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/*
 * ieee-math.c - IEEE floating point emulation code
 * Copyright (C) 1989,1990,1991,1995 by
 * Digital Equipment Corporation, Maynard, Massachusetts.
 *
 * Heavily modified for Linux/Alpha.  Changes are Copyright (c) 1995
 * by David Mosberger (davidm@azstarnet.com).
 *
 * This file may be redistributed according to the terms of the
 * GNU General Public License.
 */
/*
 * The original code did not have any comments. I have created many
 * comments as I fix the bugs in the code.  My comments are based on
 * my observation and interpretation of the code.  If the original
 * author would have spend a few minutes to comment the code, we would
 * never had a problem of misinterpretation.  -HA
 *
 * This code could probably be a lot more optimized (especially the
 * division routine).  However, my foremost concern was to get the
 * IEEE behavior right.  Performance is less critical as these
 * functions are used on exceptional numbers only (well, assuming you
 * don't turn on the "trap on inexact"...).
 */
#include "ieee-math.h"
 
#define STICKY_S        0x20000000      /* both in longword 0 of fraction */
#define STICKY_T        1
 
/*
 * Careful: order matters here!
 */
enum {
        NaN, QNaN, INFTY, ZERO, DENORM, NORMAL
};
 
enum {
        SINGLE, DOUBLE
};
 
typedef unsigned long fpclass_t;
 
#define IEEE_TMAX       0x7fefffffffffffff
#define IEEE_SMAX       0x47efffffe0000000
#define IEEE_SNaN       0xfff00000000f0000
#define IEEE_QNaN       0xfff8000000000000
#define IEEE_PINF       0x7ff0000000000000
#define IEEE_NINF       0xfff0000000000000
 
 
/*
 * The memory format of S floating point numbers differs from the
 * register format.  In the following, the bitnumbers above the
 * diagram below give the memory format while the numbers below give
 * the register format.
 *
 *        31 30      23 22                              0
 *      +-----------------------------------------------+
 * S    | s |   exp    |       fraction                 |
 *      +-----------------------------------------------+
 *        63 62      52 51                            29
 *
 * For T floating point numbers, the register and memory formats
 * match:
 *
 *      +-------------------------------------------------------------------+
 * T    | s |        exp        |           frac | tion                     |
 *      +-------------------------------------------------------------------+
 *        63 62               52 51            32 31                       0
 */
typedef struct {
        unsigned long   f[2];   /* bit 55 in f[0] is the factor of 2^0*/
        int             s;      /* 1 bit sign (0 for +, 1 for -) */
        int             e;      /* 16 bit signed exponent */
} EXTENDED;
 
 
/*
 * Return the sign of a Q integer, S or T fp number in the register
 * format.
 */
static inline int
sign (unsigned long a)
{
        if ((long) a < 0)
                return -1;
        else
                return 1;
}
 
 
static inline long
cmp128 (const long a[2], const long b[2])
{
        if (a[1] < b[1]) return -1;
        if (a[1] > b[1]) return  1;
        return a[0] - b[0];
}
 
 
static inline void
sll128 (unsigned long a[2])
{
        a[1] = (a[1] << 1) | (a[0] >> 63);
        a[0] <<= 1;
}
 
 
static inline void
srl128 (unsigned long a[2])
{
        a[0] = (a[0] >> 1) | (a[1] << 63);
        a[1] >>= 1;
}
 
 
static inline void
add128 (const unsigned long a[2], const unsigned long b[2], unsigned long c[2])
{
        unsigned long carry = a[0] > (0xffffffffffffffff - b[0]);
 
        c[0] = a[0] + b[0];
        c[1] = a[1] + b[1] + carry;
}
 
 
static inline void
sub128 (const unsigned long a[2], const unsigned long b[2], unsigned long c[2])
{
        unsigned long borrow = a[0] < b[0];
 
        c[0] = a[0] - b[0];
        c[1] = a[1] - b[1] - borrow;
}
 
 
static inline void
mul64 (const unsigned long a, const unsigned long b, unsigned long c[2])
{
        c[0] = a * b;
        asm ("umulh %1,%2,%0" : "=r"(c[1]) : "r"(a), "r"(b));
}
 
 
static void
div128 (unsigned long a[2], unsigned long b[2], unsigned long c[2])
{
        unsigned long mask[2] = {1, 0};
 
