diff options
Diffstat (limited to 'arch/x86/math-emu/poly_2xm1.c')
| -rw-r--r-- | arch/x86/math-emu/poly_2xm1.c | 146 |
1 files changed, 146 insertions, 0 deletions
diff --git a/arch/x86/math-emu/poly_2xm1.c b/arch/x86/math-emu/poly_2xm1.c new file mode 100644 index 0000000000..aa33006baf --- /dev/null +++ b/arch/x86/math-emu/poly_2xm1.c @@ -0,0 +1,146 @@ +// 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; + +} |