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/*
* License for Berkeley SoftFloat Release 3e
*
* John R. Hauser
* 2018 January 20
*
* The following applies to the whole of SoftFloat Release 3e as well as to
* each source file individually.
*
* Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Regents of the
* University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions, and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions, and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
* DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
*
* The functions listed in this file are modified versions of the ones
* from the Berkeley SoftFloat 3e Library.
*
* Their implementation correctness has been checked with the Berkeley
* TestFloat Release 3e tool for x86_64.
*/
#include "rounding.h"
#include "bitscan.h"
#include "softfloat.h"
#if defined(BIG_ENDIAN)
#define word_incr -1
#define index_word(total, n) ((total) - 1 - (n))
#define index_word_hi(total) 0
#define index_word_lo(total) ((total) - 1)
#define index_multiword_hi(total, n) 0
#define index_multiword_lo(total, n) ((total) - (n))
#define index_multiword_hi_but(total, n) 0
#define index_multiword_lo_but(total, n) (n)
#else
#define word_incr 1
#define index_word(total, n) (n)
#define index_word_hi(total) ((total) - 1)
#define index_word_lo(total) 0
#define index_multiword_hi(total, n) ((total) - (n))
#define index_multiword_lo(total, n) 0
#define index_multiword_hi_but(total, n) (n)
#define index_multiword_lo_but(total, n) 0
#endif
typedef union { double f; int64_t i; uint64_t u; } di_type;
typedef union { float f; int32_t i; uint32_t u; } fi_type;
const uint8_t count_leading_zeros8[256] = {
8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
/**
* \brief Shifts 'a' right by the number of bits given in 'dist', which must be in
* the range 1 to 63. If any nonzero bits are shifted off, they are "jammed"
* into the least-significant bit of the shifted value by setting the
* least-significant bit to 1. This shifted-and-jammed value is returned.
*
* From softfloat_shortShiftRightJam64()
*/
static inline
uint64_t _mesa_short_shift_right_jam64(uint64_t a, uint8_t dist)
{
return a >> dist | ((a & (((uint64_t) 1 << dist) - 1)) != 0);
}
/**
* \brief Shifts 'a' right by the number of bits given in 'dist', which must not
* be zero. If any nonzero bits are shifted off, they are "jammed" into the
* least-significant bit of the shifted value by setting the least-significant
* bit to 1. This shifted-and-jammed value is returned.
* The value of 'dist' can be arbitrarily large. In particular, if 'dist' is
* greater than 64, the result will be either 0 or 1, depending on whether 'a'
* is zero or nonzero.
*
* From softfloat_shiftRightJam64()
*/
static inline
uint64_t _mesa_shift_right_jam64(uint64_t a, uint32_t dist)
{
return
(dist < 63) ? a >> dist | ((uint64_t) (a << (-dist & 63)) != 0) : (a != 0);
}
/**
* \brief Shifts 'a' right by the number of bits given in 'dist', which must not be
* zero. If any nonzero bits are shifted off, they are "jammed" into the
* least-significant bit of the shifted value by setting the least-significant
* bit to 1. This shifted-and-jammed value is returned.
* The value of 'dist' can be arbitrarily large. In particular, if 'dist' is
* greater than 32, the result will be either 0 or 1, depending on whether 'a'
* is zero or nonzero.
*
* From softfloat_shiftRightJam32()
*/
static inline
uint32_t _mesa_shift_right_jam32(uint32_t a, uint16_t dist)
{
return
(dist < 31) ? a >> dist | ((uint32_t) (a << (-dist & 31)) != 0) : (a != 0);
}
/**
* \brief Extracted from softfloat_roundPackToF64()
*/
static inline
double _mesa_roundtozero_f64(int64_t s, int64_t e, int64_t m)
{
di_type result;
if ((uint64_t) e >= 0x7fd) {
if (e < 0) {
m = _mesa_shift_right_jam64(m, -e);
e = 0;
} else if ((e > 0x7fd) || (0x8000000000000000 <= m)) {
e = 0x7ff;
m = 0;
result.u = (s << 63) + (e << 52) + m;
result.u -= 1;
return result.f;
}
}
m >>= 10;
if (m == 0)
e = 0;
result.u = (s << 63) + (e << 52) + m;
return result.f;
}
/**
* \brief Extracted from softfloat_roundPackToF32()
*/
static inline
float _mesa_round_f32(int32_t s, int32_t e, int32_t m, bool rtz)
{
fi_type result;
uint8_t round_increment = rtz ? 0 : 0x40;
if ((uint32_t) e >= 0xfd) {
if (e < 0) {
m = _mesa_shift_right_jam32(m, -e);
e = 0;
} else if ((e > 0xfd) || (0x80000000 <= m + round_increment)) {
e = 0xff;
m = 0;
result.u = (s << 31) + (e << 23) + m;
result.u -= !round_increment;
return result.f;
}
}
uint8_t round_bits;
round_bits = m & 0x7f;
m = ((uint32_t) m + round_increment) >> 7;
m &= ~(uint32_t) (! (round_bits ^ 0x40) & !rtz);
if (m == 0)
e = 0;
result.u = (s << 31) + (e << 23) + m;
return result.f;
}
/**
* \brief Extracted from softfloat_roundPackToF16()
*/
static inline
uint16_t _mesa_roundtozero_f16(int16_t s, int16_t e, int16_t m)
{
if ((uint16_t) e >= 0x1d) {
if (e < 0) {
m = _mesa_shift_right_jam32(m, -e);
e = 0;
} else if (e > 0x1d) {
e = 0x1f;
m = 0;
return (s << 15) + (e << 10) + m - 1;
}
}
m >>= 4;
if (m == 0)
e = 0;
return (s << 15) + (e << 10) + m;
}
/**
* \brief Shifts the N-bit unsigned integer pointed to by 'a' left by the number of
* bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
* must be in the range 1 to 31. Any nonzero bits shifted off are lost. The
* shifted N-bit result is stored at the location pointed to by 'm_out'. Each
* of 'a' and 'm_out' points to a 'size_words'-long array of 32-bit elements
* that concatenate in the platform's normal endian order to form an N-bit
* integer.
