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b65f0b7b2e
On s390x I get the following werror when build with gcc 6.1 (or current gcc head) and -O3:
../sysdeps/ieee754/dbl-64/k_rem_pio2.c: In function ‘__kernel_rem_pio2’:
../sysdeps/ieee754/dbl-64/k_rem_pio2.c:254:18: error: array subscript is below array bounds [-Werror=array-bounds]
for (k = 1; iq[jk - k] == 0; k++)
~~^~~~~~~~
I get the same error with sysdeps/ieee754/flt-32/k_rem_pio2f.c.
This patch adds DIAG_* macros around it.
ChangeLog:
* sysdeps/ieee754/dbl-64/k_rem_pio2.c (__kernel_rem_pio2):
Use DIAG_*_NEEDS_COMMENT macro to get rid of array-bounds warning.
* sysdeps/ieee754/flt-32/k_rem_pio2f.c (__kernel_rem_pio2f):
Likewise.
363 lines
9.4 KiB
C
363 lines
9.4 KiB
C
/* @(#)k_rem_pio2.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
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#endif
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/*
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* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
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* double x[],y[]; int e0,nx,prec; int ipio2[];
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*
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* __kernel_rem_pio2 return the last three digits of N with
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* y = x - N*pi/2
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* so that |y| < pi/2.
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*
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* The method is to compute the integer (mod 8) and fraction parts of
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* (2/pi)*x without doing the full multiplication. In general we
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* skip the part of the product that are known to be a huge integer (
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* more accurately, = 0 mod 8 ). Thus the number of operations are
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* independent of the exponent of the input.
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*
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* (2/pi) is represented by an array of 24-bit integers in ipio2[].
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*
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* Input parameters:
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* x[] The input value (must be positive) is broken into nx
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* pieces of 24-bit integers in double precision format.
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* x[i] will be the i-th 24 bit of x. The scaled exponent
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* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
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* match x's up to 24 bits.
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*
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* Example of breaking a double positive z into x[0]+x[1]+x[2]:
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* e0 = ilogb(z)-23
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* z = scalbn(z,-e0)
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* for i = 0,1,2
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* x[i] = floor(z)
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* z = (z-x[i])*2**24
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*
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*
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* y[] ouput result in an array of double precision numbers.
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* The dimension of y[] is:
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* 24-bit precision 1
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* 53-bit precision 2
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* 64-bit precision 2
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* 113-bit precision 3
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* The actual value is the sum of them. Thus for 113-bit
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* precision, one may have to do something like:
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*
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* long double t,w,r_head, r_tail;
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* t = (long double)y[2] + (long double)y[1];
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* w = (long double)y[0];
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* r_head = t+w;
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* r_tail = w - (r_head - t);
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*
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* e0 The exponent of x[0]
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*
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* nx dimension of x[]
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*
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* prec an integer indicating the precision:
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* 0 24 bits (single)
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* 1 53 bits (double)
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* 2 64 bits (extended)
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* 3 113 bits (quad)
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*
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* ipio2[]
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* integer array, contains the (24*i)-th to (24*i+23)-th
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* bit of 2/pi after binary point. The corresponding
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* floating value is
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*
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* ipio2[i] * 2^(-24(i+1)).
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*
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* External function:
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* double scalbn(), floor();
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*
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*
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* Here is the description of some local variables:
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*
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* jk jk+1 is the initial number of terms of ipio2[] needed
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* in the computation. The recommended value is 2,3,4,
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* 6 for single, double, extended,and quad.
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*
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* jz local integer variable indicating the number of
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* terms of ipio2[] used.
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*
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* jx nx - 1
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*
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* jv index for pointing to the suitable ipio2[] for the
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* computation. In general, we want
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* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
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* is an integer. Thus
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* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
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* Hence jv = max(0,(e0-3)/24).
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*
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* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
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*
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* q[] double array with integral value, representing the
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* 24-bits chunk of the product of x and 2/pi.
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*
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* q0 the corresponding exponent of q[0]. Note that the
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* exponent for q[i] would be q0-24*i.
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*
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* PIo2[] double precision array, obtained by cutting pi/2
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* into 24 bits chunks.
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*
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* f[] ipio2[] in floating point
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*
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* iq[] integer array by breaking up q[] in 24-bits chunk.
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*
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* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
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*
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* ih integer. If >0 it indicates q[] is >= 0.5, hence
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* it also indicates the *sign* of the result.
