csharp/EPAM.Deltix.DFP.Benchmark/Bid64Add.cs (554 lines of code) (raw):

using static EPAM.Deltix.DFP.BidDecimalData; using static EPAM.Deltix.DFP.BidInternal; using BID_UINT64 = System.UInt64; using BID_SINT64 = System.Int64; using BID_UINT32 = System.UInt32; using _IDEC_flags = System.UInt32; using int_double = System.UInt64; using System.Runtime.CompilerServices; namespace EPAM.Deltix.DFP { internal static class Bid64Add { #if NET6_0_OR_GREATER [MethodImpl(MethodImplOptions.AggressiveOptimization)] #endif public static unsafe BID_UINT64 bid64_sub(BID_UINT64 x, BID_UINT64 y #if !IEEE_ROUND_NEAREST , int rnd_mode #endif #if BID_SET_STATUS_FLAGS , ref _IDEC_flags pfpsf #endif ) { // check if y is not NaN if (((y & NAN_MASK64) != NAN_MASK64)) y ^= 0x8000000000000000UL; return bid64_add(x, y #if !IEEE_ROUND_NEAREST , rnd_mode #endif #if BID_SET_STATUS_FLAGS , ref pfpsf #endif ); } /// <summary> /// Algorithm description: /// /// if(exponent_a < exponent_b) /// switch a, b /// diff_expon = exponent_a - exponent_b /// if(diff_expon > 16) /// return normalize(a) /// if(coefficient_a*10^diff_expon guaranteed below 2^62) /// S = sign_a*coefficient_a*10^diff_expon + sign_b*coefficient_b /// if(|S|<10^16) /// return get_BID64(sign(S),exponent_b,|S|) /// else /// determine number of extra digits in S (1, 2, or 3) /// return rounded result /// else // large exponent difference /// if(number_digits(coefficient_a*10^diff_expon) +/- 10^16) /// guaranteed the same as /// number_digits(coefficient_a*10^diff_expon) ) /// S = normalize(coefficient_a + (sign_a^sign_b)*10^(16-diff_expon)) /// corr = 10^16 + (sign_a^sign_b)*coefficient_b /// corr*10^exponent_b is rounded so it aligns with S*10^exponent_S /// return get_BID64(sign_a,exponent(S),S+rounded(corr)) /// else /// add sign_a*coefficient_a*10^diff_expon, sign_b*coefficient_b /// in 128-bit integer arithmetic, then round to 16 decimal digits /// </summary> #if NET6_0_OR_GREATER [MethodImpl(MethodImplOptions.AggressiveOptimization)] #endif public static unsafe BID_UINT64 bid64_add(BID_UINT64 x, BID_UINT64 y #if !IEEE_ROUND_NEAREST , int rnd_mode #endif #if BID_SET_STATUS_FLAGS , ref _IDEC_flags pfpsf #endif ) { BID_UINT128 CA, CT, CT_new; BID_UINT64 sign_x, sign_y, coefficient_x, coefficient_y, C64_new; BID_UINT64 valid_x, valid_y; BID_UINT64 res; BID_UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab, rem_a; BID_UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1; #if BID_SET_STATUS_FLAGS BID_UINT64 carry, tmp; #endif int_double tempx_i; int exponent_x, exponent_y, exponent_a, exponent_b, diff_dec_expon; int bin_expon_ca, extra_digits, amount, scale_k, scale_ca; int rmode; #if BID_SET_STATUS_FLAGS _IDEC_flags status; #endif //valid_x = unpack_BID64(out sign_x, out exponent_x, out coefficient_x, x); { sign_x = x & 0x8000000000000000UL; if ((x & SPECIAL_ENCODING_MASK64) != SPECIAL_ENCODING_MASK64) { // exponent exponent_x = (int)((x >> EXPONENT_SHIFT_SMALL64) & EXPONENT_MASK64); // coefficient coefficient_x = (x & SMALL_COEFF_MASK64); valid_x = coefficient_x; } else { // special encodings if ((x & INFINITY_MASK64) == INFINITY_MASK64) { exponent_x = 0; coefficient_x = x & 0xfe03ffffffffffffUL; if ((x & 0x0003ffffffffffffUL) >= 1000000000000000UL) coefficient_x = x & 0xfe00000000000000UL; if ((x & NAN_MASK64) == INFINITY_MASK64) coefficient_x = x & SINFINITY_MASK64; valid_x = 0; // NaN or Infinity } else { // coefficient BID_UINT64 coeff = (x & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64; // check for non-canonical values if (coeff >= 10000000000000000UL) coeff = 0; coefficient_x = coeff; // get exponent exponent_x = (int)((x >> EXPONENT_SHIFT_LARGE64) & EXPONENT_MASK64); valid_x = coeff; } } } //valid_y = unpack_BID64(out sign_y, out exponent_y, out coefficient_y, y); { sign_y = y & 0x8000000000000000UL; if ((y & SPECIAL_ENCODING_MASK64) != SPECIAL_ENCODING_MASK64) { // exponent exponent_y = (int)((y >> EXPONENT_SHIFT_SMALL64) & EXPONENT_MASK64); // coefficient coefficient_y = (y & SMALL_COEFF_MASK64); valid_y = coefficient_y; } else { // special encodings if ((y & INFINITY_MASK64) == INFINITY_MASK64) { exponent_y = 0; coefficient_y = y & 0xfe03ffffffffffffUL; if ((y & 0x0003ffffffffffffUL) >= 1000000000000000UL) coefficient_y = y & 0xfe00000000000000UL; if ((y & NAN_MASK64) == INFINITY_MASK64) coefficient_y = y & SINFINITY_MASK64; valid_y = 0; // NaN or Infinity } else { // coefficient BID_UINT64 coeff = (y & LARGE_COEFF_MASK64) | LARGE_COEFF_HIGH_BIT64; // check for non-canonical values if (coeff >= 10000000000000000UL) coeff = 0; coefficient_y = coeff; // get exponent exponent_y = (int)((y >> EXPONENT_SHIFT_LARGE64) & EXPONENT_MASK64); valid_y = coeff; } } } // unpack arguments, check for NaN or Infinity if (valid_x == 0) { // x is Inf. or NaN // test if x is NaN if ((x & NAN_MASK64) == NAN_MASK64) { #if BID_SET_STATUS_FLAGS if (((x & SNAN_MASK64) == SNAN_MASK64) // sNaN || ((y & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags(ref pfpsf, BID_INVALID_EXCEPTION); #endif return coefficient_x & QUIET_MASK64; } // x is Infinity? if ((x & INFINITY_MASK64) == INFINITY_MASK64) { // check if y is Inf if (((y & NAN_MASK64) == INFINITY_MASK64)) { if (sign_x == (y & 0x8000000000000000UL)) { return coefficient_x; } // return NaN { #if BID_SET_STATUS_FLAGS __set_status_flags(ref pfpsf, BID_INVALID_EXCEPTION); #endif return NAN_MASK64; } } // check if y is NaN if (((y & NAN_MASK64) == NAN_MASK64)) { res = coefficient_y & QUIET_MASK64; #if BID_SET_STATUS_FLAGS if (((y & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags(ref pfpsf, BID_INVALID_EXCEPTION); #endif return res; } // otherwise return +/-Inf { return coefficient_x; } } // x is 0 { if (((y & INFINITY_MASK64) != INFINITY_MASK64) && coefficient_y != 0) { if (exponent_y <= exponent_x) { return y; } } } } if (valid_y == 0) { // y is Inf. or NaN? if (((y & INFINITY_MASK64) == INFINITY_MASK64)) { #if BID_SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags(ref pfpsf, BID_INVALID_EXCEPTION); #endif