval.val.low; #else /* no long double */ mant_val = 52; bias_val = 0x3ff; sign = (srcval.val.high & 0x80000000) != 0; exponent = (srcval.val.high & 0x7FF00000) >> 20; mantissa0 = srcval.val.high & 0x000FFFFF; mantissa1 = srcval.val.low; #endif #ifdef HAVE_LONG_DOUBLE 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)); */ DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1)); #else TRACEPRINTF(("val_from_float(%.8X%.8X)\n", srcval.val.high, srcval.val.low)); DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1)); #endif if (result == NULL) result = calc_buffer; temp = (char*) alloca(value_size); /* CLEAR the buffer, else some bits might be uninitialized */ memset(result, 0, fc_get_buffer_length()); result->desc.exponent_size = desc->exponent_size; result->desc.mantissa_size = desc->mantissa_size; result->desc.explicit_one = desc->explicit_one; /* extract sign */ result->sign = sign; /* sign and flag suffice to identify NaN or inf, no exponent/mantissa * encoding is needed. the function can return immediately in these cases */ if (isnan(l)) { result->desc.clss = NAN; TRACEPRINTF(("val_from_float resulted in NAN\n")); return result; } else if (isinf(l)) { result->desc.clss = INF; TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : "")); return result; } /* build exponent, because input and output exponent and mantissa sizes may differ * this looks more complicated than it is: unbiased input exponent + output bias, * minus the mantissa difference which is added again later when the output float * becomes normalized */ sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result)); /* build mantissa representation */ if (exponent != 0) { /* insert the hidden bit */ sc_val_from_ulong(1, temp); sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL); _shift_left(temp, sc_get_buffer(), NULL); } else { sc_val_from_ulong(0, NULL); } _save_result(_mant(result)); /* bits from the upper word */ sc_val_from_ulong(mantissa0, temp); sc_val_from_ulong(34, NULL); _shift_left(temp, sc_get_buffer(), temp); sc_or(_mant(result), temp, _mant(result)); /* bits from the lower word */ sc_val_from_ulong(mantissa1, temp); sc_val_from_ulong(ROUNDING_BITS, NULL); _shift_left(temp, sc_get_buffer(), temp); sc_or(_mant(result), temp, _mant(result)); /* _normalize expects the radix point to be normal, so shift mantissa of subnormal * origin one to the left */ if (exponent == 0) { sc_val_from_ulong(1, NULL); _shift_left(_mant(result), sc_get_buffer(), _mant(result)); } normalize(result, result, 0); TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED))); return result; } LLDBL fc_val_to_ieee754(const fp_value *val) { fp_value *value; fp_value *temp = NULL; int byte_offset; UINT32 sign; UINT32 exponent; UINT32 mantissa0; UINT32 mantissa1; value_t buildval; ieee_descriptor_t desc; unsigned mantissa_size; #ifdef HAVE_LONG_DOUBLE desc.exponent_size = 15; desc.mantissa_size = 63; desc.explicit_one = 1; desc.clss = NORMAL; #else desc.exponent_size = 11; desc.mantissa_size = 52; desc.explicit_one = 0; desc.clss = NORMAL; #endif mantissa_size = desc.mantissa_size + desc.explicit_one; temp = (fp_value*) alloca(calc_buffer_size); value = fc_cast(val, &desc, temp); sign = value->sign; /* @@@ long double exponent is 15bit, so the use of sc_val_to_long should not * lead to wrong results */ exponent = sc_val_to_long(_exp(value)) ; sc_val_from_ulong(ROUNDING_BITS, NULL); _shift_right(_mant(value), sc_get_buffer(), _mant(value)); mantissa0 = 0; mantissa1 = 0; for (byte_offset = 0; byte_offset < 4; byte_offset++) mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3); for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++) mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3); #ifdef HAVE_LONG_DOUBLE buildval.val.high = sign << 15; buildval.val.high |= exponent; buildval.val.mid = mantissa0; buildval.val.low = mantissa1; #else /* no long double */ mantissa0 &= 0x000FFFFF; /* get rid of garbage */ buildval.val.high = sign << 31; buildval.val.high |= exponent << 20; buildval.val.high |= mantissa0; buildval.val.low = mantissa1; #endif TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1)); return buildval.d; } fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result) { char *temp; int exp_offset, val_bias, res_bias; if (result == NULL) result = calc_buffer; temp = (char*) alloca(value_size); if (value->desc.exponent_size == desc->exponent_size && value->desc.mantissa_size == desc->mantissa_size && value->desc.explicit_one == desc->explicit_one) { if (value != result) memcpy(result, value, calc_buffer_size); return