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188 lines
6.5 KiB
C
188 lines
6.5 KiB
C
/* Copyright (C) 1996-2016 Free Software Foundation, Inc.
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Contributed by David Mosberger (davidm@cs.arizona.edu).
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library. If not, see
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<http://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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#include <shlib-compat.h>
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#if !defined(_IEEE_FP_INEXACT)
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/*
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* This version is much faster than generic sqrt implementation, but
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* it doesn't handle the inexact flag. It doesn't handle exceptional
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* values either, but will defer to the full ieee754_sqrt routine which
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* can.
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*/
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/* Careful with rearranging this without consulting the assembly below. */
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const static struct sqrt_data_struct {
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unsigned long dn, up, half, almost_three_half;
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unsigned long one_and_a_half, two_to_minus_30, one, nan;
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const int T2[64];
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} sqrt_data __attribute__((used)) = {
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0x3fefffffffffffff, /* __dn = nextafter(1,-Inf) */
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0x3ff0000000000001, /* __up = nextafter(1,+Inf) */
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0x3fe0000000000000, /* half */
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0x3ff7ffffffc00000, /* almost_three_half = 1.5-2^-30 */
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0x3ff8000000000000, /* one_and_a_half */
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0x3e10000000000000, /* two_to_minus_30 */
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0x3ff0000000000000, /* one */
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0xffffffffffffffff, /* nan */
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{ 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
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0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
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0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
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0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
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0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
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0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
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0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
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0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd }
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};
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asm ("\
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/* Define offsets into the structure defined in C above. */ \n\
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$DN = 0*8 \n\
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$UP = 1*8 \n\
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$HALF = 2*8 \n\
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$ALMOST_THREE_HALF = 3*8 \n\
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$NAN = 7*8 \n\
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$T2 = 8*8 \n\
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\n\
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/* Stack variables. */ \n\
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$K = 0 \n\
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$Y = 8 \n\
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\n\
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.text \n\
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.align 5 \n\
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.globl __ieee754_sqrt \n\
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.ent __ieee754_sqrt \n\
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__ieee754_sqrt: \n\
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ldgp $29, 0($27) \n\
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subq $sp, 16, $sp \n\
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.frame $sp, 16, $26, 0\n"
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#ifdef PROF
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" lda $28, _mcount \n\
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jsr $28, ($28), _mcount\n"
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#endif
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" .prologue 1 \n\
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\n\
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.align 4 \n\
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stt $f16, $K($sp) # e0 : \n\
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mult $f31, $f31, $f31 # .. fm : \n\
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lda $4, sqrt_data # e0 : \n\
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fblt $f16, $fixup # .. fa : \n\
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\n\
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ldah $2, 0x5fe8 # e0 : \n\
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ldq $3, $K($sp) # .. e1 : \n\
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ldt $f12, $HALF($4) # e0 : \n\
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ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 : \n\
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\n\
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sll $3, 52, $5 # e0 : \n\
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lda $6, 0x7fd # .. e1 : \n\
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fnop # .. fa : \n\
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fnop # .. fm : \n\
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\n\
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subq $5, 1, $5 # e1 : \n\
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srl $3, 33, $1 # .. e0 : \n\
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cmpule $5, $6, $5 # e0 : \n\
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beq $5, $fixup # .. e1 : \n\
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\n\
