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3 |
xianfeng |
/*
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* Basic two-word fraction declaration and manipulation.
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*/
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#define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1
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#define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
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#define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
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#define _FP_FRAC_HIGH_2(X) (X##_f1)
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#define _FP_FRAC_LOW_2(X) (X##_f0)
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#define _FP_FRAC_WORD_2(X,w) (X##_f##w)
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#define _FP_FRAC_SLL_2(X,N) \
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do { \
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if ((N) < _FP_W_TYPE_SIZE) \
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{ \
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if (__builtin_constant_p(N) && (N) == 1) \
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{ \
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X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \
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X##_f0 += X##_f0; \
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} \
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else \
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{ \
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X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
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X##_f0 <<= (N); \
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} \
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} \
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else \
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{ \
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X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
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X##_f0 = 0; \
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} \
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} while (0)
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#define _FP_FRAC_SRL_2(X,N) \
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do { \
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if ((N) < _FP_W_TYPE_SIZE) \
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{ \
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X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
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X##_f1 >>= (N); \
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} \
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else \
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{ \
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X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
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X##_f1 = 0; \
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} \
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} while (0)
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/* Right shift with sticky-lsb. */
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#define _FP_FRAC_SRS_2(X,N,sz) \
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do { \
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if ((N) < _FP_W_TYPE_SIZE) \
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{ \
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X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \
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(__builtin_constant_p(N) && (N) == 1 \
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? X##_f0 & 1 \
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: (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
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X##_f1 >>= (N); \
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} \
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else \
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{ \
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X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \
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(((X##_f1 << (2 * _FP_W_TYPE_SIZE - (N))) | \
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X##_f0) != 0)); \
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X##_f1 = 0; \
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} \
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} while (0)
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#define _FP_FRAC_ADDI_2(X,I) \
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__FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
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#define _FP_FRAC_ADD_2(R,X,Y) \
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__FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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#define _FP_FRAC_SUB_2(R,X,Y) \
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__FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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#define _FP_FRAC_CLZ_2(R,X) \
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do { \
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if (X##_f1) \
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__FP_CLZ(R,X##_f1); \
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else \
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{ \
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__FP_CLZ(R,X##_f0); \
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R += _FP_W_TYPE_SIZE; \
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} \
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} while(0)
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/* Predicates */
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#define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
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#define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
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#define _FP_FRAC_OVERP_2(fs,X) (X##_f1 & _FP_OVERFLOW_##fs)
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#define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
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#define _FP_FRAC_GT_2(X, Y) \
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((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
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#define _FP_FRAC_GE_2(X, Y) \
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((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
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#define _FP_ZEROFRAC_2 0, 0
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#define _FP_MINFRAC_2 0, 1
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/*
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* Internals
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*/
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#define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
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#define __FP_CLZ_2(R, xh, xl) \
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do { \
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if (xh) \
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__FP_CLZ(R,xl); \
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else \
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{ \
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__FP_CLZ(R,xl); \
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R += _FP_W_TYPE_SIZE; \
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} \
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} while(0)
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#if 0
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#ifndef __FP_FRAC_ADDI_2
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#define __FP_FRAC_ADDI_2(xh, xl, i) \
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(xh += ((xl += i) < i))
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#endif
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#ifndef __FP_FRAC_ADD_2
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#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
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(rh = xh + yh + ((rl = xl + yl) < xl))
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#endif
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#ifndef __FP_FRAC_SUB_2
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#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
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(rh = xh - yh - ((rl = xl - yl) > xl))
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#endif
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#else
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#undef __FP_FRAC_ADDI_2
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#define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
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#undef __FP_FRAC_ADD_2
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#define __FP_FRAC_ADD_2 add_ssaaaa
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#undef __FP_FRAC_SUB_2
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#define __FP_FRAC_SUB_2 sub_ddmmss
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#endif
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/*
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* Unpack the raw bits of a native fp value. Do not classify or
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* normalize the data.
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*/
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#define _FP_UNPACK_RAW_2(fs, X, val) \
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do { \
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union _FP_UNION_##fs _flo; _flo.flt = (val); \
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\
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X##_f0 = _flo.bits.frac0; \
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X##_f1 = _flo.bits.frac1; \
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X##_e = _flo.bits.exp; \
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X##_s = _flo.bits.sign; \
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} while (0)
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/*
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* Repack the raw bits of a native fp value.