result; } if (value->desc.clss == NAN) { if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1) return fc_get_qnan(desc, result); else return fc_get_snan(desc, result); } else if (value->desc.clss == INF) { if (value->sign == 0) return fc_get_plusinf(desc, result); else return fc_get_minusinf(desc, result); } /* set the descriptor of the new value */ result->desc.exponent_size = desc->exponent_size; result->desc.mantissa_size = desc->mantissa_size; result->desc.explicit_one = desc->explicit_one; result->desc.clss = value->desc.clss; result->sign = value->sign; /* when the mantissa sizes differ normalizing has to shift to align it. * this would change the exponent, which is unwanted. So calculate this * offset and add it */ val_bias = (1 << (value->desc.exponent_size - 1)) - 1; res_bias = (1 << (desc->exponent_size - 1)) - 1; exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size); sc_val_from_long(exp_offset, temp); sc_add(_exp(value), temp, _exp(result)); /* _normalize expects normalized radix point */ if (value->desc.clss == SUBNORMAL) { sc_val_from_ulong(1, NULL); _shift_left(_mant(value), sc_get_buffer(), _mant(result)); } else if (value != result) { memcpy(_mant(result), _mant(value), value_size); } else { memmove(_mant(result), _mant(value), value_size); } normalize(result, result, 0); TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED))); return result; } fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result) { if (result == NULL) result = calc_buffer; result->desc.exponent_size = desc->exponent_size; result->desc.mantissa_size = desc->mantissa_size; result->desc.explicit_one = desc->explicit_one; result->desc.clss = NORMAL; result->sign = 0; sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result)); sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result)); sc_val_from_ulong(ROUNDING_BITS, NULL); _shift_left(_mant(result), sc_get_buffer(), _mant(result)); return result; } fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result) { if (result == NULL) result = calc_buffer; fc_get_max(desc, result); result->sign = 1; return result; } fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result) { if (result == NULL) result = calc_buffer; result->desc.exponent_size = desc->exponent_size; result->desc.mantissa_size = desc->mantissa_size; result->desc.explicit_one = desc->explicit_one; result->desc.clss = NAN; result->sign = 0; sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result)); /* signaling NaN has non-zero mantissa with msb not set */ sc_val_from_ulong(1, _mant(result)); return result; } fp_value *fc_get_qnan(const ieee_descriptor_t *desc, fp_value *result) { if (result == NULL) result = calc_buffer; result->desc.exponent_size = desc->exponent_size; result->desc.mantissa_size = desc->mantissa_size; result->desc.explicit_one = desc->explicit_one; result->desc.clss = NAN; result->sign = 0; sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result)); /* quiet NaN has the msb of the mantissa set, so shift one there */ sc_val_from_ulong(1, _mant(result)); /* mantissa_size >+< 1 because of two extra rounding bits */ sc_val_from_ulong(desc->mantissa_size + 1, NULL); _shift_left(_mant(result), sc_get_buffer(), _mant(result)); return result; } fp_value *fc_get_plusinf(const ieee_descriptor_t *desc, fp_value *result) { char *mant; if (result == NULL) result = calc_buffer; result->desc.exponent_size = desc->exponent_size; result->desc.mantissa_size = desc->mantissa_size; result->desc.explicit_one = desc->explicit_one; result->desc.clss = INF; result->sign = 0; sc_val_from_ulong((1 << desc->exponent_size) - 1, _exp(result)); mant = _mant(result); sc_val_from_ulong(0, mant); if (desc->explicit_one) { sc_set_bit_at(mant, result->desc.mantissa_size + ROUNDING_BITS); } return result; } fp_value *fc_get_minusinf(const ieee_descriptor_t *desc, fp_value *result) { if (result == NULL) result = calc_buffer; fc_get_plusinf(desc, result); result->sign = 1; return result; } int fc_comp(const fp_value *val_a, const fp_value *val_b) { int mul = 1; /* * shortcut: if both values are identical, they are either * Unordered if NaN or equal */ if (val_a == val_b) return val_a->desc.clss == NAN ? 