java/dfp/src/main/java/com/epam/deltix/dfp/JavaImplRound.java [460:545]: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - long /*BID_UINT128*/ P128_w0, P128_w1; x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // check for NaNs and infinities if ((x & MASK_NAN) == MASK_NAN) { // check for NaN if ((x & 0x0003ffffffffffffL) >= 1000000000000000L) x = x & 0xfe00000000000000L; // clear G6-G12 and the payload bits else x = x & 0xfe03ffffffffffffL; // clear G6-G12 if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN // set invalid flag // __set_status_flags(pfpsf, BID_INVALID_EXCEPTION); // return quiet (SNaN) res = x & 0xfdffffffffffffffL; } else { // QNaN res = x; } return res; } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity return x_sign | 0x7800000000000000L; } // unpack x if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11 (condition will be 0), then // the exponent is G[0:w+1] exp = (int) (((x & MASK_BINARY_EXPONENT2) >>> 51) - 398); C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (C1 > 9999999999999999L) { // non-canonical C1 = 0; } } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) exp = (int) (((x & MASK_BINARY_EXPONENT1) >>> 53) - 398); C1 = (x & MASK_BINARY_SIG1); } // if x is 0 or non-canonical if (C1 == 0) { if (exp < 0) exp = 0; return x_sign | (((long) exp + 398) << 53); } // x is a finite non-zero number (not 0, non-canonical, or special) // return 0 if (exp <= -(p+1)) if (exp <= -17) { return x_sign | 0x31c0000000000000L; } // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x if (UnsignedLong.isGreaterOrEqual(C1, 0x0020000000000000L)) { // x >= 2^53 q = 16; } else { // if x < 2^53 final long tmp1_ui64 = Double.doubleToRawLongBits((double) C1); // exact conversion x_nr_bits = 1 + ((((/*unsigned*/ int) (tmp1_ui64 >>> 52)) & 0x7ff) - 0x3ff); q = (int) bid_nr_digits_flat[((x_nr_bits - 1) << 2) /*+ 0 .digits*/]; if (q == 0) { q = (int) bid_nr_digits_flat[((x_nr_bits - 1) << 2) + 3 /*.digits1*/]; if (UnsignedLong.isGreaterOrEqual(C1, bid_nr_digits_flat[((x_nr_bits - 1) << 2) + 2 /*.threshold_lo*/])) q++; } } if (exp >= 0) { // -exp <= 0 // the argument is an integer already return x; } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q // need to shift right -exp digits from the coefficient; the exp will be 0 ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate C1 = C1 + bid_midpoint64[ind - 1]; // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by // bid_shiftright128[] and bid_maskhigh128[] // 1 <= x <= 16 // kx = 10^(-x) = bid_ten2mk64[ind - 1] // C* = (C1 + 1/2 * 10^x) * 10^(-x) // the approximation of 10^(-x) was rounded up to 64 bits //__mul_64x64_to_128(P128, C1, bid_ten2mk64[ind - 1]); { final long __CY = bid_ten2mk64[ind - 1]; P128_w1 = Mul64Impl.unsignedMultiplyHigh(C1, __CY); - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - java/dfp/src/main/java/com/epam/deltix/dfp/JavaImplRound.java [987:1072]: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - long /*BID_UINT128*/ P128_w0, P128_w1; x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // check for NaNs and infinities if ((x & MASK_NAN) == MASK_NAN) { // check for NaN if ((x & 0x0003ffffffffffffL) >= 1000000000000000L) x = x & 0xfe00000000000000L; // clear G6-G12 and the payload bits else x = x & 0xfe03ffffffffffffL; // clear G6-G12 if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN // set invalid flag // __set_status_flags(pfpsf, BID_INVALID_EXCEPTION); // return quiet (SNaN) res = x & 0xfdffffffffffffffL; } else { // QNaN res = x; } return res; } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity return x_sign | 0x7800000000000000L; } // unpack x if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11 (condition will be 0), then // the exponent is G[0:w+1] exp = (int) (((x & MASK_BINARY_EXPONENT2) >>> 51) - 398); C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (C1 > 9999999999999999L) { // non-canonical C1 = 0; } } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) exp = (int) (((x & MASK_BINARY_EXPONENT1) >>> 53) - 398); C1 = (x & MASK_BINARY_SIG1); } // if x is 0 or non-canonical if (C1 == 0) { if (exp < 0) exp = 0; return x_sign | (((long) exp + 398) << 53); } // x is a finite non-zero number (not 0, non-canonical, or special) // return 0 if (exp <= -(p+1)) if (exp <= -17) { return x_sign | 0x31c0000000000000L; } // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x if (UnsignedLong.isGreaterOrEqual(C1, 0x0020000000000000L)) { // x >= 2^53 q = 16; } else { // if x < 2^53 final long tmp1_ui64 = Double.doubleToRawLongBits((double) C1); // exact conversion x_nr_bits = 1 + ((((/*unsigned*/ int) (tmp1_ui64 >>> 52)) & 0x7ff) - 0x3ff); q = (int) bid_nr_digits_flat[((x_nr_bits - 1) << 2) /*+ 0 .digits*/]; if (q == 0) { q = (int) bid_nr_digits_flat[((x_nr_bits - 1) << 2) + 3 /*.digits1*/]; if (UnsignedLong.isGreaterOrEqual(C1, bid_nr_digits_flat[((x_nr_bits - 1) << 2) + 2 /*.threshold_lo*/])) q++; } } if (exp >= 0) { // -exp <= 0 // the argument is an integer already return x; } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q // need to shift right -exp digits from the coefficient; the exp will be 0 ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate C1 = C1 + bid_midpoint64[ind - 1]; // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by // bid_shiftright128[] and bid_maskhigh128[] // 1 <= x <= 16 // kx = 10^(-x) = bid_ten2mk64[ind - 1] // C* = (C1 + 1/2 * 10^x) * 10^(-x) // the approximation of 10^(-x) was rounded up to 64 bits //__mul_64x64_to_128(P128, C1, bid_ten2mk64[ind - 1]); { final long __CY = bid_ten2mk64[ind - 1]; P128_w1 = Mul64Impl.unsignedMultiplyHigh(C1, __CY); 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