diff options
Diffstat (limited to 'soft-fp/op-2.h')
| -rw-r--r-- | soft-fp/op-2.h | 910 |
1 files changed, 478 insertions, 432 deletions
diff --git a/soft-fp/op-2.h b/soft-fp/op-2.h index a5275d4668..1cbc1fe23f 100644 --- a/soft-fp/op-2.h +++ b/soft-fp/op-2.h @@ -37,74 +37,74 @@ #define _FP_FRAC_LOW_2(X) (X##_f0) #define _FP_FRAC_WORD_2(X,w) (X##_f##w) -#define _FP_FRAC_SLL_2(X,N) \ -(void)(((N) < _FP_W_TYPE_SIZE) \ - ? ({ \ - if (__builtin_constant_p(N) && (N) == 1) \ - { \ - X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \ - X##_f0 += X##_f0; \ - } \ - else \ - { \ - X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ - X##_f0 <<= (N); \ - } \ - 0; \ - }) \ - : ({ \ - X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ - X##_f0 = 0; \ - })) +#define _FP_FRAC_SLL_2(X,N) \ + (void)(((N) < _FP_W_TYPE_SIZE) \ + ? ({ \ + if (__builtin_constant_p(N) && (N) == 1) \ + { \ + X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \ + X##_f0 += X##_f0; \ + } \ + else \ + { \ + X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ + X##_f0 <<= (N); \ + } \ + 0; \ + }) \ + : ({ \ + X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ + X##_f0 = 0; \ + })) #define _FP_FRAC_SRL_2(X,N) \ -(void)(((N) < _FP_W_TYPE_SIZE) \ - ? ({ \ - X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ - X##_f1 >>= (N); \ - }) \ - : ({ \ - X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ - X##_f1 = 0; \ - })) + (void)(((N) < _FP_W_TYPE_SIZE) \ + ? ({ \ + X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ + X##_f1 >>= (N); \ + }) \ + : ({ \ + X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ + X##_f1 = 0; \ + })) /* Right shift with sticky-lsb. */ -#define _FP_FRAC_SRST_2(X,S, N,sz) \ -(void)(((N) < _FP_W_TYPE_SIZE) \ - ? ({ \ - S = (__builtin_constant_p(N) && (N) == 1 \ - ? X##_f0 & 1 \ - : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \ - X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \ - X##_f1 >>= (N); \ - }) \ - : ({ \ - S = ((((N) == _FP_W_TYPE_SIZE \ - ? 0 \ - : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ - | X##_f0) != 0); \ - X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \ - X##_f1 = 0; \ - })) - -#define _FP_FRAC_SRS_2(X,N,sz) \ -(void)(((N) < _FP_W_TYPE_SIZE) \ - ? ({ \ - X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \ - (__builtin_constant_p(N) && (N) == 1 \ - ? X##_f0 & 1 \ - : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ - X##_f1 >>= (N); \ - }) \ - : ({ \ - X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \ - ((((N) == _FP_W_TYPE_SIZE \ - ? 0 \ - : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ - | X##_f0) != 0)); \ - X##_f1 = 0; \ - })) +#define _FP_FRAC_SRST_2(X,S, N,sz) \ + (void)(((N) < _FP_W_TYPE_SIZE) \ + ? ({ \ + S = (__builtin_constant_p(N) && (N) == 1 \ + ? X##_f0 & 1 \ + : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \ + X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \ + X##_f1 >>= (N); \ + }) \ + : ({ \ + S = ((((N) == _FP_W_TYPE_SIZE \ + ? 0 \ + : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ + | X##_f0) != 0); \ + X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \ + X##_f1 = 0; \ + })) + +#define _FP_FRAC_SRS_2(X,N,sz) \ + (void)(((N) < _FP_W_TYPE_SIZE) \ + ? ({ \ + X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \ + | (__builtin_constant_p(N) && (N) == 1 \ + ? X##_f0 & 1 \ + : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ + X##_f1 >>= (N); \ + }) \ + : ({ \ + X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \ + | ((((N) == _FP_W_TYPE_SIZE \ + ? 