2 : 0; /* unordered if one is a NaN */ if (val_a->desc.clss == NAN || val_b->desc.clss == NAN) return 2; /* zero is equal independent of sign */ if ((val_a->desc.clss == ZERO) && (val_b->desc.clss == ZERO)) return 0; /* different signs make compare easy */ if (val_a->sign != val_b->sign) return (val_a->sign == 0) ? (1) : (-1); mul = val_a->sign ? -1 : 1; /* both infinity means equality */ if ((val_a->desc.clss == INF) && (val_b->desc.clss == INF)) return 0; /* infinity is bigger than the rest */ if (val_a->desc.clss == INF) return 1 * mul; if (val_b->desc.clss == INF) return -1 * mul; /* check first exponent, that mantissa if equal */ switch (sc_comp(_exp(val_a), _exp(val_b))) { case -1: return -1 * mul; case 1: return 1 * mul; case 0: return sc_comp(_mant(val_a), _mant(val_b)) * mul; default: return 2; } } int fc_is_zero(const fp_value *a) { return a->desc.clss == ZERO; } int fc_is_negative(const fp_value *a) { return a->sign; } int fc_is_inf(const fp_value *a) { return a->desc.clss == INF; } int fc_is_nan(const fp_value *a) { return a->desc.clss == NAN; } int fc_is_subnormal(const fp_value *a) { return a->desc.clss == SUBNORMAL; } char *fc_print(const fp_value *val, char *buf, int buflen, unsigned base) { char *mul_1; LLDBL flt_val; mul_1 = (char*) alloca(calc_buffer_size); switch (base) { case FC_DEC: switch ((value_class_t)val->desc.clss) { case INF: snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+'); break; case NAN: snprintf(buf, buflen, "NaN"); break; case ZERO: snprintf(buf, buflen, "0.0"); break; default: flt_val = fc_val_to_ieee754(val); #ifdef HAVE_LONG_DOUBLE /* XXX 30 is arbitrary */ snprintf(buf, buflen, "%.30LE", flt_val); #else snprintf(buf, buflen, "%.18E", flt_val); #endif } break; case FC_HEX: switch ((value_class_t)val->desc.clss) { case INF: snprintf(buf, buflen, "%cINF", val->sign ? '-' : '+'); break; case NAN: snprintf(buf, buflen, "NAN"); break; case ZERO: snprintf(buf, buflen, "0.0"); break; default: flt_val = fc_val_to_ieee754(val); #ifdef HAVE_LONG_DOUBLE snprintf(buf, buflen, "%LA", flt_val); #else snprintf(buf, buflen, "%A", flt_val); #endif } break; case FC_PACKED: default: snprintf(buf, buflen, "%s", sc_print(pack(val, mul_1), value_size*4, SC_HEX, 0)); buf[buflen - 1] = '\0'; break; } return buf; } unsigned char fc_sub_bits(const fp_value *value, unsigned num_bits, unsigned byte_ofs) { /* this is used to cache the packed version of the value */ static char *packed_value = NULL; if (packed_value == NULL) packed_value = XMALLOCN(char, value_size); if (value != NULL) pack(value, packed_value); return sc_sub_bits(packed_value, num_bits, byte_ofs); } /* Returns non-zero if the mantissa is zero, i.e. 1.0Exxx */ int fc_zero_mantissa(const fp_value *value) { return sc_get_lowest_set_bit(_mant(value)) == ROUNDING_BITS + value->desc.mantissa_size; } /* Returns the exponent of a value. */ int fc_get_exponent(const fp_value *value) { int exp_bias = (1 << (value->desc.exponent_size - 1)) - 1; return sc_val_to_long(_exp(value)) - exp_bias; } /* Return non-zero if a given value can be converted lossless into another precision */ int fc_can_lossless_conv_to(const fp_value *value, const ieee_descriptor_t *desc) { int v; int exp_bias; /* handle some special cases first */ switch (value->desc.clss) { case ZERO: case INF: case NAN: return 1; default: break; } /* check if the exponent can be encoded: note, 0 and all ones are reserved for the exponent */ exp_bias = (1 << (desc->exponent_size - 1)) - 1; v = fc_get_exponent(value) + exp_bias; if (0 < v && v < (1 << desc->exponent_size) - 1) { /* exponent can be encoded, now check the mantissa */ v = value->desc.mantissa_size + ROUNDING_BITS - sc_get_lowest_set_bit(_mant(value)); return v <= desc->mantissa_size; } return 0; } fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode) { if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO) rounding_mode = mode; return rounding_mode; } fc_rounding_mode_t fc_get_rounding_mode(void) { return rounding_mode; } void init_fltcalc(int precision) { if (calc_buffer == NULL) { /* does nothing if already init */ if (precision == 0) precision = FC_DEFAULT_PRECISION; init_strcalc(precision + 2 + ROUNDING_BITS); /* needs additionally rounding bits, one bit as explicit 1., and one for * addition overflow */ max_precision = sc_get_precision() - (2 + ROUNDING_BITS); if (max_precision < precision) printf("WARNING: not enough precision available, using %d\n", max_precision); rounding_mode = FC_TONEAREST; value_size = sc_get_buffer_length(); calc_buffer_size = sizeof(fp_value) + 2*value_size - 1; calc_buffer = (fp_value*) xmalloc(calc_buffer_size); memset(calc_buffer, 0, calc_buffer_size); DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\ntCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", value_size, calc_buffer_size, calc_buffer)); #ifdef HAVE_LONG_DOUBLE DEBUGPRINTF(("\tUsing long double (1-15-64) interface\n")); #else DEBUGPRINTF(("\tUsing double (1-11-52) interface\n")); #endif #ifdef WORDS_BIGENDIAN DEBUGPRINTF(("\tWord order is big endian\n\n")); #else DEBUGPRINTF(("\tWord order is little endian\n\n")); #endif } } void finish_fltcalc (void) { free(calc_buffer); calc_buffer = NULL; } #ifdef FLTCALC_TRACE_CALC static char buffer[100]; #endif /* definition of interface functions */ fp_value *fc_add(const fp_value *a, const fp_value *b, fp_value *result) { if (result == NULL) result = calc_buffer; TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); TRACEPRINTF(("+ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED))); /* make the value with the bigger exponent the first one */ if (sc_comp(_exp(a), _exp(b)) == -1) _fadd(b, a, result); else _fadd(a, b, result); TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED))); return result; } fp_value *fc_sub(const fp_value *a, const fp_value *b, fp_value *result) { fp_value *temp; if (result == NULL) result = calc_buffer; TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); TRACEPRINTF(("- %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED))); temp = (fp_value*) alloca(calc_buffer_size); memcpy(temp, b, calc_buffer_size); temp->sign = !b->sign; if (sc_comp(_exp(a), _exp(temp)) == -1) _fadd(temp, a, result); else _fadd(a, temp, result); TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED))); return result; } fp_value *fc_mul(const fp_value *a, const fp_value *b, fp_value *result) { if (result == NULL) result = calc_buffer; TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); TRACEPRINTF(("* %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED))); _fmul(a, b, result); TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED))); return result; } fp_value *fc_div(const fp_value *a, const fp_value *b, fp_value *result) { if (result == NULL) result = calc_buffer; TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); TRACEPRINTF(("/ %s ", fc_print(b, buffer, sizeof(buffer), FC_PACKED))); _fdiv(a, b, result); TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED))); return result; } fp_value *fc_neg(const fp_value *a, fp_value *result) { if (result == NULL) result = calc_buffer; TRACEPRINTF(("- %s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); if (a != result) memcpy(result, a, calc_buffer_size); result->sign = !a->sign; TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED))); return result; } fp_value *fc_int(const fp_value *a, fp_value *result) { if (result == NULL) result = calc_buffer; TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); TRACEPRINTF(("truncated to integer ")); _trunc(a, result); TRACEPRINTF(("= %s\n", fc_print(result, buffer, sizeof(buffer), FC_PACKED))); return result; } fp_value *fc_rnd(const fp_value *a, fp_value *result) { if (result == NULL) result = calc_buffer; (void) a; TRACEPRINTF(("%s ", fc_print(a, buffer, sizeof(buffer), FC_PACKED))); TRACEPRINTF(("rounded to integer ")); panic("fc_rnd() not yet implemented"); } /* * convert a floating point value into an sc value ... */ int fc_flt2int(const fp_value *a, void *result, ir_mode *dst_mode) { if (a->desc.clss == NORMAL) { int exp_bias = (1 << (a->desc.exponent_size - 1)) - 1; int exp_val = sc_val_to_long(_exp(a)) - exp_bias; int shift, highest; int mantissa_size; int tgt_bits; if (a->sign && !mode_is_signed(dst_mode)) { /* FIXME: for now we cannot convert this */ return 0; } tgt_bits = get_mode_size_bits(dst_mode); if (mode_is_signed(dst_mode)) --tgt_bits; assert(exp_val >= 0 && "floating point value not integral before fc_flt2int() call"); mantissa_size = a->desc.mantissa_size + ROUNDING_BITS; shift = exp_val - mantissa_size; if (tgt_bits < mantissa_size + 1) tgt_bits = mantissa_size + 1; if (shift > 0) { sc_shlI(_mant(a), shift, tgt_bits, 0, result); } else { sc_shrI(_mant(a), -shift, tgt_bits, 0, result); } /* check for overflow */ highest = sc_get_highest_set_bit(result); if (mode_is_signed(dst_mode)) { if (highest == sc_get_lowest_set_bit(result)) { /* need extra test for MIN_INT */ if (highest >= (int) get_mode_size_bits(dst_mode)) { /* FIXME: handle overflow */ return 0; } } else { if (highest >= (int) get_mode_size_bits(dst_mode) - 1) { /* FIXME: handle overflow */ return 0; } } } else { if (highest >= (int) get_mode_size_bits(dst_mode)) { /* FIXME: handle overflow */ return 0; } } if (a->sign) sc_neg(result, result); return 1; } else if (a->desc.clss == ZERO) { sc_zero(result); return 1; } return 0; } unsigned fc_set_immediate_precision(unsigned bits) { unsigned old = immediate_prec; immediate_prec = bits; return old; } int fc_is_exact(void) { return fc_exact; }