--- /dev/null
+/*
+ * 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) || (0x8000 <= m)) {
+ 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;
+ 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);
+ }
+ 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(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;
+ m = 0x1;
+ 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);
+}
projects / mesa.git / commitdiff