318 lines
12 KiB
C
Executable File
318 lines
12 KiB
C
Executable File
/*============================================================================
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This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2b.
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Written by John R. Hauser. This work was made possible in part by the
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International Computer Science Institute, located at Suite 600, 1947 Center
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Street, Berkeley, California 94704. Funding was partially provided by the
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National Science Foundation under grant MIP-9311980. The original version
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of this code was written as part of a project to build a fixed-point vector
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processor in collaboration with the University of California at Berkeley,
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overseen by Profs. Nelson Morgan and John Wawrzynek. More information
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is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
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arithmetic/SoftFloat.html'.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
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been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
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RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
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AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
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COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
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EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
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INSTITUTE (possibly via similar legal notice) AGAINST ALL LOSSES, COSTS, OR
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OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) the source code for the derivative work includes prominent notice that
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the work is derivative, and (2) the source code includes prominent notice with
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these four paragraphs for those parts of this code that are retained.
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=============================================================================*/
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/*============================================================================
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* Adapted for Bochs (x86 achitecture simulator) by
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* Stanislav Shwartsman (gate@fidonet.org.il)
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* ==========================================================================*/
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/*----------------------------------------------------------------------------
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| Shifts `a' right by the number of bits given in `count'. If any nonzero
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| bits are shifted off, they are ``jammed'' into the least significant bit of
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| the result by setting the least significant bit to 1. The value of `count'
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| can be arbitrarily large; in particular, if `count' is greater than 32, the
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| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
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| The result is stored in the location pointed to by `zPtr'.
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*----------------------------------------------------------------------------*/
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BX_CPP_INLINE void shift32RightJamming(Bit32u a, Bit16s count, Bit32u *zPtr)
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{
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Bit32u z;
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if (count == 0) {
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z = a;
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}
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else if (count < 32) {
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z = (a>>count) | ((a<<((-count) & 31)) != 0);
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}
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else {
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z = (a != 0);
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}
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*zPtr = z;
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}
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/*----------------------------------------------------------------------------
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| Shifts `a' right by the number of bits given in `count'. If any nonzero
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| bits are shifted off, they are ``jammed'' into the least significant bit of
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| the result by setting the least significant bit to 1. The value of `count'
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| can be arbitrarily large; in particular, if `count' is greater than 64, the
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| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
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| The result is stored in the location pointed to by `zPtr'.
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*----------------------------------------------------------------------------*/
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BX_CPP_INLINE void shift64RightJamming(Bit64u a, Bit16s count, Bit64u *zPtr)
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{
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Bit64u z;
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if (count == 0) {
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z = a;
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}
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else if (count < 64) {
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z = (a>>count) | ((a<<((-count) & 63)) != 0);
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}
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else {
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z = (a != 0);
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}
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*zPtr = z;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
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| _plus_ the number of bits given in `count'. The shifted result is at most
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| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
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| bits shifted off form a second 64-bit result as follows: The _last_ bit
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| shifted off is the most-significant bit of the extra result, and the other
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| 63 bits of the extra result are all zero if and only if _all_but_the_last_
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| bits shifted off were all zero. This extra result is stored in the location
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| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
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| (This routine makes more sense if `a0' and `a1' are considered to form
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| a fixed-point value with binary point between `a0' and `a1'. This fixed-
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| point value is shifted right by the number of bits given in `count', and
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| the integer part of the result is returned at the location pointed to by
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| `z0Ptr'. The fractional part of the result may be slightly corrupted as
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| described above, and is returned at the location pointed to by `z1Ptr'.)
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*----------------------------------------------------------------------------*/
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BX_CPP_INLINE void
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shift64ExtraRightJamming(
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Bit64u a0, Bit64u a1, Bit16s count, Bit64u *z0Ptr, Bit64u *z1Ptr)
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{
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Bit64u z0, z1;
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Bit8s negCount = (-count) & 63;
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if (count == 0) {
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z1 = a1;
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z0 = a0;
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}
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else if (count < 64) {
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z1 = (a0<<negCount) | (a1 != 0);
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z0 = a0>>count;
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}
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else {
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if (count == 64) {
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z1 = a0 | (a1 != 0);
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}
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else {
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z1 = ((a0 | a1) != 0);
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}
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z0 = 0;
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}
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
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| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
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| any carry out is lost. The result is broken into two 64-bit pieces which
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| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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BX_CPP_INLINE void
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add128(Bit64u a0, Bit64u a1, Bit64u b0, Bit64u b1, Bit64u *z0Ptr, Bit64u *z1Ptr)
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{
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Bit64u z1;
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z1 = a1 + b1;
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*z1Ptr = z1;
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*z0Ptr = a0 + b0 + (z1 < a1);
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}
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/*----------------------------------------------------------------------------
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| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
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| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
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| 2^128, so any borrow out (carry out) is lost. The result is broken into two
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| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
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| `z1Ptr'.
