poly_2xm1.c
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上传日期:2013-02-24
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- /*---------------------------------------------------------------------------+
- | 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;
- }