From: Julian Seward Date: Mon, 6 Sep 2004 14:57:52 +0000 (+0000) Subject: Test program for developing double <-> extended double conversion X-Git-Tag: svn/VALGRIND_3_0_1^2~1106 X-Git-Url: http://git.ipfire.org/gitweb.cgi?a=commitdiff_plain;h=d6b2245803cad4eef5680d246c9954edf57f2012;p=thirdparty%2Fvalgrind.git Test program for developing double <-> extended double conversion code. git-svn-id: svn://svn.valgrind.org/vex/trunk@228 --- diff --git a/VEX/useful/fp_80_64.c b/VEX/useful/fp_80_64.c new file mode 100644 index 0000000000..e874012cff --- /dev/null +++ b/VEX/useful/fp_80_64.c @@ -0,0 +1,550 @@ + +#include "../pub/libvex_basictypes.h" +#include +#include +#include +#include + + +/* 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 +UInt read_bit_array ( UChar* arr, UInt n ) +{ + UChar c = arr[n >> 3]; + c >>= (n&7); + return c & 1; +} + + +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" ); +} + +/* 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: + + * Does not handle double precision denormals. As a result, values + with magnitudes less than 1e-308 are flushed to zero when they + need not be. + + * 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 isInf; + Int bexp; + UChar sign; + + sign = (f64[7] >> 7) & 1; + bexp = (f64[7] << 4) | ((f64[6] >> 4) & 0x0F); + bexp &= 0x7FF; + + /* 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] = sign << 7; + f80[8] = f80[7] = f80[6] = f80[5] = f80[4] + = f80[3] = f80[2] = f80[1] = f80[0] = 0; + 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) { + isInf = (f64[6] & 0x0F) == 0 + && f64[5] == 0 && f64[4] == 0 && f64[3] == 0 + && f64[2] == 0 && f64[1] == 0 && f64[0] == 0; + if (isInf) { + /* Produce an appropriately signed infinity: + S 1--1 (15) 1 0--0 (63) + */ + f80[9] = (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] = (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] = (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] = (sign << 7) | ((bexp >> 8) & 0xFF); + f80[8] = bexp & 0xFF; + f80[7] = (1 << 7) | ((f64[6] << 3) & 0x78) | ((f64[5] >> 5) & 7); + f80[6] = ((f64[5] << 3) & 0xF8) | ((f64[4] >> 5) & 7); + f80[5] = ((f64[4] << 3) & 0xF8) | ((f64[3] >> 5) & 7); + f80[4] = ((f64[3] << 3) & 0xF8) | ((f64[2] >> 5) & 7); + f80[3] = ((f64[2] << 3) & 0xF8) | ((f64[1] >> 5) & 7); + f80[2] = ((f64[1] << 3) & 0xF8) | ((f64[0] >> 5) & 7); + f80[1] = ((f64[0] << 3) & 0xF8); + f80[0] = 0; +} + + +///////////////////////////////////////////////////////////////// + +/* Convert a x87 extended double (80-bit) into an IEEE 754 double + (64-bit), mimicing the hardware fairly closely. Both numbers are + stored little-endian. Limitations, all of which could be fixed, + given some level of hassle: + + * Does not create double precision denormals. As a result, values + with magnitudes less than 1e-308 are flushed to zero when they + need not be. + + * 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; + UChar sign; + + sign = (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] = 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 = (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] = (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] = (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] = (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] = (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 double. Construct a zero. Note, this + is a kludge since we could conceivably create a + denormalised number for bexp in -1 to -51, but we don't + bother. This means the conversion flushes values + approximately in the range 1e-309 to 1e-324 ish to zero + when it doesn't actually need to. This could be + improved. */ + f64[7] = sign << 7; + f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; + 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] = (f80[1] >> 3) | (f80[2] << 5); + f64[1] = (f80[2] >> 3) | (f80[3] << 5); + f64[2] = (f80[3] >> 3) | (f80[4] << 5); + f64[3] = (f80[4] >> 3) | (f80[5] << 5); + f64[4] = (f80[5] >> 3) | (f80[6] << 5); + f64[5] = (f80[6] >> 3) | (f80[7] << 5); + + f64[6] = ((bexp << 4) & 0xF0) | ((f80[7] >> 3) & 0x0F); + + f64[7] = (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) */ { + /* Round upwards. This is a kludge. Once in every 64k + roundings (statistically) the bottom two bytes are both 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 we don't round, but we should. */ + } +} + + +////////////// + +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; +} + + + +