/* This program is part of the TACLeBench benchmark suite. Version V 2.0 Name: quicksortlibm.c Author: Ian Lance Taylor Function: IEEE754 software library routines. Source: Sun Microsystems and Cygnus Original name: Unknown Changes: No major functional changes. License: See the terms below. */ #include "quicksortlibm.h" #include "math_private.h" // Often used variables/consts #ifdef __STDC__ const float #else float #endif quicksort_one = 1.0f, quicksort_half = 5.0000000000e-01f, /* 0x3f000000 */ quicksort_zero = 0.0f, quicksort_huge = 1.0e30, quicksort_tiny = 1.0e-30f, quicksort_two = 2.0, quicksort_two24 = 16777216.0; /* 0x4b800000 */ /* e_powf.c -- float version of e_pow.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ const float #else float #endif quicksort_bp[ ] = { 1.0f, 1.5f, }, quicksort_dp_h[ ] = { 0.0f, 5.84960938e-01f,}, /* 0x3f15c000 */ quicksort_dp_l[ ] = { 0.0f, 1.56322085e-06f,}, /* 0x35d1cfdc */ quicksort_L1 = 6.0000002384e-01f, /* 0x3f19999a */ quicksort_L2 = 4.2857143283e-01f, /* 0x3edb6db7 */ quicksort_L3 = 3.3333334327e-01f, /* 0x3eaaaaab */ quicksort_L4 = 2.7272811532e-01f, /* 0x3e8ba305 */ quicksort_L5 = 2.3066075146e-01f, /* 0x3e6c3255 */ quicksort_L6 = 2.0697501302e-01f, /* 0x3e53f142 */ quicksort_P1 = 1.6666667163e-01f, /* 0x3e2aaaab */ quicksort_P2 = -2.7777778450e-03f, /* 0xbb360b61 */ quicksort_P3 = 6.6137559770e-05f, /* 0x388ab355 */ quicksort_P4 = -1.6533901999e-06f, /* 0xb5ddea0e */ quicksort_P5 = 4.1381369442e-08f, /* 0x3331bb4c */ quicksort_lg2 = 6.9314718246e-01f, /* 0x3f317218 */ quicksort_lg2_h = 6.93145752e-01f, /* 0x3f317200 */ quicksort_lg2_l = 1.42860654e-06f, /* 0x35bfbe8c */ quicksort_ovt = 4.2995665694e-08f, /* -(128-log2(ovfl+.5ulp)) */ quicksort_cp = 9.6179670095e-01f, /* 0x3f76384f =2/(3ln2) */ quicksort_cp_h = 9.6179199219e-01f, /* 0x3f763800 =head of cp */ quicksort_cp_l = 4.7017383622e-06f, /* 0x369dc3a0 =tail of cp_h */ quicksort_ivln2 = 1.4426950216e+00f, /* 0x3fb8aa3b =1/ln2 */ quicksort_ivln2_h = 1.4426879883e+00f, /* 0x3fb8aa00 =16b 1/ln2*/ quicksort_ivln2_l = 7.0526075433e-06f; /* 0x36eca570 =1/ln2 tail*/ #ifdef __STDC__ float quicksort___ieee754_powf( float x, float y ) #else float quicksort___ieee754_powf( x, y ) float x, y; #endif { float z, ax, z_h, z_l, p_h, p_l; float y1, t1, t2, r, s, t, u, v, w; int i, j, k, yisint, n; int hx, hy, ix, iy, is; QUICKSORT_GET_FLOAT_WORD( hx, x ); QUICKSORT_GET_FLOAT_WORD( hy, y ); ix = hx & 0x7fffffff; iy = hy & 0x7fffffff; /* y==zero: x**0 = 1 */ if ( iy == 0 ) return ( quicksort_one ); /* x==+-1 */ if ( x == 1.0f ) return ( quicksort_one ); if ( ( x == -1.0f ) && quicksort_isinf( y ) ) return ( quicksort_one ); /* +-NaN return x+y */ if ( ( ix > 0x7f800000 ) || ( iy > 0x7f800000 ) ) return ( x + y ); /* determine if y is an odd int when x < 0 yisint = 0 ... y is not an integer yisint = 1 ... y is an odd int yisint = 2 ... y is an even int */ yisint = 0; if ( hx < 0 ) { if ( iy >= 0x4b800000 ) yisint = 2; /* even integer y */ else if ( iy >= 0x3f800000 ) { k = ( iy >> 23 ) - 0x7f; /* exponent */ j = iy >> ( 23 - k ); if ( ( j << ( 23 - k ) ) == iy ) yisint = 2 - ( j & 1 ); } } /* special value of y */ if ( iy == 