| |
| #ifndef USED_AS_INCLUDE |
| |
| #include "../pub/libvex_basictypes.h" |
| #include <stdio.h> |
| #include <malloc.h> |
| #include <stdlib.h> |
| #include <string.h> |
| #include <assert.h> |
| |
| |
| /* Test program for developing code for conversions between |
| x87 64-bit and 80-bit floats. |
| |
| 80-bit format exists only for x86/x86-64, and so the routines |
| hardwire it as little-endian. The 64-bit format (IEEE double) |
| could exist on any platform, little or big-endian and so we |
| have to take that into account. IOW, these routines have to |
| work correctly when compiled on both big- and little-endian |
| targets, but the 80-bit images only ever have to exist in |
| little-endian format. |
| */ |
| static void show_f80 ( UChar* ); |
| static void show_f64 ( UChar* ); |
| |
| 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 &= ~(1 << (n&7)); |
| c |= ((b&1) << (n&7)); |
| arr[n >> 3] = c; |
| } |
| |
| |
| static void convert_f80le_to_f64le_HW ( /*IN*/UChar* f80, /*OUT*/UChar* f64 ) |
| { |
| asm volatile ("ffree %%st(7); fldt (%0); fstpl (%1)" |
| : |
| : "r" (&f80[0]), "r" (&f64[0]) |
| : "memory" ); |
| } |
| |
| static void convert_f64le_to_f80le_HW ( /*IN*/UChar* f64, /*OUT*/UChar* f80 ) |
| { |
| asm volatile ("ffree %%st(7); fldl (%0); fstpt (%1)" |
| : |
| : "r" (&f64[0]), "r" (&f80[0]) |
| : "memory" ); |
| } |
| |
| #endif /* ndef USED_AS_INCLUDE */ |
| |
| |
| |
| /* 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. |
| */ |
| |
| /* Convert a 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. |
| */ |
| static 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 a 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. |
| */ |
| static 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. */ |
| assert(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. */ |
| } |
| } |
| |
| |
| #ifndef USED_AS_INCLUDE |
| |
| ////////////// |
| |
| static void show_f80 ( UChar* f80 ) |
| { |
| Int i; |
| printf("%d ", read_bit_array(f80, 79)); |
| |
| for (i = 78; i >= 64; i--) |
| printf("%d", read_bit_array(f80, i)); |
| |
| printf(" %d ", read_bit_array(f80, 63)); |
| |
| for (i = 62; i >= 0; i--) |
| printf("%d", read_bit_array(f80, i)); |
| } |
| |
| static void show_f64le ( UChar* f64 ) |
| { |
| Int i; |
| printf("%d ", read_bit_array(f64, 63)); |
| |
| for (i = 62; i >= 52; i--) |
| printf("%d", read_bit_array(f64, i)); |
| |
| printf(" "); |
| for (i = 51; i >= 0; i--) |
| printf("%d", read_bit_array(f64, i)); |
| } |
| |
| ////////////// |
| |
| |
| /* Convert f80 to a 64-bit IEEE double using both the hardware and the |
| soft version, and compare the results. If they differ, print |
| details and return 1. If they are identical, return 0. |
| */ |
| int do_80_to_64_test ( Int test_no, UChar* f80, UChar* f64h, UChar* f64s) |
| { |
| Char buf64s[100], buf64h[100]; |
| Bool same; |
| Int k; |
| convert_f80le_to_f64le_HW(f80, f64h); |
| convert_f80le_to_f64le(f80, f64s); |
| same = True; |
| for (k = 0; k < 8; k++) { |
| if (f64s[k] != f64h[k]) { |
| same = False; break; |
| } |
| } |
| /* bitwise identical */ |
| if (same) |
| return 0; |
| |
| sprintf(buf64s, "%.16e", *(double*)f64s); |
| sprintf(buf64h, "%.16e", *(double*)f64h); |
| |
| /* Not bitwise identical, but pretty darn close */ |
| if (0 == strcmp(buf64s, buf64h)) |
| return 0; |
| |
| printf("\n"); |
| printf("f80: "); show_f80(f80); printf("\n"); |
| printf("f64h: "); show_f64le(f64h); printf("\n"); |
| printf("f64s: "); show_f64le(f64s); printf("\n"); |