0 \ + : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ + | X##_f0) != 0)); \ + X##_f1 = 0; \ + })) #define _FP_FRAC_ADDI_2(X,I) \ __FP_FRAC_ADDI_2(X##_f1, X##_f0, I) @@ -118,16 +118,18 @@ #define _FP_FRAC_DEC_2(X,Y) \ __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0) -#define _FP_FRAC_CLZ_2(R,X) \ - do { \ - if (X##_f1) \ - __FP_CLZ(R,X##_f1); \ - else \ - { \ - __FP_CLZ(R,X##_f0); \ - R += _FP_W_TYPE_SIZE; \ - } \ - } while(0) +#define _FP_FRAC_CLZ_2(R,X) \ + do \ + { \ + if (X##_f1) \ + __FP_CLZ(R,X##_f1); \ + else \ + { \ + __FP_CLZ(R,X##_f0); \ + R += _FP_W_TYPE_SIZE; \ + } \ + } \ + while(0) /* Predicates */ #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0) @@ -152,16 +154,18 @@ #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1) -#define __FP_CLZ_2(R, xh, xl) \ - do { \ - if (xh) \ - __FP_CLZ(R,xh); \ - else \ - { \ - __FP_CLZ(R,xl); \ - R += _FP_W_TYPE_SIZE; \ - } \ - } while(0) +#define __FP_CLZ_2(R, xh, xl) \ + do \ + { \ + if (xh) \ + __FP_CLZ(R,xh); \ + else \ + { \ + __FP_CLZ(R,xl); \ + R += _FP_W_TYPE_SIZE; \ + } \ + } \ + while(0) #if 0 @@ -179,10 +183,12 @@ # endif # ifndef __FP_FRAC_DEC_2 # define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ - do { \ - UWtype _t = xl; \ - xh -= yh + ((xl -= yl) > _t); \ - } while (0) + do \ + { \ + UWtype _t = xl; \ + xh -= yh + ((xl -= yl) > _t); \ + } \ + while (0) # endif #else @@ -204,54 +210,61 @@ * normalize the data. */ -#define _FP_UNPACK_RAW_2(fs, X, val) \ - do { \ - union _FP_UNION_##fs _flo; _flo.flt = (val); \ - \ - X##_f0 = _flo.bits.frac0; \ - X##_f1 = _flo.bits.frac1; \ - X##_e = _flo.bits.exp; \ - X##_s = _flo.bits.sign; \ - } while (0) - -#define _FP_UNPACK_RAW_2_P(fs, X, val) \ - do { \ - union _FP_UNION_##fs *_flo = \ - (union _FP_UNION_##fs *)(val); \ - \ - X##_f0 = _flo->bits.frac0; \ - X##_f1 = _flo->bits.frac1; \ - X##_e = _flo->bits.exp; \ - X##_s = _flo->bits.sign; \ - } while (0) +#define _FP_UNPACK_RAW_2(fs, X, val) \ + do \ + { \ + union _FP_UNION_##fs _flo; \ + _flo.flt = (val); \ + \ + X##_f0 = _flo.bits.frac0; \ + X##_f1 = _flo.bits.frac1; \ + X##_e = _flo.bits.exp; \ + X##_s = _flo.bits.sign; \ + } \ + while (0) + +#define _FP_UNPACK_RAW_2_P(fs, X, val) \ + do \ + { \ + union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *)(val); \ + \ + X##_f0 = _flo->bits.frac0; \ + X##_f1 = _flo->bits.frac1; \ + X##_e = _flo->bits.exp; \ + X##_s = _flo->bits.sign; \ + } \ + while (0) /* * Repack the raw bits of a native fp value. */ -#define _FP_PACK_RAW_2(fs, val, X) \ - do { \ - union _FP_UNION_##fs _flo; \ - \ - _flo.bits.frac0 = X##_f0; \ - _flo.bits.frac1 = X##_f1; \ - _flo.bits.exp = X##_e; \ - _flo.bits.sign = X##_s; \ - \ - (val) = _flo.flt; \ - } while (0) - -#define _FP_PACK_RAW_2_P(fs, val, X) \ - do { \ - union _FP_UNION_##fs *_flo = \ - (union _FP_UNION_##fs *)(val); \ - \ - _flo->bits.frac0 = X##_f0; \ - _flo->bits.frac1 = X##_f1; \ - _flo->bits.exp = X##_e; \ - _flo->bits.sign = X##_s; \ - } while (0) +#define _FP_PACK_RAW_2(fs, val, X) \ + do \ + { \ + union _FP_UNION_##fs _flo; \ + \ + _flo.bits.frac0 = X##_f0; \ + _flo.bits.frac1 = X##_f1; \ + _flo.bits.exp = X##_e; \ + _flo.bits.sign = X##_s; \ + \ + (val) = _flo.flt; \ + } \ + while (0) + +#define _FP_PACK_RAW_2_P(fs, val, X) \ + do \ + { \ + union _FP_UNION_##fs *_flo = (union _FP_UNION_##fs *)(val); \ + \ + _flo->bits.frac0 = X##_f0; \ + _flo->bits.frac1 = X##_f1; \ + _flo->bits.exp = X##_e; \ + _flo->bits.sign = X##_s; \ + } \ + while (0) /* @@ -261,111 +274,127 @@ /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ #define _FP_MUL_MEAT_DW_2_wide(wfracbits, R, X, Y, doit) \ - do { \ - _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ + do \ + { \ + _FP_FRAC_DECL_2(_b); \ + _FP_FRAC_DECL_2(_c); \ \ - doit(_FP_FRAC_WORD_4(R,1), _FP_FRAC_WORD_4(R,0), X##_f0, Y##_f0); \ - doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ - doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ - doit(_FP_FRAC_WORD_4(R,3), _FP_FRAC_WORD_4(R,2), X##_f1, Y##_f1); \ + doit(_FP_FRAC_WORD_4(R,1), _FP_FRAC_WORD_4(R,0), X##_f0, Y##_f0); \ + doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ + doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ + doit(_FP_FRAC_WORD_4(R,3), _FP_FRAC_WORD_4(R,2), X##_f1, Y##_f1); \ \ - __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1), 0, _b_f1, _b_f0, \ - _FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1)); \ - __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1), 0, _c_f1, _c_f0, \ - _FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1)); \ - } while (0) + __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1), 0, _b_f1, _b_f0, \ + _FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1)); \ + __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1), 0, _c_f1, _c_f0, \ + _FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1)); \ + } \ + while (0) #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ - do { \ - _FP_FRAC_DECL_4(_z); \ + do \ + { \ + _FP_FRAC_DECL_4(_z); \ \ - _FP_MUL_MEAT_DW_2_wide(wfracbits, _z, X, Y, doit); \ + _FP_MUL_MEAT_DW_2_wide(wfracbits, _z, X, Y, doit); \ \ - /* Normalize since we know where the msb of the multiplicands \ - were (bit B), we know that the msb of the of the product is \ - at either 2B or 2B-1. */ \ - _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ - R##_f0 = _FP_FRAC_WORD_4(_z,0); \ - R##_f1 = _FP_FRAC_WORD_4(_z,1); \ - } while (0) + /* Normalize since we know where the msb of the multiplicands \ + were (bit B), we know that the msb of the of the product is \ + at either 2B or 2B-1. */ \ + _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ + R##_f0 = _FP_FRAC_WORD_4(_z,0); \ + R##_f1 = _FP_FRAC_WORD_4(_z,1); \ + } \ + while (0) /* Given a 1W * 1W => 2W primitive, do the extended multiplication. Do only 3 multiplications instead of four. This one is for machines where multiplication is much more expensive than subtraction. */ #define _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, R, X, Y, doit) \ - do { \ - _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ - _FP_W_TYPE _d; \ - int _c1, _c2; \ + do \ + { \ + _FP_FRAC_DECL_2(_b); \ + _FP_FRAC_DECL_2(_c); \ + _FP_W_TYPE _d; \ + int _c1, _c2; \ \ - _b_f0 = X##_f0 + X##_f1; \ - _c1 = _b_f0 < X##_f0; \ - _b_f1 = Y##_f0 + Y##_f1; \ - _c2 = _b_f1 < Y##_f0; \ - doit(_d, _FP_FRAC_WORD_4(R,0), X##_f0, Y##_f0); \ - doit(_FP_FRAC_WORD_4(R,2), _FP_FRAC_WORD_4(R,1), _b_f0, _b_f1); \ - doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ + _b_f0 = X##_f0 + X##_f1; \ + _c1 = _b_f0 < X##_f0; \ + _b_f1 = Y##_f0 + Y##_f1; \ + _c2 = _b_f1 < Y##_f0; \ + doit(_d, _FP_FRAC_WORD_4(R,0), X##_f0, Y##_f0); \ + doit(_FP_FRAC_WORD_4(R,2), _FP_FRAC_WORD_4(R,1), _b_f0, _b_f1); \ + doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ \ - _b_f0 &= -_c2; \ - _b_f1 &= -_c1; \ - __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1), (_c1 & _c2), 0, _d, \ - 