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 // SPDX-License-Identifier: GPL-2.0 /*---------------------------------------------------------------------------+ | poly_2xm1.c | | | | Function to compute 2^x-1 by a polynomial approximation. | | | | Copyright (C) 1992,1993,1994,1997 | | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia | | E-mail billm@suburbia.net | | | | | +---------------------------------------------------------------------------*/ #include "exception.h" #include "reg_constant.h" #include "fpu_emu.h" #include "fpu_system.h" #include "control_w.h" #include "poly.h" #define HIPOWER 11 static const unsigned long long lterms[HIPOWER] = { 0x0000000000000000LL, /* This term done separately as 12 bytes */ 0xf5fdeffc162c7543LL, 0x1c6b08d704a0bfa6LL, 0x0276556df749cc21LL, 0x002bb0ffcf14f6b8LL, 0x0002861225ef751cLL, 0x00001ffcbfcd5422LL, 0x00000162c005d5f1LL, 0x0000000da96ccb1bLL, 0x0000000078d1b897LL, 0x000000000422b029LL }; static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194); /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0, These numbers are 2^(1/4), 2^(1/2), and 2^(3/4) */ static const Xsig shiftterm0 = MK_XSIG(0, 0, 0); static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318); static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3); static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9); static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1, &shiftterm2, &shiftterm3 }; /*--- poly_2xm1() -----------------------------------------------------------+ | Requires st(0) which is TAG_Valid and < 1. | +---------------------------------------------------------------------------*/ int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result) { long int exponent, shift; unsigned long long Xll; Xsig accumulator, Denom, argSignif; u_char tag; exponent = exponent16(arg); #ifdef PARANOID if (exponent >= 0) { /* Don't want a |number| >= 1.0 */ /* Number negative, too large, or not Valid. */ EXCEPTION(EX_INTERNAL | 0x127); return 1; } #endif /* PARANOID */ argSignif.lsw = 0; XSIG_LL(argSignif) = Xll = significand(arg); if (exponent == -1) { shift = (argSignif.msw & 0x40000000) ? 3 : 2; /* subtract 0.5 or 0.75 */ exponent -= 2; XSIG_LL(argSignif) <<= 2; Xll <<= 2; } else if (exponent == -2) { shift = 1; /* subtract 0.25 */ exponent--; XSIG_LL(argSignif) <<= 1; Xll <<= 1; } else shift = 0; if (exponent < -2) { /* Shift the argument right by the required places. */ if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U) Xll++; /* round up */ } accumulator.lsw = accumulator.midw = accumulator.msw = 0; polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1); mul_Xsig_Xsig(&accumulator, &argSignif); shr_Xsig(&accumulator, 3); mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */ add_two_Xsig(&accumulator, &argSignif, &exponent); if (shift) { /* The argument is large, use the identity: f(x+a) = f(a) * (f(x) + 1) - 1; */ shr_Xsig(&accumulator, -exponent); accumulator.msw |= 0x80000000; /* add 1.0 */ mul_Xsig_Xsig(&accumulator, shiftterm[shift]); accumulator.msw &= 0x3fffffff; /* subtract 1.0 */ exponent = 1; } if (sign != SIGN_POS) { /* The argument is negative, use the identity: f(-x) = -f(x) / (1 + f(x)) */ Denom.lsw = accumulator.lsw; XSIG_LL(Denom) = XSIG_LL(accumulator); if (exponent < 0) shr_Xsig(&Denom, -exponent); else if (exponent > 0) { /* exponent must be 1 here */ XSIG_LL(Denom) <<= 1; if (Denom.lsw & 0x80000000) XSIG_LL(Denom) |= 1; (Denom.lsw) <<= 1; } Denom.msw |= 0x80000000; /* add 1.0 */ div_Xsig(&accumulator, &Denom, &accumulator); } /* Convert to 64 bit signed-compatible */ exponent += round_Xsig(&accumulator); result = &st(0); significand(result) = XSIG_LL(accumulator); setexponent16(result, exponent); tag = FPU_round(result, 1, 0, FULL_PRECISION, sign); setsign(result, sign); FPU_settag0(tag); return 0; }