0x7f800000 ) { /* y is +-inf */ if ( ix == 0x3f800000 ) return ( y - y ); /* inf**+-1 is NaN */ else if ( ix > 0x3f800000 ) /* (|x|>1)**+-inf = inf,0 */ return ( ( hy >= 0 ) ? y : quicksort_zero ); else /* (|x|<1)**-,+inf = inf,0 */ return ( ( hy < 0 ) ? -y : quicksort_zero ); } if ( iy == 0x3f800000 ) { /* y is +-1 */ if ( hy < 0 ) return ( quicksort_one / x ); else return ( x ); } if ( hy == 0x40000000 ) return ( x * x ); /* y is 2 */ if ( hy == 0x3f000000 ) { /* y is 0.5 */ if ( hx >= 0 ) /* x >= +0 */ return ( quicksort___ieee754_sqrtf( x ) ); } ax = quicksort_fabsf( x ); /* special value of x */ if ( ( ix == 0x7f800000 ) || ( ix == 0 ) || ( ix == 0x3f800000 ) ) { z = ax; /*x is +-0,+-inf,+-1*/ if ( hy < 0 ) z = quicksort_one / z; /* z = (1/|x|) */ if ( hx < 0 ) { if ( ( ( ix - 0x3f800000 ) | yisint ) == 0 ) z = ( z - z ) / ( z - z ); /* (-1)**non-int is NaN */ else if ( yisint == 1 ) z = -z; /* (x<0)**odd = -(|x|**odd) */ } return ( z ); } /* (x<0)**(non-int) is NaN */ if ( ( ( ( ( unsigned int ) hx >> 31 ) - 1 ) | yisint ) == 0 ) return ( ( x - x ) / ( x - x ) ); /* |y| is huge */ if ( iy > 0x4d000000 ) { /* if |y| > 2**27 */ /* over/underflow if x is not close to one */ if ( ix < 0x3f7ffff8 ) return ( ( hy < 0 ) ? quicksort_huge *quicksort_huge : quicksort_tiny * quicksort_tiny ); if ( ix > 0x3f800007 ) return ( ( hy > 0 ) ? quicksort_huge *quicksort_huge : quicksort_tiny * quicksort_tiny ); /* now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ t = x - 1; /* t has 20 trailing zeros */ w = ( t * t ) * ( ( float ) 0.5f - t * ( ( float ) 0.333333333333f - t * ( float ) 0.25f ) ); u = quicksort_ivln2_h * t; /* ivln2_h has 16 sig. bits */ v = t * quicksort_ivln2_l - w * quicksort_ivln2; t1 = u + v; QUICKSORT_GET_FLOAT_WORD( is, t1 ); QUICKSORT_SET_FLOAT_WORD( t1, is & 0xfffff000 ); t2 = v - ( t1 - u ); } else { float s2, s_h, s_l, t_h, t_l; n = 0; /* take care subnormal number */ if ( ix < 0x00800000 ) { ax *= quicksort_two24; n -= 24; QUICKSORT_GET_FLOAT_WORD( ix, ax ); } n += ( ( ix ) >> 23 ) - 0x7f; j = ix & 0x007fffff; /* determine interval */ ix = j | 0x3f800000; /* normalize ix */ if ( j <= 0x1cc471 ) k = 0; /* |x|> 1 ) | 0x20000000 ) + 0x0040000 + ( k << 21 ) ); t_l = ax - ( t_h - quicksort_bp[ k ] ); s_l = v * ( ( u - s_h * t_h ) - s_h * t_l ); /* compute log(ax) */ s2 = s * s; r = s2 * s2 * ( quicksort_L1 + s2 * ( quicksort_L2 + s2 * ( quicksort_L3 + s2 * ( quicksort_L4 + s2 * ( quicksort_L5 + s2 * quicksort_L6 ) ) ) ) ); r += s_l * ( s_h + s ); s2 = s_h * s_h; t_h = ( float ) 3.0f + s2 + r; QUICKSORT_GET_FLOAT_WORD( is, t_h ); QUICKSORT_SET_FLOAT_WORD( t_h, is & 0xfffff000 ); t_l = r - ( ( t_h - ( float ) 3.0f ) - s2 ); /* u+v = s*(1+...) */ u = s_h * t_h; v = s_l * t_h + t_l * s; /* 2/(3log2)*(s+...) */ p_h = u + v; QUICKSORT_GET_FLOAT_WORD( is, p_h ); QUICKSORT_SET_FLOAT_WORD( p_h, is & 0xfffff000 ); p_l = v - ( p_h - u ); z_h = quicksort_cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ z_l = quicksort_cp_l * p_h + p_l * quicksort_cp + quicksort_dp_l[ k ]; /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ t = ( float ) n; t1 = ( ( ( z_h + z_l ) + quicksort_dp_h[ k ] ) + t ); QUICKSORT_GET_FLOAT_WORD( is, t1 ); QUICKSORT_SET_FLOAT_WORD( t1, is & 0xfffff000 ); t2 = z_l - ( ( ( t1 - t ) - quicksort_dp_h[ k ] ) - z_h ); } s = quicksort_one; /* s (sign of result -ve**odd) = -1 else = 1 */ if ( ( ( ( ( unsigned int ) hx >> 31 ) - 1 ) | ( yisint - 1 ) ) == 0 ) s = -quicksort_one; /* (-ve)**(odd int) */ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ QUICKSORT_GET_FLOAT_WORD( is, y ); QUICKSORT_SET_FLOAT_WORD( y1, is & 0xfffff000 ); p_l = ( y - y1 ) * t1 + y * t2; p_h = y1 * t1; z = p_l + p_h; QUICKSORT_GET_FLOAT_WORD( j, z ); if ( j > 0x43000000 ) /* if z > 128 */ return ( s * quicksort_huge * quicksort_huge ); /* overflow */ else if ( j == 0x43000000 ) { /* if z == 128 */ if ( p_l + quicksort_ovt > z - p_h ) return ( s * quicksort_huge * quicksort_huge ); /* overflow */ } else if ( ( j & 0x7fffffff ) > 0x43160000 ) /* z <= -150 */ return ( s * quicksort_tiny * quicksort_tiny ); /* underflow */ else if ( ( unsigned int ) j == 0xc3160000 ) { /* z == -150 */ if ( p_l <= z - p_h ) return ( s * quicksort_tiny * quicksort_tiny ); /* underflow */ } /* compute 2**(p_h+p_l) */ i = j & 0x7fffffff; k = ( i >> 23 ) - 0x7f; n = 0; if ( i > 0x3f000000 ) { /* if |z| > 0.5, set n = [ z+0.5 ] */ n = j + ( 0x00800000 >> ( k + 1 ) ); k = ( ( n & 0x7fffffff ) >> 23 ) - 0x7f; /* new k for n */ QUICKSORT_SET_FLOAT_WORD( t, n & ~( 0x007fffff >> k ) ); n = ( ( n & 0x007fffff ) | 0x00800000 ) >> ( 23 - k ); if ( j < 0 ) n = -n; p_h -= t; } t = p_l + p_h; QUICKSORT_GET_FLOAT_WORD( is, t ); QUICKSORT_SET_FLOAT_WORD( t, is & 0xfffff000 ); u = t * quicksort_lg2_h; v = ( p_l - ( t - p_h ) ) * quicksort_lg2 + t * quicksort_lg2_l; z = u + v; w = v - ( z - u ); t = z * z; t1 = z - t * ( quicksort_P1 + t * ( quicksort_P2 + t * ( quicksort_P3 + t * ( quicksort_P4 + t * quicksort_P5 ) ) ) ); r = ( z * t1 ) / ( t1 - quicksort_two ) - ( w + z * w ); z = quicksort_one - ( r - z ); QUICKSORT_GET_FLOAT_WORD( j, z ); j += ( n << 23 ); if ( ( j >> 23 ) <= 0 ) z = quicksort___scalbnf( z, n ); /* subnormal output */ else QUICKSORT_SET_FLOAT_WORD( z, j ); return ( s * z ); } /* e_sqrtf.c -- float version of e_sqrt.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ float quicksort___ieee754_sqrtf( float x ) #else float quicksort___ieee754_sqrtf( x ) float x; #endif { float z; int sign = ( int ) 0x80000000; int ix, s, q, m, t, i; unsigned int r; QUICKSORT_GET_FLOAT_WORD( ix, x ); /* take care of Inf and NaN */ if ( ( ix & 0x7f800000 ) == 0x7f800000 ) return ( x * x + x ); /* sqrt(NaN)=NaN, sqrt(+inf)=+inf sqrt(-inf)=sNaN */ /* take care of zero */ if ( ix <= 0 ) { if ( ( ix & ( ~sign ) ) == 0 ) return ( x ); /* sqrt(+-0) = +-0 */ else if ( ix < 0 ) return ( ( x - x ) / ( x - x ) ); /* sqrt(-ve) = sNaN */ } /* normalize x */ m = ( ix >> 23 ); if ( m == 0 ) { /* subnormal x */ _Pragma( "loopbound min 0 max 0" ) for ( i = 0; ( ix & 0x00800000 ) == 0; i++ ) ix <<= 1; m -= i - 1; } m -= 127; /* unbias exponent */ ix = ( ix & 0x007fffff ) | 0x00800000; if ( m & 1 ) /* odd m, double x to make it even */ ix += ix; m >>= 1; /* m = [ m/2 ] */ /* generate sqrt(x) bit by bit */ ix += ix; q = s = 0; /* q = sqrt(x) */ r = 0x01000000; /* r = moving bit