        /*
         * Shift b until either the sign bit is set or until it is at
         * least as big as the dividend:
         */
        while (cmp128(b, a) < 0 && sign(b[1]) >= 0) {
                sll128(b);
                sll128(mask);
        }
        c[0] = c[1] = 0;
        do {
                if (cmp128(a, b) >= 0) {
                        sub128(a, b, a);
                        add128(mask, c, c);
                }
                srl128(mask);
                srl128(b);
        } while (mask[0] || mask[1]);
}
 
 
static void
normalize (EXTENDED *a)
{
        if (!a->f[0] && !a->f[1])
                return;         /* zero fraction, unnormalizable... */
        /*
         * In "extended" format, the "1" in "1.f" is explicit; it is
         * in bit 55 of f[0], and the decimal point is understood to
         * be between bit 55 and bit 54.  To normalize, shift the
         * fraction until we have a "1" in bit 55.
         */
        if ((a->f[0] & 0xff00000000000000) != 0 || a->f[1] != 0) {
                /*
                 * Mantissa is greater than 1.0:
                 */
                while ((a->f[0] & 0xff80000000000000) != 0x0080000000000000 ||
                       a->f[1] != 0)
                {
                        unsigned long sticky;
 
                        ++a->e;
                        sticky = a->f[0] & 1;
                        srl128(a->f);
                        a->f[0] |= sticky;
                }
                return;
        }
 
        if (!(a->f[0] & 0x0080000000000000)) {
                /*
                 * Mantissa is less than 1.0:
                 */
                while (!(a->f[0] & 0x0080000000000000)) {
                        --a->e;
                        a->f[0] <<= 1;
                }
                return;
        }
}
 
 
static inline fpclass_t
ieee_fpclass (unsigned long a)
{
        unsigned long exp, fract;
 
        exp   = (a >> 52) & 0x7ff;      /* 11 bits of exponent */
        fract = a & 0x000fffffffffffff; /* 52 bits of fraction */
        if (exp == 0) {
                if (fract == 0)
                        return ZERO;
                return DENORM;
        }
        if (exp == 0x7ff) {
                if (fract == 0)
                        return INFTY;
                if (((fract >> 51) & 1) != 0)
                        return QNaN;
                return NaN;
        }
        return NORMAL;
}
 
 
/*
 * Translate S/T fp number in register format into extended format.
 */
static fpclass_t
extend_ieee (unsigned long a, EXTENDED *b, int prec)
{
        fpclass_t result_kind;
 
        b->s = a >> 63;
        b->e = ((a >> 52) & 0x7ff) - 0x3ff;     /* remove bias */
        b->f[1] = 0;
        /*
         * We shift f[1] left three bits so that the higher order bits
         * of the fraction will reside in bits 55 through 0 of f[0].
         */
        b->f[0] = (a & 0x000fffffffffffff) << 3;
        result_kind = ieee_fpclass(a);
        if (result_kind == NORMAL) {
                /* set implied 1. bit: */
                b->f[0] |= 1UL << 55;
        } else if (result_kind == DENORM) {
                if (prec == SINGLE)
                        b->e = -126;
                else
                        b->e = -1022;
        }
        return result_kind;
}
 
 
/*
 * INPUT PARAMETERS:
 *       a           a number in EXTENDED format to be converted to
 *                   s-floating format.
 *       f           rounding mode and exception enable bits.
 * OUTPUT PARAMETERS:
 *       b          will contain the s-floating number that "a" was
 *                  converted to (in register format).
 */
static unsigned long
make_s_ieee (long f, EXTENDED *a, unsigned long *b)
{
        unsigned long res, sticky;
 
        if (!a->e && !a->f[0] && !a->f[1]) {
                *b = (unsigned long) a->s << 63;        /* return +/-0 */
                return 0;
        }
 
        normalize(a);
        res = 0;
 
        if (a->e < -0x7e) {
                res = FPCR_INE;
                if (f & IEEE_TRAP_ENABLE_UNF) {
                        res |= FPCR_UNF;
                        a->e += 0xc0;   /* scale up result by 2^alpha */
                } else {
                        /* try making denormalized number: */
                        while (a->e < -0x7e) {
                                ++a->e;
                                sticky = a->f[0] & 1;
                                srl128(a->f);
                                if (!a->f[0] && !a->f[0]) {
                                        /* underflow: replace with exact 0 */
                                        res |= FPCR_UNF;
                                        break;
                                }
                                a->f[0] |= sticky;
                        }
                        a->e = -0x3ff;
                }
        }
        if (a->e >= 0x80) {
                res = FPCR_OVF | FPCR_INE;
                if (f & IEEE_TRAP_ENABLE_OVF) {
                        a->e -= 0xc0;   /* scale down result by 2^alpha */
                } else {
                        /*
                         * Overflow without trap enabled, substitute
                         * result according to rounding mode:
                         */
                        switch (RM(f)) {
                              case ROUND_NEAR:
                                *b = IEEE_PINF;
                                break;
 
                              case ROUND_CHOP:
                                *b = IEEE_SMAX;
                                break;
 
                              case ROUND_NINF:
                                if (a->s) {
                                        *b = IEEE_PINF;
                                } else {
                                        *b = IEEE_SMAX;
                                }
                                break;
 
