LXR linux/arch/mips/math-emu/dp

   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
  12static 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
  20union 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