| |
| /*---------------------------------------------------------------*/ |
| /*--- begin guest_generic_x87.c ---*/ |
| /*---------------------------------------------------------------*/ |
| |
| /* |
| This file is part of Valgrind, a dynamic binary instrumentation |
| framework. |
| |
| Copyright (C) 2004-2010 OpenWorks LLP |
| info@open-works.net |
| |
| This program 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 2 of the |
| License, or (at your option) any later version. |
| |
| This program 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. |
| |
| You should have received a copy of the GNU General Public License |
| along with this program; if not, write to the Free Software |
| Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
| 02110-1301, USA. |
| |
| The GNU General Public License is contained in the file COPYING. |
| |
| Neither the names of the U.S. Department of Energy nor the |
| University of California nor the names of its contributors may be |
| used to endorse or promote products derived from this software |
| without prior written permission. |
| */ |
| |
| /* This file contains functions for doing some x87-specific |
| operations. Both the amd64 and x86 front ends (guests) indirectly |
| call these functions via guest helper calls. By putting them here, |
| code duplication is avoided. Some of these functions are tricky |
| and hard to verify, so there is much to be said for only having one |
| copy thereof. |
| */ |
| |
| #include "libvex_basictypes.h" |
| |
| #include "main_util.h" |
| #include "guest_generic_x87.h" |
| |
| |
| /* 80 and 64-bit floating point formats: |
| |
| 80-bit: |
| |
| S 0 0-------0 zero |
| S 0 0X------X denormals |
| S 1-7FFE 1X------X normals (all normals have leading 1) |
| S 7FFF 10------0 infinity |
| S 7FFF 10X-----X snan |
| S 7FFF 11X-----X qnan |
| |
| S is the sign bit. For runs X----X, at least one of the Xs must be |
| nonzero. Exponent is 15 bits, fractional part is 63 bits, and |
| there is an explicitly represented leading 1, and a sign bit, |
| giving 80 in total. |
| |
| 64-bit avoids the confusion of an explicitly represented leading 1 |
| and so is simpler: |
| |
| S 0 0------0 zero |
| S 0 X------X denormals |
| S 1-7FE any normals |
| S 7FF 0------0 infinity |
| S 7FF 0X-----X snan |
| S 7FF 1X-----X qnan |
| |
| Exponent is 11 bits, fractional part is 52 bits, and there is a |
| sign bit, giving 64 in total. |
| */ |
| |
| |
| static inline UInt read_bit_array ( UChar* arr, UInt n ) |
| { |
| UChar c = arr[n >> 3]; |
| c >>= (n&7); |
| return c & 1; |
| } |
| |
| static inline void write_bit_array ( UChar* arr, UInt n, UInt b ) |
| { |
| UChar c = arr[n >> 3]; |
| c = toUChar( c & ~(1 << (n&7)) ); |
| c = toUChar( c | ((b&1) << (n&7)) ); |
| arr[n >> 3] = c; |
| } |
| |
| /* Convert an IEEE754 double (64-bit) into an x87 extended double |
| (80-bit), mimicing the hardware fairly closely. Both numbers are |
| stored little-endian. Limitations, all of which could be fixed, |
| given some level of hassle: |
| |
| * Identity of NaNs is not preserved. |
| |
| See comments in the code for more details. |
| */ |
| void convert_f64le_to_f80le ( /*IN*/UChar* f64, /*OUT*/UChar* f80 ) |
| { |
| Bool mantissaIsZero; |
| Int bexp, i, j, shift; |
| UChar sign; |
| |
| sign = toUChar( (f64[7] >> 7) & 1 ); |
| bexp = (f64[7] << 4) | ((f64[6] >> 4) & 0x0F); |
