| /* Half-float conversion routines. |
| |
| Copyright (C) 2008-2021 Free Software Foundation, Inc. |
| Contributed by CodeSourcery. |
| |
| This file is free software; you can redistribute it and/or modify it |
| under the terms of the GNU General Public License as published by the |
| Free Software Foundation; either version 3, or (at your option) any |
| later version. |
| |
| This file is distributed in the hope that it will be useful, but |
| WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| General Public License for more details. |
| |
| Under Section 7 of GPL version 3, you are granted additional |
| permissions described in the GCC Runtime Library Exception, version |
| 3.1, as published by the Free Software Foundation. |
| |
| You should have received a copy of the GNU General Public License and |
| a copy of the GCC Runtime Library Exception along with this program; |
| see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| struct format |
| { |
| /* Number of bits. */ |
| unsigned long long size; |
| /* Exponent bias. */ |
| unsigned long long bias; |
| /* Exponent width in bits. */ |
| unsigned long long exponent; |
| /* Significand precision in explicitly stored bits. */ |
| unsigned long long significand; |
| }; |
| |
| static const struct format |
| binary32 = |
| { |
| 32, /* size. */ |
| 127, /* bias. */ |
| 8, /* exponent. */ |
| 23 /* significand. */ |
| }; |
| |
| static const struct format |
| binary64 = |
| { |
| 64, /* size. */ |
| 1023, /* bias. */ |
| 11, /* exponent. */ |
| 52 /* significand. */ |
| }; |
| |
| /* Function prototypes. */ |
| unsigned short __gnu_f2h_ieee (unsigned int a); |
| unsigned int __gnu_h2f_ieee (unsigned short a); |
| unsigned short __gnu_f2h_alternative (unsigned int x); |
| unsigned int __gnu_h2f_alternative (unsigned short a); |
| unsigned short __gnu_d2h_ieee (unsigned long long a); |
| unsigned short __gnu_d2h_alternative (unsigned long long x); |
| |
| static inline unsigned short |
| __gnu_float2h_internal (const struct format* fmt, |
| unsigned long long a, int ieee) |
| { |
| unsigned long long point = 1ULL << fmt->significand; |
| unsigned short sign = (a >> (fmt->size - 16)) & 0x8000; |
| int aexp; |
| unsigned long long mantissa; |
| unsigned long long mask; |
| unsigned long long increment; |
| |
| /* Get the exponent and mantissa encodings. */ |
| mantissa = a & (point - 1); |
| |
| mask = (1 << fmt->exponent) - 1; |
| aexp = (a >> fmt->significand) & mask; |
| |
| /* Infinity, NaN and alternative format special case. */ |
| if (((unsigned int) aexp) == mask) |
| { |
| if (!ieee) |
| return sign; |
| if (mantissa == 0) |
| return sign | 0x7c00; /* Infinity. */ |
| /* Remaining cases are NaNs. Convert SNaN to QNaN. */ |
| return sign | 0x7e00 | (mantissa >> (fmt->significand - 10)); |
| } |
| |
| /* Zero. */ |
| if (aexp == 0 && mantissa == 0) |
| return sign; |
| |
| /* Construct the exponent and mantissa. */ |
| aexp -= fmt->bias; |
| |
| /* Decimal point is immediately after the significand. */ |
| mantissa |= point; |
| |
| if (aexp < -14) |
| { |
| mask = point | (point - 1); |
| /* Minimum exponent for half-precision is 2^-24. */ |
| if (aexp >= -25) |
| mask >>= 25 + aexp; |
| } |
| else |
| mask = (point - 1) >> 10; |
| |
| /* Round. */ |
| if (mantissa & mask) |
| { |
| increment = (mask + 1) >> 1; |
| if ((mantissa & mask) == increment) |
| increment = mantissa & (increment << 1); |
| mantissa += increment; |
| if (mantissa >= (point << 1)) |
| { |
| mantissa >>= 1; |
| aexp++; |
| } |
| } |
| |
| if (ieee) |
| { |
| if (aexp > 15) |
| return sign | 0x7c00; |
| } |
| else |
| { |
| if (aexp > 16) |
| return sign | 0x7fff; |
| } |
| |
| if (aexp < -24) |
| return sign; |
| |
| if (aexp < -14) |
| { |
| mantissa >>= -14 - aexp; |
| aexp = -14; |
| } |
| |
| /* Encode the final 16-bit floating-point value. |
| |
| This is formed of the sign bit, the bias-adjusted exponent, and the |
| calculated mantissa, with the following caveats: |
| |
| 1. The mantissa calculated after rounding could have a leading 1. |
| To compensate for this, subtract one from the exponent bias (15) |
| before adding it to the calculated exponent. |
| 2. When we were calculating rounding, we left the mantissa with the |
| number of bits of the source operand, it needs reduced to ten |
| bits (+1 for the afforementioned leading 1) by shifting right by |
| the number of bits in the source mantissa - 10. |
| 3. To ensure the leading 1 in the mantissa is applied to the exponent |
| we need to add the mantissa rather than apply an arithmetic "or" |
| to it. */ |
| |
| return sign | (((aexp + 14) << 10) + (mantissa >> (fmt->significand - 10))); |
| } |
| |
| static inline unsigned short |
| __gnu_f2h_internal (unsigned int a, int ieee) |
| { |
| return __gnu_float2h_internal (&binary32, (unsigned long long) a, ieee); |
| } |
| |
| static inline unsigned short |
| __gnu_d2h_internal (unsigned long long a, int ieee) |
| { |
| return __gnu_float2h_internal (&binary64, a, ieee); |
| } |
| |
| static inline unsigned int |
| __gnu_h2f_internal(unsigned short a, int ieee) |
| { |
| unsigned int sign = (unsigned int)(a & 0x8000) << 16; |
| int aexp = (a >> 10) & 0x1f; |
| unsigned int mantissa = a & 0x3ff; |
| |
| if (aexp == 0x1f && ieee) |
| return sign | 0x7f800000 | (mantissa << 13); |
| |
| if (aexp == 0) |
| { |
| int shift; |
| |
| if (mantissa == 0) |
| return sign; |
| |
| shift = __builtin_clz(mantissa) - 21; |
| mantissa <<= shift; |
| aexp = -shift; |
| } |
| |
| return sign | (((aexp + 0x70) << 23) + (mantissa << 13)); |
| } |
| |
| unsigned short |
| __gnu_f2h_ieee(unsigned int a) |
| { |
| return __gnu_f2h_internal(a, 1); |
| } |
| |
| unsigned int |
| __gnu_h2f_ieee(unsigned short a) |
| { |
| return __gnu_h2f_internal(a, 1); |
| } |
| |
| unsigned short |
| __gnu_f2h_alternative(unsigned int x) |
| { |
| return __gnu_f2h_internal(x, 0); |
| } |
| |
| unsigned int |
| __gnu_h2f_alternative(unsigned short a) |
| { |
| return __gnu_h2f_internal(a, 0); |
| } |
| |
| unsigned short |
| __gnu_d2h_ieee (unsigned long long a) |
| { |
| return __gnu_d2h_internal (a, 1); |
| } |
| |
| unsigned short |
| __gnu_d2h_alternative (unsigned long long x) |
| { |
| return __gnu_d2h_internal (x, 0); |
| } |