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*----------------------------------------------------------------------------*/
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BX_CPP_INLINE void
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sub128(Bit64u a0, Bit64u a1, Bit64u b0, Bit64u b1, Bit64u *z0Ptr, Bit64u *z1Ptr)
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{
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*z1Ptr = a1 - b1;
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*z0Ptr = a0 - b0 - (a1 < b1);
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}
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/*----------------------------------------------------------------------------
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| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
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| into two 64-bit pieces which are stored at the locations pointed to by
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| `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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BX_CPP_INLINE void mul64To128(Bit64u a, Bit64u b, Bit64u *z0Ptr, Bit64u *z1Ptr)
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{
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Bit32u aHigh, aLow, bHigh, bLow;
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Bit64u z0, zMiddleA, zMiddleB, z1;
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aLow = a;
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aHigh = a>>32;
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bLow = b;
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bHigh = b>>32;
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z1 = ((Bit64u) aLow) * bLow;
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zMiddleA = ((Bit64u) aLow) * bHigh;
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zMiddleB = ((Bit64u) aHigh) * bLow;
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z0 = ((Bit64u) aHigh) * bHigh;
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zMiddleA += zMiddleB;
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z0 += (((Bit64u) (zMiddleA < zMiddleB))<<32) + (zMiddleA>>32);
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zMiddleA <<= 32;
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z1 += zMiddleA;
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z0 += (z1 < zMiddleA);
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Returns an approximation to the 64-bit integer quotient obtained by dividing
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| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
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| divisor `b' must be at least 2^63. If q is the exact quotient truncated
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| toward zero, the approximation returned lies between q and q + 2 inclusive.
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| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
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| unsigned integer is returned.
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*----------------------------------------------------------------------------*/
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static Bit64u estimateDiv128To64(Bit64u a0, Bit64u a1, Bit64u b)
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{
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Bit64u b0, b1;
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Bit64u rem0, rem1, term0, term1;
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Bit64u z;
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if (b <= a0) return BX_CONST64(0xFFFFFFFFFFFFFFFF);
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b0 = b>>32;
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z = (b0<<32 <= a0) ? BX_CONST64(0xFFFFFFFF00000000) : (a0 / b0)<<32;
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mul64To128(b, z, &term0, &term1);
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sub128(a0, a1, term0, term1, &rem0, &rem1);
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while (((Bit64s) rem0) < 0) {
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z -= BX_CONST64(0x100000000);
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b1 = b<<32;
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add128(rem0, rem1, b0, b1, &rem0, &rem1);
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}
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rem0 = (rem0<<32) | (rem1>>32);
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z |= (b0<<32 <= rem0) ? 0xFFFFFFFF : rem0 / b0;
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return z;
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}
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/*----------------------------------------------------------------------------
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| Returns an approximation to the square root of the 32-bit significand given
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| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
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| `aExp' (the least significant bit) is 1, the integer returned approximates
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| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
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| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
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| case, the approximation returned lies strictly within +/-2 of the exact
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| value.
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*----------------------------------------------------------------------------*/
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static Bit32u estimateSqrt32(Bit16s aExp, Bit32u a)
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{
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static const Bit16u sqrtOddAdjustments[] = {
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0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
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0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
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};
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static const Bit16u sqrtEvenAdjustments[] = {
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0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
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0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
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};
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Bit8s index;
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Bit32u z;
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index = (a>>27) & 15;
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if (aExp & 1) {
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z = 0x4000 + (a>>17) - sqrtOddAdjustments[index];
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z = ((a / z)<<14) + (z<<15);
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a >>= 1;
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}
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else {
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z = 0x8000 + (a>>17) - sqrtEvenAdjustments[index];
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z = a / z + z;
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z = (0x20000 <= z) ? 0xFFFF8000 : (z<<15);
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if (z <= a) return (Bit32u) (((Bit32s) a)>>1);
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}
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return ((Bit32u) ((((Bit64u) a)<<31) / z)) + (z>>1);
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}
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/*----------------------------------------------------------------------------
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| Returns the number of leading 0 bits before the most-significant 1 bit of
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| `a'. If `a' is zero, 32 is returned.
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*----------------------------------------------------------------------------*/
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static int countLeadingZeros32(Bit32u a)
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{
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static const Bit8s countLeadingZerosHigh[] = {
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8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
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3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
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2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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};
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Bit8s shiftCount;
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shiftCount = 0;
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if (a < 0x10000) {
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shiftCount += 16;
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a <<= 16;
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}
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if (a < 0x1000000) {
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shiftCount += 8;
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a <<= 8;
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}
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shiftCount += countLeadingZerosHigh[ a>>24 ];
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return shiftCount;
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}
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/*----------------------------------------------------------------------------
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| Returns the number of leading 0 bits before the most-significant 1 bit of
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| `a'. If `a' is zero, 64 is returned.
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*----------------------------------------------------------------------------*/
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static int countLeadingZeros64(Bit64u a)
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{
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Bit8s shiftCount;
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shiftCount = 0;
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if (a < ((Bit64u) 1)<<32) {
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shiftCount += 32;
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}
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else {
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a >>= 32;
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}
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shiftCount += countLeadingZeros32(a);
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return shiftCount;
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}
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