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152 lines
3.4 KiB
152 lines
3.4 KiB
// SPDX-License-Identifier: GPL-2.0-only |
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/* IEEE754 floating point arithmetic |
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* double precision square root |
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*/ |
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/* |
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* MIPS floating point support |
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* Copyright (C) 1994-2000 Algorithmics Ltd. |
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*/ |
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#include "ieee754dp.h" |
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static const unsigned int table[] = { |
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0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, |
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29598, 36145, 43202, 50740, 58733, 67158, 75992, |
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85215, 83599, 71378, 60428, 50647, 41945, 34246, |
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27478, 21581, 16499, 12183, 8588, 5674, 3403, |
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1742, 661, 130 |
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}; |
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union ieee754dp ieee754dp_sqrt(union ieee754dp x) |
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{ |
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struct _ieee754_csr oldcsr; |
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union ieee754dp y, z, t; |
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unsigned int scalx, yh; |
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COMPXDP; |
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EXPLODEXDP; |
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ieee754_clearcx(); |
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FLUSHXDP; |
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/* x == INF or NAN? */ |
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switch (xc) { |
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case IEEE754_CLASS_SNAN: |
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return ieee754dp_nanxcpt(x); |
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case IEEE754_CLASS_QNAN: |
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/* sqrt(Nan) = Nan */ |
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return x; |
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case IEEE754_CLASS_ZERO: |
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/* sqrt(0) = 0 */ |
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return x; |
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case IEEE754_CLASS_INF: |
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if (xs) { |
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/* sqrt(-Inf) = Nan */ |
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ieee754_setcx(IEEE754_INVALID_OPERATION); |
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return ieee754dp_indef(); |
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} |
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/* sqrt(+Inf) = Inf */ |
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return x; |
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case IEEE754_CLASS_DNORM: |
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DPDNORMX; |
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fallthrough; |
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case IEEE754_CLASS_NORM: |
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if (xs) { |
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/* sqrt(-x) = Nan */ |
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ieee754_setcx(IEEE754_INVALID_OPERATION); |
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return ieee754dp_indef(); |
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} |
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break; |
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} |
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/* save old csr; switch off INX enable & flag; set RN rounding */ |
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oldcsr = ieee754_csr; |
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ieee754_csr.mx &= ~IEEE754_INEXACT; |
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ieee754_csr.sx &= ~IEEE754_INEXACT; |
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ieee754_csr.rm = FPU_CSR_RN; |
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/* adjust exponent to prevent overflow */ |
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scalx = 0; |
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if (xe > 512) { /* x > 2**-512? */ |
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xe -= 512; /* x = x / 2**512 */ |
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scalx += 256; |
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} else if (xe < -512) { /* x < 2**-512? */ |
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xe += 512; /* x = x * 2**512 */ |
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scalx -= 256; |
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} |
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x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT); |
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y = x; |
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/* magic initial approximation to almost 8 sig. bits */ |
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yh = y.bits >> 32; |
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yh = (yh >> 1) + 0x1ff80000; |
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yh = yh - table[(yh >> 15) & 31]; |
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y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff); |
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/* Heron's rule once with correction to improve to ~18 sig. bits */ |
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/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */ |
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t = ieee754dp_div(x, y); |
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y = ieee754dp_add(y, t); |
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y.bits -= 0x0010000600000000LL; |
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y.bits &= 0xffffffff00000000LL; |
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/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */ |
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/* t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */ |
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t = ieee754dp_mul(y, y); |
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z = t; |
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t.bexp += 0x001; |
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t = ieee754dp_add(t, z); |
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z = ieee754dp_mul(ieee754dp_sub(x, z), y); |
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/* t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; */ |
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t = ieee754dp_div(z, ieee754dp_add(t, x)); |
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t.bexp += 0x001; |
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y = ieee754dp_add(y, t); |
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/* twiddle last bit to force y correctly rounded */ |
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/* set RZ, clear INEX flag */ |
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ieee754_csr.rm = FPU_CSR_RZ; |
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ieee754_csr.sx &= ~IEEE754_INEXACT; |
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/* t=x/y; ...chopped quotient, possibly inexact */ |
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t = ieee754dp_div(x, y); |
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if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) { |
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if (!(ieee754_csr.sx & IEEE754_INEXACT)) |
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/* t = t-ulp */ |
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t.bits -= 1; |
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/* add inexact to result status */ |
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oldcsr.cx |= IEEE754_INEXACT; |
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oldcsr.sx |= IEEE754_INEXACT; |
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switch (oldcsr.rm) { |
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case FPU_CSR_RU: |
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y.bits += 1; |
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fallthrough; |
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case FPU_CSR_RN: |
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t.bits += 1; |
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break; |
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} |
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/* y=y+t; ...chopped sum */ |
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y = ieee754dp_add(y, t); |
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/* adjust scalx for correctly rounded sqrt(x) */ |
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scalx -= 1; |
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} |
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/* py[n0]=py[n0]+scalx; ...scale back y */ |
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y.bexp += scalx; |
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/* restore rounding mode, possibly set inexact */ |
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ieee754_csr = oldcsr; |
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return y; |
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}
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