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*/
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#define _FP_PACK_RAW_2(fs, val, X) \
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do { \
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union _FP_UNION_##fs _flo; \
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\
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_flo.bits.frac0 = X##_f0; \
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_flo.bits.frac1 = X##_f1; \
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_flo.bits.exp = X##_e; \
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_flo.bits.sign = X##_s; \
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\
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(val) = _flo.flt; \
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} while (0)
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/*
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* Multiplication algorithms:
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*/
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
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#define _FP_MUL_MEAT_2_wide(fs, R, X, Y, doit) \
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do { \
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_FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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\
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doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
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doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
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doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
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doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
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\
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__FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
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0, _b_f1, _b_f0, 0, \
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_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
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__FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
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0, _c_f1, _c_f0, 0, \
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_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
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\
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/* Normalize since we know where the msb of the multiplicands \
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were (bit B), we know that the msb of the of the product is \
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at either 2B or 2B-1. */ \
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_FP_FRAC_SRS_4(_z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs); \
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R##_f0 = _FP_FRAC_WORD_4(_z,0); \
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R##_f1 = _FP_FRAC_WORD_4(_z,1); \
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} while (0)
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/* This next macro appears to be totally broken. Fortunately nowhere
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* seems to use it :-> The problem is that we define _z[4] but
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* then use it in _FP_FRAC_SRS_4, which will attempt to access
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* _z_f[n] which will cause an error. The fix probably involves
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* declaring it with _FP_FRAC_DECL_4, see previous macro. -- PMM 02/1998
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*/
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#define _FP_MUL_MEAT_2_gmp(fs, R, X, Y) \
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do { \
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_FP_W_TYPE _x[2], _y[2], _z[4]; \
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_x[0] = X##_f0; _x[1] = X##_f1; \
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_y[0] = Y##_f0; _y[1] = Y##_f1; \
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\
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| 223 |
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mpn_mul_n(_z, _x, _y, 2); \
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\
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/* Normalize since we know where the msb of the multiplicands \
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were (bit B), we know that the msb of the of the product is \
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at either 2B or 2B-1. */ \
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_FP_FRAC_SRS_4(_z, _FP_WFRACBITS##_fs-1, 2*_FP_WFRACBITS_##fs); \
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R##_f0 = _z[0]; \
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R##_f1 = _z[1]; \
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| 231 |
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} while (0)
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| 232 |
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| 233 |
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| 234 |
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/*
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| 235 |
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* Division algorithms:
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| 236 |
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* This seems to be giving me difficulties -- PMM
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| 237 |
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* Look, NetBSD seems to be able to comment algorithms. Can't you?
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| 238 |
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* I've thrown printks at the problem.
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* This now appears to work, but I still don't really know why.
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| 240 |
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* Also, I don't think the result is properly normalised...
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| 241 |
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*/
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| 242 |
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| 243 |
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#define _FP_DIV_MEAT_2_udiv_64(fs, R, X, Y) \
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| 244 |
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do { \
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| 245 |
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extern void _fp_udivmodti4(_FP_W_TYPE q[2], _FP_W_TYPE r[2], \
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| 246 |
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_FP_W_TYPE n1, _FP_W_TYPE n0, \
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| 247 |
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_FP_W_TYPE d1, _FP_W_TYPE d0); \
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| 248 |
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_FP_W_TYPE _n_f3, _n_f2, _n_f1, _n_f0, _r_f1, _r_f0; \
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| 249 |
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_FP_W_TYPE _q_f1, _q_f0, _m_f1, _m_f0; \
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| 250 |
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_FP_W_TYPE _rmem[2], _qmem[2]; \
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| 251 |