                              case ROUND_PINF:
                                if (a->s) {
                                        *b = IEEE_SMAX;
                                } else {
                                        *b = IEEE_PINF;
                                }
                                break;
                        }
                        *b |= ((unsigned long) a->s << 63);
                        return res;
                }
        }
 
        *b = (((unsigned long) a->s << 63) |
              (((unsigned long) a->e + 0x3ff) << 52) |
              ((a->f[0] >> 3) & 0x000fffffe0000000));
        return res;
}
 
 
static unsigned long
make_t_ieee (long f, EXTENDED *a, unsigned long *b)
{
        unsigned long res, sticky;
 
        if (!a->e && !a->f[0] && !a->f[1]) {
                *b = (unsigned long) a->s << 63;        /* return +/-0 */
                return 0;
        }
 
        normalize(a);
        res = 0;
        if (a->e < -0x3fe) {
                res = FPCR_INE;
                if (f & IEEE_TRAP_ENABLE_UNF) {
                        res |= FPCR_UNF;
                        a->e += 0x600;
                } else {
                        /* try making denormalized number: */
                        while (a->e < -0x3fe) {
                                ++a->e;
                                sticky = a->f[0] & 1;
                                srl128(a->f);
                                if (!a->f[0] && !a->f[0]) {
                                        /* underflow: replace with exact 0 */
                                        res |= FPCR_UNF;
                                        break;
                                }
                                a->f[0] |= sticky;
                        }
                        a->e = -0x3ff;
                }
        }
        if (a->e >= 0x3ff) {
                res = FPCR_OVF | FPCR_INE;
                if (f & IEEE_TRAP_ENABLE_OVF) {
                        a->e -= 0x600;  /* scale down result by 2^alpha */
                } else {
                        /*
                         * Overflow without trap enabled, substitute
                         * result according to rounding mode:
                         */
                        switch (RM(f)) {
                              case ROUND_NEAR:
                                *b = IEEE_PINF;
                                break;
 
                              case ROUND_CHOP:
                                *b = IEEE_TMAX;
                                break;
 
                              case ROUND_NINF:
                                if (a->s) {
                                        *b = IEEE_PINF;
                                } else {
                                        *b = IEEE_TMAX;
                                }
                                break;
 
                              case ROUND_PINF:
                                if (a->s) {
                                        *b = IEEE_TMAX;
                                } else {
                                        *b = IEEE_PINF;
                                }
                                break;
                        }
                        *b |= ((unsigned long) a->s << 63);
                        return res;
                }
        }
        *b = (((unsigned long) a->s << 63) |
              (((unsigned long) a->e + 0x3ff) << 52) |
              ((a->f[0] >> 3) & 0x000fffffffffffff));
        return res;
}
 
 
/*
 * INPUT PARAMETERS:
 *       a          EXTENDED format number to be rounded.
 *       rm         integer with value ROUND_NEAR, ROUND_CHOP, etc.
 *                  indicates how "a" should be rounded to produce "b".
 * OUTPUT PARAMETERS:
 *       b          s-floating number produced by rounding "a".
 * RETURN VALUE:
 *       if no errors occurred, will be zero.  Else will contain flags
 *       like FPCR_INE_OP, etc.
 */
static unsigned long
round_s_ieee (int f, EXTENDED *a, unsigned long *b)
{
        unsigned long diff1, diff2, res = 0;
        EXTENDED z1, z2;
 
        if (!(a->f[0] & 0xffffffff)) {
                return make_s_ieee(f, a, b);    /* no rounding error */
        }
 
        /*
         * z1 and z2 are the S-floating numbers with the next smaller/greater
         * magnitude than a, respectively.
         */
        z1.s = z2.s = a->s;
        z1.e = z2.e = a->e;
        z1.f[0] = z2.f[0] = a->f[0] & 0xffffffff00000000;
        z1.f[1] = z2.f[1] = 0;
        z2.f[0] += 0x100000000;  /* next bigger S float number */
 
        switch (RM(f)) {
              case ROUND_NEAR:
                diff1 = a->f[0] - z1.f[0];
                diff2 = z2.f[0] - a->f[0];
                if (diff1 > diff2)
                        res = make_s_ieee(f, &z2, b);
                else if (diff2 > diff1)
                        res = make_s_ieee(f, &z1, b);
                else
                        /* equal distance: round towards even */
                        if (z1.f[0] & 0x100000000)
                                res = make_s_ieee(f, &z2, b);
                        else
                                res = make_s_ieee(f, &z1, b);
                break;
 
              case ROUND_CHOP:
                res = make_s_ieee(f, &z1, b);
                break;
 
              case ROUND_PINF:
                if (a->s) {
                        res = make_s_ieee(f, &z1, b);
                } else {
                        res = make_s_ieee(f, &z2, b);
                }
                break;
 
