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ffdd5e50 | 1 | /* Single-precision floating point square root. |
0ac5ae23 | 2 | Copyright (C) 1997, 2003, 2004, 2008, 2011 Free Software Foundation, Inc. |
ffdd5e50 UD |
3 | This file is part of the GNU C Library. |
4 | ||
5 | The GNU C Library is free software; you can redistribute it and/or | |
6 | modify it under the terms of the GNU Lesser General Public | |
7 | License as published by the Free Software Foundation; either | |
8 | version 2.1 of the License, or (at your option) any later version. | |
9 | ||
10 | The GNU C Library is distributed in the hope that it will be useful, | |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 | Lesser General Public License for more details. | |
14 | ||
15 | You should have received a copy of the GNU Lesser General Public | |
16 | License along with the GNU C Library; if not, write to the Free | |
17 | Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA | |
18 | 02111-1307 USA. */ | |
19 | ||
20 | #include <math.h> | |
21 | #include <math_private.h> | |
22 | #include <fenv_libc.h> | |
23 | #include <inttypes.h> | |
24 | ||
25 | #include <sysdep.h> | |
26 | #include <ldsodefs.h> | |
ffdd5e50 UD |
27 | |
28 | static const float almost_half = 0.50000006; /* 0.5 + 2^-24 */ | |
29 | static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 }; | |
30 | static const ieee_float_shape_type a_inf = {.word = 0x7f800000 }; | |
31 | static const float two48 = 281474976710656.0; | |
32 | static const float twom24 = 5.9604644775390625e-8; | |
33 | extern const float __t_sqrt[1024]; | |
34 | ||
35 | /* The method is based on a description in | |
36 | Computation of elementary functions on the IBM RISC System/6000 processor, | |
37 | P. W. Markstein, IBM J. Res. Develop, 34(1) 1990. | |
868f7a40 | 38 | Basically, it consists of two interleaved Newton-Raphson approximations, |
ffdd5e50 UD |
39 | one to find the actual square root, and one to find its reciprocal |
40 | without the expense of a division operation. The tricky bit here | |
41 | is the use of the POWER/PowerPC multiply-add operation to get the | |
42 | required accuracy with high speed. | |
43 | ||
44 | The argument reduction works by a combination of table lookup to | |
45 | obtain the initial guesses, and some careful modification of the | |
46 | generated guesses (which mostly runs on the integer unit, while the | |
868f7a40 | 47 | Newton-Raphson is running on the FPU). */ |
ffdd5e50 | 48 | |
ffdd5e50 UD |
49 | float |
50 | __slow_ieee754_sqrtf (float x) | |
ffdd5e50 UD |
51 | { |
52 | const float inf = a_inf.value; | |
53 | ||
54 | if (x > 0) | |
55 | { | |
56 | if (x != inf) | |
57 | { | |
58 | /* Variables named starting with 's' exist in the | |
59 | argument-reduced space, so that 2 > sx >= 0.5, | |
60 | 1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... . | |
61 | Variables named ending with 'i' are integer versions of | |
62 | floating-point values. */ | |
63 | float sx; /* The value of which we're trying to find the square | |
64 | root. */ | |
65 | float sg, g; /* Guess of the square root of x. */ | |
66 | float sd, d; /* Difference between the square of the guess and x. */ | |
