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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ /***************************************************************************** * BID64 divide ***************************************************************************** * * Algorithm description: * * if(coefficient_x<coefficient_y) * p = number_digits(coefficient_y) - number_digits(coefficient_x) * A = coefficient_x*10^p * B = coefficient_y * CA= A*10^(15+j), j=0 for A>=B, 1 otherwise * Q = 0 * else * get Q=(int)(coefficient_x/coefficient_y) * (based on double precision divide) * check for exact divide case * Let R = coefficient_x - Q*coefficient_y * Let m=16-number_digits(Q) * CA=R*10^m, Q=Q*10^m * B = coefficient_y * endif * if (CA<2^64) * Q += CA/B (64-bit unsigned divide) * else * get final Q using double precision divide, followed by 3 integer * iterations * if exact result, eliminate trailing zeros * check for underflow * round coefficient to nearest * ****************************************************************************/ #include "bid_internal.h" #include "bid_div_macros.h" #ifdef UNCHANGED_BINARY_STATUS_FLAGS #include <fenv.h> #define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT #endif extern UINT32 convert_table[5][128][2]; extern SINT8 factors[][2]; extern UINT8 packed_10000_zeros[]; #if DECIMAL_CALL_BY_REFERENCE void bid64_div (UINT64 * pres, UINT64 * px, UINT64 * py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x, y; #else UINT64 bid64_div (UINT64 x, UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 CA, CT; UINT64 sign_x, sign_y, coefficient_x, coefficient_y, A, B, QX, PD; UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res; UINT64 valid_x, valid_y; SINT64 D; int_double t_scale, tempq, temp_b; int_float tempx, tempy; double da, db, dq, da_h, da_l; int exponent_x, exponent_y, bin_expon_cx; int diff_expon, ed1, ed2, bin_index; int rmode, amount; int nzeros, i, j, k, d5; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif #if DECIMAL_CALL_BY_REFERENCE #if !DECIMAL_GLOBAL_ROUNDING _IDEC_round rnd_mode = *prnd_mode; #endif x = *px; y = *py; #endif valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); // unpack arguments, check for NaN or Infinity if (!valid_x) { // x is Inf. or NaN #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // test if x is NaN if ((x & NAN_MASK64) == NAN_MASK64) { #ifdef SET_STATUS_FLAGS if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (coefficient_x & QUIET_MASK64); } // x is Infinity? if ((x & INFINITY_MASK64) == INFINITY_MASK64) { // check if y is Inf or NaN if ((y & INFINITY_MASK64) == INFINITY_MASK64) { // y==Inf, return NaN if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (NAN_MASK64); } } else { // otherwise return +/-Inf BID_RETURN (((x ^ y) & 0x8000000000000000ull) | INFINITY_MASK64); } } // x==0 if (((y & INFINITY_MASK64) != INFINITY_MASK64) && !(coefficient_y)) { // y==0 , return NaN #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (NAN_MASK64); } if (((y & INFINITY_MASK64) != INFINITY_MASK64)) { if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) exponent_y = ((UINT32) (y >> 51)) & 0x3ff; else exponent_y = ((UINT32) (y >> 53)) & 0x3ff; sign_y = y & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53)); } } if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y & NAN_MASK64) == NAN_MASK64) { #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (coefficient_y & QUIET_MASK64); } // y is Infinity? if ((y & INFINITY_MASK64) == INFINITY_MASK64) { // return +/-0 BID_RETURN (((x ^ y) & 0x8000000000000000ull)); } // y is 0 #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (coefficient_x < coefficient_y) { // get number of decimal digits for c_x, c_y //--- get number of bits in the coefficients of x and y --- tempx.d = (float) coefficient_x; tempy.d = (float) coefficient_y; bin_index = (tempy.i - tempx.i) >> 23; A = coefficient_x * power10_index_binexp[bin_index]; B = coefficient_y; temp_b.d = (double) B; // compare A, B DU = (A - B) >> 63; ed1 = 15 + (int) DU; ed2 = estimate_decimal_digits[bin_index] + ed1; T = power10_table_128[ed1].w[0]; __mul_64x64_to_128 (CA, A, T); Q = 0; diff_expon = diff_expon - ed2; // adjust double precision db, to ensure that later A/B - (int)(da/db) > -1 if (coefficient_y < 0x0020000000000000ull) { temp_b.i += 1; db = temp_b.d; } else db = (double) (B + 2 + (B & 1)); } else { // get c_x/c_y // set last bit before conversion to DP A2 = coefficient_x | 1; da = (double) A2; db = (double) coefficient_y; tempq.d = da / db; Q = (UINT64) tempq.d; R = coefficient_x - coefficient_y * Q; // will use to get number of dec. digits of Q bin_expon_cx = (tempq.i >> 52) - 0x3ff; // R<0 ? D = ((SINT64) R) >> 63; Q += D; R += (coefficient_y & D); // exact result ? if (((SINT64) R) <= 0) { // can have R==-1 for coeff_y==1 res = get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } // get decimal digits of Q DU = power10_index_binexp[bin_expon_cx] - Q - 1; DU >>= 63; ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU; T = power10_table_128[ed2].w[0]; __mul_64x64_to_128 (CA, R, T); B = coefficient_y; Q *= power10_table_128[ed2].w[0]; diff_expon -= ed2; } if (!CA.w[1]) { Q2 = CA.w[0] / B; B2 = B + B; B4 = B2 + B2; R = CA.w[0] - Q2 * B; Q += Q2; } else { // 2^64 t_scale.i = 0x43f0000000000000ull; // convert CA to DP da_h = CA.w[1]; da_l = CA.w[0]; da = da_h * t_scale.d + da_l; // quotient dq = da / db; Q2 = (UINT64) dq; // get w[0] remainder R = CA.w[0] - Q2 * B; // R<0 ? D = ((SINT64) R) >> 63; Q2 += D; R += (B & D); // now R<6*B // quick divide // 4*B B2 = B + B; B4 = B2 + B2; R = R - B4; // R<0 ? D = ((SINT64) R) >> 63; // restore R if negative R += (B4 & D); Q2 += ((~D) & 4); R = R - B2; // R<0 ? D = ((SINT64) R) >> 63; // restore R if negative R += (B2 & D); Q2 += ((~D) & 2); R = R - B; // R<0 ? D = ((SINT64) R) >> 63; // restore R if negative R += (B & D); Q2 += ((~D) & 1); Q += Q2; } #ifdef SET_STATUS_FLAGS if (R) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!R) #endif #endif #ifndef LEAVE_TRAILING_ZEROS { // eliminate trailing zeros // check whether CX, CY are short if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) { i = (int) coefficient_y - 1; j = (int) coefficient_x - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; __mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[nzeros]; Q = CT.w[1] >> amount; diff_expon += nzeros; } else { tdigit[0] = Q & 0x3ffffff; tdigit[1] = 0; QX = Q >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { __mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 amount = short_recip_scale[nzeros]; Q = CT.w[1] >> amount; } diff_expon += nzeros; } if (diff_expon >= 0) { res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if (diff_expon >= 0) { #ifdef IEEE_ROUND_NEAREST // round to nearest code // R*10 R += R; R = (R << 2) + R; B5 = B4 + B; // compare 10*R to 5*B R = B5 - R; // correction for (R==0 && (Q&1)) R -= (Q & 1); // R<0 ? D = ((UINT64) R) >> 63; Q += D; #else #ifdef IEEE_ROUND_NEAREST_TIES_AWAY // round to nearest code // R*10 R += R; R = (R << 2) + R; B5 = B4 + B; // compare 10*R to 5*B R = B5 - R; // correction for (R==0 && (Q&1)) R -= (Q & 1); // R<0 ? D = ((UINT64) R) >> 63; Q += D; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case 0: // round to nearest code case ROUNDING_TIES_AWAY: // R*10 R += R; R = (R << 2) + R; B5 = B4 + B; // compare 10*R to 5*B R = B5 - R; // correction for (R==0 && (Q&1)) R -= ((Q | (rmode >> 2)) & 1); // R<0 ? D = ((UINT64) R) >> 63; Q += D; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up Q++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y) UINT256 CA4 = { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; int_float fx, fy, f64; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, digits_q, amount; int nzeros, i, j, k, d5, done = 0; unsigned rmode; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); // unpack arguments, check for NaN or Infinity CX.w[1] = 0; if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) { #ifdef SET_STATUS_FLAGS if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN ((x & SNAN_MASK64) == SNAN_MASK64)) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // test if x is NaN if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) { res = CX.w[0]; BID_RETURN (res & QUIET_MASK64); } // x is Infinity? if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) { // check if y is Inf. if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res = (((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; BID_RETURN (res); } } // x is 0 if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) { if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } // return 0 res = ((x) ^ y.w[1]) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; res |= (((UINT64) exponent_x) << 53); BID_RETURN (res); } } exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS); if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CY.