0, _FP_FRAC_WORD_4(R,2), _FP_FRAC_WORD_4(R,1)); \ - __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _b_f0); \ - __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _b_f1); \ - __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1), \ - 0, _d, _FP_FRAC_WORD_4(R,0)); \ - __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ - _FP_FRAC_WORD_4(R,1), 0, _c_f1, _c_f0); \ - __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(R,3), _FP_FRAC_WORD_4(R,2), \ - _c_f1, _c_f0, \ - _FP_FRAC_WORD_4(R,3), _FP_FRAC_WORD_4(R,2)); \ - } while (0) + _b_f0 &= -_c2; \ + _b_f1 &= -_c1; \ + __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1), (_c1 & _c2), 0, _d, \ + 0, _FP_FRAC_WORD_4(R,2), _FP_FRAC_WORD_4(R,1)); \ + __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _b_f0); \ + __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _b_f1); \ + __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1), \ + 0, _d, _FP_FRAC_WORD_4(R,0)); \ + __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(R,3),_FP_FRAC_WORD_4(R,2), \ + _FP_FRAC_WORD_4(R,1), 0, _c_f1, _c_f0); \ + __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(R,3), _FP_FRAC_WORD_4(R,2), \ + _c_f1, _c_f0, \ + _FP_FRAC_WORD_4(R,3), _FP_FRAC_WORD_4(R,2)); \ + } \ + while (0) #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ - do { \ - _FP_FRAC_DECL_4(_z); \ - \ - _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, _z, X, Y, doit); \ + do \ + { \ + _FP_FRAC_DECL_4(_z); \ \ - /* Normalize since we know where the msb of the multiplicands \ - were (bit B), we know that the msb of the of the product is \ - at either 2B or 2B-1. */ \ - _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ - R##_f0 = _FP_FRAC_WORD_4(_z,0); \ - R##_f1 = _FP_FRAC_WORD_4(_z,1); \ - } while (0) - -#define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y) \ - do { \ - _FP_W_TYPE _x[2], _y[2]; \ - _x[0] = X##_f0; _x[1] = X##_f1; \ - _y[0] = Y##_f0; _y[1] = Y##_f1; \ + _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, _z, X, Y, doit); \ \ - mpn_mul_n(R##_f, _x, _y, 2); \ - } while (0) + /* Normalize since we know where the msb of the multiplicands \ + were (bit B), we know that the msb of the of the product is \ + at either 2B or 2B-1. */ \ + _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ + R##_f0 = _FP_FRAC_WORD_4(_z,0); \ + R##_f1 = _FP_FRAC_WORD_4(_z,1); \ + } \ + while (0) + +#define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y) \ + do \ + { \ + _FP_W_TYPE _x[2], _y[2]; \ + _x[0] = X##_f0; \ + _x[1] = X##_f1; \ + _y[0] = Y##_f0; \ + _y[1] = Y##_f1; \ + \ + mpn_mul_n(R##_f, _x, _y, 2); \ + } \ + while (0) #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ - do { \ - _FP_FRAC_DECL_4(_z); \ + do \ + { \ + _FP_FRAC_DECL_4(_z); \ \ - _FP_MUL_MEAT_DW_2_gmp(wfracbits, _z, X, Y); \ + _FP_MUL_MEAT_DW_2_gmp(wfracbits, _z, X, Y); \ \ - /* Normalize since we know where the msb of the multiplicands \ - were (bit B), we know that the msb of the of the product is \ - at either 2B or 2B-1. */ \ - _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ - R##_f0 = _z_f[0]; \ - R##_f1 = _z_f[1]; \ - } while (0) + /* Normalize since we know where the msb of the multiplicands \ + were (bit B), we know that the msb of the of the product is \ + at either 2B or 2B-1. */ \ + _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ + R##_f0 = _z_f[0]; \ + R##_f1 = _z_f[1]; \ + } \ + while (0) /* Do at most 120x120=240 bits multiplication using double floating point multiplication. This