--- /dev/null
+
+#include "../pub/libvex_basictypes.h"
+#include <stdio.h>
+#include <malloc.h>
+#include <stdlib.h>
+#include <string.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
+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;
+}
+
+
+
+
projects / thirdparty / valgrind.git / commitdiff
