util: add softfloat functions to operate with doubles and floats

Implemented fadd, fsub, fmul and ffma for doubles and ffma for floats,
rounding to zero, using a modified implementation from Berkely
Softfloat 3e Library.

Their implementation correctness has been checked with the Berkeley
TestFloat Release 3e tool for x86_64.

v2:
- Reuse util_last_bit64() in _mesa_count_leading_zeros64()
  implementation (Connor).

v3:
- Add a specific ffma for floats version (Connor).
- Implement the ffma for doubles version (Andres).
- Lots of fixes in fadd, fsub and fmul (Andres).
- Improved documentation (Andres).

v4:
- Added f64 -> f32 conversion function (Andres).
- Added f32 -> f16 RTZ conversion function (Andres).

Signed-off-by: Samuel Iglesias Gonsálvez <[email protected]>
Signed-off-by: Andres Gomez <[email protected]>
Tested-by: Andres Gomez <[email protected]>
Acked-by: Caio Marcelo de Oliveira Filho <[email protected]>

4 files changed, 1544 insertions, 0 deletions

diff --git a/src/util/Makefile.sources b/src/util/Makefile.sources
index fdb9b6dd135..e4d9d73ce8a 100644
--- a/src/util/Makefile.sources
+++ b/src/util/Makefile.sources
@@ -56,6 +56,8 @@ MESA_UTIL_FILES := \
 	simple_mtx.h \
 	slab.c \
 	slab.h \
+	softfloat.c \
+	softfloat.h \
 	string_buffer.c \
 	string_buffer.h \
 	strndup.h \
diff --git a/src/util/meson.build b/src/util/meson.build
index 3e65a36fdb5..8326691f408 100644
--- a/src/util/meson.build
+++ b/src/util/meson.build
@@ -78,6 +78,8 @@ files_mesa_util = files(
   'simple_mtx.h',
   'slab.c',
   'slab.h',
+  'softfloat.c',
+  'softfloat.h',
   'string_buffer.c',
   'string_buffer.h',
   'strndup.h',
diff --git a/src/util/softfloat.c b/src/util/softfloat.c
new file mode 100644
index 00000000000..591128efd47
--- /dev/null
+++ b/src/util/softfloat.c
@@ -0,0 +1,1475 @@
+/*
+ * 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);
+}
diff --git a/src/util/softfloat.h b/src/util/softfloat.h
new file mode 100644
index 00000000000..4e48c6548b9
--- /dev/null
+++ b/src/util/softfloat.h
@@ -0,0 +1,65 @@
+/*
+ * 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.
+ */
+
+#ifndef _SOFTFLOAT_H_
+#define _SOFTFLOAT_H_
+
+#include <stdbool.h>
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+double _mesa_double_add_rtz(double a, double b);
+double _mesa_double_sub_rtz(double a, double b);
+double _mesa_double_mul_rtz(double a, double b);
+double _mesa_double_fma_rtz(double a, double b, double c);
+float _mesa_float_fma_rtz(float a, float b, float c);
+float _mesa_double_to_f32(double x, bool rtz);
+uint16_t _mesa_float_to_half_rtz(float x);
+
+#ifdef __cplusplus
+} /* extern C */
+#endif
+
+#endif  /* _SOFTFLOAT_H */