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softfp_template.h
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softfp_template.h
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/*
* SoftFP Library
*
* Copyright (c) 2016 Fabrice Bellard
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#if F_SIZE == 32
#define F_UINT uint32_t
#define F_ULONG uint64_t
#define MANT_SIZE 23
#define EXP_SIZE 8
#elif F_SIZE == 64
#define F_UHALF uint32_t
#define F_UINT uint64_t
#ifdef HAVE_INT128
#define F_ULONG uint128_t
#endif
#define MANT_SIZE 52
#define EXP_SIZE 11
#elif F_SIZE == 128
#define F_UHALF uint64_t
#define F_UINT uint128_t
#define MANT_SIZE 112
#define EXP_SIZE 15
#else
#error unsupported F_SIZE
#endif
#define EXP_MASK ((1 << EXP_SIZE) - 1)
#define MANT_MASK (((F_UINT)1 << MANT_SIZE) - 1)
#define SIGN_MASK ((F_UINT)1 << (F_SIZE - 1))
#define IMANT_SIZE (F_SIZE - 2) /* internal mantissa size */
#define RND_SIZE (IMANT_SIZE - MANT_SIZE)
#define QNAN_MASK ((F_UINT)1 << (MANT_SIZE - 1))
/* quiet NaN */
#define F_QNAN glue(F_QNAN, F_SIZE)
#define clz glue(clz, F_SIZE)
#define pack_sf glue(pack_sf, F_SIZE)
#define unpack_sf glue(unpack_sf, F_SIZE)
#define rshift_rnd glue(rshift_rnd, F_SIZE)
#define round_pack_sf glue(roundpack_sf, F_SIZE)
#define normalize_sf glue(normalize_sf, F_SIZE)
#define normalize2_sf glue(normalize2_sf, F_SIZE)
#define issignan_sf glue(issignan_sf, F_SIZE)
#define isnan_sf glue(isnan_sf, F_SIZE)
#define add_sf glue(add_sf, F_SIZE)
#define mul_sf glue(mul_sf, F_SIZE)
#define fma_sf glue(fma_sf, F_SIZE)
#define div_sf glue(div_sf, F_SIZE)
#define sqrt_sf glue(sqrt_sf, F_SIZE)
#define normalize_subnormal_sf glue(normalize_subnormal_sf, F_SIZE)
#define divrem_u glue(divrem_u, F_SIZE)
#define sqrtrem_u glue(sqrtrem_u, F_SIZE)
#define mul_u glue(mul_u, F_SIZE)
#define cvt_sf32_sf glue(cvt_sf32_sf, F_SIZE)
#define cvt_sf64_sf glue(cvt_sf64_sf, F_SIZE)
static const F_UINT F_QNAN = (((F_UINT)EXP_MASK << MANT_SIZE) | ((F_UINT)1 << (MANT_SIZE - 1)));
static inline F_UINT pack_sf(uint32_t a_sign, uint32_t a_exp, F_UINT a_mant)
{
return ((F_UINT)a_sign << (F_SIZE - 1)) |
((F_UINT)a_exp << MANT_SIZE) |
(a_mant & MANT_MASK);
}
static inline F_UINT unpack_sf(uint32_t *pa_sign, int32_t *pa_exp,
F_UINT a)
{
*pa_sign = a >> (F_SIZE - 1);
*pa_exp = (a >> MANT_SIZE) & EXP_MASK;
return a & MANT_MASK;
}
static F_UINT rshift_rnd(F_UINT a, int d)
{
F_UINT mask;
if (d != 0) {
if (d >= F_SIZE) {
a = (a != 0);
} else {
mask = ((F_UINT)1 << d) - 1;
a = (a >> d) | ((a & mask) != 0);
}
}
return a;
}
/* a_mant is considered to have its MSB at F_SIZE - 2 bits */
static F_UINT round_pack_sf(uint32_t a_sign, int a_exp, F_UINT a_mant,
