{
switch (a->cls) {
case float_class_snan:
- float_raise(float_flag_invalid, s);
+ float_raise(float_flag_invalid | float_flag_invalid_snan, s);
if (s->default_nan_mode) {
parts_default_nan(a, s);
} else {
float_status *s)
{
if (is_snan(a->cls) || is_snan(b->cls)) {
- float_raise(float_flag_invalid, s);
+ float_raise(float_flag_invalid | float_flag_invalid_snan, s);
}
if (s->default_nan_mode) {
int which;
if (unlikely(abc_mask & float_cmask_snan)) {
- float_raise(float_flag_invalid, s);
+ float_raise(float_flag_invalid | float_flag_invalid_snan, s);
}
which = pickNaNMulAdd(a->cls, b->cls, c->cls,
* fraction; these bits will be removed. The exponent will be biased
* by EXP_BIAS and must be bounded by [EXP_MAX-1, 0].
*/
-static void partsN(uncanon)(FloatPartsN *p, float_status *s,
- const FloatFmt *fmt)
+static void partsN(uncanon_normal)(FloatPartsN *p, float_status *s,
+ const FloatFmt *fmt)
{
const int exp_max = fmt->exp_max;
const int frac_shift = fmt->frac_shift;
- const uint64_t frac_lsb = fmt->frac_lsb;
- const uint64_t frac_lsbm1 = fmt->frac_lsbm1;
const uint64_t round_mask = fmt->round_mask;
- const uint64_t roundeven_mask = fmt->roundeven_mask;
+ const uint64_t frac_lsb = round_mask + 1;
+ const uint64_t frac_lsbm1 = round_mask ^ (round_mask >> 1);
+ const uint64_t roundeven_mask = round_mask | frac_lsb;
uint64_t inc;
- bool overflow_norm;
+ bool overflow_norm = false;
int exp, flags = 0;
- if (unlikely(p->cls != float_class_normal)) {
- switch (p->cls) {
- case float_class_zero:
- p->exp = 0;
- frac_clear(p);
- return;
- case float_class_inf:
- g_assert(!fmt->arm_althp);
- p->exp = fmt->exp_max;
- frac_clear(p);
- return;
- case float_class_qnan:
- case float_class_snan:
- g_assert(!fmt->arm_althp);
- p->exp = fmt->exp_max;
- frac_shr(p, fmt->frac_shift);
- return;
- default:
- break;
- }
- g_assert_not_reached();
- }
-
switch (s->float_rounding_mode) {
case float_round_nearest_even:
- overflow_norm = false;
- inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1 ? frac_lsbm1 : 0);
+ if (N > 64 && frac_lsb == 0) {
+ inc = ((p->frac_hi & 1) || (p->frac_lo & round_mask) != frac_lsbm1
+ ? frac_lsbm1 : 0);
+ } else {
+ inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
+ ? frac_lsbm1 : 0);
+ }
break;
case float_round_ties_away:
- overflow_norm = false;
inc = frac_lsbm1;
break;
case float_round_to_zero:
break;
case float_round_to_odd:
overflow_norm = true;
- inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+ /* fall through */
+ case float_round_to_odd_inf:
+ if (N > 64 && frac_lsb == 0) {
+ inc = p->frac_hi & 1 ? 0 : round_mask;
+ } else {
+ inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+ }
break;
default:
g_assert_not_reached();
p->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
exp++;
}
+ p->frac_lo &= ~round_mask;
}
- frac_shr(p, frac_shift);
if (fmt->arm_althp) {
/* ARM Alt HP eschews Inf and NaN for a wider exponent. */
flags = float_flag_invalid;
exp = exp_max;
frac_allones(p);
+ p->frac_lo &= ~round_mask;
}
} else if (unlikely(exp >= exp_max)) {
- flags |= float_flag_overflow | float_flag_inexact;
- if (overflow_norm) {
+ flags |= float_flag_overflow;
+ if (s->rebias_overflow) {
+ exp -= fmt->exp_re_bias;
+ } else if (overflow_norm) {
+ flags |= float_flag_inexact;
exp = exp_max - 1;
frac_allones(p);
+ p->frac_lo &= ~round_mask;
} else {
+ flags |= float_flag_inexact;
p->cls = float_class_inf;
exp = exp_max;
frac_clear(p);
}
}
+ frac_shr(p, frac_shift);
+ } else if (unlikely(s->rebias_underflow)) {
+ flags |= float_flag_underflow;
+ exp += fmt->exp_re_bias;
+ if (p->frac_lo & round_mask) {
+ flags |= float_flag_inexact;
+ if (frac_addi(p, p, inc)) {
+ frac_shr(p, 1);
+ p->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
+ exp++;
+ }
+ p->frac_lo &= ~round_mask;
+ }
+ frac_shr(p, frac_shift);
} else if (s->flush_to_zero) {
flags |= float_flag_output_denormal;
p->cls = float_class_zero;
/* Need to recompute round-to-even/round-to-odd. */
switch (s->float_rounding_mode) {
case float_round_nearest_even:
- inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
- ? frac_lsbm1 : 0);
+ if (N > 64 && frac_lsb == 0) {
+ inc = ((p->frac_hi & 1) ||
+ (p->frac_lo & round_mask) != frac_lsbm1
+ ? frac_lsbm1 : 0);
+ } else {
+ inc = ((p->frac_lo & roundeven_mask) != frac_lsbm1
+ ? frac_lsbm1 : 0);
+ }
break;
case float_round_to_odd:
- inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+ case float_round_to_odd_inf:
+ if (N > 64 && frac_lsb == 0) {
+ inc = p->frac_hi & 1 ? 0 : round_mask;
+ } else {
+ inc = p->frac_lo & frac_lsb ? 0 : round_mask;
+ }
break;
default:
break;
}
flags |= float_flag_inexact;
frac_addi(p, p, inc);
+ p->frac_lo &= ~round_mask;
}
exp = (p->frac_hi & DECOMPOSED_IMPLICIT_BIT) != 0;
float_raise(flags, s);
}
+static void partsN(uncanon)(FloatPartsN *p, float_status *s,
+ const FloatFmt *fmt)
+{
+ if (likely(p->cls == float_class_normal)) {
+ parts_uncanon_normal(p, s, fmt);
+ } else {
+ switch (p->cls) {
+ case float_class_zero:
+ p->exp = 0;
+ frac_clear(p);
+ return;
+ case float_class_inf:
+ g_assert(!fmt->arm_althp);
+ p->exp = fmt->exp_max;
+ frac_clear(p);
+ return;
+ case float_class_qnan:
+ case float_class_snan:
+ g_assert(!fmt->arm_althp);
+ p->exp = fmt->exp_max;
+ frac_shr(p, fmt->frac_shift);
+ return;
+ default:
+ break;
+ }
+ g_assert_not_reached();
+ }
+}
+
/*
* Returns the result of adding or subtracting the values of the
* floating-point values `a' and `b'. The operation is performed
return a;
}
/* Inf - Inf */
- float_raise(float_flag_invalid, s);
+ float_raise(float_flag_invalid | float_flag_invalid_isi, s);
parts_default_nan(a, s);
return a;
}
p_nan:
return parts_pick_nan(a, b, s);
}
+
+/*
+ * Returns the result of multiplying the floating-point values `a' and
+ * `b'. The operation is performed according to the IEC/IEEE Standard
+ * for Binary Floating-Point Arithmetic.
+ */
+static FloatPartsN *partsN(mul)(FloatPartsN *a, FloatPartsN *b,
+ float_status *s)
+{
+ int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+ bool sign = a->sign ^ b->sign;
+
+ if (likely(ab_mask == float_cmask_normal)) {
+ FloatPartsW tmp;
+
+ frac_mulw(&tmp, a, b);
+ frac_truncjam(a, &tmp);
+
+ a->exp += b->exp + 1;
+ if (!(a->frac_hi & DECOMPOSED_IMPLICIT_BIT)) {
+ frac_add(a, a, a);
+ a->exp -= 1;
+ }
+
+ a->sign = sign;
+ return a;
+ }
+
+ /* Inf * Zero == NaN */
+ if (unlikely(ab_mask == float_cmask_infzero)) {
+ float_raise(float_flag_invalid | float_flag_invalid_imz, s);
+ parts_default_nan(a, s);
+ return a;
+ }
+
+ if (unlikely(ab_mask & float_cmask_anynan)) {
+ return parts_pick_nan(a, b, s);
+ }
+
+ /* Multiply by 0 or Inf */
+ if (ab_mask & float_cmask_inf) {
+ a->cls = float_class_inf;
+ a->sign = sign;
+ return a;
+ }
+
+ g_assert(ab_mask & float_cmask_zero);
+ a->cls = float_class_zero;
+ a->sign = sign;
+ return a;
+}
+
+/*
+ * Returns the result of multiplying the floating-point values `a' and
+ * `b' then adding 'c', with no intermediate rounding step after the
+ * multiplication. The operation is performed according to the
+ * IEC/IEEE Standard for Binary Floating-Point Arithmetic 754-2008.
+ * The flags argument allows the caller to select negation of the
+ * addend, the intermediate product, or the final result. (The
+ * difference between this and having the caller do a separate
+ * negation is that negating externally will flip the sign bit on NaNs.)
+ *
+ * Requires A and C extracted into a double-sized structure to provide the
+ * extra space for the widening multiply.
+ */
+static FloatPartsN *partsN(muladd)(FloatPartsN *a, FloatPartsN *b,
+ FloatPartsN *c, int flags, float_status *s)
+{
+ int ab_mask, abc_mask;
+ FloatPartsW p_widen, c_widen;
+
+ ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+ abc_mask = float_cmask(c->cls) | ab_mask;
+
+ /*
+ * It is implementation-defined whether the cases of (0,inf,qnan)
+ * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
+ * they return if they do), so we have to hand this information
+ * off to the target-specific pick-a-NaN routine.