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*
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*/
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/*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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#include <math.h>
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#include <math_private.h>
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#include <libc-internal.h>
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static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
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static const double PIo2[] = {
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1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
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7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
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5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
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3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
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1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
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1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
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2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
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2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
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};
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static const double
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zero = 0.0,
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one = 1.0,
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
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int
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__kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec,
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const int32_t *ipio2)
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{
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int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih;
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double z, fw, f[20], fq[20], q[20];
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/* initialize jk*/
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jk = init_jk[prec];
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jp = jk;
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/* determine jx,jv,q0, note that 3>q0 */
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jx = nx - 1;
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jv = (e0 - 3) / 24; if (jv < 0)
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jv = 0;
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q0 = e0 - 24 * (jv + 1);
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/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
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j = jv - jx; m = jx + jk;
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for (i = 0; i <= m; i++, j++)
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f[i] = (j < 0) ? zero : (double) ipio2[j];
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/* compute q[0],q[1],...q[jk] */
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for (i = 0; i <= jk; i++)
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{
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for (j = 0, fw = 0.0; j <= jx; j++)
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fw += x[j] * f[jx + i - j];
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q[i] = fw;
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}
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jz = jk;
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recompute:
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/* distill q[] into iq[] reversingly */
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for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
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{
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fw = (double) ((int32_t) (twon24 * z));
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iq[i] = (int32_t) (z - two24 * fw);
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z = q[j - 1] + fw;
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}
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/* compute n */
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z = __scalbn (z, q0); /* actual value of z */
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z -= 8.0 * __floor (z * 0.125); /* trim off integer >= 8 */
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n = (int32_t) z;
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z -= (double) n;
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ih = 0;
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if (q0 > 0) /* need iq[jz-1] to determine n */
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{
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i = (iq[jz - 1] >> (24 - q0)); n += i;
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iq[jz - 1] -= i << (24 - q0);
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ih = iq[jz - 1] >> (23 - q0);
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}
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else if (q0 == 0)
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ih = iq[jz - 1] >> 23;
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else if (z >= 0.5)
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ih = 2;
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if (ih > 0) /* q > 0.5 */
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{
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n += 1; carry = 0;
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for (i = 0; i < jz; i++) /* compute 1-q */
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{
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j = iq[i];
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if (carry == 0)
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{
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if (j != 0)
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{
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carry = 1; iq[i] = 0x1000000 - j;
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}
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}
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else
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iq[i] = 0xffffff - j;
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}
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if (q0 > 0) /* rare case: chance is 1 in 12 */
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{
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switch (q0)
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{
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case 1:
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iq[jz - 1] &= 0x7fffff; break;
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case 2:
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iq[jz - 1] &= 0x3fffff; break;
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}
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}
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if (ih == 2)
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{
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z = one - z;
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if (carry != 0)
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z -= __scalbn (one, q0);
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}
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}
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/* check if recomputation is needed */
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if (z == zero)
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{
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j = 0;
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for (i = jz - 1; i >= jk; i--)
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j |= iq[i];
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if (j == 0) /* need recomputation */
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{
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/* On s390x gcc 6.1 -O3 produces the warning "array subscript is below
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array bounds [-Werror=array-bounds]". Only __ieee754_rem_pio2l
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calls __kernel_rem_pio2 for normal numbers and |x| > pi/4 in case
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of ldbl-96 and |x| > 3pi/4 in case of ldbl-128[ibm].
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Thus x can't be zero and ipio2 is not zero, too. Thus not all iq[]
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values can't be zero. */
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DIAG_PUSH_NEEDS_COMMENT;
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DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds");
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for (k = 1; iq[jk - k] == 0; k++)
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; /* k = no. of terms needed */
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DIAG_POP_NEEDS_COMMENT;
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for (i = jz + 1; i <= jz + k; i++) /* add q[jz+1] to q[jz+k] */
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{
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f[jx + i] = (double) ipio2[jv + i];
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for (j = 0, fw = 0.0; j <= jx; j++)
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fw += x[j] * f[jx + i - j];
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q[i] = fw;
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}
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jz += k;
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goto recompute;
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}
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}
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/* chop off zero terms */
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if (z == 0.0)
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{
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jz -= 1; q0 -= 24;
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while (iq[jz] == 0)
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{
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jz--; q0 -= 24;
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}
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}
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else /* break z into 24-bit if necessary */
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{
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z = __scalbn (z, -q0);
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if (z >= two24)
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{
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fw = (double) ((int32_t) (twon24 * z));
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iq[jz] = (int32_t) (z - two24 * fw);
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jz += 1; q0 += 24;
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iq[jz] = (int32_t) fw;
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}
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else
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iq[jz] = (int32_t) z;
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}
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/* convert integer "bit" chunk to floating-point value */
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fw = __scalbn (one, q0);
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for (i = jz; i >= 0; i--)
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{
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q[i] = fw * (double) iq[i]; fw *= twon24;
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}
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/* compute PIo2[0,...,jp]*q[jz,...,0] */
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for (i = jz; i >= 0; i--)
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{
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for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
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fw += PIo2[k] * q[i + k];
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fq[jz - i] = fw;
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}
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/* compress fq[] into y[] */
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switch (prec)
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{
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case 0:
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fw = 0.0;
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for (i = jz; i >= 0; i--)
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fw += fq[i];
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y[0] = (ih == 0) ? fw : -fw;
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break;
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case 1:
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case 2:;
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double fv = 0.0;
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for (i = jz; i >= 0; i--)
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fv = math_narrow_eval (fv + fq[i]);
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y[0] = (ih == 0) ? fv : -fv;
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fv = math_narrow_eval (fq[0] - fv);
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for (i = 1; i <= jz; i++)
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fv = math_narrow_eval (fv + fq[i]);
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y[1] = (ih == 0) ? fv : -fv;
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break;
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case 3: /* painful */
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for (i = jz; i > 0; i--)
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{
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double fv = math_narrow_eval (fq[i - 1] + fq[i]);
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fq[i] += fq[i - 1] - fv;
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fq[i - 1] = fv;
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}
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for (i = jz; i > 1; i--)
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{
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double fv = math_narrow_eval (fq[i - 1] + fq[i]);
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fq[i] += fq[i - 1] - fv;
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fq[i - 1] = fv;
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}
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for (fw = 0.0, i = jz; i >= 2; i--)
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fw += fq[i];
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if (ih == 0)
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{
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y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
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}
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else
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{
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y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
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}
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}
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return n & 7;
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}
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