*
* From softfloat_shortShiftLeftM()
*/
static inline void
_mesa_short_shift_left_m(uint8_t size_words, const uint32_t *a, uint8_t dist, uint32_t *m_out)
{
uint8_t neg_dist;
unsigned index, last_index;
uint32_t part_word, a_word;
neg_dist = -dist;
index = index_word_hi(size_words);
last_index = index_word_lo(size_words);
part_word = a[index] << dist;
while (index != last_index) {
a_word = a[index - word_incr];
m_out[index] = part_word | a_word >> (neg_dist & 31);
index -= word_incr;
part_word = a_word << dist;
}
m_out[index] = part_word;
}
/**
* \brief Shifts the N-bit unsigned integer pointed to by 'a' left by the number of
* bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
* must not be zero. Any nonzero bits shifted off are lost. The shifted
* N-bit result is stored at the location pointed to by 'm_out'. Each of 'a'
* and 'm_out' points to a 'size_words'-long array of 32-bit elements that
* concatenate in the platform's normal endian order to form an N-bit
* integer. The value of 'dist' can be arbitrarily large. In particular, if
* 'dist' is greater than N, the stored result will be 0.
*
* From softfloat_shiftLeftM()
*/
static inline void
_mesa_shift_left_m(uint8_t size_words, const uint32_t *a, uint32_t dist, uint32_t *m_out)
{
uint32_t word_dist;
uint8_t inner_dist;
uint8_t i;
word_dist = dist >> 5;
if (word_dist < size_words) {
a += index_multiword_lo_but(size_words, word_dist);
inner_dist = dist & 31;
if (inner_dist) {
_mesa_short_shift_left_m(size_words - word_dist, a, inner_dist,
m_out + index_multiword_hi_but(size_words, word_dist));
if (!word_dist)
return;
} else {
uint32_t *dest = m_out + index_word_hi(size_words);
a += index_word_hi(size_words - word_dist);
for (i = size_words - word_dist; i; --i) {
*dest = *a;
a -= word_incr;
dest -= word_incr;
}
}
m_out += index_multiword_lo(size_words, word_dist);
} else {
word_dist = size_words;
}
do {
*m_out++ = 0;
--word_dist;
} while (word_dist);
}
/**
* \brief Shifts the N-bit unsigned integer pointed to by 'a' right by the number of
* bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
* must be in the range 1 to 31. Any nonzero bits shifted off are lost. The
* shifted N-bit result is stored at the location pointed to by 'm_out'. Each
* of 'a' and 'm_out' points to a 'size_words'-long array of 32-bit elements
* that concatenate in the platform's normal endian order to form an N-bit
* integer.
*
* From softfloat_shortShiftRightM()
*/
static inline void
_mesa_short_shift_right_m(uint8_t size_words, const uint32_t *a, uint8_t dist, uint32_t *m_out)
{
uint8_t neg_dist;
unsigned index, last_index;
uint32_t part_word, a_word;
neg_dist = -dist;
index = index_word_lo(size_words);
last_index = index_word_hi(size_words);
part_word = a[index] >> dist;
while (index != last_index) {
a_word = a[index + word_incr];
m_out[index] = a_word << (neg_dist & 31) | part_word;
index += word_incr;
part_word = a_word >> dist;
}
m_out[index] = part_word;
}
/**
* \brief Shifts the N-bit unsigned integer pointed to by 'a' right by the number of
* bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
* must be in the range 1 to 31. If any nonzero bits are shifted off, they
* are "jammed" into the least-significant bit of the shifted value by setting
* the least-significant bit to 1. This shifted-and-jammed N-bit result is
* stored at the location pointed to by 'm_out'. Each of 'a' and 'm_out'
* points to a 'size_words'-long array of 32-bit elements that concatenate in
* the platform's normal endian order to form an N-bit integer.
*
*
* From softfloat_shortShiftRightJamM()
*/
static inline void
_mesa_short_shift_right_jam_m(uint8_t size_words, const uint32_t *a, uint8_t dist, uint32_t *m_out)
{
uint8_t neg_dist;
unsigned index, last_index;
uint64_t part_word, a_word;
neg_dist = -dist;
index = index_word_lo(size_words);
last_index = index_word_hi(size_words);
a_word = a[index];
part_word = a_word >> dist;
if (part_word << dist != a_word )
part_word |= 1;
while (index != last_index) {
a_word = a[index + word_incr];
m_out[index] = a_word << (neg_dist & 31) | part_word;
index += word_incr;
part_word = a_word >> dist;
}
m_out[index] = part_word;
}
/**
* \brief Shifts the N-bit unsigned integer pointed to by 'a' right by the number of
* bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
* must not be zero. If any nonzero bits are shifted off, they are "jammed"
* into the least-significant bit of the shifted value by setting the
* least-significant bit to 1. This shifted-and-jammed N-bit result is stored
* at the location pointed to by 'm_out'. Each of 'a' and 'm_out' points to a
* 'size_words'-long array of 32-bit elements that concatenate in the
* platform's normal endian order to form an N-bit integer. The value of
* 'dist' can be arbitrarily large. In particular, if 'dist' is greater than
* N, the stored result will be either 0 or 1, depending on whether the
* original N bits are all zeros.