+ */
+ if (unlikely(abc_mask & float_cmask_anynan)) {
+ return parts_pick_nan_muladd(a, b, c, s, ab_mask, abc_mask);
+ }
+
+ if (flags & float_muladd_negate_c) {
+ c->sign ^= 1;
+ }
+
+ /* Compute the sign of the product into A. */
+ a->sign ^= b->sign;
+ if (flags & float_muladd_negate_product) {
+ a->sign ^= 1;
+ }
+
+ if (unlikely(ab_mask != float_cmask_normal)) {
+ if (unlikely(ab_mask == float_cmask_infzero)) {
+ float_raise(float_flag_invalid | float_flag_invalid_imz, s);
+ goto d_nan;
+ }
+
+ if (ab_mask & float_cmask_inf) {
+ if (c->cls == float_class_inf && a->sign != c->sign) {
+ float_raise(float_flag_invalid | float_flag_invalid_isi, s);
+ goto d_nan;
+ }
+ goto return_inf;
+ }
+
+ g_assert(ab_mask & float_cmask_zero);
+ if (c->cls == float_class_normal) {
+ *a = *c;
+ goto return_normal;
+ }
+ if (c->cls == float_class_zero) {
+ if (a->sign != c->sign) {
+ goto return_sub_zero;
+ }
+ goto return_zero;
+ }
+ g_assert(c->cls == float_class_inf);
+ }
+
+ if (unlikely(c->cls == float_class_inf)) {
+ a->sign = c->sign;
+ goto return_inf;
+ }
+
+ /* Perform the multiplication step. */
+ p_widen.sign = a->sign;
+ p_widen.exp = a->exp + b->exp + 1;
+ frac_mulw(&p_widen, a, b);
+ if (!(p_widen.frac_hi & DECOMPOSED_IMPLICIT_BIT)) {
+ frac_add(&p_widen, &p_widen, &p_widen);
+ p_widen.exp -= 1;
+ }
+
+ /* Perform the addition step. */
+ if (c->cls != float_class_zero) {
+ /* Zero-extend C to less significant bits. */
+ frac_widen(&c_widen, c);
+ c_widen.exp = c->exp;
+
+ if (a->sign == c->sign) {
+ parts_add_normal(&p_widen, &c_widen);
+ } else if (!parts_sub_normal(&p_widen, &c_widen)) {
+ goto return_sub_zero;
+ }
+ }
+
+ /* Narrow with sticky bit, for proper rounding later. */
+ frac_truncjam(a, &p_widen);
+ a->sign = p_widen.sign;
+ a->exp = p_widen.exp;
+
+ return_normal:
+ if (flags & float_muladd_halve_result) {
+ a->exp -= 1;
+ }
+ finish_sign:
+ if (flags & float_muladd_negate_result) {
+ a->sign ^= 1;
+ }
+ return a;
+
+ return_sub_zero:
+ a->sign = s->float_rounding_mode == float_round_down;
+ return_zero:
+ a->cls = float_class_zero;
+ goto finish_sign;
+
+ return_inf:
+ a->cls = float_class_inf;
+ goto finish_sign;
+
+ d_nan:
+ parts_default_nan(a, s);
+ return a;
+}
+
+/*
+ * Returns the result of dividing the floating-point value `a' by the
+ * corresponding value `b'. The operation is performed according to
+ * the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ */
+static FloatPartsN *partsN(div)(FloatPartsN *a, FloatPartsN *b,
+ float_status *s)
+{
+ int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+ bool sign = a->sign ^ b->sign;
+
+ if (likely(ab_mask == float_cmask_normal)) {
+ a->sign = sign;
+ a->exp -= b->exp + frac_div(a, b);
+ return a;
+ }
+
+ /* 0/0 or Inf/Inf => NaN */
+ if (unlikely(ab_mask == float_cmask_zero)) {
+ float_raise(float_flag_invalid | float_flag_invalid_zdz, s);
+ goto d_nan;
+ }
+ if (unlikely(ab_mask == float_cmask_inf)) {
+ float_raise(float_flag_invalid | float_flag_invalid_idi, s);
+ goto d_nan;
+ }
+
+ /* All the NaN cases */
+ if (unlikely(ab_mask & float_cmask_anynan)) {
+ return parts_pick_nan(a, b, s);
+ }
+
+ a->sign = sign;
+
+ /* Inf / X */
+ if (a->cls == float_class_inf) {
+ return a;
+ }
+
+ /* 0 / X */
+ if (a->cls == float_class_zero) {
+ return a;
+ }
+
+ /* X / Inf */
+ if (b->cls == float_class_inf) {
+ a->cls = float_class_zero;
+ return a;
+ }
+
+ /* X / 0 => Inf */
+ g_assert(b->cls == float_class_zero);
+ float_raise(float_flag_divbyzero, s);
+ a->cls = float_class_inf;
+ return a;
+
+ d_nan:
+ parts_default_nan(a, s);
+ return a;
+}
+
+/*
+ * Floating point remainder, per IEC/IEEE, or modulus.
+ */
+static FloatPartsN *partsN(modrem)(FloatPartsN *a, FloatPartsN *b,
+ uint64_t *mod_quot, float_status *s)
+{
+ int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+
+ if (likely(ab_mask == float_cmask_normal)) {
+ frac_modrem(a, b, mod_quot);
+ return a;
+ }
+
+ if (mod_quot) {
+ *mod_quot = 0;
+ }
+
+ /* All the NaN cases */
+ if (unlikely(ab_mask & float_cmask_anynan)) {
+ return parts_pick_nan(a, b, s);
+ }
+
+ /* Inf % N; N % 0 */
+ if (a->cls == float_class_inf || b->cls == float_class_zero) {
+ float_raise(float_flag_invalid, s);
+ parts_default_nan(a, s);
+ return a;
+ }
+
+ /* N % Inf; 0 % N */
+ g_assert(b->cls == float_class_inf || a->cls == float_class_zero);
+ return a;
+}
+
+/*
+ * Square Root
+ *
+ * The base algorithm is lifted from
+ * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrtf.c
+ * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrt.c
+ * https://git.musl-libc.org/cgit/musl/tree/src/math/sqrtl.c
+ * and is thus MIT licenced.