is useful if floating point @@ -376,190 +405,203 @@ SETFETZ is a macro which will disable all FPU exceptions and set rounding towards zero, RESETFE should optionally reset it back. */ -#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ - do { \ - static const double _const[] = { \ - /* 2^-24 */ 5.9604644775390625e-08, \ - /* 2^-48 */ 3.5527136788005009e-15, \ - /* 2^-72 */ 2.1175823681357508e-22, \ - /* 2^-96 */ 1.2621774483536189e-29, \ - /* 2^28 */ 2.68435456e+08, \ - /* 2^4 */ 1.600000e+01, \ - /* 2^-20 */ 9.5367431640625e-07, \ - /* 2^-44 */ 5.6843418860808015e-14, \ - /* 2^-68 */ 3.3881317890172014e-21, \ - /* 2^-92 */ 2.0194839173657902e-28, \ - /* 2^-116 */ 1.2037062152420224e-35}; \ - double _a240, _b240, _c240, _d240, _e240, _f240, \ - _g240, _h240, _i240, _j240, _k240; \ - union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ - _p240, _q240, _r240, _s240; \ - UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ - \ - if (wfracbits < 106 || wfracbits > 120) \ - abort(); \ - \ - setfetz; \ - \ - _e240 = (double)(long)(X##_f0 & 0xffffff); \ - _j240 = (double)(long)(Y##_f0 & 0xffffff); \ - _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \ - _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \ - _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ - _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ - _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \ - _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \ - _a240 = (double)(long)(X##_f1 >> 32); \ - _f240 = (double)(long)(Y##_f1 >> 32); \ - _e240 *= _const[3]; \ - _j240 *= _const[3]; \ - _d240 *= _const[2]; \ - _i240 *= _const[2]; \ - _c240 *= _const[1]; \ - _h240 *= _const[1]; \ - _b240 *= _const[0]; \ - _g240 *= _const[0]; \ - _s240.d = _e240*_j240;\ - _r240.d = _d240*_j240 + _e240*_i240;\ - _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\ - _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\ - _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\ - _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ - _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ - _l240.d = _a240*_g240 + _b240*_f240; \ - _k240 = _a240*_f240; \ - _r240.d += _s240.d; \ - _q240.d += _r240.d; \ - _p240.d += _q240.d; \ - _o240.d += _p240.d; \ - _n240.d += _o240.d; \ - _m240.d += _n240.d; \ - _l240.d += _m240.d; \ - _k240 += _l240.d; \ - _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ - _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ - _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ - _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ - _o240.d += _const[7]; \ - _n240.d += _const[6]; \ - _m240.d += _const[5]; \ - _l240.d += _const[4]; \ - if (_s240.d != 0.0) _y240 = 1; \ - if (_r240.d != 0.0) _y240 = 1; \ - if (_q240.d != 0.0) _y240 = 1; \ - if (_p240.d != 0.0) _y240 = 1; \ - _t240 = (DItype)_k240; \ - _u240 = _l240.i; \ - _v240 = _m240.i; \ - _w240 = _n240.i; \ - _x240 = _o240.i; \ - R##_f1 = (_t240 << (128 - (wfracbits - 1))) \ - | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \ - R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ - | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ - | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ - | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ - | _y240; \ - resetfe; \ - } while (0) +#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ + do \ + { \ + static const double _const[] = \ + { \ + /* 2^-24 */ 5.9604644775390625e-08, \ + /* 2^-48 */ 