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/* k_rem_pio2f.c -- float version of k_rem_pio2.c
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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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_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $";
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#endif
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#include <math.h>
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#include <math-narrow-eval.h>
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#include <math_private.h>
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#include <libc-diag.h>
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/* In the float version, the input parameter x contains 8 bit
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integers, not 24 bit integers. 113 bit precision is not supported. */
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static const int init_jk[] = {4,7,9}; /* initial value for jk */
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static const float PIo2[] = {
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1.5703125000e+00, /* 0x3fc90000 */
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4.5776367188e-04, /* 0x39f00000 */
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2.5987625122e-05, /* 0x37da0000 */
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7.5437128544e-08, /* 0x33a20000 */
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6.0026650317e-11, /* 0x2e840000 */
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7.3896444519e-13, /* 0x2b500000 */
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5.3845816694e-15, /* 0x27c20000 */
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5.6378512969e-18, /* 0x22d00000 */
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8.3009228831e-20, /* 0x1fc40000 */
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3.2756352257e-22, /* 0x1bc60000 */
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6.3331015649e-25, /* 0x17440000 */
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};
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static const float
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zero = 0.0,
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one = 1.0,
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two8 = 2.5600000000e+02, /* 0x43800000 */
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twon8 = 3.9062500000e-03; /* 0x3b800000 */
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int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, 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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float 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)/8; if(jv<0) jv=0;
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q0 = e0-8*(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++) f[i] = (j<0)? zero : (float) 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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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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fw = (float)((int32_t)(twon8* z));
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iq[i] = (int32_t)(z-two8*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 = __scalbnf(z,q0); /* actual value of z */
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z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */
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n = (int32_t) z;
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z -= (float)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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i = (iq[jz-1]>>(8-q0)); n += i;
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iq[jz-1] -= i<<(8-q0);
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ih = iq[jz-1]>>(7-q0);
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}
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else if(q0==0) ih = iq[jz-1]>>7;
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else if(z>=(float)0.5) ih=2;
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if(ih>0) { /* q > 0.5 */
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n += 1; carry = 0;
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for(i=0;i
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j = iq[i];
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if(carry==0) {
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if(j!=0) {
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carry = 1; iq[i] = 0x100- j;
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}
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} else iq[i] = 0xff - j;
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}
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if(q0>0) { /* rare case: chance is 1 in 12 */
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switch(q0) {
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case 1:
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iq[jz-1] &= 0x7f; break;
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case 2:
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iq[jz-1] &= 0x3f; break;
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}
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}
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if(ih==2) {
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z = one - z;
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if(carry!=0) z -= __scalbnf(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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j = 0;
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for (i=jz-1;i>=jk;i--) j |= iq[i];
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if(j==0) { /* need recomputation */
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/* On s390x gcc 6.1 -O3 produces the warning "array subscript is
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below array bounds [-Werror=array-bounds]". Only
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__ieee754_rem_pio2f calls __kernel_rem_pio2f for normal
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numbers and |x| ~> 2^7*(pi/2). Thus x can't be zero and
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ipio2 is not zero, too. Thus not all iq[] values can't be
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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++); /* 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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f[jx+i] = (float) ipio2[jv+i];
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for(j=0,fw=0.0;j<=jx;j++) 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==(float)0.0) {
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jz -= 1; q0 -= 8;
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while(iq[jz]==0) { jz--; q0-=8;}
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} else { /* break z into 8-bit if necessary */
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z = __scalbnf(z,-q0);
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if(z>=two8) {
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fw = (float)((int32_t)(twon8*z));
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iq[jz] = (int32_t)(z-two8*fw);
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jz += 1; q0 += 8;
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iq[jz] = (int32_t) fw;
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} else 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 = __scalbnf(one,q0);
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for(i=jz;i>=0;i--) {
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q[i] = fw*(float)iq[i]; fw*=twon8;
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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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for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) 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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case 0:
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fw = 0.0;
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for (i=jz;i>=0;i--) 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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float fv = 0.0;
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for (i=jz;i>=0;i--) fv = math_narrow_eval (fv + fq[i]);
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y[0] = (ih==0)? fv: -fv;
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/* GCC mainline (to be GCC 9), as of 2018-05-22 on
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i686, warns that fq[0] may be used uninitialized.
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This is not possible because jz is always
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nonnegative when the above loop initializing fq is
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executed, because the result is never zero to full
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precision (this function is not called for zero
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arguments). */
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DIAG_PUSH_NEEDS_COMMENT;
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DIAG_IGNORE_NEEDS_COMMENT (9, "-Wmaybe-uninitialized");
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fv = math_narrow_eval (fq[0]-fv);
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DIAG_POP_NEEDS_COMMENT;
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for (i=1;i<=jz;i++) 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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float 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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float 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--) fw += fq[i];
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if(ih==0) {
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y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
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} else {
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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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