*
* From softfloat_shiftRightJamM()
*/
static inline void
_mesa_shift_right_jam_m(uint8_t size_words, const uint32_t *a, uint32_t dist, uint32_t *m_out)
{
uint32_t word_jam, word_dist, *tmp;
uint8_t i, inner_dist;
word_jam = 0;
word_dist = dist >> 5;
tmp = NULL;
if (word_dist) {
if (size_words < word_dist)
word_dist = size_words;
tmp = (uint32_t *) (a + index_multiword_lo(size_words, word_dist));
i = word_dist;
do {
word_jam = *tmp++;
if (word_jam)
break;
--i;
} while (i);
tmp = m_out;
}
if (word_dist < size_words) {
a += index_multiword_hi_but(size_words, word_dist);
inner_dist = dist & 31;
if (inner_dist) {
_mesa_short_shift_right_jam_m(size_words - word_dist, a, inner_dist,
m_out + index_multiword_lo_but(size_words, word_dist));
if (!word_dist) {
if (word_jam)
m_out[index_word_lo(size_words)] |= 1;
return;
}
} else {
a += index_word_lo(size_words - word_dist);
tmp = m_out + index_word_lo(size_words);
for (i = size_words - word_dist; i; --i) {
*tmp = *a;
a += word_incr;
tmp += word_incr;
}
}
tmp = m_out + index_multiword_hi(size_words, word_dist);
}
if (tmp) {
do {
*tmp++ = 0;
--word_dist;
} while (word_dist);
}
if (word_jam)
m_out[index_word_lo(size_words)] |= 1;
}
/**
* \brief Calculate a + b but rounding to zero.
*
* Notice that this mainly differs from the original Berkeley SoftFloat 3e
* implementation in that we don't really treat NaNs, Zeroes nor the
* signalling flags. Any NaN is good for us and the sign of the Zero is not
* important.
*
* From f64_add()
*/
double
_mesa_double_add_rtz(double a, double b)
{
const di_type a_di = {a};
uint64_t a_flt_m = a_di.u & 0x0fffffffffffff;
uint64_t a_flt_e = (a_di.u >> 52) & 0x7ff;
uint64_t a_flt_s = (a_di.u >> 63) & 0x1;
const di_type b_di = {b};
uint64_t b_flt_m = b_di.u & 0x0fffffffffffff;
uint64_t b_flt_e = (b_di.u >> 52) & 0x7ff;
uint64_t b_flt_s = (b_di.u >> 63) & 0x1;
int64_t s, e, m = 0;
s = a_flt_s;
const int64_t exp_diff = a_flt_e - b_flt_e;
/* Handle special cases */
if (a_flt_s != b_flt_s) {
return _mesa_double_sub_rtz(a, -b);
} else if ((a_flt_e == 0) && (a_flt_m == 0)) {
/* 'a' is zero, return 'b' */
return b;
} else if ((b_flt_e == 0) && (b_flt_m == 0)) {
/* 'b' is zero, return 'a' */
return a;
} else if (a_flt_e == 0x7ff && a_flt_m != 0) {
/* 'a' is a NaN, return NaN */
return a;
} else if (b_flt_e == 0x7ff && b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
} else if (a_flt_e == 0x7ff && a_flt_m == 0) {
/* Inf + x = Inf */
return a;
} else if (b_flt_e == 0x7ff && b_flt_m == 0) {
/* x + Inf = Inf */
return b;
} else if (exp_diff == 0 && a_flt_e == 0) {
di_type result_di;
result_di.u = a_di.u + b_flt_m;
return result_di.f;
} else if (exp_diff == 0) {
e = a_flt_e;
m = 0x0020000000000000 + a_flt_m + b_flt_m;
m <<= 9;
} else if (exp_diff < 0) {
a_flt_m <<= 9;
b_flt_m <<= 9;
e = b_flt_e;
if (a_flt_e != 0)
a_flt_m += 0x2000000000000000;
else
a_flt_m <<= 1;
a_flt_m = _mesa_shift_right_jam64(a_flt_m, -exp_diff);
m = 0x2000000000000000 + a_flt_m + b_flt_m;
if (m < 0x4000000000000000) {
--e;
m <<= 1;
}
} else {
a_flt_m <<= 9;
b_flt_m <<= 9;
e = a_flt_e;
if (b_flt_e != 0)
b_flt_m += 0x2000000000000000;
else
b_flt_m <<= 1;
b_flt_m = _mesa_shift_right_jam64(b_flt_m, exp_diff);
m = 0x2000000000000000 + a_flt_m + b_flt_m;
if (m < 0x4000000000000000) {
--e;
m <<= 1;
}
}
return _mesa_roundtozero_f64(s, e, m);
}
/**
* \brief Returns the number of leading 0 bits before the most-significant 1 bit of
* 'a'. If 'a' is zero, 64 is returned.
*/
static inline unsigned
_mesa_count_leading_zeros64(uint64_t a)
{
return 64 - util_last_bit64(a);
}
/**
* \brief Returns the number of leading 0 bits before the most-significant 1 bit of
* 'a'. If 'a' is zero, 32 is returned.
