636 lines
19 KiB
C
636 lines
19 KiB
C
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#ifndef USED_AS_INCLUDE
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#include "../pub/libvex_basictypes.h"
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#include <stdio.h>
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#include <malloc.h>
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#include <stdlib.h>
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#include <string.h>
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#include <assert.h>
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/* Test program for developing code for conversions between
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x87 64-bit and 80-bit floats.
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80-bit format exists only for x86/x86-64, and so the routines
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hardwire it as little-endian. The 64-bit format (IEEE double)
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could exist on any platform, little or big-endian and so we
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have to take that into account. IOW, these routines have to
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work correctly when compiled on both big- and little-endian
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targets, but the 80-bit images only ever have to exist in
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little-endian format.
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*/
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static void show_f80 ( UChar* );
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static void show_f64 ( UChar* );
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static inline
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UInt read_bit_array ( UChar* arr, UInt n )
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{
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UChar c = arr[n >> 3];
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c >>= (n&7);
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return c & 1;
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}
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static inline
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void write_bit_array ( UChar* arr, UInt n, UInt b )
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{
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UChar c = arr[n >> 3];
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c &= ~(1 << (n&7));
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c |= ((b&1) << (n&7));
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arr[n >> 3] = c;
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}
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static void convert_f80le_to_f64le_HW ( /*IN*/UChar* f80, /*OUT*/UChar* f64 )
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{
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asm volatile ("ffree %%st(7); fldt (%0); fstpl (%1)"
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:
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: "r" (&f80[0]), "r" (&f64[0])
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: "memory" );
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}
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static void convert_f64le_to_f80le_HW ( /*IN*/UChar* f64, /*OUT*/UChar* f80 )
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{
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asm volatile ("ffree %%st(7); fldl (%0); fstpt (%1)"
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:
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: "r" (&f64[0]), "r" (&f80[0])
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: "memory" );
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}
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#endif /* ndef USED_AS_INCLUDE */
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/* 80 and 64-bit floating point formats:
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80-bit:
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S 0 0-------0 zero
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S 0 0X------X denormals
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S 1-7FFE 1X------X normals (all normals have leading 1)
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S 7FFF 10------0 infinity
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S 7FFF 10X-----X snan
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S 7FFF 11X-----X qnan
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S is the sign bit. For runs X----X, at least one of the Xs must be
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nonzero. Exponent is 15 bits, fractional part is 63 bits, and
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there is an explicitly represented leading 1, and a sign bit,
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giving 80 in total.
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64-bit avoids the confusion of an explicitly represented leading 1
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and so is simpler:
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S 0 0------0 zero
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S 0 X------X denormals
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S 1-7FE any normals
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S 7FF 0------0 infinity
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S 7FF 0X-----X snan
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S 7FF 1X-----X qnan
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Exponent is 11 bits, fractional part is 52 bits, and there is a
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sign bit, giving 64 in total.
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*/
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/* Convert a IEEE754 double (64-bit) into an x87 extended double
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(80-bit), mimicing the hardware fairly closely. Both numbers are
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stored little-endian. Limitations, all of which could be fixed,
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given some level of hassle:
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* Identity of NaNs is not preserved.
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See comments in the code for more details.
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*/
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static void convert_f64le_to_f80le ( /*IN*/UChar* f64, /*OUT*/UChar* f80 )
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{
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Bool mantissaIsZero;
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Int bexp, i, j, shift;
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UChar sign;
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sign = toUChar( (f64[7] >> 7) & 1 );
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bexp = (f64[7] << 4) | ((f64[6] >> 4) & 0x0F);
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bexp &= 0x7FF;
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mantissaIsZero = False;
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if (bexp == 0 || bexp == 0x7FF) {
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/* We'll need to know whether or not the mantissa (bits 51:0) is
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all zeroes in order to handle these cases. So figure it
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out. */
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mantissaIsZero
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= toBool(
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(f64[6] & 0x0F) == 0
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&& f64[5] == 0 && f64[4] == 0 && f64[3] == 0
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&& f64[2] == 0 && f64[1] == 0 && f64[0] == 0
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);
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}
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/* If the exponent is zero, either we have a zero or a denormal.