RoundingModeEnum rm, uint32_t *pfflags)
{
int diff;
uint32_t addend, rnd_bits;
switch(rm) {
case RM_RNE:
case RM_RMM:
addend = (1 << (RND_SIZE - 1));
break;
case RM_RTZ:
addend = 0;
break;
default:
case RM_RDN:
case RM_RUP:
// printf("s=%d rm=%d m=%x\n", a_sign, rm, a_mant);
if (a_sign ^ (rm & 1))
addend = (1 << RND_SIZE) - 1;
else
addend = 0;
break;
}
/* potentially subnormal */
if (a_exp <= 0) {
BOOL is_subnormal;
/* Note: we set the underflow flag if the rounded result
is subnormal and inexact */
is_subnormal = (a_exp < 0 ||
(a_mant + addend) < ((F_UINT)1 << (F_SIZE - 1)));
diff = 1 - a_exp;
a_mant = rshift_rnd(a_mant, diff);
rnd_bits = a_mant & ((1 << RND_SIZE ) - 1);
if (is_subnormal && rnd_bits != 0) {
*pfflags |= FFLAG_UNDERFLOW;
}
a_exp = 1;
} else {
rnd_bits = a_mant & ((1 << RND_SIZE ) - 1);
}
if (rnd_bits != 0)
*pfflags |= FFLAG_INEXACT;
a_mant = (a_mant + addend) >> RND_SIZE;
/* half way: select even result */
if (rm == RM_RNE && rnd_bits == (1 << (RND_SIZE - 1)))
a_mant &= ~1;
/* Note the rounding adds at least 1, so this is the maximum
value */
a_exp += a_mant >> (MANT_SIZE + 1);
if (a_mant <= MANT_MASK) {
/* denormalized or zero */
a_exp = 0;
} else if (a_exp >= EXP_MASK) {
/* overflow */
if (addend == 0) {
a_exp = EXP_MASK - 1;
a_mant = MANT_MASK;
} else {
/* infinity */
a_exp = EXP_MASK;
a_mant = 0;
}
*pfflags |= FFLAG_OVERFLOW | FFLAG_INEXACT;
}
return pack_sf(a_sign, a_exp, a_mant);
}
/* a_mant is considered to have at most F_SIZE - 1 bits */
static F_UINT normalize_sf(uint32_t a_sign, int a_exp, F_UINT a_mant,
RoundingModeEnum rm, uint32_t *pfflags)
{
int shift;
shift = clz(a_mant) - (F_SIZE - 1 - IMANT_SIZE);
assert(shift >= 0);
a_exp -= shift;
a_mant <<= shift;
return round_pack_sf(a_sign, a_exp, a_mant, rm, pfflags);
}
/* same as normalize_sf() but with a double word mantissa. a_mant1 is
considered to have at most F_SIZE - 1 bits */
static F_UINT normalize2_sf(uint32_t a_sign, int a_exp, F_UINT a_mant1, F_UINT a_mant0,
RoundingModeEnum rm, uint32_t *pfflags)
{
int l, shift;
if (a_mant1 == 0) {
l = F_SIZE + clz(a_mant0);
} else {
l = clz(a_mant1);
}
shift = l - (F_SIZE - 1 - IMANT_SIZE);
assert(shift >= 0);
a_exp -= shift;
if (shift == 0) {
a_mant1 |= (a_mant0 != 0);
} else if (shift < F_SIZE) {
a_mant1 = (a_mant1 << shift) | (a_mant0 >> (F_SIZE - shift));
a_mant0 <<= shift;
a_mant1 |= (a_mant0 != 0);
} else {
a_mant1 = a_mant0 << (shift - F_SIZE);
}
return round_pack_sf(a_sign, a_exp, a_mant1, rm, pfflags);
}
BOOL issignan_sf(F_UINT a)
{
uint32_t a_exp1;
F_UINT a_mant;
a_exp1 = (a >> (MANT_SIZE - 1)) & ((1 << (EXP_SIZE + 1)) - 1);
a_mant = a & MANT_MASK;
return (a_exp1 == (2 * EXP_MASK) && a_mant != 0);