*/
static inline unsigned
_mesa_count_leading_zeros32(uint32_t a)
{
return 32 - util_last_bit(a);
}
static inline double
_mesa_norm_round_pack_f64(int64_t s, int64_t e, int64_t m)
{
int8_t shift_dist;
shift_dist = _mesa_count_leading_zeros64(m) - 1;
e -= shift_dist;
if ((10 <= shift_dist) && ((unsigned) e < 0x7fd)) {
di_type result;
result.u = (s << 63) + ((m ? e : 0) << 52) + (m << (shift_dist - 10));
return result.f;
} else {
return _mesa_roundtozero_f64(s, e, m << shift_dist);
}
}
/**
* \brief Replaces the N-bit unsigned integer pointed to by 'm_out' by the
* 2s-complement of itself, where N = 'size_words' * 32. Argument 'm_out'
* points to a 'size_words'-long array of 32-bit elements that concatenate in
* the platform's normal endian order to form an N-bit integer.
*
* From softfloat_negXM()
*/
static inline void
_mesa_neg_x_m(uint8_t size_words, uint32_t *m_out)
{
unsigned index, last_index;
uint8_t carry;
uint32_t word;
index = index_word_lo(size_words);
last_index = index_word_hi(size_words);
carry = 1;
for (;;) {
word = ~m_out[index] + carry;
m_out[index] = word;
if (index == last_index)
break;
index += word_incr;
if (word)
carry = 0;
}
}
/**
* \brief Adds the two N-bit integers pointed to by 'a' and 'b', where N =
* 'size_words' * 32. The addition is modulo 2^N, so any carry out is
* lost. The N-bit sum is stored at the location pointed to by 'm_out'. Each
* of 'a', 'b', and 'm_out' points to a 'size_words'-long array of 32-bit
* elements that concatenate in the platform's normal endian order to form an
* N-bit integer.
*
* From softfloat_addM()
*/
static inline void
_mesa_add_m(uint8_t size_words, const uint32_t *a, const uint32_t *b, uint32_t *m_out)
{
unsigned index, last_index;
uint8_t carry;
uint32_t a_word, word;
index = index_word_lo(size_words);
last_index = index_word_hi(size_words);
carry = 0;
for (;;) {
a_word = a[index];
word = a_word + b[index] + carry;
m_out[index] = word;
if (index == last_index)
break;
if (word != a_word)
carry = (word < a_word);
index += word_incr;
}
}
/**
* \brief Subtracts the two N-bit integers pointed to by 'a' and 'b', where N =
* 'size_words' * 32. The subtraction is modulo 2^N, so any borrow out (carry
* out) is lost. The N-bit difference is stored at the location pointed to by
* 'm_out'. Each of 'a', 'b', and 'm_out' points to a 'size_words'-long array
* of 32-bit elements that concatenate in the platform's normal endian order
* to form an N-bit integer.
*
* From softfloat_subM()
*/
static inline void
_mesa_sub_m(uint8_t size_words, const uint32_t *a, const uint32_t *b, uint32_t *m_out)
{
unsigned index, last_index;
uint8_t borrow;
uint32_t a_word, b_word;
index = index_word_lo(size_words);
last_index = index_word_hi(size_words);
borrow = 0;
for (;;) {
a_word = a[index];
b_word = b[index];
m_out[index] = a_word - b_word - borrow;
if (index == last_index)
break;
borrow = borrow ? (a_word <= b_word) : (a_word < b_word);
index += word_incr;
}
}
/* Calculate a - b but rounding to zero.
*
* Notice that this mainly differs from the original Berkeley SoftFloat 3e
* implementation in that we don't really treat NaNs, Zeroes nor the
* signalling flags. Any NaN is good for us and the sign of the Zero is not
* important.
*
* From f64_sub()
*/
double
_mesa_double_sub_rtz(double a, double b)
{
const di_type a_di = {a};
uint64_t a_flt_m = a_di.u & 0x0fffffffffffff;
uint64_t a_flt_e = (a_di.u >> 52) & 0x7ff;
uint64_t a_flt_s = (a_di.u >> 63) & 0x1;
const di_type b_di = {b};
uint64_t b_flt_m = b_di.u & 0x0fffffffffffff;
uint64_t b_flt_e = (b_di.u >> 52) & 0x7ff;
uint64_t b_flt_s = (b_di.u >> 63) & 0x1;
int64_t s, e, m = 0;
int64_t m_diff = 0;
unsigned shift_dist = 0;
s = a_flt_s;
const int64_t exp_diff = a_flt_e - b_flt_e;
/* Handle special cases */
if (a_flt_s != b_flt_s) {
return _mesa_double_add_rtz(a, -b);
} else if ((a_flt_e == 0) && (a_flt_m == 0)) {
/* 'a' is zero, return '-b' */
return -b;
} else if ((b_flt_e == 0) && (b_flt_m == 0)) {
/* 'b' is zero, return 'a' */
return a;
} else if (a_flt_e == 0x7ff && a_flt_m != 0) {
/* 'a' is a NaN, return NaN */
return a;
} else if (b_flt_e == 0x7ff && b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
} else if (a_flt_e == 0x7ff && a_flt_m == 0) {
if (b_flt_e == 0x7ff && b_flt_m == 0) {
/* Inf - Inf = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
/* Inf - x = Inf */
return a;
} else if (b_flt_e == 0x7ff && b_flt_m == 0) {