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Produce a zero. This is a hack in that it forces denormals to
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zero. Could do better. */
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if (bexp == 0) {
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f80[9] = toUChar( sign << 7 );
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f80[8] = f80[7] = f80[6] = f80[5] = f80[4]
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= f80[3] = f80[2] = f80[1] = f80[0] = 0;
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if (mantissaIsZero)
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/* It really is zero, so that's all we can do. */
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return;
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/* There is at least one 1-bit in the mantissa. So it's a
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potentially denormalised double -- but we can produce a
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normalised long double. Count the leading zeroes in the
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mantissa so as to decide how much to bump the exponent down
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by. Note, this is SLOW. */
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shift = 0;
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for (i = 51; i >= 0; i--) {
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if (read_bit_array(f64, i))
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break;
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shift++;
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}
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/* and copy into place as many bits as we can get our hands on. */
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j = 63;
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for (i = 51 - shift; i >= 0; i--) {
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write_bit_array( f80, j,
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read_bit_array( f64, i ) );
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j--;
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}
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/* Set the exponent appropriately, and we're done. */
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bexp -= shift;
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bexp += (16383 - 1023);
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f80[9] = toUChar( (sign << 7) | ((bexp >> 8) & 0xFF) );
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f80[8] = toUChar( bexp & 0xFF );
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return;
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}
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/* If the exponent is 7FF, this is either an Infinity, a SNaN or
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QNaN, as determined by examining bits 51:0, thus:
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0 ... 0 Inf
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0X ... X SNaN
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1X ... X QNaN
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where at least one of the Xs is not zero.
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*/
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if (bexp == 0x7FF) {
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if (mantissaIsZero) {
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/* Produce an appropriately signed infinity:
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S 1--1 (15) 1 0--0 (63)
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*/
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f80[9] = toUChar( (sign << 7) | 0x7F );
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f80[8] = 0xFF;
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f80[7] = 0x80;
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f80[6] = f80[5] = f80[4] = f80[3]
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= f80[2] = f80[1] = f80[0] = 0;
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return;
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}
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/* So it's either a QNaN or SNaN. Distinguish by considering
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bit 51. Note, this destroys all the trailing bits
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(identity?) of the NaN. IEEE754 doesn't require preserving
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these (it only requires that there be one QNaN value and one
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SNaN value), but x87 does seem to have some ability to
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preserve them. Anyway, here, the NaN's identity is
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destroyed. Could be improved. */
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if (f64[6] & 8) {
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/* QNaN. Make a QNaN:
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S 1--1 (15) 1 1--1 (63)
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*/
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f80[9] = toUChar( (sign << 7) | 0x7F );
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f80[8] = 0xFF;
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f80[7] = 0xFF;
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f80[6] = f80[5] = f80[4] = f80[3]
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= f80[2] = f80[1] = f80[0] = 0xFF;
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} else {
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/* SNaN. Make a SNaN:
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S 1--1 (15) 0 1--1 (63)
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*/
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f80[9] = toUChar( (sign << 7) | 0x7F );
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f80[8] = 0xFF;
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f80[7] = 0x7F;
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f80[6] = f80[5] = f80[4] = f80[3]
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= f80[2] = f80[1] = f80[0] = 0xFF;
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}
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return;
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}
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/* It's not a zero, denormal, infinity or nan. So it must be a
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normalised number. Rebias the exponent and build the new
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number. */
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bexp += (16383 - 1023);
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f80[9] = toUChar( (sign << 7) | ((bexp >> 8) & 0xFF) );
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f80[8] = toUChar( bexp & 0xFF );
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f80[7] = toUChar( (1 << 7) | ((f64[6] << 3) & 0x78)
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| ((f64[5] >> 5) & 7) );
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f80[6] = toUChar( ((f64[5] << 3) & 0xF8) | ((f64[4] >> 5) & 7) );
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f80[5] = toUChar( ((f64[4] << 3) & 0xF8) | ((f64[3] >> 5) & 7) );
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f80[4] = toUChar( ((f64[3] << 3) & 0xF8) | ((f64[2] >> 5) & 7) );
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f80[3] = toUChar( ((f64[2] << 3) & 0xF8) | ((f64[1] >> 5) & 7) );
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f80[2] = toUChar( ((f64[1] << 3) & 0xF8) | ((f64[0] >> 5) & 7) );
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f80[1] = toUChar( ((f64[0] << 3) & 0xF8) );
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f80[0] = toUChar( 0 );
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}
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/* Convert a x87 extended double (80-bit) into an IEEE 754 double
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(64-bit), mimicking the hardware fairly closely. Both numbers are
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stored little-endian. Limitations, both of which could be fixed,
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given some level of hassle:
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* Rounding following truncation could be a bit better.
