| /* |
| * 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); |
| } |