}
BOOL isnan_sf(F_UINT a)
{
uint32_t a_exp;
F_UINT a_mant;
a_exp = (a >> MANT_SIZE) & EXP_MASK;
a_mant = a & MANT_MASK;
return (a_exp == EXP_MASK && a_mant != 0);
}
F_UINT add_sf(F_UINT a, F_UINT b, RoundingModeEnum rm,
uint32_t *pfflags)
{
uint32_t a_sign, b_sign, a_exp, b_exp;
F_UINT tmp, a_mant, b_mant;
/* swap so that abs(a) >= abs(b) */
if ((a & ~SIGN_MASK) < (b & ~SIGN_MASK)) {
tmp = a;
a = b;
b = tmp;
}
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
a_exp = (a >> MANT_SIZE) & EXP_MASK;
b_exp = (b >> MANT_SIZE) & EXP_MASK;
a_mant = (a & MANT_MASK) << 3;
b_mant = (b & MANT_MASK) << 3;
if (unlikely(a_exp == EXP_MASK)) {
if (a_mant != 0) {
/* NaN result */
if (!(a_mant & (QNAN_MASK << 3)) || issignan_sf(b))
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else if (b_exp == EXP_MASK && a_sign != b_sign) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else {
/* infinity */
return a;
}
}
if (a_exp == 0) {
a_exp = 1;
} else {
a_mant |= (F_UINT)1 << (MANT_SIZE + 3);
}
if (b_exp == 0) {
b_exp = 1;
} else {
b_mant |= (F_UINT)1 << (MANT_SIZE + 3);
}
b_mant = rshift_rnd(b_mant, a_exp - b_exp);
if (a_sign == b_sign) {
/* same signs : add the absolute values */
a_mant += b_mant;
} else {
/* different signs : subtract the absolute values */
a_mant -= b_mant;
if (a_mant == 0) {
/* zero result : the sign needs a specific handling */
a_sign = (rm == RM_RDN);
}
}
a_exp += (RND_SIZE - 3);
return normalize_sf(a_sign, a_exp, a_mant, rm, pfflags);
}
F_UINT glue(sub_sf, F_SIZE)(F_UINT a, F_UINT b, RoundingModeEnum rm,
uint32_t *pfflags)
{
return add_sf(a, b ^ SIGN_MASK, rm, pfflags);
}
static inline F_UINT normalize_subnormal_sf(int32_t *pa_exp, F_UINT a_mant)
{
int shift;
shift = MANT_SIZE - ((F_SIZE - 1 - clz(a_mant)));
*pa_exp = 1 - shift;
return a_mant << shift;
}
#ifdef F_ULONG
static F_UINT mul_u(F_UINT *plow, F_UINT a, F_UINT b)
{
F_ULONG r;
r = (F_ULONG)a * (F_ULONG)b;
*plow = r;
return r >> F_SIZE;
}
#else
#define FH_SIZE (F_SIZE / 2)
static F_UINT mul_u(F_UINT *plow, F_UINT a, F_UINT b)
{
F_UHALF a0, a1, b0, b1, r0, r1, r2, r3;
F_UINT r00, r01, r10, r11, c;
a0 = a;
a1 = a >> FH_SIZE;
b0 = b;
b1 = b >> FH_SIZE;
r00 = (F_UINT)a0 * (F_UINT)b0;
r01 = (F_UINT)a0 * (F_UINT)b1;
r10 = (F_UINT)a1 * (F_UINT)b0;
r11 = (F_UINT)a1 * (F_UINT)b1;
r0 = r00;
c = (r00 >> FH_SIZE) + (F_UHALF)r01 + (F_UHALF)r10;
r1 = c;
c = (c >> FH_SIZE) + (r01 >> FH_SIZE) + (r10 >> FH_SIZE) + (F_UHALF)r11;
r2 = c;
r3 = (c >> FH_SIZE) + (r11 >> FH_SIZE);
*plow = ((F_UINT)r1 << FH_SIZE) | r0;
return ((F_UINT)r3 << FH_SIZE) | r2;
}
#undef FH_SIZE
#endif
F_UINT mul_sf(F_UINT a, F_UINT b, RoundingModeEnum rm,
uint32_t *pfflags)