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* Identity of NaNs is not preserved.
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See comments in the code for more details.
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*/
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static void convert_f80le_to_f64le ( /*IN*/UChar* f80, /*OUT*/UChar* f64 )
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{
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Bool isInf;
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Int bexp, i, j;
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UChar sign;
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sign = toUChar((f80[9] >> 7) & 1);
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bexp = (((UInt)f80[9]) << 8) | (UInt)f80[8];
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bexp &= 0x7FFF;
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/* If the exponent is zero, either we have a zero or a denormal.
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But an extended precision denormal becomes a double precision
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zero, so in either case, just produce the appropriately signed
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zero. */
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if (bexp == 0) {
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f64[7] = toUChar(sign << 7);
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f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
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return;
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}
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/* If the exponent is 7FFF, this is either an Infinity, a SNaN or
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QNaN, as determined by examining bits 62:0, thus:
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0 ... 0 Inf
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0X ... X SNaN
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1X ... X QNaN
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where at least one of the Xs is not zero.
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*/
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if (bexp == 0x7FFF) {
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isInf = toBool(
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(f80[7] & 0x7F) == 0
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&& f80[6] == 0 && f80[5] == 0 && f80[4] == 0
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&& f80[3] == 0 && f80[2] == 0 && f80[1] == 0
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&& f80[0] == 0
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);
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if (isInf) {
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if (0 == (f80[7] & 0x80))
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goto wierd_NaN;
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/* Produce an appropriately signed infinity:
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S 1--1 (11) 0--0 (52)
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*/
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f64[7] = toUChar((sign << 7) | 0x7F);
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f64[6] = 0xF0;
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f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
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return;
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}
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/* So it's either a QNaN or SNaN. Distinguish by considering
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bit 62. Note, this destroys all the trailing bits
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(identity?) of the NaN. IEEE754 doesn't require preserving
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these (it only requires that there be one QNaN value and one
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SNaN value), but x87 does seem to have some ability to
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preserve them. Anyway, here, the NaN's identity is
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destroyed. Could be improved. */
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if (f80[8] & 0x40) {
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/* QNaN. Make a QNaN:
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S 1--1 (11) 1 1--1 (51)
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*/
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f64[7] = toUChar((sign << 7) | 0x7F);
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f64[6] = 0xFF;
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f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF;
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} else {
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/* SNaN. Make a SNaN:
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S 1--1 (11) 0 1--1 (51)
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*/
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f64[7] = toUChar((sign << 7) | 0x7F);
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f64[6] = 0xF7;
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f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF;
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}
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return;
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}
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/* If it's not a Zero, NaN or Inf, and the integer part (bit 62) is
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zero, the x87 FPU appears to consider the number denormalised
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and converts it to a QNaN. */
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if (0 == (f80[7] & 0x80)) {
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wierd_NaN:
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/* Strange hardware QNaN:
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S 1--1 (11) 1 0--0 (51)
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*/
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/* On a PIII, these QNaNs always appear with sign==1. I have
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no idea why. */
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f64[7] = (1 /*sign*/ << 7) | 0x7F;
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f64[6] = 0xF8;
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f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
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return;
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}
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/* It's not a zero, denormal, infinity or nan. So it must be a
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normalised number. Rebias the exponent and consider. */
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bexp -= (16383 - 1023);
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if (bexp >= 0x7FF) {
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/* It's too big for a double. Construct an infinity. */
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f64[7] = toUChar((sign << 7) | 0x7F);
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f64[6] = 0xF0;
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f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
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return;
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}
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if (bexp <= 0) {
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/* It's too small for a normalised double. First construct a
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zero and then see if it can be improved into a denormal. */
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f64[7] = toUChar(sign << 7);
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f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
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if (bexp < -52)
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/* Too small even for a denormal. */
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return;
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/* Ok, let's make a denormal. Note, this is SLOW. */
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/* Copy bits 63, 62, 61, etc of the src mantissa into the dst,
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indexes 52+bexp, 51+bexp, etc, until k+bexp < 0. */
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/* bexp is in range -52 .. 0 inclusive */
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for (i = 63; i >= 0; i--) {
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j = i - 12 + bexp;
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if (j < 0) break;
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/* We shouldn't really call vassert from generated code. */
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assert(j >= 0 && j < 52);
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write_bit_array ( f64,
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j,
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read_bit_array ( f80, i ) );
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}
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/* and now we might have to round ... */
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if (read_bit_array(f80, 10+1 - bexp) == 1)
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goto do_rounding;
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return;
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}
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/* Ok, it's a normalised number which is representable as a double.