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // y is Infinity? if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res = sign_x ^ sign_y; BID_RETURN (res); } // y is 0, return +/-Inf res = (((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN (res); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (__unsigned_compare_gt_128 (CY, CX)) { // CX < CY // 2^64 f64.i = 0x5f800000; // fx ~ CX, fy ~ CY fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; // expon_cy - expon_cx bin_index = (fy.i - fx.i) >> 23; if (CX.w[1]) { T = power10_index_binexp_128[bin_index].w[0]; __mul_64x128_short (CA, T, CX); } else { T128 = power10_index_binexp_128[bin_index]; __mul_64x128_short (CA, CX.w[0], T128); } ed2 = 15; if (__unsigned_compare_gt_128 (CY, CA)) ed2++; T128 = power10_table_128[ed2]; __mul_128x128_to_256 (CA4, CA, T128); ed2 += estimate_decimal_digits[bin_index]; CQ.w[0] = CQ.w[1] = 0; diff_expon = diff_expon - ed2; } else { // get CQ = CX/CY __div_128_by_128 (&CQ, &CR, CX, CY); // get number of decimal digits in CQ // 2^64 f64.i = 0x5f800000; fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; // binary expon. of CQ bin_expon = (fx.i - 0x3f800000) >> 23; digits_q = estimate_decimal_digits[bin_expon]; TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; if (__unsigned_compare_ge_128 (CQ, TP128)) digits_q++; if (digits_q <= 16) { if (!CR.w[1] && !CR.w[0]) { res = get_BID64 (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } ed2 = 16 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; __mul_64x128_to_192 (CA4, (T128.w[0]), CR); diff_expon = diff_expon - ed2; CQ.w[0] *= T128.w[0]; } else { ed2 = digits_q - 16; diff_expon += ed2; T128 = reciprocals10_128[ed2]; __mul_128x128_to_256 (P256, CQ, T128); amount = recip_scale[ed2]; CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); CQ.w[1] = 0; __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; CA4.w[1] = CX.w[1] - QB256.w[1]; CA4.w[0] = CX.w[0] - QB256.w[0]; if (CX.w[0] < QB256.w[0]) CA4.w[1]--; if (CR.w[0] || CR.w[1]) CA4.w[0] |= 1; done = 1; } } if (!done) { __div_256_by_128 (&CQ, &CA4, CY); } #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!CA4.w[0] && !CA4.w[1]) #endif #endif #ifndef LEAVE_TRAILING_ZEROS // check whether result is exact { // check whether CX, CY are short if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { i = (int) CY.w[0] - 1; j = (int) CX.w[0] - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128_long (CQ, Qh, amount); diff_expon += nzeros; } else { // decompose Q as Qh*10^17 + Ql Q_low = CQ.w[0]; { tdigit[0] = Q_low & 0x3ffffff; tdigit[1] = 0; QX = Q_low >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } if (tdigit[1] >= 100000000) { tdigit[1] -= 100000000; if (tdigit[1] >= 100000000) tdigit[1] -= 100000000; } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128 (CQ, Qh, amount); } diff_expon += nzeros; } } if(diff_expon>=0){ res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if (diff_expon >= 0) { #ifdef IEEE_ROUND_NEAREST // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; #else #ifdef IEEE_ROUND_NEAREST_TIES_AWAY // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case ROUNDING_TO_NEAREST: // round to nearest code // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_TIES_AWAY: // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up CQ.w[0]++; if (!CQ.w[0]) CQ.w[1]++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } //#define LEAVE_TRAILING_ZEROS TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y) UINT256 CA4 = { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y; int_float fx, fy, f64; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, digits_q, amount; int nzeros, i, j, k, d5, done = 0; unsigned rmode; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y)); // unpack arguments, check for NaN or Infinity if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { // test if x is NaN if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN (y & 0x7e00000000000000ull) == 0x7e00000000000000ull) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CX.