+ */
+static void partsN(sqrt)(FloatPartsN *a, float_status *status,
+ const FloatFmt *fmt)
+{
+ const uint32_t three32 = 3u << 30;
+ const uint64_t three64 = 3ull << 62;
+ uint32_t d32, m32, r32, s32, u32; /* 32-bit computation */
+ uint64_t d64, m64, r64, s64, u64; /* 64-bit computation */
+ uint64_t dh, dl, rh, rl, sh, sl, uh, ul; /* 128-bit computation */
+ uint64_t d0h, d0l, d1h, d1l, d2h, d2l;
+ uint64_t discard;
+ bool exp_odd;
+ size_t index;
+
+ if (unlikely(a->cls != float_class_normal)) {
+ switch (a->cls) {
+ case float_class_snan:
+ case float_class_qnan:
+ parts_return_nan(a, status);
+ return;
+ case float_class_zero:
+ return;
+ case float_class_inf:
+ if (unlikely(a->sign)) {
+ goto d_nan;
+ }
+ return;
+ default:
+ g_assert_not_reached();
+ }
+ }
+
+ if (unlikely(a->sign)) {
+ goto d_nan;
+ }
+
+ /*
+ * Argument reduction.
+ * x = 4^e frac; with integer e, and frac in [1, 4)
+ * m = frac fixed point at bit 62, since we're in base 4.
+ * If base-2 exponent is odd, exchange that for multiply by 2,
+ * which results in no shift.
+ */
+ exp_odd = a->exp & 1;
+ index = extract64(a->frac_hi, 57, 6) | (!exp_odd << 6);
+ if (!exp_odd) {
+ frac_shr(a, 1);
+ }
+
+ /*
+ * Approximate r ~= 1/sqrt(m) and s ~= sqrt(m) when m in [1, 4).
+ *
+ * Initial estimate:
+ * 7-bit lookup table (1-bit exponent and 6-bit significand).
+ *
+ * The relative error (e = r0*sqrt(m)-1) of a linear estimate
+ * (r0 = a*m + b) is |e| < 0.085955 ~ 0x1.6p-4 at best;
+ * a table lookup is faster and needs one less iteration.
+ * The 7-bit table gives |e| < 0x1.fdp-9.
+ *
+ * A Newton-Raphson iteration for r is
+ * s = m*r
+ * d = s*r
+ * u = 3 - d
+ * r = r*u/2
+ *
+ * Fixed point representations:
+ * m, s, d, u, three are all 2.30; r is 0.32
+ */
+ m64 = a->frac_hi;
+ m32 = m64 >> 32;
+
+ r32 = rsqrt_tab[index] << 16;
+ /* |r*sqrt(m) - 1| < 0x1.FDp-9 */
+
+ s32 = ((uint64_t)m32 * r32) >> 32;
+ d32 = ((uint64_t)s32 * r32) >> 32;
+ u32 = three32 - d32;
+
+ if (N == 64) {
+ /* float64 or smaller */
+
+ r32 = ((uint64_t)r32 * u32) >> 31;
+ /* |r*sqrt(m) - 1| < 0x1.7Bp-16 */
+
+ s32 = ((uint64_t)m32 * r32) >> 32;
+ d32 = ((uint64_t)s32 * r32) >> 32;
+ u32 = three32 - d32;
+
+ if (fmt->frac_size <= 23) {
+ /* float32 or smaller */
+
+ s32 = ((uint64_t)s32 * u32) >> 32; /* 3.29 */
+ s32 = (s32 - 1) >> 6; /* 9.23 */
+ /* s < sqrt(m) < s + 0x1.08p-23 */
+
+ /* compute nearest rounded result to 2.23 bits */
+ uint32_t d0 = (m32 << 16) - s32 * s32;
+ uint32_t d1 = s32 - d0;
+ uint32_t d2 = d1 + s32 + 1;
+ s32 += d1 >> 31;
+ a->frac_hi = (uint64_t)s32 << (64 - 25);
+
+ /* increment or decrement for inexact */
+ if (d2 != 0) {
+ a->frac_hi += ((int32_t)(d1 ^ d2) < 0 ? -1 : 1);
+ }
+ goto done;
+ }
+
+ /* float64 */
+
+ r64 = (uint64_t)r32 * u32 * 2;
+ /* |r*sqrt(m) - 1| < 0x1.37-p29; convert to 64-bit arithmetic */
+ mul64To128(m64, r64, &s64, &discard);
+ mul64To128(s64, r64, &d64, &discard);
+ u64 = three64 - d64;
+
+ mul64To128(s64, u64, &s64, &discard); /* 3.61 */
+ s64 = (s64 - 2) >> 9; /* 12.52 */
+
+ /* Compute nearest rounded result */
+ uint64_t d0 = (m64 << 42) - s64 * s64;
+ uint64_t d1 = s64 - d0;
+ uint64_t d2 = d1 + s64 + 1;
+ s64 += d1 >> 63;
+ a->frac_hi = s64 << (64 - 54);
+
+ /* increment or decrement for inexact */
+ if (d2 != 0) {
+ a->frac_hi += ((int64_t)(d1 ^ d2) < 0 ? -1 : 1);
+ }
+ goto done;
+ }
+
+ r64 = (uint64_t)r32 * u32 * 2;
+ /* |r*sqrt(m) - 1| < 0x1.7Bp-16; convert to 64-bit arithmetic */