              case ROUND_NINF:
                if (a->s) {
                        res = make_s_ieee(f, &z2, b);
                } else {
                        res = make_s_ieee(f, &z1, b);
                }
                break;
        }
        return FPCR_INE | res;
}
 
 
static unsigned long
round_t_ieee (int f, EXTENDED *a, unsigned long *b)
{
        unsigned long diff1, diff2, res;
        EXTENDED z1, z2;
 
        if (!(a->f[0] & 0x7)) {
                /* no rounding error */
                return make_t_ieee(f, a, b);
        }
 
        z1.s = z2.s = a->s;
        z1.e = z2.e = a->e;
        z1.f[0] = z2.f[0] = a->f[0] & ~0x7;
        z1.f[1] = z2.f[1] = 0;
        z2.f[0] += (1 << 3);
 
        res = 0;
        switch (RM(f)) {
              case ROUND_NEAR:
                diff1 = a->f[0] - z1.f[0];
                diff2 = z2.f[0] - a->f[0];
                if (diff1 > diff2)
                        res = make_t_ieee(f, &z2, b);
                else if (diff2 > diff1)
                        res = make_t_ieee(f, &z1, b);
                else
                        /* equal distance: round towards even */
                        if (z1.f[0] & (1 << 3))
                                res = make_t_ieee(f, &z2, b);
                        else
                                res = make_t_ieee(f, &z1, b);
                break;
 
              case ROUND_CHOP:
                res = make_t_ieee(f, &z1, b);
                break;
 
              case ROUND_PINF:
                if (a->s) {
                        res = make_t_ieee(f, &z1, b);
                } else {
                        res = make_t_ieee(f, &z2, b);
                }
                break;
 
              case ROUND_NINF:
                if (a->s) {
                        res = make_t_ieee(f, &z2, b);
                } else {
                        res = make_t_ieee(f, &z1, b);
                }
                break;
        }
        return FPCR_INE | res;
}
 
 
static fpclass_t
add_kernel_ieee (EXTENDED *op_a, EXTENDED *op_b, EXTENDED *op_c)
{
        unsigned long mask, fa, fb, fc;
        int diff;
 
        diff = op_a->e - op_b->e;
        fa = op_a->f[0];
        fb = op_b->f[0];
        if (diff < 0) {
                diff = -diff;
                op_c->e = op_b->e;
                mask = (1UL << diff) - 1;
                fa >>= diff;
                if (op_a->f[0] & mask) {
                        fa |= 1;                /* set sticky bit */
                }
        } else {
                op_c->e = op_a->e;
                mask = (1UL << diff) - 1;
                fb >>= diff;
                if (op_b->f[0] & mask) {
                        fb |= 1;                /* set sticky bit */
                }
        }
        if (op_a->s)
                fa = -fa;
        if (op_b->s)
                fb = -fb;
        fc = fa + fb;
        op_c->f[1] = 0;
        op_c->s = fc >> 63;
        if (op_c->s) {
                fc = -fc;
        }
        op_c->f[0] = fc;
        normalize(op_c);
        return 0;
}
 
 
/*
 * converts s-floating "a" to t-floating "b".
 *
 * INPUT PARAMETERS:
 *       a           a s-floating number to be converted
 *       f           the rounding mode (ROUND_NEAR, etc. )
 * OUTPUT PARAMETERS:
 *       b           the t-floating number that "a" is converted to.
 * RETURN VALUE:
 *       error flags - i.e., zero if no errors occurred,
 *       FPCR_INV if invalid operation occurred, etc.
 */
unsigned long
ieee_CVTST (int f, unsigned long a, unsigned long *b)
{
        EXTENDED temp;
        fpclass_t a_type;
 
        a_type = extend_ieee(a, &temp, SINGLE);
        if (a_type >= NaN && a_type <= INFTY) {
                *b = a;
                if (a_type == NaN) {
                        *b |= (1UL << 51);      /* turn SNaN into QNaN */
                        return FPCR_INV;
                }
                return 0;
        }
        return round_t_ieee(f, &temp, b);
}
 
 
/*
 * converts t-floating "a" to s-floating "b".
 *
 * INPUT PARAMETERS:
 *       a           a t-floating number to be converted
 *       f           the rounding mode (ROUND_NEAR, etc. )
 * OUTPUT PARAMETERS:
 *       b           the s-floating number that "a" is converted to.
 * RETURN VALUE:
 *       error flags - i.e., zero if no errors occurred,
 *       FPCR_INV if invalid operation occurred, etc.
 */
unsigned long
ieee_CVTTS (int f, unsigned long a, unsigned long *b)
{
        EXTENDED temp;
        fpclass_t a_type;
 
        a_type = extend_ieee(a, &temp, DOUBLE);
        if (a_type >= NaN && a_type <= INFTY) {
                *b = a;
                if (a_type == NaN) {
                        *b |= (1UL << 51);      /* turn SNaN into QNaN */
                        return FPCR_INV;
                }
                return 0;
        }
        return round_s_ieee(f, &temp, b);
}
 
