1 // SPDX-License-Identifier: GPL-2.0 2 /*---------------------------------------------------------------------------+ 3 | poly_2xm1.c | 4 | | 5 | Function to compute 2^x-1 by a polynomial approximation. | 6 | | 7 | Copyright (C) 1992,1993,1994,1997 | 8 | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia | 9 | E-mail billm@suburbia.net | 10 | | 11 | | 12 +---------------------------------------------------------------------------*/ 13 14 #include "exception.h" 15 #include "reg_constant.h" 16 #include "fpu_emu.h" 17 #include "fpu_system.h" 18 #include "control_w.h" 19 #include "poly.h" 20 21 #define HIPOWER 11 22 static const unsigned long long lterms[HIPOWER] = { 23 0x0000000000000000LL, /* This term done separately as 12 bytes */ 24 0xf5fdeffc162c7543LL, 25 0x1c6b08d704a0bfa6LL, 26 0x0276556df749cc21LL, 27 0x002bb0ffcf14f6b8LL, 28 0x0002861225ef751cLL, 29 0x00001ffcbfcd5422LL, 30 0x00000162c005d5f1LL, 31 0x0000000da96ccb1bLL, 32 0x0000000078d1b897LL, 33 0x000000000422b029LL 34 }; 35 36 static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194); 37 38 /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0, 39 These numbers are 2^(1/4), 2^(1/2), and 2^(3/4) 40 */ 41 static const Xsig shiftterm0 = MK_XSIG(0, 0, 0); 42 static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318); 43 static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3); 44 static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9); 45 46 static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1, 47 &shiftterm2, &shiftterm3 48 }; 49 50 /*--- poly_2xm1() -----------------------------------------------------------+ 51 | Requires st(0) which is TAG_Valid and < 1. | 52 +---------------------------------------------------------------------------*/ poly_2xm1(u_char sign,FPU_REG * arg,FPU_REG * result)53 int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result) 54 { 55 long int exponent, shift; 56 unsigned long long Xll; 57 Xsig accumulator, Denom, argSignif; 58 u_char tag; 59 60 exponent = exponent16(arg); 61 62 #ifdef PARANOID 63 if (exponent >= 0) { /* Don't want a |number| >= 1.0 */ 64 /* Number negative, too large, or not Valid. */ 65 EXCEPTION(EX_INTERNAL | 0x127); 66 return 1; 67 } 68 #endif /* PARANOID */ 69 70 argSignif.lsw = 0; 71 XSIG_LL(argSignif) = Xll = significand(arg); 72 73 if (exponent == -1) { 74 shift = (argSignif.msw & 0x40000000) ? 3 : 2; 75 /* subtract 0.5 or 0.75 */ 76 exponent -= 2; 77 XSIG_LL(argSignif) <<= 2; 78 Xll <<= 2; 79 } else if (exponent == -2) { 80 shift = 1; 81 /* subtract 0.25 */ 82 exponent--; 83 XSIG_LL(argSignif) <<= 1; 84 Xll <<= 1; 85 } else 86 shift = 0; 87 88 if (exponent < -2) { 89 /* Shift the argument right by the required places. */ 90 if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U) 91 Xll++; /* round up */ 92 } 93 94 accumulator.lsw = accumulator.midw = accumulator.msw = 0; 95 polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1); 96 mul_Xsig_Xsig(&accumulator, &argSignif); 97 shr_Xsig(&accumulator, 3); 98 99 mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */ 100 add_two_Xsig(&accumulator, &argSignif, &exponent); 101 102 if (shift) { 103 /* The argument is large, use the identity: 104 f(x+a) = f(a) * (f(x) + 1) - 1; 105 */ 106 shr_Xsig(&accumulator, -exponent); 107 accumulator.msw |= 0x80000000; /* add 1.0 */ 108 mul_Xsig_Xsig(&accumulator, shiftterm[shift]); 109 accumulator.msw &= 0x3fffffff; /* subtract 1.0 */ 110 exponent = 1; 111 } 112 113 if (sign != SIGN_POS) { 114 /* The argument is negative, use the identity: 115 f(-x) = -f(x) / (1 + f(x)) 116 */ 117 Denom.lsw = accumulator.lsw; 118 XSIG_LL(Denom) = XSIG_LL(accumulator); 119 if (exponent < 0) 120 shr_Xsig(&Denom, -exponent); 121 else if (exponent > 0) { 122 /* exponent must be 1 here */ 123 XSIG_LL(Denom) <<= 1; 124 if (Denom.lsw & 0x80000000) 125 XSIG_LL(Denom) |= 1; 126 (Denom.lsw) <<= 1; 127 } 128 Denom.msw |= 0x80000000; /* add 1.0 */ 129 div_Xsig(&accumulator, &Denom, &accumulator); 130 } 131 132 /* Convert to 64 bit signed-compatible */ 133 exponent += round_Xsig(&accumulator); 134 135 result = &st(0); 136 significand(result) = XSIG_LL(accumulator); 137 setexponent16(result, exponent); 138 139 tag = FPU_round(result, 1, 0, FULL_PRECISION, sign); 140 141 setsign(result, sign); 142 FPU_settag0(tag); 143 144 return 0; 145 146 } 147