+
+ mul64To128(m64, r64, &s64, &discard);
+ mul64To128(s64, r64, &d64, &discard);
+ u64 = three64 - d64;
+ mul64To128(u64, r64, &r64, &discard);
+ r64 <<= 1;
+ /* |r*sqrt(m) - 1| < 0x1.a5p-31 */
+
+ mul64To128(m64, r64, &s64, &discard);
+ mul64To128(s64, r64, &d64, &discard);
+ u64 = three64 - d64;
+ mul64To128(u64, r64, &rh, &rl);
+ add128(rh, rl, rh, rl, &rh, &rl);
+ /* |r*sqrt(m) - 1| < 0x1.c001p-59; change to 128-bit arithmetic */
+
+ mul128To256(a->frac_hi, a->frac_lo, rh, rl, &sh, &sl, &discard, &discard);
+ mul128To256(sh, sl, rh, rl, &dh, &dl, &discard, &discard);
+ sub128(three64, 0, dh, dl, &uh, &ul);
+ mul128To256(uh, ul, sh, sl, &sh, &sl, &discard, &discard); /* 3.125 */
+ /* -0x1p-116 < s - sqrt(m) < 0x3.8001p-125 */
+
+ sub128(sh, sl, 0, 4, &sh, &sl);
+ shift128Right(sh, sl, 13, &sh, &sl); /* 16.112 */
+ /* s < sqrt(m) < s + 1ulp */
+
+ /* Compute nearest rounded result */
+ mul64To128(sl, sl, &d0h, &d0l);
+ d0h += 2 * sh * sl;
+ sub128(a->frac_lo << 34, 0, d0h, d0l, &d0h, &d0l);
+ sub128(sh, sl, d0h, d0l, &d1h, &d1l);
+ add128(sh, sl, 0, 1, &d2h, &d2l);
+ add128(d2h, d2l, d1h, d1l, &d2h, &d2l);
+ add128(sh, sl, 0, d1h >> 63, &sh, &sl);
+ shift128Left(sh, sl, 128 - 114, &sh, &sl);
+
+ /* increment or decrement for inexact */
+ if (d2h | d2l) {
+ if ((int64_t)(d1h ^ d2h) < 0) {
+ sub128(sh, sl, 0, 1, &sh, &sl);
+ } else {
+ add128(sh, sl, 0, 1, &sh, &sl);
+ }
+ }
+ a->frac_lo = sl;
+ a->frac_hi = sh;
+
+ done:
+ /* Convert back from base 4 to base 2. */
+ a->exp >>= 1;
+ if (!(a->frac_hi & DECOMPOSED_IMPLICIT_BIT)) {
+ frac_add(a, a, a);
+ } else {
+ a->exp += 1;
+ }
+ return;
+
+ d_nan:
+ float_raise(float_flag_invalid | float_flag_invalid_sqrt, status);
+ parts_default_nan(a, status);
+}
+
+/*
+ * Rounds the floating-point value `a' to an integer, and returns the
+ * result as a floating-point value. The operation is performed
+ * according to the IEC/IEEE Standard for Binary Floating-Point
+ * Arithmetic.
+ *
+ * parts_round_to_int_normal is an internal helper function for
+ * normal numbers only, returning true for inexact but not directly
+ * raising float_flag_inexact.
+ */
+static bool partsN(round_to_int_normal)(FloatPartsN *a, FloatRoundMode rmode,
+ int scale, int frac_size)
+{
+ uint64_t frac_lsb, frac_lsbm1, rnd_even_mask, rnd_mask, inc;
+ int shift_adj;
+
+ scale = MIN(MAX(scale, -0x10000), 0x10000);
+ a->exp += scale;
+
+ if (a->exp < 0) {
+ bool one;
+
+ /* All fractional */
+ switch (rmode) {
+ case float_round_nearest_even:
+ one = false;
+ if (a->exp == -1) {
+ FloatPartsN tmp;
+ /* Shift left one, discarding DECOMPOSED_IMPLICIT_BIT */
+ frac_add(&tmp, a, a);
+ /* Anything remaining means frac > 0.5. */
+ one = !frac_eqz(&tmp);
+ }
+ break;
+ case float_round_ties_away:
+ one = a->exp == -1;
+ break;
+ case float_round_to_zero:
+ one = false;
+ break;
+ case float_round_up:
+ one = !a->sign;
+ break;
+ case float_round_down:
+ one = a->sign;
+ break;
+ case float_round_to_odd:
+ one = true;
+ break;
+ default:
+ g_assert_not_reached();
+ }
+
+ frac_clear(a);
+ a->exp = 0;
+ if (one) {
+ a->frac_hi = DECOMPOSED_IMPLICIT_BIT;
+ } else {
+ a->cls = float_class_zero;
+ }
+ return true;
+ }
+
+ if (a->exp >= frac_size) {
+ /* All integral */
+ return false;
+ }
+
+ if (N > 64 && a->exp < N - 64) {
+ /*
+ * Rounding is not in the low word -- shift lsb to bit 2,
+ * which leaves room for sticky and rounding bit.