 
/*
 * converts q-format (64-bit integer) "a" to s-floating "b".
 *
 * INPUT PARAMETERS:
 *       a           an 64-bit integer to be converted.
 *       f           the rounding mode (ROUND_NEAR, etc. )
 * OUTPUT PARAMETERS:
 *       b           the s-floating number "a" is converted to.
 * RETURN VALUE:
 *       error flags - i.e., zero if no errors occurred,
 *       FPCR_INV if invalid operation occurred, etc.
 */
unsigned long
ieee_CVTQS (int f, unsigned long a, unsigned long *b)
{
        EXTENDED op_b;
 
        op_b.s    = 0;
        op_b.f[0] = a;
        op_b.f[1] = 0;
        if (sign(a) < 0) {
                op_b.s = 1;
                op_b.f[0] = -a;
        }
        op_b.e = 55;
        normalize(&op_b);
        return round_s_ieee(f, &op_b, b);
}
 
 
/*
 * converts 64-bit integer "a" to t-floating "b".
 *
 * INPUT PARAMETERS:
 *       a           a 64-bit integer to be converted.
 *       f           the rounding mode (ROUND_NEAR, etc.)
 * OUTPUT PARAMETERS:
 *       b           the t-floating number "a" is converted to.
 * RETURN VALUE:
 *       error flags - i.e., zero if no errors occurred,
 *       FPCR_INV if invalid operation occurred, etc.
 */
unsigned long
ieee_CVTQT (int f, unsigned long a, unsigned long *b)
{
        EXTENDED op_b;
 
        op_b.s    = 0;
        op_b.f[0] = a;
        op_b.f[1] = 0;
        if (sign(a) < 0) {
                op_b.s = 1;
                op_b.f[0] = -a;
        }
        op_b.e = 55;
        normalize(&op_b);
        return round_t_ieee(f, &op_b, b);
}
 
 
/*
 * converts t-floating "a" to 64-bit integer (q-format) "b".
 *
 * INPUT PARAMETERS:
 *       a           a t-floating number to be converted.
 *       f           the rounding mode (ROUND_NEAR, etc. )
 * OUTPUT PARAMETERS:
 *       b           the 64-bit integer "a" is converted to.
 * RETURN VALUE:
 *       error flags - i.e., zero if no errors occurred,
 *       FPCR_INV if invalid operation occurred, etc.
 */
unsigned long
ieee_CVTTQ (int f, unsigned long a, unsigned long *pb)
{
        unsigned int midway;
        unsigned long ov, uv, res, b;
        fpclass_t a_type;
        EXTENDED temp;
 
        a_type = extend_ieee(a, &temp, DOUBLE);
 
        b = 0x7fffffffffffffff;
        res = FPCR_INV;
        if (a_type == NaN || a_type == INFTY)
                goto out;
 
        res = 0;
        if (a_type == QNaN)
                goto out;
 
        if (temp.e > 0) {
                ov = 0;
                while (temp.e > 0) {
                        --temp.e;
                        ov |= temp.f[1] >> 63;
                        sll128(temp.f);
                }
                if (ov || (temp.f[1] & 0xffc0000000000000))
                        res |= FPCR_IOV | FPCR_INE;
        }
        else if (temp.e < 0) {
                while (temp.e < 0) {
                        ++temp.e;
                        uv = temp.f[0] & 1;              /* save sticky bit */
                        srl128(temp.f);
                        temp.f[0] |= uv;
                }
        }
        b = (temp.f[1] << 9) | (temp.f[0] >> 55);
 
        /*
         * Notice: the fraction is only 52 bits long.  Thus, rounding
         * cannot possibly result in an integer overflow.
         */
        switch (RM(f)) {
              case ROUND_NEAR:
                if (temp.f[0] & 0x0040000000000000) {
                        midway = (temp.f[0] & 0x003fffffffffffff) == 0;
                        if ((midway && (temp.f[0] & 0x0080000000000000)) ||
                            !midway)
                                ++b;
                }
                break;
 
              case ROUND_PINF:
                if ((temp.f[0] & 0x007fffffffffffff) != 0)
                        ++b;
                break;
 
              case ROUND_NINF:
                if ((temp.f[0] & 0x007fffffffffffff) != 0)
                        --b;
                break;
 
              case ROUND_CHOP:
                /* no action needed */
                break;
        }
        if ((temp.f[0] & 0x007fffffffffffff) != 0)
                res |= FPCR_INE;
 
        if (temp.s) {
                b = -b;
        }
 
out:
        *pb = b;
        return res;
}
 
 
unsigned long
ieee_CMPTEQ (unsigned long a, unsigned long b, unsigned long *c)
{
        EXTENDED op_a, op_b;
        fpclass_t a_type, b_type;
 