| bexp &= 0x7FF; |
| |
| mantissaIsZero = False; |
| if (bexp == 0 || bexp == 0x7FF) { |
| /* We'll need to know whether or not the mantissa (bits 51:0) is |
| all zeroes in order to handle these cases. So figure it |
| out. */ |
| mantissaIsZero |
| = toBool( |
| (f64[6] & 0x0F) == 0 |
| && f64[5] == 0 && f64[4] == 0 && f64[3] == 0 |
| && f64[2] == 0 && f64[1] == 0 && f64[0] == 0 |
| ); |
| } |
| |
| /* If the exponent is zero, either we have a zero or a denormal. |
| Produce a zero. This is a hack in that it forces denormals to |
| zero. Could do better. */ |
| if (bexp == 0) { |
| f80[9] = toUChar( sign << 7 ); |
| f80[8] = f80[7] = f80[6] = f80[5] = f80[4] |
| = f80[3] = f80[2] = f80[1] = f80[0] = 0; |
| |
| if (mantissaIsZero) |
| /* It really is zero, so that's all we can do. */ |
| return; |
| |
| /* There is at least one 1-bit in the mantissa. So it's a |
| potentially denormalised double -- but we can produce a |
| normalised long double. Count the leading zeroes in the |
| mantissa so as to decide how much to bump the exponent down |
| by. Note, this is SLOW. */ |
| shift = 0; |
| for (i = 51; i >= 0; i--) { |
| if (read_bit_array(f64, i)) |
| break; |
| shift++; |
| } |
| |
| /* and copy into place as many bits as we can get our hands on. */ |
| j = 63; |
| for (i = 51 - shift; i >= 0; i--) { |
| write_bit_array( f80, j, |
| read_bit_array( f64, i ) ); |
| j--; |
| } |
| |
| /* Set the exponent appropriately, and we're done. */ |
| bexp -= shift; |
| bexp += (16383 - 1023); |
| f80[9] = toUChar( (sign << 7) | ((bexp >> 8) & 0xFF) ); |
| f80[8] = toUChar( bexp & 0xFF ); |
| return; |
| } |
| |
| /* If the exponent is 7FF, this is either an Infinity, a SNaN or |
| QNaN, as determined by examining bits 51:0, thus: |
| 0 ... 0 Inf |
| 0X ... X SNaN |
| 1X ... X QNaN |
| where at least one of the Xs is not zero. |
| */ |
| if (bexp == 0x7FF) { |
| if (mantissaIsZero) { |
| /* Produce an appropriately signed infinity: |
| S 1--1 (15) 1 0--0 (63) |
| */ |
| f80[9] = toUChar( (sign << 7) | 0x7F ); |
| f80[8] = 0xFF; |
| f80[7] = 0x80; |
| f80[6] = f80[5] = f80[4] = f80[3] |
| = f80[2] = f80[1] = f80[0] = 0; |
| return; |
| } |
| /* So it's either a QNaN or SNaN. Distinguish by considering |
| bit 51. Note, this destroys all the trailing bits |
| (identity?) of the NaN. IEEE754 doesn't require preserving |
| these (it only requires that there be one QNaN value and one |
| SNaN value), but x87 does seem to have some ability to |
| preserve them. Anyway, here, the NaN's identity is |
| destroyed. Could be improved. */ |
| if (f64[6] & 8) { |
| /* QNaN. Make a QNaN: |
| S 1--1 (15) 1 1--1 (63) |
| */ |
| f80[9] = toUChar( (sign << 7) | 0x7F ); |
| f80[8] = 0xFF; |
| f80[7] = 0xFF; |
| f80[6] = f80[5] = f80[4] = f80[3] |
| = f80[2] = f80[1] = f80[0] = 0xFF; |
| } else { |
| /* SNaN. Make a SNaN: |
| S 1--1 (15) 0 1--1 (63) |
| */ |
| f80[9] = toUChar( (sign << 7) | 0x7F ); |
| f80[8] = 0xFF; |
| f80[7] = 0x7F; |
| f80[6] = f80[5] = f80[4] = f80[3] |
| = f80[2] = f80[1] = f80[0] = 0xFF; |
| } |
| return; |
| } |
| |
| /* It's not a zero, denormal, infinity or nan. So it must be a |
| normalised number. Rebias the exponent and build the new |
| number. */ |
| bexp += (16383 - 1023); |
| |
| f80[9] = toUChar( (sign << 7) | ((bexp >> 8) & 0xFF) ); |
| f80[8] = toUChar( bexp & 0xFF ); |