return coefficient_y & QUIET_MASK64; } // y is 0 if (coefficient_x == 0) { // x==0 if (exponent_x <= exponent_y) res = ((BID_UINT64)exponent_x) << 53; else res = ((BID_UINT64)exponent_y) << 53; if (sign_x == sign_y) res |= sign_x; #if !IEEE_ROUND_NEAREST_TIES_AWAY #if !IEEE_ROUND_NEAREST if (rnd_mode == BID_ROUNDING_DOWN && sign_x != sign_y) res |= 0x8000000000000000UL; #endif #endif return res; } else if (exponent_y >= exponent_x) { return x; } } // sort arguments by exponent if (exponent_x < exponent_y) { sign_a = sign_y; exponent_a = exponent_y; coefficient_a = coefficient_y; sign_b = sign_x; exponent_b = exponent_x; coefficient_b = coefficient_x; } else { sign_a = sign_x; exponent_a = exponent_x; coefficient_a = coefficient_x; sign_b = sign_y; exponent_b = exponent_y; coefficient_b = coefficient_y; } // exponent difference diff_dec_expon = exponent_a - exponent_b; /* get binary coefficients of x and y */ //--- get number of bits in the coefficients of x and y --- // version 2 (original) tempx_i = doubleToBits((double)coefficient_a); bin_expon_ca = (int)(((tempx_i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff); if (diff_dec_expon > MAX_FORMAT_DIGITS) { // normalize a to a 16-digit coefficient scale_ca = bid_estimate_decimal_digits[bin_expon_ca]; if (coefficient_a >= bid_power10_table_128[scale_ca].w0) scale_ca++; scale_k = 16 - scale_ca; coefficient_a *= bid_power10_table_128[scale_k].w0; diff_dec_expon -= scale_k; exponent_a -= scale_k; /* get binary coefficients of x and y */ //--- get number of bits in the coefficients of x and y --- tempx_i = doubleToBits((double)coefficient_a); bin_expon_ca = (int)(((tempx_i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff); if (diff_dec_expon > MAX_FORMAT_DIGITS) { #if BID_SET_STATUS_FLAGS if (coefficient_b != 0) { __set_status_flags(ref pfpsf, BID_INEXACT_EXCEPTION); } #endif #if !IEEE_ROUND_NEAREST_TIES_AWAY #if !IEEE_ROUND_NEAREST if (((rnd_mode) & 3) != 0 && coefficient_b != 0) // not BID_ROUNDING_TO_NEAREST { switch (rnd_mode) { case BID_ROUNDING_DOWN: if (sign_b != 0) { coefficient_a -= (BID_UINT64)((((BID_SINT64)sign_a) >> 63) | 1); if (coefficient_a < 1000000000000000UL) { exponent_a--; coefficient_a = 9999999999999999UL; } else if (coefficient_a >= 10000000000000000UL) { exponent_a++; coefficient_a = 1000000000000000UL; } } break; case BID_ROUNDING_UP: if (sign_b == 0) { coefficient_a += (BID_UINT64)((((BID_SINT64)sign_a) >> 63) | 1); if (coefficient_a < 1000000000000000UL) { exponent_a--; coefficient_a = 9999999999999999UL; } else if (coefficient_a >= 10000000000000000UL) { exponent_a++; coefficient_a = 1000000000000000UL; } } break; default: // RZ if (sign_a != sign_b) { coefficient_a--; if (coefficient_a < 1000000000000000UL) { exponent_a--; coefficient_a = 9999999999999999UL; } } break; } } else #endif #endif // check special case here if ((coefficient_a == 1000000000000000UL) && (diff_dec_expon == MAX_FORMAT_DIGITS + 1) && (sign_a ^ sign_b) != 0 && (coefficient_b > 5000000000000000UL)) { coefficient_a = 9999999999999999UL; exponent_a--; } return fast_get_BID64_check_OF(sign_a, exponent_a, coefficient_a #if !IEEE_ROUND_NEAREST , rnd_mode #endif #if BID_SET_STATUS_FLAGS , ref pfpsf #endif ); } } // test whether coefficient_a*10^(exponent_a-exponent_b) may exceed 2^62 if (bin_expon_ca + bid_estimate_bin_expon[diff_dec_expon] < 60) { // coefficient_a*10^(exponent_a-exponent_b)<2^63 // multiply by 10^(exponent_a-exponent_b) coefficient_a *= bid_power10_table_128[diff_dec_expon].w0; // sign mask sign_b = (BID_UINT64)(((BID_SINT64)sign_b) >> 63); // apply sign to coeff. of b coefficient_b = (coefficient_b + sign_b) ^ sign_b; // apply sign to coefficient a sign_a = (BID_UINT64)(((BID_SINT64)sign_a) >> 63); coefficient_a = (coefficient_a + sign_a) ^ sign_a; coefficient_a += coefficient_b; // get sign sign_s = (BID_UINT64)(((BID_SINT64)coefficient_a) >> 63); coefficient_a = (coefficient_a + sign_s) ^ sign_s; sign_s &= 0x8000000000000000UL; // coefficient_a < 10^16 ? if (coefficient_a < bid_power10_table_128[MAX_FORMAT_DIGITS].w0) { #if !IEEE_ROUND_NEAREST_TIES_AWAY #if !IEEE_ROUND_NEAREST if (rnd_mode == BID_ROUNDING_DOWN && (coefficient_a == 0) && sign_a != sign_b) sign_s = 0x8000000000000000UL; #endif #endif return very_fast_get_BID64(sign_s, exponent_b, coefficient_a); } // otherwise rounding is necessary // already know coefficient_a<10^19 // coefficient_a < 10^17 ? if (coefficient_a < bid_power10_table_128[17].w0) extra_digits = 1; else if (coefficient_a < bid_power10_table_128[18].w0) extra_digits = 2; else extra_digits = 3; #if !IEEE_ROUND_NEAREST_TIES_AWAY #if !IEEE_ROUND_NEAREST rmode = rnd_mode; if (sign_s != 0 && (uint)(rmode - 1) < 2) rmode = 3 - rmode; #else rmode = 0; #endif #else rmode = 0; #endif coefficient_a += bid_round_const_table[rmode, extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits //__mul_64x64_to_128(out CT, coefficient_a, bid_reciprocals10_64[extra_digits]); { BID_UINT64 CXH, CXL, CYH, CYL, PL, PH, PM, PM2; CXH = (coefficient_a) >> 32; CXL = (BID_UINT32)(coefficient_a); BID_UINT64 CY = bid_reciprocals10_64[extra_digits]; CYH = (CY) >> 32; CYL = (BID_UINT32)(CY); PM = CXH * CYL; PH = CXH * CYH; PL = CXL * CYL; PM2 = CXL * CYH; PH += (PM >> 32); PM = (BID_UINT64)((BID_UINT32)PM) + PM2 + (PL >> 32); CT.w1 = PH + (PM >> 32); CT.w0 = (PM << 32) + (BID_UINT32)PL; } // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = bid_short_recip_scale[extra_digits]; C64 = CT.w1 >> amount; } else { // coefficient_a*10^(exponent_a-exponent_b) is large sign_s = sign_a; #if !IEEE_ROUND_NEAREST_TIES_AWAY #if !IEEE_ROUND_NEAREST rmode = rnd_mode; if (sign_s != 0 && (uint)(rmode - 1) < 2) rmode = 3 - rmode; #else rmode = 0; #endif #else rmode = 0; #endif // check whether we can take faster path scale_ca = bid_estimate_decimal_digits[bin_expon_ca]; sign_ab = sign_a ^ sign_b; sign_ab = (BID_UINT64)(((BID_SINT64)sign_ab) >> 63); // T1 = 10^(16-diff_dec_expon) T1 = bid_power10_table_128[16 - diff_dec_expon].w0; // get