/* x - Inf = -Inf */
return -b;
} else if (exp_diff == 0) {
m_diff = a_flt_m - b_flt_m;
if (m_diff == 0)
return 0;
if (a_flt_e)
--a_flt_e;
if (m_diff < 0) {
s = !s;
m_diff = -m_diff;
}
shift_dist = _mesa_count_leading_zeros64(m_diff) - 11;
e = a_flt_e - shift_dist;
if (e < 0) {
shift_dist = a_flt_e;
e = 0;
}
di_type result;
result.u = (s << 63) + (e << 52) + (m_diff << shift_dist);
return result.f;
} else if (exp_diff < 0) {
a_flt_m <<= 10;
b_flt_m <<= 10;
s = !s;
a_flt_m += (a_flt_e) ? 0x4000000000000000 : a_flt_m;
a_flt_m = _mesa_shift_right_jam64(a_flt_m, -exp_diff);
b_flt_m |= 0x4000000000000000;
e = b_flt_e;
m = b_flt_m - a_flt_m;
} else {
a_flt_m <<= 10;
b_flt_m <<= 10;
b_flt_m += (b_flt_e) ? 0x4000000000000000 : b_flt_m;
b_flt_m = _mesa_shift_right_jam64(b_flt_m, exp_diff);
a_flt_m |= 0x4000000000000000;
e = a_flt_e;
m = a_flt_m - b_flt_m;
}
return _mesa_norm_round_pack_f64(s, e - 1, m);
}
static inline void
_mesa_norm_subnormal_mantissa_f64(uint64_t m, uint64_t *exp, uint64_t *m_out)
{
int shift_dist;
shift_dist = _mesa_count_leading_zeros64(m) - 11;
*exp = 1 - shift_dist;
*m_out = m << shift_dist;
}
static inline void
_mesa_norm_subnormal_mantissa_f32(uint32_t m, uint32_t *exp, uint32_t *m_out)
{
int shift_dist;
shift_dist = _mesa_count_leading_zeros32(m) - 8;
*exp = 1 - shift_dist;
*m_out = m << shift_dist;
}
/**
* \brief Multiplies 'a' and 'b' and stores the 128-bit product at the location
* pointed to by 'zPtr'. Argument 'zPtr' points to an array of four 32-bit
* elements that concatenate in the platform's normal endian order to form a
* 128-bit integer.
*
* From softfloat_mul64To128M()
*/
static inline void
_mesa_softfloat_mul_f64_to_f128_m(uint64_t a, uint64_t b, uint32_t *m_out)
{
uint32_t a32, a0, b32, b0;
uint64_t z0, mid1, z64, mid;
a32 = a >> 32;
a0 = a;
b32 = b >> 32;
b0 = b;
z0 = (uint64_t) a0 * b0;
mid1 = (uint64_t) a32 * b0;
mid = mid1 + (uint64_t) a0 * b32;
z64 = (uint64_t) a32 * b32;
z64 += (uint64_t) (mid < mid1) << 32 | mid >> 32;
mid <<= 32;
z0 += mid;
m_out[index_word(4, 1)] = z0 >> 32;
m_out[index_word(4, 0)] = z0;
z64 += (z0 < mid);
m_out[index_word(4, 3)] = z64 >> 32;
m_out[index_word(4, 2)] = z64;
}
/* Calculate a * b but rounding to zero.
*
* Notice that this mainly differs from the original Berkeley SoftFloat 3e
* implementation in that we don't really treat NaNs, Zeroes nor the
* signalling flags. Any NaN is good for us and the sign of the Zero is not
* important.
*
* From f64_mul()
*/
double
_mesa_double_mul_rtz(double a, double b)
{
const di_type a_di = {a};
uint64_t a_flt_m = a_di.u & 0x0fffffffffffff;
uint64_t a_flt_e = (a_di.u >> 52) & 0x7ff;
uint64_t a_flt_s = (a_di.u >> 63) & 0x1;
const di_type b_di = {b};
uint64_t b_flt_m = b_di.u & 0x0fffffffffffff;
uint64_t b_flt_e = (b_di.u >> 52) & 0x7ff;
uint64_t b_flt_s = (b_di.u >> 63) & 0x1;
int64_t s, e, m = 0;
s = a_flt_s ^ b_flt_s;
if (a_flt_e == 0x7ff) {
if (a_flt_m != 0) {
/* 'a' is a NaN, return NaN */
return a;
} else if (b_flt_e == 0x7ff && b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
}
if (!(b_flt_e | b_flt_m)) {
/* Inf * 0 = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
/* Inf * x = Inf */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0;
return result.f;
}
if (b_flt_e == 0x7ff) {
if (b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
}
if (!(a_flt_e | a_flt_m)) {
/* 0 * Inf = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
/* x * Inf = Inf */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0;
return result.f;
}
if (a_flt_e == 0) {
if (a_flt_m == 0) {
/* 'a' is zero. Return zero */
di_type result;
result.u = (s << 63) + 0;
return result.f;
}
_mesa_norm_subnormal_mantissa_f64(a_flt_m , &a_flt_e, &a_flt_m);
}
if (b_flt_e == 0) {
if (b_flt_m == 0) {
/* 'b' is zero. Return zero */
di_type result;
result.u = (s << 63) + 0;
return result.f;
}
_mesa_norm_subnormal_mantissa_f64(b_flt_m , &b_flt_e, &b_flt_m);
}
e = a_flt_e + b_flt_e - 0x3ff;
a_flt_m = (a_flt_m | 0x0010000000000000) << 10;
b_flt_m = (b_flt_m | 0x0010000000000000) << 11;
uint32_t m_128[4];
_mesa_softfloat_mul_f64_to_f128_m(a_flt_m, b_flt_m, m_128);
m = (uint64_t) m_128[index_word(4, 3)] << 32 | m_128[index_word(4, 2)];
if (m_128[index_word(4, 1)] || m_128[index_word(4, 0)])
m |= 1;
if (m < 0x4000000000000000) {
--e;
m <<= 1;
}
return _mesa_roundtozero_f64(s, e, m);
}
/**
* \brief Calculate a * b + c but rounding to zero.