| f80[7] = toUChar( (1 << 7) | ((f64[6] << 3) & 0x78) |
| | ((f64[5] >> 5) & 7) ); |
| f80[6] = toUChar( ((f64[5] << 3) & 0xF8) | ((f64[4] >> 5) & 7) ); |
| f80[5] = toUChar( ((f64[4] << 3) & 0xF8) | ((f64[3] >> 5) & 7) ); |
| f80[4] = toUChar( ((f64[3] << 3) & 0xF8) | ((f64[2] >> 5) & 7) ); |
| f80[3] = toUChar( ((f64[2] << 3) & 0xF8) | ((f64[1] >> 5) & 7) ); |
| f80[2] = toUChar( ((f64[1] << 3) & 0xF8) | ((f64[0] >> 5) & 7) ); |
| f80[1] = toUChar( ((f64[0] << 3) & 0xF8) ); |
| f80[0] = toUChar( 0 ); |
| } |
| |
| |
| /* Convert an x87 extended double (80-bit) into an IEEE 754 double |
| (64-bit), mimicking the hardware fairly closely. Both numbers are |
| stored little-endian. Limitations, both of which could be fixed, |
| given some level of hassle: |
| |
| * Rounding following truncation could be a bit better. |
| |
| * Identity of NaNs is not preserved. |
| |
| See comments in the code for more details. |
| */ |
| void convert_f80le_to_f64le ( /*IN*/UChar* f80, /*OUT*/UChar* f64 ) |
| { |
| Bool isInf; |
| Int bexp, i, j; |
| UChar sign; |
| |
| sign = toUChar((f80[9] >> 7) & 1); |
| bexp = (((UInt)f80[9]) << 8) | (UInt)f80[8]; |
| bexp &= 0x7FFF; |
| |
| /* If the exponent is zero, either we have a zero or a denormal. |
| But an extended precision denormal becomes a double precision |
| zero, so in either case, just produce the appropriately signed |
| zero. */ |
| if (bexp == 0) { |
| f64[7] = toUChar(sign << 7); |
| f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| return; |
| } |
| |
| /* If the exponent is 7FFF, this is either an Infinity, a SNaN or |
| QNaN, as determined by examining bits 62:0, thus: |
| 0 ... 0 Inf |
| 0X ... X SNaN |
| 1X ... X QNaN |
| where at least one of the Xs is not zero. |
| */ |
| if (bexp == 0x7FFF) { |
| isInf = toBool( |
| (f80[7] & 0x7F) == 0 |
| && f80[6] == 0 && f80[5] == 0 && f80[4] == 0 |
| && f80[3] == 0 && f80[2] == 0 && f80[1] == 0 |
| && f80[0] == 0 |
| ); |
| if (isInf) { |
| if (0 == (f80[7] & 0x80)) |
| goto wierd_NaN; |
| /* Produce an appropriately signed infinity: |
| S 1--1 (11) 0--0 (52) |
| */ |
| f64[7] = toUChar((sign << 7) | 0x7F); |
| f64[6] = 0xF0; |
| f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| return; |
| } |
| /* So it's either a QNaN or SNaN. Distinguish by considering |
| bit 62. Note, this destroys all the trailing bits |
| (identity?) of the NaN. IEEE754 doesn't require preserving |
| these (it only requires that there be one QNaN value and one |
| SNaN value), but x87 does seem to have some ability to |
| preserve them. Anyway, here, the NaN's identity is |
| destroyed. Could be improved. */ |
| if (f80[8] & 0x40) { |
| /* QNaN. Make a QNaN: |
| S 1--1 (11) 1 1--1 (51) |
| */ |
| f64[7] = toUChar((sign << 7) | 0x7F); |
| f64[6] = 0xFF; |
| f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF; |
| } else { |
| /* SNaN. Make a SNaN: |
| S 1--1 (11) 0 1--1 (51) |
| */ |
| f64[7] = toUChar((sign << 7) | 0x7F); |
| f64[6] = 0xF7; |
| f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF; |
| } |
| return; |
| } |
| |
| /* If it's not a Zero, NaN or Inf, and the integer part (bit 62) is |
| zero, the x87 FPU appears to consider the number denormalised |
| and converts it to a QNaN. */ |
| if (0 == (f80[7] & 0x80)) { |
| wierd_NaN: |
| /* Strange hardware QNaN: |
| S 1--1 (11) 1 0--0 (51) |
| */ |