+ */
+ shift_adj = (N - 1) - (a->exp + 2);
+ frac_shrjam(a, shift_adj);
+ frac_lsb = 1 << 2;
+ } else {
+ shift_adj = 0;
+ frac_lsb = DECOMPOSED_IMPLICIT_BIT >> (a->exp & 63);
+ }
+
+ frac_lsbm1 = frac_lsb >> 1;
+ rnd_mask = frac_lsb - 1;
+ rnd_even_mask = rnd_mask | frac_lsb;
+
+ if (!(a->frac_lo & rnd_mask)) {
+ /* Fractional bits already clear, undo the shift above. */
+ frac_shl(a, shift_adj);
+ return false;
+ }
+
+ switch (rmode) {
+ case float_round_nearest_even:
+ inc = ((a->frac_lo & rnd_even_mask) != frac_lsbm1 ? frac_lsbm1 : 0);
+ break;
+ case float_round_ties_away:
+ inc = frac_lsbm1;
+ break;
+ case float_round_to_zero:
+ inc = 0;
+ break;
+ case float_round_up:
+ inc = a->sign ? 0 : rnd_mask;
+ break;
+ case float_round_down:
+ inc = a->sign ? rnd_mask : 0;
+ break;
+ case float_round_to_odd:
+ inc = a->frac_lo & frac_lsb ? 0 : rnd_mask;
+ break;
+ default:
+ g_assert_not_reached();
+ }
+
+ if (shift_adj == 0) {
+ if (frac_addi(a, a, inc)) {
+ frac_shr(a, 1);
+ a->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
+ a->exp++;
+ }
+ a->frac_lo &= ~rnd_mask;
+ } else {
+ frac_addi(a, a, inc);
+ a->frac_lo &= ~rnd_mask;
+ /* Be careful shifting back, not to overflow */
+ frac_shl(a, shift_adj - 1);
+ if (a->frac_hi & DECOMPOSED_IMPLICIT_BIT) {
+ a->exp++;
+ } else {
+ frac_add(a, a, a);
+ }
+ }
+ return true;
+}
+
+static void partsN(round_to_int)(FloatPartsN *a, FloatRoundMode rmode,
+ int scale, float_status *s,
+ const FloatFmt *fmt)
+{
+ switch (a->cls) {
+ case float_class_qnan:
+ case float_class_snan:
+ parts_return_nan(a, s);
+ break;
+ case float_class_zero:
+ case float_class_inf:
+ break;
+ case float_class_normal:
+ if (parts_round_to_int_normal(a, rmode, scale, fmt->frac_size)) {
+ float_raise(float_flag_inexact, s);
+ }
+ break;
+ default:
+ g_assert_not_reached();
+ }
+}
+
+/*
+ * Returns the result of converting the floating-point value `a' to
+ * the two's complement integer format. The conversion is performed
+ * according to the IEC/IEEE Standard for Binary Floating-Point
+ * Arithmetic---which means in particular that the conversion is
+ * rounded according to the current rounding mode. If `a' is a NaN,
+ * the largest positive integer is returned. Otherwise, if the
+ * conversion overflows, the largest integer with the same sign as `a'
+ * is returned.
+ */
+static int64_t partsN(float_to_sint)(FloatPartsN *p, FloatRoundMode rmode,
+ int scale, int64_t min, int64_t max,
+ float_status *s)
+{
+ int flags = 0;
+ uint64_t r;
+
+ switch (p->cls) {
+ case float_class_snan:
+ flags |= float_flag_invalid_snan;
+ /* fall through */
+ case float_class_qnan:
+ flags |= float_flag_invalid;
+ r = max;
+ break;
+
+ case float_class_inf:
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = p->sign ? min : max;
+ break;
+
+ case float_class_zero:
+ return 0;
+
+ case float_class_normal:
+ /* TODO: N - 2 is frac_size for rounding; could use input fmt. */
+ if (parts_round_to_int_normal(p, rmode, scale, N - 2)) {
+ flags = float_flag_inexact;
+ }
+
+ if (p->exp <= DECOMPOSED_BINARY_POINT) {
+ r = p->frac_hi >> (DECOMPOSED_BINARY_POINT - p->exp);
+ } else {
+ r = UINT64_MAX;
+ }
+ if (p->sign) {
+ if (r <= -(uint64_t)min) {
+ r = -r;
+ } else {
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = min;
+ }
+ } else if (r > max) {
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = max;
+ }
+ break;
+
+ default:
+ g_assert_not_reached();
+ }
+
+ float_raise(flags, s);
+ return r;
+}
+
+/*
+ * Returns the result of converting the floating-point value `a' to
+ * the unsigned integer format. The conversion is performed according
+ * to the IEC/IEEE Standard for Binary Floating-Point
+ * Arithmetic---which means in particular that the conversion is
+ * rounded according to the current rounding mode. If `a' is a NaN,
+ * the largest unsigned integer is returned. Otherwise, if the
+ * conversion overflows, the largest unsigned integer is returned. If
+ * the 'a' is negative, the result is rounded and zero is returned;
+ * values that do not round to zero will raise the inexact exception
+ * flag.
+ */
+static uint64_t partsN(float_to_uint)(FloatPartsN *p, FloatRoundMode rmode,
+ int scale, uint64_t max, float_status *s)
+{
+ int flags = 0;
+ uint64_t r;
+
+ switch (p->cls) {
+ case float_class_snan:
+ flags |= float_flag_invalid_snan;
+ /* fall through */
+ case float_class_qnan:
+ flags |= float_flag_invalid;
+ r = max;
+ break;
+
+ case float_class_inf:
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = p->sign ? 0 : max;
+ break;
+
+ case float_class_zero:
+ return 0;
+
+ case float_class_normal:
+ /* TODO: N - 2 is frac_size for rounding; could use input fmt. */
+ if (parts_round_to_int_normal(p, rmode, scale, N - 2)) {
+ flags = float_flag_inexact;
+ if (p->cls == float_class_zero) {
+ r = 0;
+ break;
+ }
+ }
+
+ if (p->sign) {
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = 0;
+ } else if (p->exp > DECOMPOSED_BINARY_POINT) {
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = max;
+ } else {
+ r = p->frac_hi >> (DECOMPOSED_BINARY_POINT - p->exp);
+ if (r > max) {
+ flags = float_flag_invalid | float_flag_invalid_cvti;
+ r = max;
+ }
+ }
+ break;
+
+ default:
+ g_assert_not_reached();
+ }
+
+ float_raise(flags, s);
+ return r;
+}
+
+/*
+ * Integer to float conversions
+ *
+ * Returns the result of converting the two's complement integer `a'
+ * to the floating-point format. The conversion is performed according
+ * to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ */
+static void partsN(sint_to_float)(FloatPartsN *p, int64_t a,
+ int scale, float_status *s)
+{
+ uint64_t f = a;
+ int shift;
+
+ memset(p, 0, sizeof(*p));
+
+ if (a == 0) {
+ p->cls = float_class_zero;
+ return;
+ }
+
+ p->cls = float_class_normal;
+ if (a < 0) {
+ f = -f;
+ p->sign = true;
+ }
+ shift = clz64(f);
+ scale = MIN(MAX(scale, -0x10000), 0x10000);
+
+ p->exp = DECOMPOSED_BINARY_POINT - shift + scale;
+ p->frac_hi = f << shift;
+}
+
+/*
+ * Unsigned Integer to float conversions
+ *
+ * Returns the result of converting the unsigned integer `a' to the
+ * floating-point format. The conversion is performed according to the
+ * IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+ */
+static void partsN(uint_to_float)(FloatPartsN *p, uint64_t a,
+ int scale, float_status *status)
+{
+ memset(p, 0, sizeof(*p));
+
+ if (a == 0) {
+ p->cls = float_class_zero;
+ } else {
+ int shift = clz64(a);
+ scale = MIN(MAX(scale, -0x10000), 0x10000);
+ p->cls = float_class_normal;
+ p->exp = DECOMPOSED_BINARY_POINT - shift + scale;
+ p->frac_hi = a << shift;
+ }
+}
+
+/*
+ * Float min/max.