number of digits in coefficient_a if (coefficient_a >= bid_power10_table_128[scale_ca].w0) { scale_ca++; } scale_k = 16 - scale_ca; // addition saved_ca = coefficient_a - T1; coefficient_a = (BID_UINT64)((BID_SINT64)saved_ca * (BID_SINT64)bid_power10_table_128[scale_k].w0); extra_digits = diff_dec_expon - scale_k; // apply sign saved_cb = (coefficient_b + sign_ab) ^ sign_ab; // add 10^16 and rounding constant coefficient_b = saved_cb + 10000000000000000UL + bid_round_const_table[rmode, extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits //__mul_64x64_to_128(out CT, coefficient_b, bid_reciprocals10_64[extra_digits]); { BID_UINT64 CXH, CXL, CYH, CYL, PL, PH, PM, PM2; CXH = (coefficient_b) >> 32; CXL = (BID_UINT32)(coefficient_b); BID_UINT64 CY = bid_reciprocals10_64[extra_digits]; CYH = (CY) >> 32; CYL = (BID_UINT32)(CY); PM = CXH * CYL; PH = CXH * CYH; PL = CXL * CYL; PM2 = CXL * CYH; PH += (PM >> 32); PM = (BID_UINT64)((BID_UINT32)PM) + PM2 + (PL >> 32); CT.w1 = PH + (PM >> 32); CT.w0 = (PM << 32) + (BID_UINT32)PL; } // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = bid_short_recip_scale[extra_digits]; C0_64 = CT.w1 >> amount; // result coefficient C64 = C0_64 + coefficient_a; // filter out difficult (corner) cases // this test ensures the number of digits in coefficient_a does not change // after adding (the appropriately scaled and rounded) coefficient_b if ((BID_UINT64)(C64 - 1000000000000000UL - 1) > 9000000000000000UL - 2) { if (C64 >= 10000000000000000UL) { // result has more than 16 digits if (scale_k == 0) { // must divide coeff_a by 10 saved_ca = saved_ca + T1; //__mul_64x64_to_128(out CA, saved_ca, 0x3333333333333334UL); { BID_UINT64 CXH, CXL/*, CYH, CYL*/, PL, PH, PM, PM2; CXH = (saved_ca) >> 32; CXL = (BID_UINT32)(saved_ca); /*CYH = 0x33333333U;*/ /*CYL = 0x33333334U;*/ PM = CXH * 0x33333334U /*CYL*/; PH = CXH * 0x33333333U /*CYH*/; PL = CXL * 0x33333334U /*CYL*/; PM2 = CXL * 0x33333333U /*CYH*/; PH += (PM >> 32); PM = (BID_UINT64)((BID_UINT32)PM) + PM2 + (PL >> 32); CA.w1 = PH + (PM >> 32); CA.w0 = (PM << 32) + (BID_UINT32)PL; } //reciprocals10_64[1]); coefficient_a = CA.w1 >> 1; rem_a = saved_ca - (coefficient_a << 3) - (coefficient_a << 1); coefficient_a = coefficient_a - T1; saved_cb += rem_a * bid_power10_table_128[diff_dec_expon].w0; } else coefficient_a = (BID_UINT64)((BID_SINT64)(saved_ca - T1 - (T1 << 3)) * (BID_SINT64)bid_power10_table_128[scale_k - 1].w0); extra_digits++; coefficient_b = saved_cb + 100000000000000000UL + bid_round_const_table[rmode, extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits //__mul_64x64_to_128(out CT, coefficient_b, bid_reciprocals10_64[extra_digits]); { BID_UINT64 CXH, CXL, CYH, CYL, PL, PH, PM, PM2; CXH = (coefficient_b) >> 32; CXL = (BID_UINT32)(coefficient_b); BID_UINT64 CY = bid_reciprocals10_64[extra_digits]; CYH = (CY) >> 32; CYL = (BID_UINT32)(CY); PM = CXH * CYL; PH = CXH * CYH; PL = CXL * CYL; PM2 = CXL * CYH; PH += (PM >> 32); PM = (BID_UINT64)((BID_UINT32)PM) + PM2 + (PL >> 32); CT.w1 = PH + (PM >> 32); CT.w0 = (PM << 32) + (BID_UINT32)PL; } // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = bid_short_recip_scale[extra_digits]; C0_64 = CT.w1 >> amount; // result coefficient C64 = C0_64 + coefficient_a; } else if (C64 <= 1000000000000000UL) { // less than 16 digits in result coefficient_a = (BID_UINT64)((BID_SINT64)saved_ca * (BID_SINT64)bid_power10_table_128[scale_k + 1].w0); //extra_digits --; exponent_b--; coefficient_b = (saved_cb << 3) + (saved_cb << 1) + 100000000000000000UL + bid_round_const_table[rmode, extra_digits]; // get P*(2^M[extra_digits])/10^extra_digits //__mul_64x64_to_128(out CT_new, coefficient_b, bid_reciprocals10_64[extra_digits]); { BID_UINT64 CXH, CXL, CYH, CYL, PL, PH, PM, PM2; CXH = (coefficient_b) >> 32; CXL = (BID_UINT32)(coefficient_b); BID_UINT64 CY = bid_reciprocals10_64[extra_digits]; CYH = (CY) >> 32; CYL = (BID_UINT32)(CY); PM = CXH * CYL; PH = CXH * CYH; PL = CXL * CYL; PM2 = CXL * CYH; PH += (PM >> 32); PM = (BID_UINT64)((BID_UINT32)PM) + PM2 + (PL >> 32); CT_new.w1 = PH + (PM >> 32); CT_new.w0 = (PM << 32) + (BID_UINT32)PL; } // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = bid_short_recip_scale[extra_digits]; C0_64 = CT_new.w1 >> amount; // result coefficient C64_new = C0_64 + coefficient_a; if (C64_new < 10000000000000000UL) { C64 = C64_new; //#if BID_SET_STATUS_FLAGS CT = CT_new; //#endif } else exponent_b++; } } } #if !IEEE_ROUND_NEAREST_TIES_AWAY #if !IEEE_ROUND_NEAREST if (rmode == 0) //BID_ROUNDING_TO_NEAREST #endif if ((C64 & 1) != 0) { // check whether fractional part of initial_P/10^extra_digits is // exactly .5 // this is the same as fractional part of // (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero // get remainder remainder_h = CT.w1 << (64 - amount); // test whether fractional part is 0 if (remainder_h == 0 && (CT.w0 < bid_reciprocals10_64[extra_digits])) { C64--; } } #endif #if BID_SET_STATUS_FLAGS status = BID_INEXACT_EXCEPTION; // get remainder remainder_h = CT.w1 << (64 - amount); switch (rmode) { case BID_ROUNDING_TO_NEAREST: case BID_ROUNDING_TIES_AWAY: // test whether fractional part is 0 if ((remainder_h == 0x8000000000000000UL) && (CT.w0 < bid_reciprocals10_64[extra_digits])) status = BID_EXACT_STATUS; break; case BID_ROUNDING_DOWN: case BID_ROUNDING_TO_ZERO: if (remainder_h == 0 && (CT.w0 < bid_reciprocals10_64[extra_digits])) status = BID_EXACT_STATUS; //if(!C64 && rmode==BID_ROUNDING_DOWN) sign_s=sign_y; break; default: // round up //__add_carry_out(out tmp, out carry, CT.w0, bid_reciprocals10_64[extra_digits]); { tmp = CT.w0 + bid_reciprocals10_64[extra_digits]; carry = (tmp < CT.w0) ? 1UL : 0; } if ((remainder_h >> (64 - amount)) + carry >= (((BID_UINT64)1) << amount)) status = BID_EXACT_STATUS; break; } __set_status_flags(ref pfpsf, status); #endif return fast_get_BID64_check_OF(sign_s, exponent_b + extra_digits, C64 #if !IEEE_ROUND_NEAREST , rnd_mode #endif #if BID_SET_STATUS_FLAGS , ref pfpsf #endif ); } } }