67 | float sy; /* Estimate of 1/2g (overestimated by 1ulp). */ | |
68 | float sy2; /* 2*sy */ | |
69 | float e; /* Difference between y*g and 1/2 (note that e==se). */ | |
70 | float shx; /* == sx * fsg */ | |
71 | float fsg; /* sg*fsg == g. */ | |
72 | fenv_t fe; /* Saved floating-point environment (stores rounding | |
73 | mode and whether the inexact exception is | |
74 | enabled). */ | |
75 | uint32_t xi, sxi, fsgi; | |
76 | const float *t_sqrt; | |
77 | ||
78 | GET_FLOAT_WORD (xi, x); | |
79 | fe = fegetenv_register (); | |
80 | relax_fenv_state (); | |
81 | sxi = (xi & 0x3fffffff) | 0x3f000000; | |
82 | SET_FLOAT_WORD (sx, sxi); | |
83 | t_sqrt = __t_sqrt + (xi >> (23 - 8 - 1) & 0x3fe); | |
84 | sg = t_sqrt[0]; | |
85 | sy = t_sqrt[1]; | |
86 | ||
868f7a40 | 87 | /* Here we have three Newton-Raphson iterations each of a |
ffdd5e50 UD |
88 | division and a square root and the remainder of the |
89 | argument reduction, all interleaved. */ | |
90 | sd = -(sg * sg - sx); | |
91 | fsgi = (xi + 0x40000000) >> 1 & 0x7f800000; | |
92 | sy2 = sy + sy; | |
93 | sg = sy * sd + sg; /* 16-bit approximation to sqrt(sx). */ | |
94 | e = -(sy * sg - almost_half); | |
95 | SET_FLOAT_WORD (fsg, fsgi); | |
96 | sd = -(sg * sg - sx); | |
97 | sy = sy + e * sy2; | |
98 | if ((xi & 0x7f800000) == 0) | |
99 | goto denorm; | |
100 | shx = sx * fsg; | |
101 | sg = sg + sy * sd; /* 32-bit approximation to sqrt(sx), | |
102 | but perhaps rounded incorrectly. */ | |
103 | sy2 = sy + sy; | |
104 | g = sg * fsg; | |
105 | e = -(sy * sg - almost_half); | |
106 | d = -(g * sg - shx); | |
107 | sy = sy + e * sy2; | |
108 | fesetenv_register (fe); | |
109 | return g + sy * d; | |
110 | denorm: | |
111 | /* For denormalised numbers, we normalise, calculate the | |
112 | square root, and return an adjusted result. */ | |
113 | fesetenv_register (fe); | |
114 | return __slow_ieee754_sqrtf (x * two48) * twom24; | |
115 | } | |
116 | } | |
117 | else if (x < 0) | |
118 | { | |
119 | /* For some reason, some PowerPC32 processors don't implement | |
0ac5ae23 | 120 | FE_INVALID_SQRT. */ |
ffdd5e50 UD |
121 | #ifdef FE_INVALID_SQRT |
122 | feraiseexcept (FE_INVALID_SQRT); | |
c3a0ead4 UD |
123 | |
124 | fenv_union_t u = { .fenv = fegetenv_register () }; | |
125 | if ((u.l[1] & FE_INVALID) == 0) | |
ffdd5e50 UD |
126 | #endif |
127 | feraiseexcept (FE_INVALID); | |
128 | x = a_nan.value; | |
129 | } | |
130 | return f_washf (x); | |
131 | } | |
132 | ||
133 | ||
ffdd5e50 UD |
134 | float |
135 | __ieee754_sqrtf (float x) | |
ffdd5e50 UD |
136 | { |
137 | double z; | |
138 | ||
433f49c4 UD |
139 | /* If the CPU is 64-bit we can use the optional FP instructions. */ |
140 | if (__CPU_HAS_FSQRT) | |
ffdd5e50 | 141 | { |
c3a0ead4 | 142 | /* Volatile is required to prevent the compiler from moving the |
0ac5ae23 | 143 | fsqrt instruction above the branch. */ |
ffdd5e50 UD |
144 | __asm __volatile (" fsqrts %0,%1\n" |
145 | :"=f" (z):"f" (x)); | |
146 | } | |
147 | else | |
148 | z = __slow_ieee754_sqrtf (x); | |
149 | ||
150 | return z; | |
151 | } | |
0ac5ae23 | 152 | strong_alias (__ieee754_sqrtf, __sqrtf_finite) |