{
uint32_t a_sign, b_sign, r_sign;
int32_t a_exp, b_exp, r_exp;
F_UINT a_mant, b_mant, r_mant, r_mant_low;
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
r_sign = a_sign ^ b_sign;
a_exp = (a >> MANT_SIZE) & EXP_MASK;
b_exp = (b >> MANT_SIZE) & EXP_MASK;
a_mant = a & MANT_MASK;
b_mant = b & MANT_MASK;
if (a_exp == EXP_MASK || b_exp == EXP_MASK) {
if (isnan_sf(a) || isnan_sf(b)) {
if (issignan_sf(a) || issignan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN;
} else {
/* infinity */
if ((a_exp == EXP_MASK && (b_exp == 0 && b_mant == 0)) ||
(b_exp == EXP_MASK && (a_exp == 0 && a_mant == 0))) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else {
return pack_sf(r_sign, EXP_MASK, 0);
}
}
}
if (a_exp == 0) {
if (a_mant == 0)
return pack_sf(r_sign, 0, 0); /* zero */
a_mant = normalize_subnormal_sf(&a_exp, a_mant);
} else {
a_mant |= (F_UINT)1 << MANT_SIZE;
}
if (b_exp == 0) {
if (b_mant == 0)
return pack_sf(r_sign, 0, 0); /* zero */
b_mant = normalize_subnormal_sf(&b_exp, b_mant);
} else {
b_mant |= (F_UINT)1 << MANT_SIZE;
}
r_exp = a_exp + b_exp - (1 << (EXP_SIZE - 1)) + 2;
r_mant = mul_u(&r_mant_low,a_mant << RND_SIZE, b_mant << (RND_SIZE + 1));
r_mant |= (r_mant_low != 0);
return normalize_sf(r_sign, r_exp, r_mant, rm, pfflags);
}
/* fused multiply and add */
F_UINT fma_sf(F_UINT a, F_UINT b, F_UINT c, RoundingModeEnum rm,
uint32_t *pfflags)
{
uint32_t a_sign, b_sign, c_sign, r_sign;
int32_t a_exp, b_exp, c_exp, r_exp, shift;
F_UINT a_mant, b_mant, c_mant, r_mant1, r_mant0, c_mant1, c_mant0, mask;
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
c_sign = c >> (F_SIZE - 1);
r_sign = a_sign ^ b_sign;
a_exp = (a >> MANT_SIZE) & EXP_MASK;
b_exp = (b >> MANT_SIZE) & EXP_MASK;
c_exp = (c >> MANT_SIZE) & EXP_MASK;
a_mant = a & MANT_MASK;
b_mant = b & MANT_MASK;
c_mant = c & MANT_MASK;
if (a_exp == EXP_MASK || b_exp == EXP_MASK || c_exp == EXP_MASK) {
if (isnan_sf(a) || isnan_sf(b) || isnan_sf(c)) {
if (issignan_sf(a) || issignan_sf(b) || issignan_sf(c)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN;
} else {
/* infinities */
if ((a_exp == EXP_MASK && (b_exp == 0 && b_mant == 0)) ||
(b_exp == EXP_MASK && (a_exp == 0 && a_mant == 0)) ||
((a_exp == EXP_MASK || b_exp == EXP_MASK) &&
(c_exp == EXP_MASK && r_sign != c_sign))) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else if (c_exp == EXP_MASK) {
return pack_sf(c_sign, EXP_MASK, 0);
} else {
return pack_sf(r_sign, EXP_MASK, 0);
}
}
}
if (a_exp == 0) {
if (a_mant == 0)
goto mul_zero;
a_mant = normalize_subnormal_sf(&a_exp, a_mant);
} else {
a_mant |= (F_UINT)1 << MANT_SIZE;
}
if (b_exp == 0) {
if (b_mant == 0) {
mul_zero:
if (c_exp == 0 && c_mant == 0) {