+ */
+static FloatPartsN *partsN(minmax)(FloatPartsN *a, FloatPartsN *b,
+ float_status *s, int flags)
+{
+ int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+ int a_exp, b_exp, cmp;
+
+ if (unlikely(ab_mask & float_cmask_anynan)) {
+ /*
+ * For minNum/maxNum (IEEE 754-2008)
+ * or minimumNumber/maximumNumber (IEEE 754-2019),
+ * if one operand is a QNaN, and the other
+ * operand is numerical, then return numerical argument.
+ */
+ if ((flags & (minmax_isnum | minmax_isnumber))
+ && !(ab_mask & float_cmask_snan)
+ && (ab_mask & ~float_cmask_qnan)) {
+ return is_nan(a->cls) ? b : a;
+ }
+
+ /*
+ * In IEEE 754-2019, minNum, maxNum, minNumMag and maxNumMag
+ * are removed and replaced with minimum, minimumNumber, maximum
+ * and maximumNumber.
+ * minimumNumber/maximumNumber behavior for SNaN is changed to:
+ * If both operands are NaNs, a QNaN is returned.
+ * If either operand is a SNaN,
+ * an invalid operation exception is signaled,
+ * but unless both operands are NaNs,
+ * the SNaN is otherwise ignored and not converted to a QNaN.
+ */
+ if ((flags & minmax_isnumber)
+ && (ab_mask & float_cmask_snan)
+ && (ab_mask & ~float_cmask_anynan)) {
+ float_raise(float_flag_invalid, s);
+ return is_nan(a->cls) ? b : a;
+ }
+
+ return parts_pick_nan(a, b, s);
+ }
+
+ a_exp = a->exp;
+ b_exp = b->exp;
+
+ if (unlikely(ab_mask != float_cmask_normal)) {
+ switch (a->cls) {
+ case float_class_normal:
+ break;
+ case float_class_inf:
+ a_exp = INT16_MAX;
+ break;
+ case float_class_zero:
+ a_exp = INT16_MIN;
+ break;
+ default:
+ g_assert_not_reached();
+ break;
+ }
+ switch (b->cls) {
+ case float_class_normal:
+ break;
+ case float_class_inf:
+ b_exp = INT16_MAX;
+ break;
+ case float_class_zero:
+ b_exp = INT16_MIN;
+ break;
+ default:
+ g_assert_not_reached();
+ break;
+ }
+ }
+
+ /* Compare magnitudes. */
+ cmp = a_exp - b_exp;
+ if (cmp == 0) {
+ cmp = frac_cmp(a, b);
+ }
+
+ /*
+ * Take the sign into account.
+ * For ismag, only do this if the magnitudes are equal.
+ */
+ if (!(flags & minmax_ismag) || cmp == 0) {
+ if (a->sign != b->sign) {
+ /* For differing signs, the negative operand is less. */
+ cmp = a->sign ? -1 : 1;
+ } else if (a->sign) {
+ /* For two negative operands, invert the magnitude comparison. */
+ cmp = -cmp;
+ }
+ }
+
+ if (flags & minmax_ismin) {
+ cmp = -cmp;
+ }
+ return cmp < 0 ? b : a;
+}
+
+/*
+ * Floating point compare
+ */
+static FloatRelation partsN(compare)(FloatPartsN *a, FloatPartsN *b,
+ float_status *s, bool is_quiet)
+{
+ int ab_mask = float_cmask(a->cls) | float_cmask(b->cls);
+
+ if (likely(ab_mask == float_cmask_normal)) {
+ FloatRelation cmp;
+
+ if (a->sign != b->sign) {
+ goto a_sign;
+ }
+ if (a->exp == b->exp) {
+ cmp = frac_cmp(a, b);
+ } else if (a->exp < b->exp) {
+ cmp = float_relation_less;
+ } else {
+ cmp = float_relation_greater;
+ }
+ if (a->sign) {
+ cmp = -cmp;
+ }
+ return cmp;
+ }
+
+ if (unlikely(ab_mask & float_cmask_anynan)) {
+ if (ab_mask & float_cmask_snan) {
+ float_raise(float_flag_invalid | float_flag_invalid_snan, s);
+ } else if (!is_quiet) {
+ float_raise(float_flag_invalid, s);
+ }
+ return float_relation_unordered;
+ }
+
+ if (ab_mask & float_cmask_zero) {
+ if (ab_mask == float_cmask_zero) {
+ return float_relation_equal;
+ } else if (a->cls == float_class_zero) {
+ goto b_sign;
+ } else {
+ goto a_sign;
+ }
+ }
+
+ if (ab_mask == float_cmask_inf) {
+ if (a->sign == b->sign) {
+ return float_relation_equal;
+ }
+ } else if (b->cls == float_class_inf) {
+ goto b_sign;
+ } else {
+ g_assert(a->cls == float_class_inf);
+ }
+
+ a_sign:
+ return a->sign ? float_relation_less : float_relation_greater;
+ b_sign:
+ return b->sign ? float_relation_greater : float_relation_less;
+}
+
+/*
+ * Multiply A by 2 raised to the power N.