*
* Notice that this mainly differs from the original Berkeley SoftFloat 3e
* implementation in that we don't really treat NaNs, Zeroes nor the
* signalling flags. Any NaN is good for us and the sign of the Zero is not
* important.
*
* From f64_mulAdd()
*/
double
_mesa_double_fma_rtz(double a, double b, double c)
{
const di_type a_di = {a};
uint64_t a_flt_m = a_di.u & 0x0fffffffffffff;
uint64_t a_flt_e = (a_di.u >> 52) & 0x7ff;
uint64_t a_flt_s = (a_di.u >> 63) & 0x1;
const di_type b_di = {b};
uint64_t b_flt_m = b_di.u & 0x0fffffffffffff;
uint64_t b_flt_e = (b_di.u >> 52) & 0x7ff;
uint64_t b_flt_s = (b_di.u >> 63) & 0x1;
const di_type c_di = {c};
uint64_t c_flt_m = c_di.u & 0x0fffffffffffff;
uint64_t c_flt_e = (c_di.u >> 52) & 0x7ff;
uint64_t c_flt_s = (c_di.u >> 63) & 0x1;
int64_t s, e, m = 0;
c_flt_s ^= 0;
s = a_flt_s ^ b_flt_s ^ 0;
if (a_flt_e == 0x7ff) {
if (a_flt_m != 0) {
/* 'a' is a NaN, return NaN */
return a;
} else if (b_flt_e == 0x7ff && b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
} else if (c_flt_e == 0x7ff && c_flt_m != 0) {
/* 'c' is a NaN, return NaN */
return c;
}
if (!(b_flt_e | b_flt_m)) {
/* Inf * 0 + y = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
if ((c_flt_e == 0x7ff && c_flt_m == 0) && (s != c_flt_s)) {
/* Inf * x - Inf = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
/* Inf * x + y = Inf */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0;
return result.f;
}
if (b_flt_e == 0x7ff) {
if (b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
} else if (c_flt_e == 0x7ff && c_flt_m != 0) {
/* 'c' is a NaN, return NaN */
return c;
}
if (!(a_flt_e | a_flt_m)) {
/* 0 * Inf + y = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
if ((c_flt_e == 0x7ff && c_flt_m == 0) && (s != c_flt_s)) {
/* x * Inf - Inf = NaN */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0x1;
return result.f;
}
/* x * Inf + y = Inf */
di_type result;
e = 0x7ff;
result.u = (s << 63) + (e << 52) + 0;
return result.f;
}
if (c_flt_e == 0x7ff) {
if (c_flt_m != 0) {
/* 'c' is a NaN, return NaN */
return c;
}
/* x * y + Inf = Inf */
return c;
}
if (a_flt_e == 0) {
if (a_flt_m == 0) {
/* 'a' is zero, return 'c' */
return c;
}
_mesa_norm_subnormal_mantissa_f64(a_flt_m , &a_flt_e, &a_flt_m);
}
if (b_flt_e == 0) {
if (b_flt_m == 0) {
/* 'b' is zero, return 'c' */
return c;
}
_mesa_norm_subnormal_mantissa_f64(b_flt_m , &b_flt_e, &b_flt_m);
}
e = a_flt_e + b_flt_e - 0x3fe;
a_flt_m = (a_flt_m | 0x0010000000000000) << 10;
b_flt_m = (b_flt_m | 0x0010000000000000) << 11;
uint32_t m_128[4];
_mesa_softfloat_mul_f64_to_f128_m(a_flt_m, b_flt_m, m_128);
m = (uint64_t) m_128[index_word(4, 3)] << 32 | m_128[index_word(4, 2)];
int64_t shift_dist = 0;
if (!(m & 0x4000000000000000)) {
--e;
shift_dist = -1;
}
if (c_flt_e == 0) {
if (c_flt_m == 0) {
/* 'c' is zero, return 'a * b' */
if (shift_dist)
m <<= 1;
if (m_128[index_word(4, 1)] || m_128[index_word(4, 0)])
m |= 1;
return _mesa_roundtozero_f64(s, e - 1, m);
}
_mesa_norm_subnormal_mantissa_f64(c_flt_m , &c_flt_e, &c_flt_m);
}
c_flt_m = (c_flt_m | 0x0010000000000000) << 10;
uint32_t c_flt_m_128[4];
int64_t exp_diff = e - c_flt_e;
if (exp_diff < 0) {
e = c_flt_e;
if ((s == c_flt_s) || (exp_diff < -1)) {
shift_dist -= exp_diff;
if (shift_dist) {
m = _mesa_shift_right_jam64(m, shift_dist);
}
} else {
if (!shift_dist) {
_mesa_short_shift_right_m(4, m_128, 1, m_128);
}
}
} else {
if (shift_dist)
_mesa_add_m(4, m_128, m_128, m_128);
if (!exp_diff) {
m = (uint64_t) m_128[index_word(4, 3)] << 32
| m_128[index_word(4, 2)];
} else {
c_flt_m_128[index_word(4, 3)] = c_flt_m >> 32;
c_flt_m_128[index_word(4, 2)] = c_flt_m;
c_flt_m_128[index_word(4, 1)] = 0;
c_flt_m_128[index_word(4, 0)] = 0;
_mesa_shift_right_jam_m(4, c_flt_m_128, exp_diff, c_flt_m_128);
}
}
if (s == c_flt_s) {
if (exp_diff <= 0) {
m += c_flt_m;
} else {
_mesa_add_m(4, m_128, c_flt_m_128, m_128);