if (c_sign != r_sign)
r_sign = (rm == RM_RDN);
return pack_sf(r_sign, 0, 0);
} else {
return c;
}
}
b_mant = normalize_subnormal_sf(&b_exp, b_mant);
} else {
b_mant |= (F_UINT)1 << MANT_SIZE;
}
/* multiply */
r_exp = a_exp + b_exp - (1 << (EXP_SIZE - 1)) + 3;
r_mant1 = mul_u(&r_mant0, a_mant << RND_SIZE, b_mant << RND_SIZE);
/* normalize to F_SIZE - 3 */
if (r_mant1 < ((F_UINT)1 << (F_SIZE - 3))) {
r_mant1 = (r_mant1 << 1) | (r_mant0 >> (F_SIZE - 1));
r_mant0 <<= 1;
r_exp--;
}
/* add */
if (c_exp == 0) {
if (c_mant == 0) {
/* add zero */
r_mant1 |= (r_mant0 != 0);
return normalize_sf(r_sign, r_exp, r_mant1, rm, pfflags);
}
c_mant = normalize_subnormal_sf(&c_exp, c_mant);
} else {
c_mant |= (F_UINT)1 << MANT_SIZE;
}
c_exp++;
c_mant1 = c_mant << (RND_SIZE - 1);
c_mant0 = 0;
// printf("r_s=%d r_exp=%d r_mant=%08x %08x\n", r_sign, r_exp, (uint32_t)r_mant1, (uint32_t)r_mant0);
// printf("c_s=%d c_exp=%d c_mant=%08x %08x\n", c_sign, c_exp, (uint32_t)c_mant1, (uint32_t)c_mant0);
/* ensure that abs(r) >= abs(c) */
if (!(r_exp > c_exp || (r_exp == c_exp && r_mant1 >= c_mant1))) {
F_UINT tmp;
int32_t c_tmp;
/* swap */
tmp = r_mant1; r_mant1 = c_mant1; c_mant1 = tmp;
tmp = r_mant0; r_mant0 = c_mant0; c_mant0 = tmp;
c_tmp = r_exp; r_exp = c_exp; c_exp = c_tmp;
c_tmp = r_sign; r_sign = c_sign; c_sign = c_tmp;
}
/* right shift c_mant */
shift = r_exp - c_exp;
if (shift >= 2 * F_SIZE) {
c_mant0 = (c_mant0 | c_mant1) != 0;
c_mant1 = 0;
} else if (shift >= F_SIZE + 1) {
c_mant0 = rshift_rnd(c_mant1, shift - F_SIZE);
c_mant1 = 0;
} else if (shift == F_SIZE) {
c_mant0 = c_mant1 | (c_mant0 != 0);
c_mant1 = 0;
} else if (shift != 0) {
mask = ((F_UINT)1 << shift) - 1;
c_mant0 = (c_mant1 << (F_SIZE - shift)) | (c_mant0 >> shift) | ((c_mant0 & mask) != 0);
c_mant1 = c_mant1 >> shift;
}
// printf(" r_mant=%08x %08x\n", (uint32_t)r_mant1, (uint32_t)r_mant0);
// printf(" c_mant=%08x %08x\n", (uint32_t)c_mant1, (uint32_t)c_mant0);
/* add or subtract */
if (r_sign == c_sign) {
r_mant0 += c_mant0;
r_mant1 += c_mant1 + (r_mant0 < c_mant0);
} else {
F_UINT tmp;
tmp = r_mant0;
r_mant0 -= c_mant0;
r_mant1 = r_mant1 - c_mant1 - (r_mant0 > tmp);
if ((r_mant0 | r_mant1) == 0) {
/* zero result : the sign needs a specific handling */
r_sign = (rm == RM_RDN);
}
}
#if 0
// printf(" r1_mant=%08x %08x\n", (uint32_t)r_mant1, (uint32_t)r_mant0);
/* normalize */
if (r_mant1 == 0) {
r_mant1 = r_mant0;
r_exp -= F_SIZE;
} else {
shift = clz(r_mant1) - (F_SIZE - 1 - IMANT_SIZE);
if (shift != 0) {
r_mant1 = (r_mant1 << shift) | (r_mant0 >> (F_SIZE - shift));
r_mant0 <<= shift;
r_exp -= shift;
}
r_mant1 |= (r_mant0 != 0);
}
return normalize_sf(r_sign, r_exp, r_mant1, rm, pfflags);