| |
| printf("[test %d] %.16Le -> (hw %s, sw %s)\n", |
| test_no, *(long double*)f80, |
| buf64h, buf64s ); |
| |
| return 1; |
| } |
| |
| |
| /* Convert an IEEE 64-bit double to a x87 extended double (80 bit) |
| using both the hardware and the soft version, and compare the |
| results. If they differ, print details and return 1. If they are |
| identical, return 0. |
| */ |
| int do_64_to_80_test ( Int test_no, UChar* f64, UChar* f80h, UChar* f80s) |
| { |
| Char buf80s[100], buf80h[100]; |
| Bool same; |
| Int k; |
| convert_f64le_to_f80le_HW(f64, f80h); |
| convert_f64le_to_f80le(f64, f80s); |
| same = True; |
| for (k = 0; k < 10; k++) { |
| if (f80s[k] != f80h[k]) { |
| same = False; break; |
| } |
| } |
| /* bitwise identical */ |
| if (same) |
| return 0; |
| |
| sprintf(buf80s, "%.20Le", *(long double*)f80s); |
| sprintf(buf80h, "%.20Le", *(long double*)f80h); |
| |
| /* Not bitwise identical, but pretty darn close */ |
| if (0 == strcmp(buf80s, buf80h)) |
| return 0; |
| |
| printf("\n"); |
| printf("f64: "); show_f64le(f64); printf("\n"); |
| printf("f80h: "); show_f80(f80h); printf("\n"); |
| printf("f80s: "); show_f80(f80s); printf("\n"); |
| |
| printf("[test %d] %.16e -> (hw %s, sw %s)\n", |
| test_no, *(double*)f64, |
| buf80h, buf80s ); |
| |
| return 1; |
| } |
| |
| |
| |
| void do_80_to_64_tests ( void ) |
| { |
| UInt b9,b8,b7,i, j; |
| Int fails=0, tests=0; |
| UChar* f64h = malloc(8); |
| UChar* f64s = malloc(8); |
| UChar* f80 = malloc(10); |
| int STEP = 1; |
| |
| srandom(4343); |
| |
| /* Ten million random bit patterns */ |
| for (i = 0; i < 10000000; i++) { |
| tests++; |
| for (j = 0; j < 10; j++) |
| f80[j] = (random() >> 7) & 255; |
| |
| fails += do_80_to_64_test(tests, f80, f64h, f64s); |
| } |
| |
| /* 2^24 numbers in which the first 24 bits are tested exhaustively |
| -- this covers the sign, exponent and leading part of the |
| mantissa. */ |
| for (b9 = 0; b9 < 256; b9 += STEP) { |
| for (b8 = 0; b8 < 256; b8 += STEP) { |
| for (b7 = 0; b7 < 256; b7 += STEP) { |
| tests++; |
| for (i = 0; i < 10; i++) |
| f80[i] = 0; |
| for (i = 0; i < 8; i++) |
| f64h[i] = f64s[i] = 0; |
| f80[9] = b9; |
| f80[8] = b8; |
| f80[7] = b7; |
| |
| fails += do_80_to_64_test(tests, f80, f64h, f64s); |
| }}} |
| |
| printf("\n80 -> 64: %d tests, %d fails\n\n", tests, fails); |
| } |
| |
| |
| void do_64_to_80_tests ( void ) |
| { |
| UInt b7,b6,b5,i, j; |
| Int fails=0, tests=0; |
| UChar* f80h = malloc(10); |
| UChar* f80s = malloc(10); |
| UChar* f64 = malloc(8); |
| int STEP = 1; |
| |
| srandom(2323); |
| |
| /* Ten million random bit patterns */ |
| for (i = 0; i < 10000000; i++) { |
| tests++; |
| for (j = 0; j < 8; j++) |
| f64[j] = (random() >> 13) & 255; |
| |
| fails += do_64_to_80_test(tests, f64, f80h, f80s); |
| } |
| |
| /* 2^24 numbers in which the first 24 bits are tested exhaustively |
| -- this covers the sign, exponent and leading part of the |
| mantissa. */ |
| for (b7 = 0; b7 < 256; b7 += STEP) { |
| for (b6 = 0; b6 < 256; b6 += STEP) { |
| for (b5 = 0; b5 < 256; b5 += STEP) { |
| tests++; |
| for (i = 0; i < 8; i++) |
| f64[i] = 0; |
| for (i = 0; i < 10; i++) |
| f80h[i] = f80s[i] = 0; |
| f64[7] = b7; |
| f64[6] = b6; |
| f64[5] = b5; |
| |
| fails += do_64_to_80_test(tests, f64, f80h, f80s); |
| }}} |
| |
| printf("\n64 -> 80: %d tests, %d fails\n\n", tests, fails); |
| } |
| |
| |
| int main ( void ) |
| { |
| do_80_to_64_tests(); |
| do_64_to_80_tests(); |
| return 0; |
| } |
| |
| #endif /* ndef USED_AS_INCLUDE */ |