m = (uint64_t) m_128[index_word(4, 3)] << 32
| m_128[index_word(4, 2)];
}
if (m & 0x8000000000000000) {
e++;
m = _mesa_short_shift_right_jam64(m, 1);
}
} else {
if (exp_diff < 0) {
s = c_flt_s;
if (exp_diff < -1) {
m = c_flt_m - m;
if (m_128[index_word(4, 1)] || m_128[index_word(4, 0)]) {
m = (m - 1) | 1;
}
if (!(m & 0x4000000000000000)) {
--e;
m <<= 1;
}
return _mesa_roundtozero_f64(s, e - 1, m);
} else {
c_flt_m_128[index_word(4, 3)] = c_flt_m >> 32;
c_flt_m_128[index_word(4, 2)] = c_flt_m;
c_flt_m_128[index_word(4, 1)] = 0;
c_flt_m_128[index_word(4, 0)] = 0;
_mesa_sub_m(4, c_flt_m_128, m_128, m_128);
}
} else if (!exp_diff) {
m -= c_flt_m;
if (!m && !m_128[index_word(4, 1)] && !m_128[index_word(4, 0)]) {
/* Return zero */
di_type result;
result.u = (s << 63) + 0;
return result.f;
}
m_128[index_word(4, 3)] = m >> 32;
m_128[index_word(4, 2)] = m;
if (m & 0x8000000000000000) {
s = !s;
_mesa_neg_x_m(4, m_128);
}
} else {
_mesa_sub_m(4, m_128, c_flt_m_128, m_128);
if (1 < exp_diff) {
m = (uint64_t) m_128[index_word(4, 3)] << 32
| m_128[index_word(4, 2)];
if (!(m & 0x4000000000000000)) {
--e;
m <<= 1;
}
if (m_128[index_word(4, 1)] || m_128[index_word(4, 0)])
m |= 1;
return _mesa_roundtozero_f64(s, e - 1, m);
}
}
shift_dist = 0;
m = (uint64_t) m_128[index_word(4, 3)] << 32
| m_128[index_word(4, 2)];
if (!m) {
shift_dist = 64;
m = (uint64_t) m_128[index_word(4, 1)] << 32
| m_128[index_word(4, 0)];
}
shift_dist += _mesa_count_leading_zeros64(m) - 1;
if (shift_dist) {
e -= shift_dist;
_mesa_shift_left_m(4, m_128, shift_dist, m_128);
m = (uint64_t) m_128[index_word(4, 3)] << 32
| m_128[index_word(4, 2)];
}
}
if (m_128[index_word(4, 1)] || m_128[index_word(4, 0)])
m |= 1;
return _mesa_roundtozero_f64(s, e - 1, m);
}
/**
* \brief Calculate a * b + c but rounding to zero.
*
* Notice that this mainly differs from the original Berkeley SoftFloat 3e
* implementation in that we don't really treat NaNs, Zeroes nor the
* signalling flags. Any NaN is good for us and the sign of the Zero is not
* important.
*
* From f32_mulAdd()
*/
float
_mesa_float_fma_rtz(float a, float b, float c)
{
const fi_type a_fi = {a};
uint32_t a_flt_m = a_fi.u & 0x07fffff;
uint32_t a_flt_e = (a_fi.u >> 23) & 0xff;
uint32_t a_flt_s = (a_fi.u >> 31) & 0x1;
const fi_type b_fi = {b};
uint32_t b_flt_m = b_fi.u & 0x07fffff;
uint32_t b_flt_e = (b_fi.u >> 23) & 0xff;
uint32_t b_flt_s = (b_fi.u >> 31) & 0x1;
const fi_type c_fi = {c};
uint32_t c_flt_m = c_fi.u & 0x07fffff;
uint32_t c_flt_e = (c_fi.u >> 23) & 0xff;
uint32_t c_flt_s = (c_fi.u >> 31) & 0x1;
int32_t s, e, m = 0;
c_flt_s ^= 0;
s = a_flt_s ^ b_flt_s ^ 0;
if (a_flt_e == 0xff) {
if (a_flt_m != 0) {
/* 'a' is a NaN, return NaN */
return a;
} else if (b_flt_e == 0xff && b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
} else if (c_flt_e == 0xff && c_flt_m != 0) {
/* 'c' is a NaN, return NaN */
return c;
}
if (!(b_flt_e | b_flt_m)) {
/* Inf * 0 + y = NaN */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + 0x1;
return result.f;
}
if ((c_flt_e == 0xff && c_flt_m == 0) && (s != c_flt_s)) {
/* Inf * x - Inf = NaN */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + 0x1;
return result.f;
}
/* Inf * x + y = Inf */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + 0;
return result.f;
}
if (b_flt_e == 0xff) {
if (b_flt_m != 0) {
/* 'b' is a NaN, return NaN */
return b;
} else if (c_flt_e == 0xff && c_flt_m != 0) {
/* 'c' is a NaN, return NaN */
return c;
}
if (!(a_flt_e | a_flt_m)) {
/* 0 * Inf + y = NaN */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + 0x1;
return result.f;
}
if ((c_flt_e == 0xff && c_flt_m == 0) && (s != c_flt_s)) {
/* x * Inf - Inf = NaN */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + 0x1;
return result.f;
}
/* x * Inf + y = Inf */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + 0;
return result.f;
}
if (c_flt_e == 0xff) {
if (c_flt_m != 0) {