        *c = 0;
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if (a_type == NaN || b_type == NaN)
                return FPCR_INV;
        if (a_type == QNaN || b_type == QNaN)
                return 0;
 
        if ((op_a.e == op_b.e && op_a.s == op_b.s &&
             op_a.f[0] == op_b.f[0] && op_a.f[1] == op_b.f[1]) ||
            (a_type == ZERO && b_type == ZERO))
                *c = 0x4000000000000000;
        return 0;
}
 
 
unsigned long
ieee_CMPTLT (unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b;
 
        *c = 0;
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if (a_type == NaN || b_type == NaN)
                return FPCR_INV;
        if (a_type == QNaN || b_type == QNaN)
                return 0;
 
        if ((op_a.s == 1 && op_b.s == 0 &&
             (a_type != ZERO || b_type != ZERO)) ||
            (op_a.s == 1 && op_b.s == 1 &&
             (op_a.e > op_b.e || (op_a.e == op_b.e &&
                                  cmp128(op_a.f, op_b.f) > 0))) ||
            (op_a.s == 0 && op_b.s == 0 &&
             (op_a.e < op_b.e || (op_a.e == op_b.e &&
                                  cmp128(op_a.f,op_b.f) < 0))))
                *c = 0x4000000000000000;
        return 0;
}
 
 
unsigned long
ieee_CMPTLE (unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b;
 
        *c = 0;
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if (a_type == NaN || b_type == NaN)
                return FPCR_INV;
        if (a_type == QNaN || b_type == QNaN)
                return 0;
 
        if ((a_type == ZERO && b_type == ZERO) ||
            (op_a.s == 1 && op_b.s == 0) ||
            (op_a.s == 1 && op_b.s == 1 &&
             (op_a.e > op_b.e || (op_a.e == op_b.e &&
                                  cmp128(op_a.f,op_b.f) >= 0))) ||
            (op_a.s == 0 && op_b.s == 0 &&
             (op_a.e < op_b.e || (op_a.e == op_b.e &&
                                  cmp128(op_a.f,op_b.f) <= 0))))
                *c = 0x4000000000000000;
        return 0;
}
 
 
unsigned long
ieee_CMPTUN (unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b;
 
        *c = 0x4000000000000000;
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if (a_type == NaN || b_type == NaN)
                return FPCR_INV;
        if (a_type == QNaN || b_type == QNaN)
                return 0;
        *c = 0;
        return 0;
}
 
 
/*
 * Add a + b = c, where a, b, and c are ieee s-floating numbers.  "f"
 * contains the rounding mode etc.
 */
unsigned long
ieee_ADDS (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        a_type = extend_ieee(a, &op_a, SINGLE);
        b_type = extend_ieee(b, &op_b, SINGLE);
        if ((a_type >= NaN && a_type <= INFTY) ||
            (b_type >= NaN && b_type <= INFTY))
        {
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                if (a_type == INFTY && b_type == INFTY && sign(a) != sign(b)) {
                        *c = IEEE_QNaN;
                        return FPCR_INV;
                }
                if (a_type == INFTY)
                        *c = a;
                else
                        *c = b;
                return 0;
        }
 
        add_kernel_ieee(&op_a, &op_b, &op_c);
        /* special case for -0 + -0 ==> -0 */
        if (a_type == ZERO && b_type == ZERO)
                op_c.s = op_a.s && op_b.s;
        return round_s_ieee(f, &op_c, c);
}
 
 
/*
 * Add a + b = c, where a, b, and c are ieee t-floating numbers.  "f"
 * contains the rounding mode etc.
 */
unsigned long
ieee_ADDT (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if ((a_type >= NaN && a_type <= INFTY) ||
            (b_type >= NaN && b_type <= INFTY))
        {
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                if (a_type == INFTY && b_type == INFTY && sign(a) != sign(b)) {
                        *c = IEEE_QNaN;
                        return FPCR_INV;
                }
                if (a_type == INFTY)
                        *c = a;
                else
                        *c = b;
                return 0;
        }
        add_kernel_ieee(&op_a, &op_b, &op_c);
        /* special case for -0 + -0 ==> -0 */
        if (a_type == ZERO && b_type == ZERO)
                op_c.s = op_a.s && op_b.s;
 
        return round_t_ieee(f, &op_c, c);
}
 
 
/*
 * Subtract a - b = c, where a, b, and c are ieee s-floating numbers.
 * "f" contains the rounding mode etc.
 */
unsigned long
ieee_SUBS (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        a_type = extend_ieee(a, &op_a, SINGLE);
        b_type = extend_ieee(b, &op_b, SINGLE);
        if ((a_type >= NaN && a_type <= INFTY) ||
            (b_type >= NaN && b_type <= INFTY))
        {
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                if (a_type == INFTY && b_type == INFTY && sign(a) == sign(b)) {
                        *c = IEEE_QNaN;
                        return FPCR_INV;
                }
                if (a_type == INFTY)
                        *c = a;
                else
                        *c = b ^ (1UL << 63);
                return 0;
        }
        op_b.s = !op_b.s;
        add_kernel_ieee(&op_a, &op_b, &op_c);
        /* special case for -0 - +0 ==> -0 */
        if (a_type == ZERO && b_type == ZERO)
                op_c.s = op_a.s && op_b.s;
 