#else
return normalize2_sf(r_sign, r_exp, r_mant1, r_mant0, rm, pfflags);
#endif
}
#ifdef F_ULONG
static F_UINT divrem_u(F_UINT *pr, F_UINT ah, F_UINT al, F_UINT b)
{
F_ULONG a;
a = ((F_ULONG)ah << F_SIZE) | al;
*pr = a % b;
return a / b;
}
#else
/* XXX: optimize */
static F_UINT divrem_u(F_UINT *pr, F_UINT a1, F_UINT a0, F_UINT b)
{
int i, qb, ab;
assert(a1 < b);
for(i = 0; i < F_SIZE; i++) {
ab = a1 >> (F_SIZE - 1);
a1 = (a1 << 1) | (a0 >> (F_SIZE - 1));
if (ab || a1 >= b) {
a1 -= b;
qb = 1;
} else {
qb = 0;
}
a0 = (a0 << 1) | qb;
}
*pr = a1;
return a0;
}
#endif
F_UINT div_sf(F_UINT a, F_UINT b, RoundingModeEnum rm,
uint32_t *pfflags)
{
uint32_t a_sign, b_sign, r_sign;
int32_t a_exp, b_exp, r_exp;
F_UINT a_mant, b_mant, r_mant, r;
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
r_sign = a_sign ^ b_sign;
a_exp = (a >> MANT_SIZE) & EXP_MASK;
b_exp = (b >> MANT_SIZE) & EXP_MASK;
a_mant = a & MANT_MASK;
b_mant = b & MANT_MASK;
if (a_exp == EXP_MASK) {
if (a_mant != 0 || isnan_sf(b)) {
if (issignan_sf(a) || issignan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN;
} else if (b_exp == EXP_MASK) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else {
return pack_sf(r_sign, EXP_MASK, 0);
}
} else if (b_exp == EXP_MASK) {
if (b_mant != 0) {
if (issignan_sf(a) || issignan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN;
} else {
return pack_sf(r_sign, 0, 0);
}
}
if (b_exp == 0) {
if (b_mant == 0) {
/* zero */
if (a_exp == 0 && a_mant == 0) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else {
*pfflags |= FFLAG_DIVIDE_ZERO;
return pack_sf(r_sign, EXP_MASK, 0);
}
}
b_mant = normalize_subnormal_sf(&b_exp, b_mant);
} else {
b_mant |= (F_UINT)1 << MANT_SIZE;
}
if (a_exp == 0) {
if (a_mant == 0)
return pack_sf(r_sign, 0, 0); /* zero */
a_mant = normalize_subnormal_sf(&a_exp, a_mant);
} else {
a_mant |= (F_UINT)1 << MANT_SIZE;
}
r_exp = a_exp - b_exp + (1 << (EXP_SIZE - 1)) - 1;
r_mant = divrem_u(&r, a_mant, 0, b_mant << 2);
if (r != 0)
r_mant |= 1;
return normalize_sf(r_sign, r_exp, r_mant, rm, pfflags);
}
#ifdef F_ULONG
/* compute sqrt(a) with a = ah*2^F_SIZE+al and a < 2^(F_SIZE - 2)
return true if not exact square. */
static int sqrtrem_u(F_UINT *pr, F_UINT ah, F_UINT al)
{
F_ULONG a, u, s;
int l, inexact;
/* 2^l >= a */
if (ah != 0) {
l = 2 * F_SIZE - clz(ah - 1);
} else {
if (al == 0) {
*pr = 0;
return 0;
}
l = F_SIZE - clz(al - 1);
}
a = ((F_ULONG)ah << F_SIZE) | al;
u = (F_ULONG)1 << ((l + 1) / 2);
for(;;) {
s = u;
u = ((a / s) + s) / 2;
if (u >= s)
break;
}
inexact = (a - s * s) != 0;
*pr = s;
return inexact;
}
#else
static int sqrtrem_u(F_UINT *pr, F_UINT a1, F_UINT a0)
