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 fallthrough; 56 case IEEE754_CLASS_NORM: 57 if (xs) { 58 /* sqrt(-x) = Nan */ 59 ieee754_setcx(IEEE754_INVALID_OPERATION); 60 return ieee754dp_indef(); 61 } 62 break; 63 } 64 65 /* save old csr; switch off INX enable & flag; set RN rounding */ 66 oldcsr = ieee754_csr; 67 ieee754_csr.mx &= ~IEEE754_INEXACT; 68 ieee754_csr.sx &= ~IEEE754_INEXACT; 69 ieee754_csr.rm = FPU_CSR_RN; 70 71 /* adjust exponent to prevent overflow */ 72 scalx = 0; 73 if (xe > 512) { /* x > 2**-512? */ 74 xe -= 512; /* x = x / 2**512 */ 75 scalx += 256; 76 } else if (xe < -512) { /* x < 2**-512? */ 77 xe += 512; /* x = x * 2**512 */ 78 scalx -= 256; 79 } 80 81 x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT); 82 y = x; 83 84 /* magic initial approximation to almost 8 sig. bits */ 85 yh = y.bits >> 32; 86 yh = (yh >> 1) + 0x1ff80000; 87 yh = yh - table[(yh >> 15) & 31]; 88 y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff); 89 90 /* Heron's rule once with correction to improve to ~18 sig. bits */ 91 /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */ 92 t = ieee754dp_div(x, y); 93 y = ieee754dp_add(y, t); 94 y.bits -= 0x0010000600000000LL; 95 y.bits &= 0xffffffff00000000LL; 96 97 /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */ 98 /* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */ 99 t = ieee754dp_mul(y, y); 100 z = t; 101 t.bexp += 0x001; 102 t = ieee754dp_add(t, z); 103 z = ieee754dp_mul(ieee754dp_sub(x, z), y); 104 105 /* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */ 106 t = ieee754dp_div(z, ieee754dp_add(t, x)); 107 t.bexp += 0x001; 108 y = ieee754dp_add(y, t); 109 110 /* twiddle last bit to force y correctly rounded */ 111 112 /* set RZ, clear INEX flag */ 113 ieee754_csr.rm = FPU_CSR_RZ; 114 ieee754_csr.sx &= ~IEEE754_INEXACT; 115 116 /* t=x/y; ...chopped quotient, possibly inexact */ 117 t = ieee754dp_div(x, y); 118 119 if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) { 120 121 if (!(ieee754_csr.sx & IEEE754_INEXACT)) 122 /* t = t-ulp */ 123 t.bits -= 1; 124 125 /* add inexact to result status */ 126 oldcsr.cx |= IEEE754_INEXACT; 127 oldcsr.sx |= IEEE754_INEXACT; 128 129 switch (oldcsr.rm) { 130 case FPU_CSR_RU: 131 y.bits += 1; 132 fallthrough; 133 case FPU_CSR_RN: 134 t.bits += 1; 135 break; 136 } 137 138 /* y=y+t; ...chopped sum */ 139 y = ieee754dp_add(y, t); 140 141 /* adjust scalx for correctly rounded sqrt(x) */ 142 scalx -= 1; 143 } 144 145 /* py[n0]=py[n0]+scalx; ...scale back y */ 146 y.bexp += scalx; 147 148 /* restore rounding mode, possibly set inexact */ 149 ieee754_csr = oldcsr; 150 151 return y; 152 } 153