/* 'c' is a NaN, return NaN */
return c;
}
/* x * y + Inf = Inf */
return c;
}
if (a_flt_e == 0) {
if (a_flt_m == 0) {
/* 'a' is zero, return 'c' */
return c;
}
_mesa_norm_subnormal_mantissa_f32(a_flt_m , &a_flt_e, &a_flt_m);
}
if (b_flt_e == 0) {
if (b_flt_m == 0) {
/* 'b' is zero, return 'c' */
return c;
}
_mesa_norm_subnormal_mantissa_f32(b_flt_m , &b_flt_e, &b_flt_m);
}
e = a_flt_e + b_flt_e - 0x7e;
a_flt_m = (a_flt_m | 0x00800000) << 7;
b_flt_m = (b_flt_m | 0x00800000) << 7;
uint64_t m_64 = (uint64_t) a_flt_m * b_flt_m;
if (m_64 < 0x2000000000000000) {
--e;
m_64 <<= 1;
}
if (c_flt_e == 0) {
if (c_flt_m == 0) {
/* 'c' is zero, return 'a * b' */
m = _mesa_short_shift_right_jam64(m_64, 31);
return _mesa_round_f32(s, e - 1, m, true);
}
_mesa_norm_subnormal_mantissa_f32(c_flt_m , &c_flt_e, &c_flt_m);
}
c_flt_m = (c_flt_m | 0x00800000) << 6;
int16_t exp_diff = e - c_flt_e;
if (s == c_flt_s) {
if (exp_diff <= 0) {
e = c_flt_e;
m = c_flt_m + _mesa_shift_right_jam64(m_64, 32 - exp_diff);
} else {
m_64 += _mesa_shift_right_jam64((uint64_t) c_flt_m << 32, exp_diff);
m = _mesa_short_shift_right_jam64(m_64, 32);
}
if (m < 0x40000000) {
--e;
m <<= 1;
}
} else {
uint64_t c_flt_m_64 = (uint64_t) c_flt_m << 32;
if (exp_diff < 0) {
s = c_flt_s;
e = c_flt_e;
m_64 = c_flt_m_64 - _mesa_shift_right_jam64(m_64, -exp_diff);
} else if (!exp_diff) {
m_64 -= c_flt_m_64;
if (!m_64) {
/* Return zero */
fi_type result;
result.u = (s << 31) + 0;
return result.f;
}
if (m_64 & 0x8000000000000000) {
s = !s;
m_64 = -m_64;
}
} else {
m_64 -= _mesa_shift_right_jam64(c_flt_m_64, exp_diff);
}
int8_t shift_dist = _mesa_count_leading_zeros64(m_64) - 1;
e -= shift_dist;
shift_dist -= 32;
if (shift_dist < 0) {
m = _mesa_short_shift_right_jam64(m_64, -shift_dist);
} else {
m = (uint32_t) m_64 << shift_dist;
}
}
return _mesa_round_f32(s, e, m, true);
}
/**
* \brief Converts from 64bits to 32bits float and rounds according to
* instructed.
*
* From f64_to_f32()
*/
float
_mesa_double_to_f32(double val, bool rtz)
{
const di_type di = {val};
uint64_t flt_m = di.u & 0x0fffffffffffff;
uint64_t flt_e = (di.u >> 52) & 0x7ff;
uint64_t flt_s = (di.u >> 63) & 0x1;
int32_t s, e, m = 0;
s = flt_s;
if (flt_e == 0x7ff) {
if (flt_m != 0) {
/* 'val' is a NaN, return NaN */
fi_type result;
e = 0xff;
m = 0x1;
result.u = (s << 31) + (e << 23) + m;
return result.f;
}
/* 'val' is Inf, return Inf */
fi_type result;
e = 0xff;
result.u = (s << 31) + (e << 23) + m;
return result.f;
}
if (!(flt_e | flt_m)) {
/* 'val' is zero, return zero */
fi_type result;
e = 0;
result.u = (s << 31) + (e << 23) + m;
return result.f;
}
m = _mesa_short_shift_right_jam64(flt_m, 22);
if ( ! (flt_e | m) ) {
/* 'val' is denorm, return zero */
fi_type result;
e = 0;
result.u = (s << 31) + (e << 23) + m;
return result.f;
}
return _mesa_round_f32(s, flt_e - 0x381, m | 0x40000000, rtz);
}
/**
* \brief Converts from 32bits to 16bits float and rounds the result to zero.
*
* From f32_to_f16()
*/
uint16_t
_mesa_float_to_half_rtz_slow(float val)
{
const fi_type fi = {val};
const uint32_t flt_m = fi.u & 0x7fffff;
const uint32_t flt_e = (fi.u >> 23) & 0xff;
const uint32_t flt_s = (fi.u >> 31) & 0x1;
int16_t s, e, m = 0;
s = flt_s;
if (flt_e == 0xff) {
if (flt_m != 0) {
/* 'val' is a NaN, return NaN */
e = 0x1f;
/* Retain the top bits of a NaN to make sure that the quiet/signaling
* status stays the same.
*/
m = flt_m >> 13;
if (!m)
m = 1;
return (s << 15) + (e << 10) + m;
}
/* 'val' is Inf, return Inf */
e = 0x1f;
return (s << 15) + (e << 10) + m;
}
if (!(flt_e | flt_m)) {
/* 'val' is zero, return zero */
e = 0;
return (s << 15) + (e << 10) + m;
}
m = flt_m >> 9 | ((flt_m & 0x1ff) != 0);
if ( ! (flt_e | m) ) {
/* 'val' is denorm, return zero */
e = 0;
return (s << 15) + (e << 10) + m;
}
return _mesa_roundtozero_f16(s, flt_e - 0x71, m | 0x4000);
}
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