{
int l, inexact;
F_UINT u, s, r, q, sq0, sq1;
/* 2^l >= a */
if (a1 != 0) {
l = 2 * F_SIZE - clz(a1 - 1);
} else {
if (a0 == 0) {
*pr = 0;
return 0;
}
l = F_SIZE - clz(a0 - 1);
}
u = (F_UINT)1 << ((l + 1) / 2);
for(;;) {
s = u;
q = divrem_u(&r, a1, a0, s);
u = (q + s) / 2;
if (u >= s)
break;
}
sq1 = mul_u(&sq0, s, s);
inexact = (sq0 != a0 || sq1 != a1);
*pr = s;
return inexact;
}
#endif
F_UINT sqrt_sf(F_UINT a, RoundingModeEnum rm,
uint32_t *pfflags)
{
uint32_t a_sign;
int32_t a_exp;
F_UINT a_mant;
a_sign = a >> (F_SIZE - 1);
a_exp = (a >> MANT_SIZE) & EXP_MASK;
a_mant = a & MANT_MASK;
if (a_exp == EXP_MASK) {
if (a_mant != 0) {
if (issignan_sf(a)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN;
} else if (a_sign) {
goto neg_error;
} else {
return a; /* +infinity */
}
}
if (a_sign) {
if (a_exp == 0 && a_mant == 0)
return a; /* -zero */
neg_error:
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
}
if (a_exp == 0) {
if (a_mant == 0)
return pack_sf(0, 0, 0); /* zero */
a_mant = normalize_subnormal_sf(&a_exp, a_mant);
} else {
a_mant |= (F_UINT)1 << MANT_SIZE;
}
a_exp -= EXP_MASK / 2;
/* simpler to handle an even exponent */
if (a_exp & 1) {
a_exp--;
a_mant <<= 1;
}
a_exp = (a_exp >> 1) + EXP_MASK / 2;
a_mant <<= (F_SIZE - 4 - MANT_SIZE);
if (sqrtrem_u(&a_mant, a_mant, 0))
a_mant |= 1;
return normalize_sf(a_sign, a_exp, a_mant, rm, pfflags);
}
/* comparisons */
F_UINT glue(min_sf, F_SIZE)(F_UINT a, F_UINT b, uint32_t *pfflags)
{
uint32_t a_sign, b_sign;
if (isnan_sf(a) || isnan_sf(b)) {
if (issignan_sf(a) || issignan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else if (isnan_sf(a)) {
if (isnan_sf(b))
return F_QNAN;
else
return b;
} else {
return a;
}
}
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
if (a_sign != b_sign) {
if (a_sign)
return a;
else
return b;
} else {
if ((a < b) ^ a_sign)
return a;
else
return b;
}
}
F_UINT glue(max_sf, F_SIZE)(F_UINT a, F_UINT b, uint32_t *pfflags)
{
uint32_t a_sign, b_sign;
if (isnan_sf(a) || isnan_sf(b)) {
if (issignan_sf(a) || issignan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
return F_QNAN;
} else if (isnan_sf(a)) {
if (isnan_sf(b))
return F_QNAN;
else
return b;
} else {
return a;
}
}
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
if (a_sign != b_sign) {
if (a_sign)
return b;
else
return a;
} else {
if ((a < b) ^ a_sign)
return b;
else
return a;
}
}
int glue(eq_quiet_sf, F_SIZE)(F_UINT a, F_UINT b, uint32_t *pfflags)
{
if (isnan_sf(a) || isnan_sf(b)) {
if (issignan_sf(a) || issignan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
}
return 0;
}
if ((F_UINT)((a | b) << 1) == 0)
return 1; /* zero case */
return (a == b);
}