+ */
+static void partsN(scalbn)(FloatPartsN *a, int n, float_status *s)
+{
+ switch (a->cls) {
+ case float_class_snan:
+ case float_class_qnan:
+ parts_return_nan(a, s);
+ break;
+ case float_class_zero:
+ case float_class_inf:
+ break;
+ case float_class_normal:
+ a->exp += MIN(MAX(n, -0x10000), 0x10000);
+ break;
+ default:
+ g_assert_not_reached();
+ }
+}
+
+/*
+ * Return log2(A)
+ */
+static void partsN(log2)(FloatPartsN *a, float_status *s, const FloatFmt *fmt)
+{
+ uint64_t a0, a1, r, t, ign;
+ FloatPartsN f;
+ int i, n, a_exp, f_exp;
+
+ if (unlikely(a->cls != float_class_normal)) {
+ switch (a->cls) {
+ case float_class_snan:
+ case float_class_qnan:
+ parts_return_nan(a, s);
+ return;
+ case float_class_zero:
+ float_raise(float_flag_divbyzero, s);
+ /* log2(0) = -inf */
+ a->cls = float_class_inf;
+ a->sign = 1;
+ return;
+ case float_class_inf:
+ if (unlikely(a->sign)) {
+ goto d_nan;
+ }
+ return;
+ default:
+ break;
+ }
+ g_assert_not_reached();
+ }
+ if (unlikely(a->sign)) {
+ goto d_nan;
+ }
+
+ /* TODO: This algorithm looses bits too quickly for float128. */
+ g_assert(N == 64);
+
+ a_exp = a->exp;
+ f_exp = -1;
+
+ r = 0;
+ t = DECOMPOSED_IMPLICIT_BIT;
+ a0 = a->frac_hi;
+ a1 = 0;
+
+ n = fmt->frac_size + 2;
+ if (unlikely(a_exp == -1)) {
+ /*
+ * When a_exp == -1, we're computing the log2 of a value [0.5,1.0).
+ * When the value is very close to 1.0, there are lots of 1's in
+ * the msb parts of the fraction. At the end, when we subtract
+ * this value from -1.0, we can see a catastrophic loss of precision,
+ * as 0x800..000 - 0x7ff..ffx becomes 0x000..00y, leaving only the
+ * bits of y in the final result. To minimize this, compute as many
+ * digits as we can.
+ * ??? This case needs another algorithm to avoid this.
+ */
+ n = fmt->frac_size * 2 + 2;
+ /* Don't compute a value overlapping the sticky bit */
+ n = MIN(n, 62);
+ }
+
+ for (i = 0; i < n; i++) {
+ if (a1) {
+ mul128To256(a0, a1, a0, a1, &a0, &a1, &ign, &ign);
+ } else if (a0 & 0xffffffffull) {
+ mul64To128(a0, a0, &a0, &a1);
+ } else if (a0 & ~DECOMPOSED_IMPLICIT_BIT) {
+ a0 >>= 32;
+ a0 *= a0;
+ } else {
+ goto exact;
+ }
+
+ if (a0 & DECOMPOSED_IMPLICIT_BIT) {
+ if (unlikely(a_exp == 0 && r == 0)) {
+ /*
+ * When a_exp == 0, we're computing the log2 of a value
+ * [1.0,2.0). When the value is very close to 1.0, there
+ * are lots of 0's in the msb parts of the fraction.
+ * We need to compute more digits to produce a correct
+ * result -- restart at the top of the fraction.
+ * ??? This is likely to lose precision quickly, as for
+ * float128; we may need another method.
+ */
+ f_exp -= i;
+ t = r = DECOMPOSED_IMPLICIT_BIT;
+ i = 0;
+ } else {
+ r |= t;
+ }
+ } else {
+ add128(a0, a1, a0, a1, &a0, &a1);
+ }
+ t >>= 1;
+ }
+
+ /* Set sticky for inexact. */
+ r |= (a1 || a0 & ~DECOMPOSED_IMPLICIT_BIT);
+
+ exact:
+ parts_sint_to_float(a, a_exp, 0, s);
+ if (r == 0) {
+ return;
+ }
+
+ memset(&f, 0, sizeof(f));
+ f.cls = float_class_normal;
+ f.frac_hi = r;
+ f.exp = f_exp - frac_normalize(&f);
+
+ if (a_exp < 0) {
+ parts_sub_normal(a, &f);
+ } else if (a_exp > 0) {
+ parts_add_normal(a, &f);
+ } else {
+ *a = f;
+ }
+ return;
+
+ d_nan:
+ float_raise(float_flag_invalid, s);
+ parts_default_nan(a, s);
+}
projects / mirror_qemu.git / blobdiff