/* Copyright (C) 2007-2019 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 . */ #include "bid_internal.h" /***************************************************************************** * BID64 nextup ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_nextup (UINT64 * pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else UINT64 bid64_nextup (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; UINT64 x_sign; UINT64 x_exp; BID_UI64DOUBLE tmp1; int x_nr_bits; int q1, ind; UINT64 C1; // C1 represents x_signif (UINT64) // check for NaNs and infinities if ((x & MASK_NAN) == MASK_NAN) { // check for NaN if ((x & 0x0003ffffffffffffull) > 999999999999999ull) x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits else x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return quiet (SNaN) res = x & 0xfdffffffffffffffull; } else { // QNaN res = x; } BID_RETURN (res); } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity if (!(x & 0x8000000000000000ull)) { // x is +inf res = 0x7800000000000000ull; } else { // x is -inf res = 0xf7fb86f26fc0ffffull; // -MAXFP = -999...99 * 10^emax } BID_RETURN (res); } // unpack the argument x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } // check for zeros (possibly from non-canonical values) if (C1 == 0x0ull) { // x is 0 res = 0x0000000000000001ull; // MINFP = 1 * 10^emin } else { // x is not special and is not zero if (x == 0x77fb86f26fc0ffffull) { // x = +MAXFP = 999...99 * 10^emax res = 0x7800000000000000ull; // +inf } else if (x == 0x8000000000000001ull) { // x = -MINFP = 1...99 * 10^emin res = 0x8000000000000000ull; // -0 } else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp // can add/subtract 1 ulp to the significand // Note: we could check here if x >= 10^16 to speed up the case q1 =16 // q1 = nr. of decimal digits in x (1 <= q1 <= 54) // determine first the nr. of bits in x if (C1 >= MASK_BINARY_OR2) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors if (C1 >= 0x0000000100000000ull) { // x >= 2^32 tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // x < 2^32 tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if x < 2^53 tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } q1 = nr_digits[x_nr_bits - 1].digits; if (q1 == 0) { q1 = nr_digits[x_nr_bits - 1].digits1; if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q1++; } // if q1 < P16 then pad the significand with zeros if (q1 < P16) { if (x_exp > (UINT64) (P16 - q1)) { ind = P16 - q1; // 1 <= ind <= P16 - 1 // pad with P16 - q1 zeros, until exponent = emin // C1 = C1 * 10^ind C1 = C1 * ten2k64[ind]; x_exp = x_exp - ind; } else { // pad with zeros until the exponent reaches emin ind = x_exp; C1 = C1 * ten2k64[ind]; x_exp = EXP_MIN; } } if (!x_sign) { // x > 0 // add 1 ulp (add 1 to the significand) C1++; if (C1 == 0x002386f26fc10000ull) { // if C1 = 10^16 C1 = 0x00038d7ea4c68000ull; // C1 = 10^15 x_exp++; } // Ok, because MAXFP = 999...99 * 10^emax was caught already } else { // x < 0 // subtract 1 ulp (subtract 1 from the significand) C1--; if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) { // if C1 = 10^15 - 1 C1 = 0x002386f26fc0ffffull; // C1 = 10^16 - 1 x_exp--; } } // assemble the result // if significand has 54 bits if (C1 & MASK_BINARY_OR2) { res = x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 & MASK_BINARY_SIG2); } else { // significand fits in 53 bits res = x_sign | (x_exp << 53) | C1; } } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp } // end x is not special and is not zero BID_RETURN (res); } /***************************************************************************** * BID64 nextdown ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_nextdown (UINT64 * pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else UINT64 bid64_nextdown (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; UINT64 x_sign; UINT64 x_exp; BID_UI64DOUBLE tmp1; int x_nr_bits; int q1, ind; UINT64 C1; // C1 represents x_signif (UINT64) // check for NaNs and infinities if ((x & MASK_NAN) == MASK_NAN) { // check for NaN if ((x & 0x0003ffffffffffffull) > 999999999999999ull) x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits else x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return quiet (SNaN) res = x & 0xfdffffffffffffffull; } else { // QNaN res = x; } BID_RETURN (res); } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity if (x & 0x8000000000000000ull) { // x is -inf res = 0xf800000000000000ull; } else { // x is +inf res = 0x77fb86f26fc0ffffull; // +MAXFP = +999...99 * 10^emax } BID_RETURN (res); } // unpack the argument x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } // check for zeros (possibly from non-canonical values) if (C1 == 0x0ull) { // x is 0 res = 0x8000000000000001ull; // -MINFP = -1 * 10^emin } else { // x is not special and is not zero if (x == 0xf7fb86f26fc0ffffull) { // x = -MAXFP = -999...99 * 10^emax res = 0xf800000000000000ull; // -inf } else if (x == 0x0000000000000001ull) { // x = +MINFP = 1...99 * 10^emin res = 0x0000000000000000ull; // -0 } else { // -MAXFP + 1ulp <= x <= -MINFP OR MINFP + 1 ulp <= x <= MAXFP // can add/subtract 1 ulp to the significand // Note: we could check here if x >= 10^16 to speed up the case q1 =16 // q1 = nr. of decimal digits in x (1 <= q1 <= 16) // determine first the nr. of bits in x if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid // rounding errors if (C1 >= 0x0000000100000000ull) { // x >= 2^32 tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // x < 2^32 tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if x < 2^53 tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } q1 = nr_digits[x_nr_bits - 1].digits; if (q1 == 0) { q1 = nr_digits[x_nr_bits - 1].digits1; if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q1++; } // if q1 < P16 then pad the significand with zeros if (q1 < P16) { if (x_exp > (UINT64) (P16 - q1)) { ind = P16 - q1; // 1 <= ind <= P16 - 1 // pad with P16 - q1 zeros, until exponent = emin // C1 = C1 * 10^ind C1 = C1 * ten2k64[ind]; x_exp = x_exp - ind; } else { // pad with zeros until the exponent reaches emin ind = x_exp; C1 = C1 * ten2k64[ind]; x_exp = EXP_MIN; } } if (x_sign) { // x < 0 // add 1 ulp (add 1 to the significand) C1++; if (C1 == 0x002386f26fc10000ull) { // if C1 = 10^16 C1 = 0x00038d7ea4c68000ull; // C1 = 10^15 x_exp++; // Ok, because -MAXFP = -999...99 * 10^emax was caught already } } else { // x > 0 // subtract 1 ulp (subtract 1 from the significand) C1--; if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) { // if C1 = 10^15 - 1 C1 = 0x002386f26fc0ffffull; // C1 = 10^16 - 1 x_exp--; } } // assemble the result // if significand has 54 bits if (C1 & MASK_BINARY_OR2) { res = x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 & MASK_BINARY_SIG2); } else { // significand fits in 53 bits res = x_sign | (x_exp << 53) | C1; } } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp } // end x is not special and is not zero BID_RETURN (res); } /***************************************************************************** * BID64 nextafter ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_nextafter (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else UINT64 bid64_nextafter (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; UINT64 tmp1, tmp2; FPSC tmp_fpsf = 0; // dummy fpsf for calls to comparison functions int res1, res2; // check for NaNs or infinities if (((x & MASK_SPECIAL) == MASK_SPECIAL) || ((y & MASK_SPECIAL) == MASK_SPECIAL)) { // x is NaN or infinity or y is NaN or infinity if ((x & MASK_NAN) == MASK_NAN) { // x is NAN if ((x & 0x0003ffffffffffffull) > 999999999999999ull) x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits else x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return quiet (x) res = x & 0xfdffffffffffffffull; } else { // x is QNaN if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN // set invalid flag *pfpsf |= INVALID_EXCEPTION; } // return x res = x; } BID_RETURN (res); } else if ((y & MASK_NAN) == MASK_NAN) { // y is NAN if ((y & 0x0003ffffffffffffull) > 999999999999999ull) y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits else y = y & 0xfe03ffffffffffffull; // clear G6-G12 if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return quiet (y) res = y & 0xfdffffffffffffffull; } else { // y is QNaN // return y res = y; } BID_RETURN (res); } else { // at least one is infinity if ((x & MASK_ANY_INF) == MASK_INF) { // x = inf x = x & (MASK_SIGN | MASK_INF); } if ((y & MASK_ANY_INF) == MASK_INF) { // y = inf y = y & (MASK_SIGN | MASK_INF); } } } // neither x nor y is NaN // if not infinity, check for non-canonical values x (treated as zero) if ((x & MASK_ANY_INF) != MASK_INF) { // x != inf // 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] if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); } } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) x is unch. ; // canonical } } // no need to check for non-canonical y // neither x nor y is NaN tmp_fpsf = *pfpsf; // save fpsf #if DECIMAL_CALL_BY_REFERENCE bid64_quiet_equal (&res1, px, py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64_quiet_greater (&res2, px, py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res1 = bid64_quiet_equal (x, y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res2 = bid64_quiet_greater (x, y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif *pfpsf = tmp_fpsf; // restore fpsf if (res1) { // x = y // return x with the sign of y res = (y & 0x8000000000000000ull) | (x & 0x7fffffffffffffffull); } else if (res2) { // x > y #if DECIMAL_CALL_BY_REFERENCE bid64_nextdown (&res, px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res = bid64_nextdown (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif } else { // x < y #if DECIMAL_CALL_BY_REFERENCE bid64_nextup (&res, px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res = bid64_nextup (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif } // if the operand x is finite but the result is infinite, signal // overflow and inexact if (((x & MASK_INF) != MASK_INF) && ((res & MASK_INF) == MASK_INF)) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // set the overflow flag *pfpsf |= OVERFLOW_EXCEPTION; } // if the result is in (-10^emin, 10^emin), and is different from the // operand x, signal underflow and inexact tmp1 = 0x00038d7ea4c68000ull; // +100...0[16] * 10^emin tmp2 = res & 0x7fffffffffffffffull; tmp_fpsf = *pfpsf; // save fpsf #if DECIMAL_CALL_BY_REFERENCE bid64_quiet_greater (&res1, &tmp1, &tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); bid64_quiet_not_equal (&res2, &x, &res _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #else res1 = bid64_quiet_greater (tmp1, tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); res2 = bid64_quiet_not_equal (x, res _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG); #endif *pfpsf = tmp_fpsf; // restore fpsf if (res1 && res2) { // if (bid64_quiet_greater (tmp1, tmp2, &tmp_fpsf) && // bid64_quiet_not_equal (x, res, &tmp_fpsf)) { // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; // set the underflow flag *pfpsf |= UNDERFLOW_EXCEPTION; } BID_RETURN (res); }