int glue(le_sf, F_SIZE)(F_UINT a, F_UINT b, uint32_t *pfflags)
{
uint32_t a_sign, b_sign;
if (isnan_sf(a) || isnan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
return 0;
}
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
if (a_sign != b_sign) {
return (a_sign || ((F_UINT)((a | b) << 1) == 0));
} else {
if (a_sign) {
return (a >= b);
} else {
return (a <= b);
}
}
}
int glue(lt_sf, F_SIZE)(F_UINT a, F_UINT b, uint32_t *pfflags)
{
uint32_t a_sign, b_sign;
if (isnan_sf(a) || isnan_sf(b)) {
*pfflags |= FFLAG_INVALID_OP;
return 0;
}
a_sign = a >> (F_SIZE - 1);
b_sign = b >> (F_SIZE - 1);
if (a_sign != b_sign) {
return (a_sign && ((F_UINT)((a | b) << 1) != 0));
} else {
if (a_sign) {
return (a > b);
} else {
return (a < b);
}
}
}
uint32_t glue(fclass_sf, F_SIZE)(F_UINT a)
{
uint32_t a_sign;
int32_t a_exp;
F_UINT a_mant;
uint32_t ret;
a_sign = a >> (F_SIZE - 1);
a_exp = (a >> MANT_SIZE) & EXP_MASK;
a_mant = a & MANT_MASK;
if (a_exp == EXP_MASK) {
if (a_mant != 0) {
if (a_mant & QNAN_MASK)
ret = FCLASS_QNAN;
else
ret = FCLASS_SNAN;
} else {
if (a_sign)
ret = FCLASS_NINF;
else
ret = FCLASS_PINF;
}
} else if (a_exp == 0) {
if (a_mant == 0) {
if (a_sign)
ret = FCLASS_NZERO;
else
ret = FCLASS_PZERO;
} else {
if (a_sign)
ret = FCLASS_NSUBNORMAL;
else
ret = FCLASS_PSUBNORMAL;
}
} else {
if (a_sign)
ret = FCLASS_NNORMAL;
else
ret = FCLASS_PNORMAL;
}
return ret;
}
/* conversions between floats */
#if F_SIZE >= 64
F_UINT cvt_sf32_sf(uint32_t a, uint32_t *pfflags)
{
uint32_t a_sign;
int32_t a_exp;
F_UINT a_mant;
a_mant = unpack_sf32(&a_sign, &a_exp, a);
if (a_exp == 0xff) {
if (a_mant != 0) {
/* NaN */
if (issignan_sf32(a)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN;
} else {
/* infinity */
return pack_sf(a_sign, EXP_MASK, 0);
}
}
if (a_exp == 0) {
if (a_mant == 0)
return pack_sf(a_sign, 0, 0); /* zero */
a_mant = normalize_subnormal_sf32(&a_exp, a_mant);
}
/* convert the exponent value */
a_exp = a_exp - 0x7f + (EXP_MASK / 2);
/* shift the mantissa */
a_mant <<= (MANT_SIZE - 23);
/* We assume the target float is large enough to that no
normalization is necessary */
return pack_sf(a_sign, a_exp, a_mant);
}
uint32_t glue(glue(cvt_sf, F_SIZE), _sf32)(F_UINT a, RoundingModeEnum rm,
uint32_t *pfflags)
{
uint32_t a_sign;
int32_t a_exp;
F_UINT a_mant;
a_mant = unpack_sf(&a_sign, &a_exp, a);
if (a_exp == EXP_MASK) {
if (a_mant != 0) {
/* NaN */
if (issignan_sf(a)) {
*pfflags |= FFLAG_INVALID_OP;
}
return F_QNAN32;
} else {
/* infinity */
return pack_sf32(a_sign, 0xff, 0);
}
}
if (a_exp == 0) {
if (a_mant == 0)
return pack_sf32(a_sign, 0, 0); /* zero */
normalize_subnormal_sf(&a_exp, a_mant);
} else {
a_mant |= (F_UINT)1 << MANT_SIZE;