| /* On a PIII, these QNaNs always appear with sign==1. I have |
| no idea why. */ |
| f64[7] = (1 /*sign*/ << 7) | 0x7F; |
| f64[6] = 0xF8; |
| f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| return; |
| } |
| |
| /* It's not a zero, denormal, infinity or nan. So it must be a |
| normalised number. Rebias the exponent and consider. */ |
| bexp -= (16383 - 1023); |
| if (bexp >= 0x7FF) { |
| /* It's too big for a double. Construct an infinity. */ |
| f64[7] = toUChar((sign << 7) | 0x7F); |
| f64[6] = 0xF0; |
| f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| return; |
| } |
| |
| if (bexp <= 0) { |
| /* It's too small for a normalised double. First construct a |
| zero and then see if it can be improved into a denormal. */ |
| f64[7] = toUChar(sign << 7); |
| f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| |
| if (bexp < -52) |
| /* Too small even for a denormal. */ |
| return; |
| |
| /* Ok, let's make a denormal. Note, this is SLOW. */ |
| /* Copy bits 63, 62, 61, etc of the src mantissa into the dst, |
| indexes 52+bexp, 51+bexp, etc, until k+bexp < 0. */ |
| /* bexp is in range -52 .. 0 inclusive */ |
| for (i = 63; i >= 0; i--) { |
| j = i - 12 + bexp; |
| if (j < 0) break; |
| /* We shouldn't really call vassert from generated code. */ |
| vassert(j >= 0 && j < 52); |
| write_bit_array ( f64, |
| j, |
| read_bit_array ( f80, i ) ); |
| } |
| /* and now we might have to round ... */ |
| if (read_bit_array(f80, 10+1 - bexp) == 1) |
| goto do_rounding; |
| |
| return; |
| } |
| |
| /* Ok, it's a normalised number which is representable as a double. |
| Copy the exponent and mantissa into place. */ |
| /* |
| for (i = 0; i < 52; i++) |
| write_bit_array ( f64, |
| i, |
| read_bit_array ( f80, i+11 ) ); |
| */ |
| f64[0] = toUChar( (f80[1] >> 3) | (f80[2] << 5) ); |
| f64[1] = toUChar( (f80[2] >> 3) | (f80[3] << 5) ); |
| f64[2] = toUChar( (f80[3] >> 3) | (f80[4] << 5) ); |
| f64[3] = toUChar( (f80[4] >> 3) | (f80[5] << 5) ); |
| f64[4] = toUChar( (f80[5] >> 3) | (f80[6] << 5) ); |
| f64[5] = toUChar( (f80[6] >> 3) | (f80[7] << 5) ); |
| |
| f64[6] = toUChar( ((bexp << 4) & 0xF0) | ((f80[7] >> 3) & 0x0F) ); |
| |
| f64[7] = toUChar( (sign << 7) | ((bexp >> 4) & 0x7F) ); |
| |
| /* Now consider any rounding that needs to happen as a result of |
| truncating the mantissa. */ |
| if (f80[1] & 4) /* read_bit_array(f80, 10) == 1) */ { |
| |
| /* If the bottom bits of f80 are "100 0000 0000", then the |
| infinitely precise value is deemed to be mid-way between the |
| two closest representable values. Since we're doing |
| round-to-nearest (the default mode), in that case it is the |
| bit immediately above which indicates whether we should round |
| upwards or not -- if 0, we don't. All that is encapsulated |
| in the following simple test. */ |
| if ((f80[1] & 0xF) == 4/*0100b*/ && f80[0] == 0) |
| return; |
| |
| do_rounding: |
| /* Round upwards. This is a kludge. Once in every 2^24 |
| roundings (statistically) the bottom three bytes are all 0xFF |
| and so we don't round at all. Could be improved. */ |
| if (f64[0] != 0xFF) { |
| f64[0]++; |
| } |
| else |
| if (f64[0] == 0xFF && f64[1] != 0xFF) { |
| f64[0] = 0; |
| f64[1]++; |
| } |
| else |
| if (f64[0] == 0xFF && f64[1] == 0xFF && f64[2] != 0xFF) { |
| f64[0] = 0; |
| f64[1] = 0; |
| f64[2]++; |
| } |
| /* else we don't round, but we should. */ |