        return round_s_ieee(f, &op_c, c);
}
 
 
/*
 * Subtract a - b = c, where a, b, and c are ieee t-floating numbers.
 * "f" contains the rounding mode etc.
 */
unsigned long
ieee_SUBT (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if ((a_type >= NaN && a_type <= INFTY) ||
            (b_type >= NaN && b_type <= INFTY))
        {
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                if (a_type == INFTY && b_type == INFTY && sign(a) == sign(b)) {
                        *c = IEEE_QNaN;
                        return FPCR_INV;
                }
                if (a_type == INFTY)
                        *c = a;
                else
                        *c = b ^ (1UL << 63);
                return 0;
        }
        op_b.s = !op_b.s;
        add_kernel_ieee(&op_a, &op_b, &op_c);
        /* special case for -0 - +0 ==> -0 */
        if (a_type == ZERO && b_type == ZERO)
                op_c.s = op_a.s && op_b.s;
 
        return round_t_ieee(f, &op_c, c);
}
 
 
/*
 * Multiply a x b = c, where a, b, and c are ieee s-floating numbers.
 * "f" contains the rounding mode.
 */
unsigned long
ieee_MULS (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        a_type = extend_ieee(a, &op_a, SINGLE);
        b_type = extend_ieee(b, &op_b, SINGLE);
        if ((a_type >= NaN && a_type <= INFTY) ||
            (b_type >= NaN && b_type <= INFTY))
        {
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                if ((a_type == INFTY && b_type == ZERO) ||
                    (b_type == INFTY && a_type == ZERO))
                {
                        *c = IEEE_QNaN;         /* return canonical QNaN */
                        return FPCR_INV;
                }
                if (a_type == INFTY)
                        *c = a ^ ((b >> 63) << 63);
                else if (b_type == INFTY)
                        *c = b ^ ((a >> 63) << 63);
                else
                        /* either of a and b are +/-0 */
                        *c = ((unsigned long) op_a.s ^ op_b.s) << 63;
                return 0;
        }
        op_c.s = op_a.s ^ op_b.s;
        op_c.e = op_a.e + op_b.e - 55;
        mul64(op_a.f[0], op_b.f[0], op_c.f);
 
        return round_s_ieee(f, &op_c, c);
}
 
 
/*
 * Multiply a x b = c, where a, b, and c are ieee t-floating numbers.
 * "f" contains the rounding mode.
 */
unsigned long
ieee_MULT (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        *c = IEEE_QNaN;
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if ((a_type >= NaN && a_type <= ZERO) ||
            (b_type >= NaN && b_type <= ZERO))
        {
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                if ((a_type == INFTY && b_type == ZERO) ||
                    (b_type == INFTY && a_type == ZERO))
                {
                        *c = IEEE_QNaN;         /* return canonical QNaN */
                        return FPCR_INV;
                }
                if (a_type == INFTY)
                        *c = a ^ ((b >> 63) << 63);
                else if (b_type == INFTY)
                        *c = b ^ ((a >> 63) << 63);
                else
                        /* either of a and b are +/-0 */
                        *c = ((unsigned long) op_a.s ^ op_b.s) << 63;
                return 0;
        }
        op_c.s = op_a.s ^ op_b.s;
        op_c.e = op_a.e + op_b.e - 55;
        mul64(op_a.f[0], op_b.f[0], op_c.f);
 
        return round_t_ieee(f, &op_c, c);
}
 
 
/*
 * Divide a / b = c, where a, b, and c are ieee s-floating numbers.
 * "f" contains the rounding mode etc.
 */
unsigned long
ieee_DIVS (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        a_type = extend_ieee(a, &op_a, SINGLE);
        b_type = extend_ieee(b, &op_b, SINGLE);
        if ((a_type >= NaN && a_type <= ZERO) ||
            (b_type >= NaN && b_type <= ZERO))
        {
                unsigned long res;
 