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/* I think this check is to ensure that the result is normalised. \
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| 252 |
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* Assuming X,Y normalised (ie in [1.0,2.0)) X/Y will be in \
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| 253 |
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* [0.5,2.0). Furthermore, it will be less than 1.0 iff X < Y. \
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| 254 |
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* In this case we tweak things. (this is based on comments in \
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| 255 |
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* the NetBSD FPU emulation code. ) \
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| 256 |
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* We know X,Y are normalised because we ensure this as part of \
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| 257 |
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* the unpacking process. -- PMM \
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| 258 |
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*/ \
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| 259 |
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if (_FP_FRAC_GT_2(X, Y)) \
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| 260 |
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{ \
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| 261 |
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/* R##_e++; */ \
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| 262 |
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_n_f3 = X##_f1 >> 1; \
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| 263 |
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_n_f2 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
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| 264 |
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_n_f1 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
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| 265 |
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_n_f0 = 0; \
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| 266 |
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} \
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| 267 |
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else \
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| 268 |
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{ \
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| 269 |
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R##_e--; \
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| 270 |
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_n_f3 = X##_f1; \
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| 271 |
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_n_f2 = X##_f0; \
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| 272 |
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_n_f1 = _n_f0 = 0; \
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| 273 |
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} \
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| 274 |
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\
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| 275 |
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/* Normalize, i.e. make the most significant bit of the \
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| 276 |
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denominator set. CHANGED: - 1 to nothing -- PMM */ \
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| 277 |
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_FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs /* -1 */); \
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| 278 |
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\
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| 279 |
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/* Do the 256/128 bit division given the 128-bit _fp_udivmodtf4 \
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| 280 |
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primitive snagged from libgcc2.c. */ \
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| 281 |
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\
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| 282 |
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_fp_udivmodti4(_qmem, _rmem, _n_f3, _n_f2, 0, Y##_f1); \
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| 283 |
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_q_f1 = _qmem[0]; \
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| 284 |
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umul_ppmm(_m_f1, _m_f0, _q_f1, Y##_f0); \
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| 285 |
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_r_f1 = _rmem[0]; \
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| 286 |
|
|
_r_f0 = _n_f1; \
|
| 287 |
|
|
if (_FP_FRAC_GT_2(_m, _r)) \
|
| 288 |
|
|
{ \
|
| 289 |
|
|
_q_f1--; \
|
| 290 |
|
|
_FP_FRAC_ADD_2(_r, _r, Y); \
|
| 291 |
|
|
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
| 292 |
|
|
{ \
|
| 293 |
|
|
_q_f1--; \
|
| 294 |
|
|
_FP_FRAC_ADD_2(_r, _r, Y); \
|
| 295 |
|
|
} \
|
| 296 |
|
|
} \
|
| 297 |
|
|
_FP_FRAC_SUB_2(_r, _r, _m); \
|
| 298 |
|
|
\
|
| 299 |
|
|
_fp_udivmodti4(_qmem, _rmem, _r_f1, _r_f0, 0, Y##_f1); \
|
| 300 |
|
|
_q_f0 = _qmem[0]; \
|
| 301 |
|
|
umul_ppmm(_m_f1, _m_f0, _q_f0, Y##_f0); \
|
| 302 |
|
|
_r_f1 = _rmem[0]; \
|
| 303 |
|
|
_r_f0 = _n_f0; \
|
| 304 |
|
|
if (_FP_FRAC_GT_2(_m, _r)) \
|
| 305 |
|
|
{ \
|
| 306 |
|
|
_q_f0--; \
|
| 307 |
|
|
_FP_FRAC_ADD_2(_r, _r, Y); \
|
| 308 |
|
|
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
| 309 |
|
|
{ \
|
| 310 |
|
|
_q_f0--; \
|
| 311 |
|
|
_FP_FRAC_ADD_2(_r, _r, Y); \
|
| 312 |
|
|
} \
|
| 313 |
|
|
} \
|
| 314 |
|
|
_FP_FRAC_SUB_2(_r, _r, _m); \
|
| 315 |
|
|
\
|
| 316 |
|
|
R##_f1 = _q_f1; \
|
| 317 |
|
|
R##_f0 = _q_f0 | ((_r_f1 | _r_f0) != 0); \
|
| 318 |
|
|
/* adjust so answer is normalized again. I'm not sure what the \
|
| 319 |
|
|
* final sz param should be. In practice it's never used since \
|
| 320 |
|
|
* N is 1 which is always going to be < _FP_W_TYPE_SIZE... \
|
| 321 |
|
|
*/ \
|
| 322 |
|
|
/* _FP_FRAC_SRS_2(R,1,_FP_WFRACBITS_##fs); */ \
|
| 323 |
|
|
} while (0)
|
| 324 |
|
|
|
| 325 |
|
|
|
| 326 |
|
|
#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
|
| 327 |
|
|
do { \
|
| 328 |
|
|
_FP_W_TYPE _x[4], _y[2], _z[4]; \
|
| 329 |
|
|
_y[0] = Y##_f0; _y[1] = Y##_f1; \
|
| 330 |
|
|
_x[0] = _x[3] = 0; \
|
| 331 |
|
|
if (_FP_FRAC_GT_2(X, Y)) \
|
| 332 |
|
|
{ \
|
| 333 |
|
|
R##_e++; \
|
| 334 |
|
|
_x[1] = (X##_f0 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE) | \
|
| 335 |
|
|
X##_f1 >> (_FP_W_TYPE_SIZE - \
|
| 336 |
|
|
(_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE))); \
|
| 337 |
|
|
_x[2] = X##_f1 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE); \
|
| 338 |
|
|
} \
|
| 339 |
|
|
else \
|
| 340 |
|
|
{ \
|
| 341 |
|
|
_x[1] = (X##_f0 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE) | \
|
| 342 |
|
|
X##_f1 >> (_FP_W_TYPE_SIZE - \
|
| 343 |
|
|
(_FP_WFRACBITS - _FP_W_TYPE_SIZE))); \
|
| 344 |
|
|
_x[2] = X##_f1 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE); \
|
| 345 |
|
|
} \
|
| 346 |
|
|
\
|
| 347 |
|
|
(void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
|
| 348 |
|
|
R##_f1 = _z[1]; \
|
| 349 |
|
|
R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \
|
| 350 |
|
|
} while (0)
|
| 351 |
|
|
|
| 352 |
|
|
|
| 353 |
|
|
/*
|
| 354 |
|
|
* Square root algorithms:
|
| 355 |
|
|
* We have just one right now, maybe Newton approximation
|
| 356 |
|
|
* should be added for those machines where division is fast.
