1 // SPDX-License-Identifier: GPL-2.0-only 2 /* IEEE754 floating point arithmetic 3 * double precision square root 4 */ 5 /* 6 * MIPS floating point support 7 * Copyright (C) 1994-2000 Algorithmics Ltd. 8 */ 9 10 #include "ieee754dp.h" 11 12 static const unsigned int table[] = { 13 0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, 14 29598, 36145, 43202, 50740, 58733, 67158, 75992, 15 85215, 83599, 71378, 60428, 50647, 41945, 34246, 16 27478, 21581, 16499, 12183, 8588, 5674, 3403, 17 1742, 661, 130 18 }; 19 20 union ieee754dp ieee754dp_sqrt(union ieee754dp x) 21 { 22 struct _ieee754_csr oldcsr; 23 union ieee754dp y, z, t; 24 unsigned int scalx, yh; 25 COMPXDP; 26 27 EXPLODEXDP; 28 ieee754_clearcx(); 29 FLUSHXDP; 30 31 /* x == INF or NAN? */ 32 switch (xc) { 33 case IEEE754_CLASS_SNAN: 34 return ieee754dp_nanxcpt(x); 35 36 case IEEE754_CLASS_QNAN: 37 /* sqrt(Nan) = Nan */ 38 return x; 39 40 case IEEE754_CLASS_ZERO: 41 /* sqrt(0) = 0 */ 42 return x; 43 44 case IEEE754_CLASS_INF: 45 if (xs) { 46 /* sqrt(-Inf) = Nan */ 47 ieee754_setcx(IEEE754_INVALID_OPERATION); 48 return ieee754dp_indef(); 49 } 50 /* sqrt(+Inf) = Inf */ 51 return x; 52 53 case IEEE754_CLASS_DNORM: 54 DPDNORMX; 55 /* fall through */ 56 57 case IEEE754_CLASS_NORM: 58 if (xs) { 59 /* sqrt(-x) = Nan */ 60 ieee754_setcx(IEEE754_INVALID_OPERATION); 61 return ieee754dp_indef(); 62 } 63 break; 64 } 65 66 /* save old csr; switch off INX enable & flag; set RN rounding */ 67 oldcsr = ieee754_csr; 68 ieee754_csr.mx &= ~IEEE754_INEXACT; 69 ieee754_csr.sx &= ~IEEE754_INEXACT; 70 ieee754_csr.rm = FPU_CSR_RN; 71 72 /* adjust exponent to prevent overflow */ 73 scalx = 0; 74 if (xe > 512) { /* x > 2**-512? */ 75 xe -= 512; /* x = x / 2**512 */ 76 scalx += 256; 77 } else if (xe < -512) { /* x < 2**-512? */ 78 xe += 512; /* x = x * 2**512 */ 79 scalx -= 256; 80 } 81 82 x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT); 83 y = x; 84 85 /* magic initial approximation to almost 8 sig. bits */ 86 yh = y.bits >> 32; 87 yh = (yh >> 1) + 0x1ff80000; 88 yh = yh - table[(yh >> 15) & 31]; 89 y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff); 90 91 /* Heron's rule once with correction to improve to ~18 sig. bits */ 92 /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */ 93 t = ieee754dp_div(x, y); 94 y = ieee754dp_add(y, t); 95 y.bits -= 0x0010000600000000LL; 96 y.bits &= 0xffffffff00000000LL; 97 98 /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */ 99 /* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */ 100 t = ieee754dp_mul(y, y); 101 z = t; 102 t.bexp += 0x001; 103 t = ieee754dp_add(t, z); 104 z = ieee754dp_mul(ieee754dp_sub(x, z), y); 105 106 /* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */ 107 t = ieee754dp_div(z, ieee754dp_add(t, x)); 108 t.bexp += 0x001; 109 y = ieee754dp_add(y, t); 110 111 /* twiddle last bit to force y correctly rounded */ 112 113 /* set RZ, clear INEX flag */ 114 ieee754_csr.rm = FPU_CSR_RZ; 115 ieee754_csr.sx &= ~IEEE754_INEXACT; 116 117 /* t=x/y; ...chopped quotient, possibly inexact */ 118 t = ieee754dp_div(x, y); 119 120 if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) { 121 122 if (!(ieee754_csr.sx & IEEE754_INEXACT)) 123 /* t = t-ulp */ 124 t.bits -= 1; 125 126 /* add inexact to result status */ 127 oldcsr.cx |= IEEE754_INEXACT; 128 oldcsr.sx |= IEEE754_INEXACT; 129 130 switch (oldcsr.rm) { 131 case FPU_CSR_RU: 132 y.bits += 1; 133 /* fall through */ 134 case FPU_CSR_RN: 135 t.bits += 1; 136 break; 137 } 138 139 /* y=y+t; ...chopped sum */ 140 y = ieee754dp_add(y, t); 141 142 /* adjust scalx for correctly rounded sqrt(x) */ 143 scalx -= 1; 144 } 145 146 /* py[n0]=py[n0]+scalx; ...scale back y */ 147 y.bexp += scalx; 148 149 /* restore rounding mode, possibly set inexact */ 150 ieee754_csr = oldcsr; 151 152 return y; 153 } 154