| } |
| } |
| |
| |
| /* CALLED FROM GENERATED CODE: CLEAN HELPER */ |
| /* Extract the signed significand or exponent component as per |
| fxtract. Arg and result are doubles travelling under the guise of |
| ULongs. Returns significand when getExp is zero and exponent |
| otherwise. */ |
| ULong x86amd64g_calculate_FXTRACT ( ULong arg, HWord getExp ) |
| { |
| ULong uSig, uExp; |
| /* Long sSig; */ |
| Int sExp, i; |
| UInt sign, expExp; |
| |
| /* |
| S 7FF 0------0 infinity |
| S 7FF 0X-----X snan |
| S 7FF 1X-----X qnan |
| */ |
| const ULong posInf = 0x7FF0000000000000ULL; |
| const ULong negInf = 0xFFF0000000000000ULL; |
| const ULong nanMask = 0x7FF0000000000000ULL; |
| const ULong qNan = 0x7FF8000000000000ULL; |
| const ULong posZero = 0x0000000000000000ULL; |
| const ULong negZero = 0x8000000000000000ULL; |
| const ULong bit51 = 1ULL << 51; |
| const ULong bit52 = 1ULL << 52; |
| const ULong sigMask = bit52 - 1; |
| |
| /* Mimic PIII behaviour for special cases. */ |
| if (arg == posInf) |
| return getExp ? posInf : posInf; |
| if (arg == negInf) |
| return getExp ? posInf : negInf; |
| if ((arg & nanMask) == nanMask) |
| return qNan; |
| if (arg == posZero) |
| return getExp ? negInf : posZero; |
| if (arg == negZero) |
| return getExp ? negInf : negZero; |
| |
| /* Split into sign, exponent and significand. */ |
| sign = ((UInt)(arg >> 63)) & 1; |
| |
| /* Mask off exponent & sign. uSig is in range 0 .. 2^52-1. */ |
| uSig = arg & sigMask; |
| |
| /* Get the exponent. */ |
| sExp = ((Int)(arg >> 52)) & 0x7FF; |
| |
| /* Deal with denormals: if the exponent is zero, then the |
| significand cannot possibly be zero (negZero/posZero are handled |
| above). Shift the significand left until bit 51 of it becomes |
| 1, and decrease the exponent accordingly. |
| */ |
| if (sExp == 0) { |
| for (i = 0; i < 52; i++) { |
| if (uSig & bit51) |
| break; |
| uSig <<= 1; |
| sExp--; |
| } |
| uSig <<= 1; |
| } else { |
| /* Add the implied leading-1 in the significand. */ |
| uSig |= bit52; |
| } |
| |
| /* Roll in the sign. */ |
| /* sSig = uSig; */ |
| /* if (sign) sSig =- sSig; */ |
| |
| /* Convert sig into a double. This should be an exact conversion. |
| Then divide by 2^52, which should give a value in the range 1.0 |
| to 2.0-epsilon, at least for normalised args. */ |
| /* dSig = (Double)sSig; */ |
| /* dSig /= 67108864.0; */ /* 2^26 */ |
| /* dSig /= 67108864.0; */ /* 2^26 */ |
| uSig &= sigMask; |
| uSig |= 0x3FF0000000000000ULL; |
| if (sign) |
| uSig ^= negZero; |
| |
| /* Convert exp into a double. Also an exact conversion. */ |
| /* dExp = (Double)(sExp - 1023); */ |
| sExp -= 1023; |
| if (sExp == 0) { |
| uExp = 0; |
| } else { |
| uExp = sExp < 0 ? -sExp : sExp; |
| expExp = 0x3FF +52; |
| /* 1 <= uExp <= 1074 */ |
| /* Skip first 42 iterations of normalisation loop as we know they |
| will always happen */ |
| uExp <<= 42; |
| expExp -= 42; |
| for (i = 0; i < 52-42; i++) { |
| if (uExp & bit52) |
| break; |
| uExp <<= 1; |
| expExp--; |
| } |
| uExp &= sigMask; |
| uExp |= ((ULong)expExp) << 52; |
| if (sExp < 0) uExp ^= negZero; |
| } |
| |
| return getExp ? uExp : uSig; |
| } |
| |
| |
| /*---------------------------------------------------------------*/ |
| /*--- end guest_generic_x87.c ---*/ |
| /*---------------------------------------------------------------*/ |