|
| 357 |
|
|
*/
|
| 358 |
|
|
|
| 359 |
|
|
#define _FP_SQRT_MEAT_2(R, S, T, X, q) \
|
| 360 |
|
|
do { \
|
| 361 |
|
|
while (q) \
|
| 362 |
|
|
{ \
|
| 363 |
|
|
T##_f1 = S##_f1 + q; \
|
| 364 |
|
|
if (T##_f1 <= X##_f1) \
|
| 365 |
|
|
{ \
|
| 366 |
|
|
S##_f1 = T##_f1 + q; \
|
| 367 |
|
|
X##_f1 -= T##_f1; \
|
| 368 |
|
|
R##_f1 += q; \
|
| 369 |
|
|
} \
|
| 370 |
|
|
_FP_FRAC_SLL_2(X, 1); \
|
| 371 |
|
|
q >>= 1; \
|
| 372 |
|
|
} \
|
| 373 |
|
|
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 374 |
|
|
while (q) \
|
| 375 |
|
|
{ \
|
| 376 |
|
|
T##_f0 = S##_f0 + q; \
|
| 377 |
|
|
T##_f1 = S##_f1; \
|
| 378 |
|
|
if (T##_f1 < X##_f1 || \
|
| 379 |
|
|
(T##_f1 == X##_f1 && T##_f0 < X##_f0)) \
|
| 380 |
|
|
{ \
|
| 381 |
|
|
S##_f0 = T##_f0 + q; \
|
| 382 |
|
|
if (((_FP_WS_TYPE)T##_f0) < 0 && \
|
| 383 |
|
|
((_FP_WS_TYPE)S##_f0) >= 0) \
|
| 384 |
|
|
S##_f1++; \
|
| 385 |
|
|
_FP_FRAC_SUB_2(X, X, T); \
|
| 386 |
|
|
R##_f0 += q; \
|
| 387 |
|
|
} \
|
| 388 |
|
|
_FP_FRAC_SLL_2(X, 1); \
|
| 389 |
|
|
q >>= 1; \
|
| 390 |
|
|
} \
|
| 391 |
|
|
} while (0)
|
| 392 |
|
|
|
| 393 |
|
|
|
| 394 |
|
|
/*
|
| 395 |
|
|
* Assembly/disassembly for converting to/from integral types.
|
| 396 |
|
|
* No shifting or overflow handled here.
|
| 397 |
|
|
*/
|
| 398 |
|
|
|
| 399 |
|
|
#define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
|
| 400 |
|
|
do { \
|
| 401 |
|
|
if (rsize <= _FP_W_TYPE_SIZE) \
|
| 402 |
|
|
r = X##_f0; \
|
| 403 |
|
|
else \
|
| 404 |
|
|
{ \
|
| 405 |
|
|
r = X##_f1; \
|
| 406 |
|
|
r <<= _FP_W_TYPE_SIZE; \
|
| 407 |
|
|
r += X##_f0; \
|
| 408 |
|
|
} \
|
| 409 |
|
|
} while (0)
|
| 410 |
|
|
|
| 411 |
|
|
#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
|
| 412 |
|
|
do { \
|
| 413 |
|
|
X##_f0 = r; \
|
| 414 |
|
|
X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
|
| 415 |
|
|
} while (0)
|
| 416 |
|
|
|
| 417 |
|
|
/*
|
| 418 |
|
|
* Convert FP values between word sizes
|
| 419 |
|
|
*/
|
| 420 |
|
|
|
| 421 |
|
|
#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \
|
| 422 |
|
|
do { \
|
| 423 |
|
|
_FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
|
| 424 |
|
|
_FP_WFRACBITS_##sfs); \
|
| 425 |
|
|
D##_f = S##_f0; \
|
| 426 |
|
|
} while (0)
|
| 427 |
|
|
|
| 428 |
|
|
#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \
|
| 429 |
|
|
do { \
|
| 430 |
|
|
D##_f0 = S##_f; \
|
| 431 |
|
|
D##_f1 = 0; \
|
| 432 |
|
|
_FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
|
| 433 |
|
|
} while (0)
|
| 434 |
|
|
|