3.5527136788005009e-15, \ + /* 2^-72 */ 2.1175823681357508e-22, \ + /* 2^-96 */ 1.2621774483536189e-29, \ + /* 2^28 */ 2.68435456e+08, \ + /* 2^4 */ 1.600000e+01, \ + /* 2^-20 */ 9.5367431640625e-07, \ + /* 2^-44 */ 5.6843418860808015e-14, \ + /* 2^-68 */ 3.3881317890172014e-21, \ + /* 2^-92 */ 2.0194839173657902e-28, \ + /* 2^-116 */ 1.2037062152420224e-35 \ + }; \ + double _a240, _b240, _c240, _d240, _e240, _f240, \ + _g240, _h240, _i240, _j240, _k240; \ + union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ + _p240, _q240, _r240, _s240; \ + UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ + \ + if (wfracbits < 106 || wfracbits > 120) \ + abort(); \ + \ + setfetz; \ + \ + _e240 = (double)(long)(X##_f0 & 0xffffff); \ + _j240 = (double)(long)(Y##_f0 & 0xffffff); \ + _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \ + _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \ + _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ + _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ + _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \ + _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \ + _a240 = (double)(long)(X##_f1 >> 32); \ + _f240 = (double)(long)(Y##_f1 >> 32); \ + _e240 *= _const[3]; \ + _j240 *= _const[3]; \ + _d240 *= _const[2]; \ + _i240 *= _const[2]; \ + _c240 *= _const[1]; \ + _h240 *= _const[1]; \ + _b240 *= _const[0]; \ + _g240 *= _const[0]; \ + _s240.d = _e240*_j240; \ + _r240.d = _d240*_j240 + _e240*_i240; \ + _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240; \ + _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240; \ + _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240; \ + _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ + _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ + _l240.d = _a240*_g240 + _b240*_f240; \ + _k240 = _a240*_f240; \ + _r240.d += _s240.d; \ + _q240.d += _r240.d; \ + _p240.d += _q240.d; \ + _o240.d += _p240.d; \ + _n240.d += _o240.d; \ + _m240.d += _n240.d; \ + _l240.d += _m240.d; \ + _k240 += _l240.d; \ + _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ + _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ + _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ + _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ + _o240.d += _const[7]; \ + _n240.d += _const[6]; \ + _m240.d += _const[5]; \ + _l240.d += _const[4]; \ + if (_s240.d != 0.0) \ + _y240 = 1; \ + if (_r240.d != 0.0) \ + _y240 = 1; \ + if (_q240.d != 0.0) \ + _y240 = 1; \ + if (_p240.d != 0.0) \ + _y240 = 1; \ + _t240 = (DItype)_k240; \ + _u240 = _l240.i; \ + _v240 = _m240.i; \ + _w240 = _n240.i; \ + _x240 = _o240.i; \ + R##_f1 = ((_t240 << (128 - (wfracbits - 1))) \ + | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104))); \ + R##_f0 = (((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ + | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ + | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ + | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ + | _y240); \ + resetfe; \ + } \ + while (0) /* * Division algorithms: */ #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ - do { \ - _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ - if (_FP_FRAC_GE_2(X, Y)) \ - { \ - _n_f2 = X##_f1 >> 1; \ - _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ - _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ - } \ - else \ - { \ - R##_e--; \ - _n_f2 = X##_f1; \ - _n_f1 = X##_f0; \ - _n_f0 = 0; \ - } \ + do \ + { \ + _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ + if (_FP_FRAC_GE_2(X, Y)) \ + { \ + _n_f2 = X##_f1 >> 1; \ + _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ + _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ + } \ + else \ + { \ + R##_e--; \ + _n_f2 = X##_f1; \ + _n_f1 = X##_f0; \ + _n_f0 = 0; \ + } \ \ - /* Normalize, i.e. make the most significant bit of the \ - denominator set. */ \ - _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \ + /* Normalize, i.e. make the most significant bit of the \ + denominator set. */ \ + _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \ \ - udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \ - umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ - _r_f0 = _n_f0; \ - if (_FP_FRAC_GT_2(_m, _r)) \ - { \ - R##_f1--; \ - _FP_FRAC_ADD_2(_r, Y, _r); \ - if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ - { \ - R##_f1--; \ - _FP_FRAC_ADD_2(_r, Y, _r); \ - } \ - } \ - _FP_FRAC_DEC_2(_r, _m); \ + udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \ + umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ + _r_f0 = _n_f0; \ + if (_FP_FRAC_GT_2(_m, _r)) \ + { \ + R##_f1--; \ + _FP_FRAC_ADD_2(_r, Y, _r); \ + if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ + { \ + R##_f1--; \ + _FP_FRAC_ADD_2(_r, Y, _r); \ + } \ + } \ + _FP_FRAC_DEC_2(_r, _m); \ \ - if (_r_f1 == Y##_f1) \ - { \ - /* This is a special case, not an optimization \ - (_r/Y##_f1 would not fit into UWtype). \ - As _r is guaranteed to be < Y, R##_f0 can be either \ - (UWtype)-1 or (UWtype)-2. But as we know what kind \ - of bits it is (sticky, guard, round), we don't care. \ - We also don't care what the reminder is, because the \ - guard bit will be set anyway. -jj */ \ - R##_f0 = -1; \ - } \ - else \ - { \ - udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \ - umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ - _r_f0 = 0; \ - if (_FP_FRAC_GT_2(_m, _r)) \ - { \ - R##_f0--; \ - _FP_FRAC_ADD_2(_r, Y, _r); \ - if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ - { \ - R##_f0--; \ - _FP_FRAC_ADD_2(_r, Y, _r); \ - } \ - } \ - if (!_FP_FRAC_EQ_2(_r, _m)) \ - R##_f0 |= _FP_WORK_STICKY; \ - } \ - } while (0) + if (_r_f1 == Y##_f1) \ + { \ + /* This is a special case, not an optimization \ + (_r/Y##_f1 would not fit into UWtype). \ + As _r is guaranteed to be < Y, R##_f0 can be either \ + (UWtype)-1 or (UWtype)-2. But as we know what kind \ + of bits it is (sticky, guard, round), we don't care. \ + We also don't care what the reminder is, because the \ + guard bit will be set anyway. -jj */ \ + R##_f0 = -1; \ + } \ + else \ + { \ + udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \ + umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ + _r_f0 = 0; \ + if (_FP_FRAC_GT_2(_m, _r)) \ + { \ + R##_f0--; \ + _FP_FRAC_ADD_2(_r, Y, _r); \ + if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ + { \ + R##_f0--; \ + _FP_FRAC_ADD_2(_r, Y, _r); \ + } \ + } \ + if (!_FP_FRAC_EQ_2(_r, _m)) \ + R##_f0 |= _FP_WORK_STICKY; \ + } \ + } \ + while (0) #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ - do { \ - _FP_W_TYPE _x[4], _y[2], _z[4]; \ - _y[0] = Y##_f0; _y[1] = Y##_f1; \ - _x[0] = _x[3] = 0; \ - if (_FP_FRAC_GE_2(X, Y)) \ - { \ - _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \ - X##_f1 >> (_FP_W_TYPE_SIZE - \ - (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ - _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ - } \ - else \ - { \ - R##_e--; \ - _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \ - X##_f1 >> (_FP_W_TYPE_SIZE - \ - (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ - _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ - } \ + do \ + { \ + _FP_W_TYPE _x[4], _y[2], _z[4]; \ + _y[0] = Y##_f0; \ + _y[1] = Y##_f1; \ + _x[0] = _x[3] = 0; \ + if (_FP_FRAC_GE_2(X, Y)) \ + { \ + _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) \ + | X##_f1 >> (_FP_W_TYPE_SIZE - \ + (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ + _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ + } \ + else \ + { \ + R##_e--; \ + _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) \ + | X##_f1 >> (_FP_W_TYPE_SIZE - \ + (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ + _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ + } \ \ - (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ - R##_f1 = _z[1]; \ - R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ - } while (0) + (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ + R##_f1 = _z[1]; \ + R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ + } \ + while (0) /* @@ -568,44 +610,46 @@ * should be added for those machines where division is fast. */ -#define _FP_SQRT_MEAT_2(R, S, T, X, q) \ - do { \ - while (q) \ - { \ - T##_f1 = S##_f1 + q; \ - if (T##_f1 <= X##_f1) \ - { \ - S##_f1 = T##_f1 + q; \ - X##_f1 -= T##_f1; \ - R##_f1 += q; \ - } \ - _FP_FRAC_SLL_2(X, 1); \ - q >>= 1; \ - } \ - q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ - while (q != _FP_WORK_ROUND) \ - { \ - T##_f0 = S##_f0 + q; \ - T##_f1 = S##_f1; \ - if (T##_f1 < X##_f1 || \ - (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ - { \ - S##_f0 = T##_f0 + q; \ - S##_f1 += (T##_f0 > S##_f0); \ - _FP_FRAC_DEC_2(X, T); \ - R##_f0 += q; \ - } \ - _FP_FRAC_SLL_2(X, 1); \ - q >>= 1; \ - } \ - if (X##_f0 | X##_f1) \ - { \ - if (S##_f1 < X##_f1 || \ - (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ - R##_f0 |= _FP_WORK_ROUND; \ - R##_f0 |= _FP_WORK_STICKY; \ - } \ - } while (0) +#define _FP_SQRT_MEAT_2(R, S, T, X, q) \ + do \ + { \ + while (q) \ + { \ + T##_f1 = S##_f1 + q; \ + if (T##_f1 <= X##_f1) \ + { \ + S##_f1 = T##_f1 + q; \ + X##_f1 -= T##_f1; \ + R##_f1 += q; \ + } \ + _FP_FRAC_SLL_2(X, 1); \ + q >>= 1; \ + } \ + q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ + while (q != _FP_WORK_ROUND) \ + { \ + T##_f0 = S##_f0 + q; \ + T##_f1 = S##_f1; \ + if (T##_f1 < X##_f1 \ + || (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ + { \ + S##_f0 = T##_f0 + q; \ + S##_f1 += (T##_f0 > S##_f0); \ + _FP_FRAC_DEC_2(X, T); \ + R##_f0 += q; \ + } \ + _FP_FRAC_SLL_2(X, 1); \ + q >>= 1; \ + } \ + if (X##_f0 | X##_f1) \ + { \ + if (S##_f1 < X##_f1 \ + || (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ + R##_f0 |= _FP_WORK_ROUND; \ + R##_f0 |= _FP_WORK_STICKY; \ + } \ + } \ + while (0) /* @@ -614,19 +658,21 @@ */ #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ -(void)((rsize <= _FP_W_TYPE_SIZE) \ - ? ({ r = X##_f0; }) \ - : ({ \ - r = X##_f1; \ - r <<= _FP_W_TYPE_SIZE; \ - r += X##_f0; \ - })) + (void)((rsize <= _FP_W_TYPE_SIZE) \ + ? ({ r = X##_f0; }) \ + : ({ \ + r = X##_f1; \ + r <<= _FP_W_TYPE_SIZE; \ + r += X##_f0; \ + })) #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ - do { \ - X##_f0 = r; \ - X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ - } while (0) + do \ + { \ + X##_f0 = r; \ + X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ + } \ + while (0) /* * Convert FP values between word sizes |