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Copy the exponent and mantissa into place. */
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/*
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for (i = 0; i < 52; i++)
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write_bit_array ( f64,
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i,
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read_bit_array ( f80, i+11 ) );
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*/
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f64[0] = toUChar( (f80[1] >> 3) | (f80[2] << 5) );
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f64[1] = toUChar( (f80[2] >> 3) | (f80[3] << 5) );
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f64[2] = toUChar( (f80[3] >> 3) | (f80[4] << 5) );
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f64[3] = toUChar( (f80[4] >> 3) | (f80[5] << 5) );
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f64[4] = toUChar( (f80[5] >> 3) | (f80[6] << 5) );
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f64[5] = toUChar( (f80[6] >> 3) | (f80[7] << 5) );
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f64[6] = toUChar( ((bexp << 4) & 0xF0) | ((f80[7] >> 3) & 0x0F) );
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f64[7] = toUChar( (sign << 7) | ((bexp >> 4) & 0x7F) );
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/* Now consider any rounding that needs to happen as a result of
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truncating the mantissa. */
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if (f80[1] & 4) /* read_bit_array(f80, 10) == 1) */ {
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/* If the bottom bits of f80 are "100 0000 0000", then the
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infinitely precise value is deemed to be mid-way between the
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two closest representable values. Since we're doing
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round-to-nearest (the default mode), in that case it is the
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bit immediately above which indicates whether we should round
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upwards or not -- if 0, we don't. All that is encapsulated
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in the following simple test. */
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if ((f80[1] & 0xF) == 4/*0100b*/ && f80[0] == 0)
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return;
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do_rounding:
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/* Round upwards. This is a kludge. Once in every 2^24
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roundings (statistically) the bottom three bytes are all 0xFF
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and so we don't round at all. Could be improved. */
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if (f64[0] != 0xFF) {
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f64[0]++;
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}
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else
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if (f64[0] == 0xFF && f64[1] != 0xFF) {
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f64[0] = 0;
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f64[1]++;
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}
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else
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if (f64[0] == 0xFF && f64[1] == 0xFF && f64[2] != 0xFF) {
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f64[0] = 0;
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f64[1] = 0;
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f64[2]++;
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}
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/* else we don't round, but we should. */
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}
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}
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#ifndef USED_AS_INCLUDE
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//////////////
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static void show_f80 ( UChar* f80 )
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{
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Int i;
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printf("%d ", read_bit_array(f80, 79));
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for (i = 78; i >= 64; i--)
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printf("%d", read_bit_array(f80, i));
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printf(" %d ", read_bit_array(f80, 63));
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for (i = 62; i >= 0; i--)
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printf("%d", read_bit_array(f80, i));
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}
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static void show_f64le ( UChar* f64 )
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{
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Int i;
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printf("%d ", read_bit_array(f64, 63));
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for (i = 62; i >= 52; i--)
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printf("%d", read_bit_array(f64, i));
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printf(" ");
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for (i = 51; i >= 0; i--)
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printf("%d", read_bit_array(f64, i));
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}
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//////////////
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|
|
/* 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 */
|