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mult $f16, $f12, $f11 # fm : $f11 = x * 0.5 \n\
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subl $2, $1, $2 # .. e0 : \n\
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addt $f12, $f12, $f17 # .. fa : $f17 = 1.0 \n\
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srl $2, 12, $1 # e0 : \n\
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\n\
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and $1, 0xfc, $1 # e0 : \n\
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addq $1, $4, $1 # e1 : \n\
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ldl $1, $T2($1) # e0 : \n\
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addt $f12, $f17, $f15 # .. fa : $f15 = 1.5 \n\
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\n\
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subl $2, $1, $2 # e0 : \n\
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ldt $f14, $DN($4) # .. e1 : \n\
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sll $2, 32, $2 # e0 : \n\
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stq $2, $Y($sp) # e0 : \n\
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\n\
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ldt $f13, $Y($sp) # e0 : \n\
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mult/su $f11, $f13, $f10 # fm 2: $f10 = (x * 0.5) * y \n\
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mult $f10, $f13, $f10 # fm 4: $f10 = ((x*0.5)*y)*y \n\
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subt $f15, $f10, $f1 # fa 4: $f1 = (1.5-0.5*x*y*y) \n\
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\n\
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mult $f13, $f1, $f13 # fm 4: yp = y*(1.5-0.5*x*y^2)\n\
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mult/su $f11, $f13, $f1 # fm 4: $f11 = x * 0.5 * yp \n\
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mult $f1, $f13, $f11 # fm 4: $f11 = (x*0.5*yp)*yp \n\
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subt $f18, $f11, $f1 # fa 4: $f1=(1.5-2^-30)-x/2*yp^2\n\
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\n\
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mult $f13, $f1, $f13 # fm 4: ypp = $f13 = yp*$f1 \n\
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subt $f15, $f12, $f1 # .. fa : $f1 = (1.5 - 0.5) \n\
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ldt $f15, $UP($4) # .. e0 : \n\
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mult/su $f16, $f13, $f10 # fm 4: z = $f10 = x * ypp \n\
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\n\
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mult $f10, $f13, $f11 # fm 4: $f11 = z*ypp \n\
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mult $f10, $f12, $f12 # fm : $f12 = z*0.5 \n\
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subt $f1, $f11, $f1 # fa 4: $f1 = 1 - z*ypp \n\
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mult $f12, $f1, $f12 # fm 4: $f12 = z/2*(1 - z*ypp)\n\
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\n\
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addt $f10, $f12, $f0 # fa 4: zp=res= z+z/2*(1-z*ypp)\n\
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mult/c $f0, $f14, $f12 # fm 4: zmi = zp * DN \n\
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mult/c $f0, $f15, $f11 # fm : zpl = zp * UP \n\
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mult/c $f0, $f12, $f1 # fm : $f1 = zp * zmi \n\
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\n\
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mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl \n\
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subt/su $f1, $f16, $f13 # .. fa : y1 = zp*zmi - x \n\
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subt/su $f15, $f16, $f14 # fa 4: y2 = zp*zpl - x \n\
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fcmovge $f13, $f12, $f0 # fa 3: res = (y1>=0)?zmi:res \n\
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\n\
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fcmovlt $f14, $f11, $f0 # fa 4: res = (y2<0)?zpl:res \n\
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addq $sp, 16, $sp # .. e0 : \n\
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ret # .. e1 : \n\
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\n\
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.align 4 \n\
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$fixup: \n\
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addq $sp, 16, $sp \n\
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br __full_ieee754_sqrt !samegp \n\
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\n\
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.end __ieee754_sqrt");
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/* Avoid the __sqrt_finite alias that dbl-64/e_sqrt.c would give... */
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#undef strong_alias
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#define strong_alias(a,b)
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/* ... defining our own. */
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#if SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18)
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asm (".global __sqrt_finite1; __sqrt_finite1 = __ieee754_sqrt");
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#else
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asm (".global __sqrt_finite; __sqrt_finite = __ieee754_sqrt");
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#endif
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static double __full_ieee754_sqrt(double) __attribute_used__;
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#define __ieee754_sqrt __full_ieee754_sqrt
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#elif SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18)
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# define __sqrt_finite __sqrt_finite1
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#endif /* _IEEE_FP_INEXACT */
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#include <sysdeps/ieee754/dbl-64/e_sqrt.c>
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/* Work around forgotten symbol in alphaev6 build. */
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#if SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18)
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# undef __sqrt_finite
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# undef __ieee754_sqrt
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compat_symbol (libm, __sqrt_finite1, __sqrt_finite, GLIBC_2_15);
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versioned_symbol (libm, __ieee754_sqrt, __sqrt_finite, GLIBC_2_18);
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#endif
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