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                res = 0;
                *c = IEEE_PINF;
                if (a_type == INFTY) {
                        if (b_type == INFTY) {
                                *c = IEEE_QNaN;
                                return FPCR_INV;
                        }
                } else if (b_type == ZERO) {
                        if (a_type == ZERO) {
                                *c = IEEE_QNaN;
                                return FPCR_INV;
                        }
                        res = FPCR_DZE;
                } else
                        /* a_type == ZERO || b_type == INFTY */
                        *c = 0;
                *c |= (unsigned long) (op_a.s ^ op_b.s) << 63;
                return res;
        }
        op_c.s = op_a.s ^ op_b.s;
        op_c.e = op_a.e - op_b.e;
 
        op_a.f[1] = op_a.f[0];
        op_a.f[0] = 0;
        div128(op_a.f, op_b.f, op_c.f);
        if (a_type != ZERO)
                /* force a sticky bit because DIVs never hit exact .5: */
                op_c.f[0] |= STICKY_S;
        normalize(&op_c);
        op_c.e -= 9;            /* remove excess exp from original shift */
        return round_s_ieee(f, &op_c, c);
}
 
 
/*
 * Divide a/b = c, where a, b, and c are ieee t-floating numbers.  "f"
 * contains the rounding mode etc.
 */
unsigned long
ieee_DIVT (int f, unsigned long a, unsigned long b, unsigned long *c)
{
        fpclass_t a_type, b_type;
        EXTENDED op_a, op_b, op_c;
 
        *c = IEEE_QNaN;
        a_type = extend_ieee(a, &op_a, DOUBLE);
        b_type = extend_ieee(b, &op_b, DOUBLE);
        if ((a_type >= NaN && a_type <= ZERO) ||
            (b_type >= NaN && b_type <= ZERO))
        {
                unsigned long res;
 
                /* propagate NaNs according to arch. ref. handbook: */
                if (b_type == QNaN)
                        *c = b;
                else if (b_type == NaN)
                        *c = b | (1UL << 51);
                else if (a_type == QNaN)
                        *c = a;
                else if (a_type == NaN)
                        *c = a | (1UL << 51);
 
                if (a_type == NaN || b_type == NaN)
                        return FPCR_INV;
                if (a_type == QNaN || b_type == QNaN)
                        return 0;
 
                res = 0;
                *c = IEEE_PINF;
                if (a_type == INFTY) {
                        if (b_type == INFTY) {
                                *c = IEEE_QNaN;
                                return FPCR_INV;
                        }
                } else if (b_type == ZERO) {
                        if (a_type == ZERO) {
                                *c = IEEE_QNaN;
                                return FPCR_INV;
                        }
                        res = FPCR_DZE;
                } else
                        /* a_type == ZERO || b_type == INFTY */
                        *c = 0;
                *c |= (unsigned long) (op_a.s ^ op_b.s) << 63;
                return res;
        }
        op_c.s = op_a.s ^ op_b.s;
        op_c.e = op_a.e - op_b.e;
 
        op_a.f[1] = op_a.f[0];
        op_a.f[0] = 0;
        div128(op_a.f, op_b.f, op_c.f);
        if (a_type != ZERO)
                /* force a sticky bit because DIVs never hit exact .5 */
                op_c.f[0] |= STICKY_T;
        normalize(&op_c);
        op_c.e -= 9;            /* remove excess exp from original shift */
        return round_t_ieee(f, &op_c, c);
}
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[/] [or1k/] [trunk/] [uclinux/] [uClinux-2.0.x/] [arch/] [alpha/] [math-emu/] [ieee-math.c] - Blame information for rev 1765

Line No.	Rev	Author	Line
1	199	simons	`/*`
2			`* ieee-math.c - IEEE floating point emulation code`
3			`* Copyright (C) 1989,1990,1991,1995 by`
4			`* Digital Equipment Corporation, Maynard, Massachusetts.`
5			`*`
6			`* Heavily modified for Linux/Alpha. Changes are Copyright (c) 1995`
7			`* by David Mosberger (davidm@azstarnet.com).`
8			`*`
9			`* This file may be redistributed according to the terms of the`
10			`* GNU General Public License.`
11			`*/`
12			`/*`
13			`* The original code did not have any comments. I have created many`
14			`* comments as I fix the bugs in the code. My comments are based on`
15			`* my observation and interpretation of the code. If the original`
16			`* author would have spend a few minutes to comment the code, we would`
17			`* never had a problem of misinterpretation. -HA`
18			`*`
19			`* This code could probably be a lot more optimized (especially the`
20			`* division routine). However, my foremost concern was to get the`
21			`* IEEE behavior right. Performance is less critical as these`
22			`* functions are used on exceptional numbers only (well, assuming you`
23			`* don't turn on the "trap on inexact"...).`
24			`*/`
25			`#include "ieee-math.h"`
26
27			`#define STICKY_S 0x20000000 /* both in longword 0 of fraction */`
28			`#define STICKY_T 1`
29
30			`/*`
31			`* Careful: order matters here!`
32			`*/`
33			`enum {`
34			`NaN, QNaN, INFTY, ZERO, DENORM, NORMAL`
35			`};`
36
37			`enum {`
38			`SINGLE, DOUBLE`
39			`};`
40