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // x is Infinity? if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // check if y is Inf. if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res = ((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; BID_RETURN (res); } } // x is 0 if (((y & INFINITY_MASK64) != INFINITY_MASK64) && !(CY.w[0])) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } // return 0 if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) { if (!CY.w[0]) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } exponent_x = exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + (DECIMAL_EXPONENT_BIAS << 1); if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53); BID_RETURN (res); } } CY.w[1] = 0; if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y & NAN_MASK64) == NAN_MASK64) { #ifdef SET_STATUS_FLAGS if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif BID_RETURN (CY.w[0] & QUIET_MASK64); } // y is Infinity? if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res = sign_x ^ sign_y; BID_RETURN (res); } // y is 0, return +/-Inf res = ((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN (res); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + (DECIMAL_EXPONENT_BIAS << 1); if (__unsigned_compare_gt_128 (CY, CX)) { // CX < CY // 2^64 f64.i = 0x5f800000; // fx ~ CX, fy ~ CY fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; // expon_cy - expon_cx bin_index = (fy.i - fx.i) >> 23; if (CX.w[1]) { T = power10_index_binexp_128[bin_index].w[0]; __mul_64x128_short (CA, T, CX); } else { T128 = power10_index_binexp_128[bin_index]; __mul_64x128_short (CA, CX.w[0], T128); } ed2 = 15; if (__unsigned_compare_gt_128 (CY, CA)) ed2++; T128 = power10_table_128[ed2]; __mul_128x128_to_256 (CA4, CA, T128); ed2 += estimate_decimal_digits[bin_index]; CQ.w[0] = CQ.w[1] = 0; diff_expon = diff_expon - ed2; } else { // get CQ = CX/CY __div_128_by_128 (&CQ, &CR, CX, CY); // get number of decimal digits in CQ // 2^64 f64.i = 0x5f800000; fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; // binary expon. of CQ bin_expon = (fx.i - 0x3f800000) >> 23; digits_q = estimate_decimal_digits[bin_expon]; TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; if (__unsigned_compare_ge_128 (CQ, TP128)) digits_q++; if (digits_q <= 16) { if (!CR.w[1] && !CR.w[0]) { res = get_BID64 (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } ed2 = 16 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; __mul_64x128_to_192 (CA4, (T128.w[0]), CR); diff_expon = diff_expon - ed2; CQ.w[0] *= T128.w[0]; } else { ed2 = digits_q - 16; diff_expon += ed2; T128 = reciprocals10_128[ed2]; __mul_128x128_to_256 (P256, CQ, T128); amount = recip_scale[ed2]; CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); CQ.w[1] = 0; __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; CA4.w[1] = CX.w[1] - QB256.w[1]; CA4.w[0] = CX.w[0] - QB256.w[0]; if (CX.w[0] < QB256.w[0]) CA4.w[1]--; if (CR.w[0] || CR.w[1]) CA4.w[0] |= 1; done = 1; if(CA4.w[1]|CA4.w[0]) { __mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); } } } if (!done) { __div_256_by_128 (&CQ, &CA4, CY); } #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!CA4.w[0] && !CA4.w[1]) #endif #endif #ifndef LEAVE_TRAILING_ZEROS // check whether result is exact { if(!done) { // check whether CX, CY are short if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { i = (int) CY.w[0] - 1; j = (int) CX.w[0] - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128_long (CQ, Qh, amount); diff_expon += nzeros; } else { // decompose Q as Qh*10^17 + Ql //T128 = reciprocals10_128[17]; Q_low = CQ.w[0]; { tdigit[0] = Q_low & 0x3ffffff; tdigit[1] = 0; QX = Q_low >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } if (tdigit[1] >= 100000000) { tdigit[1] -= 100000000; if (tdigit[1] >= 100000000) tdigit[1] -= 100000000; } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128 (CQ, Qh, amount); } diff_expon += nzeros; } } } if(diff_expon>=0){ res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if (diff_expon >= 0) { #ifdef IEEE_ROUND_NEAREST // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; //if(CQ.w[0]<carry64) //CQ.w[1] ++; #else #ifdef IEEE_ROUND_NEAREST_TIES_AWAY // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case ROUNDING_TO_NEAREST: // round to nearest code // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_TIES_AWAY: // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up CQ.w[0]++; if (!CQ.w[0]) CQ.w[1]++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } //#define LEAVE_TRAILING_ZEROS extern UINT32 convert_table[5][128][2]; extern SINT8 factors[][2]; extern UINT8 packed_10000_zeros[]; //UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf) TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y) UINT256 CA4 = { {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Ql, Tmp; UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; int_float fx, fy, f64; UINT32 QX32, tdigit[3], digit, digit_h, digit_low; int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, digits_q, amount; int nzeros, i, j, k, d5, done = 0; unsigned rmode; #ifdef UNCHANGED_BINARY_STATUS_FLAGS fexcept_t binaryflags = 0; #endif valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); // unpack arguments, check for NaN or Infinity if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { // test if x is NaN if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN (y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CX.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // x is Infinity? if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // check if y is Inf. if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) // return NaN { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif res = 0x7c00000000000000ull; BID_RETURN (res); } if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { // otherwise return +/-Inf res = ((x.w[1] ^ y. w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; BID_RETURN (res); } } // x is 0 if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) { if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif // x=y=0, return NaN res = 0x7c00000000000000ull; BID_RETURN (res); } // return 0 res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull; exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (exponent_x > DECIMAL_MAX_EXPON_64) exponent_x = DECIMAL_MAX_EXPON_64; else if (exponent_x < 0) exponent_x = 0; res |= (((UINT64) exponent_x) << 53); BID_RETURN (res); } } if (!valid_y) { // y is Inf. or NaN // test if y is NaN if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { #ifdef SET_STATUS_FLAGS if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN __set_status_flags (pfpsf, INVALID_EXCEPTION); #endif Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); Tmp.w[0] = CY.w[0]; TP128 = reciprocals10_128[18]; __mul_128x128_full (Qh, Ql, Tmp, TP128); amount = recip_scale[18]; __shr_128 (Tmp, Qh, amount); res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; BID_RETURN (res); } // y is Infinity? if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { // return +/-0 res = sign_x ^ sign_y; BID_RETURN (res); } // y is 0, return +/-Inf res = ((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; #ifdef SET_STATUS_FLAGS __set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); #endif BID_RETURN (res); } #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; if (__unsigned_compare_gt_128 (CY, CX)) { // CX < CY // 2^64 f64.i = 0x5f800000; // fx ~ CX, fy ~ CY fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; // expon_cy - expon_cx bin_index = (fy.i - fx.i) >> 23; if (CX.w[1]) { T = power10_index_binexp_128[bin_index].w[0]; __mul_64x128_short (CA, T, CX); } else { T128 = power10_index_binexp_128[bin_index]; __mul_64x128_short (CA, CX.w[0], T128); } ed2 = 15; if (__unsigned_compare_gt_128 (CY, CA)) ed2++; T128 = power10_table_128[ed2]; __mul_128x128_to_256 (CA4, CA, T128); ed2 += estimate_decimal_digits[bin_index]; CQ.w[0] = CQ.w[1] = 0; diff_expon = diff_expon - ed2; } else { // get CQ = CX/CY __div_128_by_128 (&CQ, &CR, CX, CY); // get number of decimal digits in CQ // 2^64 f64.i = 0x5f800000; fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; // binary expon. of CQ bin_expon = (fx.i - 0x3f800000) >> 23; digits_q = estimate_decimal_digits[bin_expon]; TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; if (__unsigned_compare_ge_128 (CQ, TP128)) digits_q++; if (digits_q <= 16) { if (!CR.w[1] && !CR.w[0]) { res = get_BID64 (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } ed2 = 16 - digits_q; T128.w[0] = power10_table_128[ed2].w[0]; __mul_64x128_to_192 (CA4, (T128.w[0]), CR); diff_expon = diff_expon - ed2; CQ.w[0] *= T128.w[0]; } else { ed2 = digits_q - 16; diff_expon += ed2; T128 = reciprocals10_128[ed2]; __mul_128x128_to_256 (P256, CQ, T128); amount = recip_scale[ed2]; CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); CQ.w[1] = 0; __mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); __mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; CA4.w[1] = CX.w[1] - QB256.w[1]; CA4.w[0] = CX.w[0] - QB256.w[0]; if (CX.w[0] < QB256.w[0]) CA4.w[1]--; if (CR.w[0] || CR.w[1]) CA4.w[0] |= 1; done = 1; if(CA4.w[1]|CA4.w[0]) { __mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); } } } if (!done) { __div_256_by_128 (&CQ, &CA4, CY); } #ifdef SET_STATUS_FLAGS if (CA4.w[0] || CA4.w[1]) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #ifndef LEAVE_TRAILING_ZEROS else #endif #else #ifndef LEAVE_TRAILING_ZEROS if (!CA4.w[0] && !CA4.w[1]) #endif #endif #ifndef LEAVE_TRAILING_ZEROS // check whether result is exact { if(!done) { // check whether CX, CY are short if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { i = (int) CY.w[0] - 1; j = (int) CX.w[0] - 1; // difference in powers of 2 factors for Y and X nzeros = ed2 - factors[i][0] + factors[j][0]; // difference in powers of 5 factors d5 = ed2 - factors[i][1] + factors[j][1]; if (d5 < nzeros) nzeros = d5; // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); //__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128_long (CQ, Qh, amount); diff_expon += nzeros; } else { // decompose Q as Qh*10^17 + Ql //T128 = reciprocals10_128[17]; Q_low = CQ.w[0]; { tdigit[0] = Q_low & 0x3ffffff; tdigit[1] = 0; QX = Q_low >> 26; QX32 = QX; nzeros = 0; for (j = 0; QX32; j++, QX32 >>= 7) { k = (QX32 & 127); tdigit[0] += convert_table[j][k][0]; tdigit[1] += convert_table[j][k][1]; if (tdigit[0] >= 100000000) { tdigit[0] -= 100000000; tdigit[1]++; } } if (tdigit[1] >= 100000000) { tdigit[1] -= 100000000; if (tdigit[1] >= 100000000) tdigit[1] -= 100000000; } digit = tdigit[0]; if (!digit && !tdigit[1]) nzeros += 16; else { if (!digit) { nzeros += 8; digit = tdigit[1]; } // decompose digit PD = (UINT64) digit *0x068DB8BBull; digit_h = (UINT32) (PD >> 40); digit_low = digit - digit_h * 10000; if (!digit_low) nzeros += 4; else digit_h = digit_low; if (!(digit_h & 1)) nzeros += 3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> (digit_h & 7)); } if (nzeros) { // get P*(2^M[extra_digits])/10^extra_digits __mul_128x128_full (Qh, Ql, CQ, reciprocals10_128[nzeros]); // now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 amount = recip_scale[nzeros]; __shr_128 (CQ, Qh, amount); } diff_expon += nzeros; } } } if(diff_expon>=0){ res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } } #endif if(diff_expon>=0) { #ifdef IEEE_ROUND_NEAREST // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; //if(CQ.w[0]<carry64) //CQ.w[1] ++; #else #ifdef IEEE_ROUND_NEAREST_TIES_AWAY // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; #else rmode = rnd_mode; if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) rmode = 3 - rmode; switch (rmode) { case ROUNDING_TO_NEAREST: // round to nearest code // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_TIES_AWAY: // rounding // 2*CA4 - CY CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); CA4r.w[0] = CA4.w[0] + CA4.w[0]; __sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; CQ.w[0] += carry64; if (CQ.w[0] < carry64) CQ.w[1]++; break; case ROUNDING_DOWN: case ROUNDING_TO_ZERO: break; default: // rounding up CQ.w[0]++; if (!CQ.w[0]) CQ.w[1]++; break; } #endif #endif res = fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } else { // UF occurs #ifdef SET_STATUS_FLAGS if ((diff_expon + 16 < 0)) { // set status flags __set_status_flags (pfpsf, INEXACT_EXCEPTION); } #endif rmode = rnd_mode; res = get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); #ifdef UNCHANGED_BINARY_STATUS_FLAGS (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); #endif BID_RETURN (res); } }
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