from right to left */ _Pragma( "loopbound min 25 max 25" ) while ( r != 0 ) { t = s + r; if ( t <= ix ) { s = t + r; ix -= t; q += r; } ix += ix; r >>= 1; } /* use floating add to find out rounding direction */ if ( ix != 0 ) { z = quicksort_one - quicksort_tiny; /* trigger inexact flag */ if ( z >= quicksort_one ) { z = quicksort_one + quicksort_tiny; if ( z > quicksort_one ) q += 2; else q += ( q & 1 ); } } ix = ( q >> 1 ) + 0x3f000000; ix += ( m << 23 ); QUICKSORT_SET_FLOAT_WORD( z, ix ); return ( z ); } /* s_copysignf.c -- float version of s_copysign.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ /* copysignf(float x, float y) copysignf(x,y) returns a value with the magnitude of x and with the sign bit of y. */ #ifdef __STDC__ float quicksort___copysignf( float x, float y ) #else float quicksort___copysignf( x, y ) float x, y; #endif { unsigned int ix, iy; QUICKSORT_GET_FLOAT_WORD( ix, x ); QUICKSORT_GET_FLOAT_WORD( iy, y ); QUICKSORT_SET_FLOAT_WORD( x, ( ix & 0x7fffffff ) | ( iy & 0x80000000 ) ); return ( x ); } /* e_rem_pio2f.c -- float version of e_rem_pio2.c Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ /* __ieee754_rem_pio2f(x,y) return the remainder of x rem pi/2 in y[ 0 ]+y[ 1 ] use __kernel_rem_pio2f() */ /* This array is like the one in e_rem_pio2.c, but the numbers are single precision and the last 8 bits are forced to 0. */ #ifdef __STDC__ const int quicksort_npio2_hw[ ] = { #else int quicksort_npio2_hw[ ] = { #endif 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, 0x4242c700, 0x42490f00 }; /* invpio2: 24 bits of 2/pi pio2_1: first 17 bit of pi/2 pio2_1t: pi/2 - pio2_1 pio2_2: second 17 bit of pi/2 pio2_2t: pi/2 - (pio2_1+pio2_2) pio2_3: third 17 bit of pi/2 pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ #ifdef __STDC__ const float #else float #endif quicksort_invpio2 = 6.3661980629e-01f, /* 0x3f22f984 */ quicksort_pio2_1 = 1.5707855225e+00f, /* 0x3fc90f80 */ quicksort_pio2_1t = 1.0804334124e-05f, /* 0x37354443 */ quicksort_pio2_2 = 1.0804273188e-05f, /* 0x37354400 */ quicksort_pio2_2t = 6.0770999344e-11f, /* 0x2e85a308 */ quicksort_pio2_3 = 6.0770943833e-11f, /* 0x2e85a300 */ quicksort_pio2_3t = 6.1232342629e-17f; /* 0x248d3132 */ #ifdef __STDC__ int quicksort___ieee754_rem_pio2f( float x, float *y ) #else int quicksort___ieee754_rem_pio2f( x, y ) float x, y[ ]; #endif { float z, w, t, r, fn; int i, j, n, ix, hx; QUICKSORT_GET_FLOAT_WORD( hx, x ); ix = hx & 0x7fffffff; if ( ix <= 0x3f490fd8 ) { /* |x| ~<= pi/4 , no need for reduction */ y[ 0 ] = x; y[ 1 ] = 0; return ( 0 ); } if ( ix < 0x4016cbe4 ) { /* |x| < 3pi/4, special case with n=+-1 */ if ( hx > 0 ) { z = x - quicksort_pio2_1; if ( ( ix & 0xfffffff0 ) != 0x3fc90fd0 ) { /* 24+24 bit pi OK */ y[ 0 ] = z - quicksort_pio2_1t; y[ 1 ] = ( z - y[ 0 ] ) - quicksort_pio2_1t; } else { /* near pi/2, use 24+24+24 bit pi */ z -= quicksort_pio2_2; y[ 0 ] = z - quicksort_pio2_2t; y[ 1 ] = ( z - y[ 0 ] ) - quicksort_pio2_2t; } return ( 1 ); } else { /* negative x */ z = x + quicksort_pio2_1; if ( ( ix & 0xfffffff0 ) != 0x3fc90fd0 ) { /* 24+24 bit pi OK */ y[ 0 ] = z + quicksort_pio2_1t; y[ 1 ] = ( z - y[ 0 ] ) + quicksort_pio2_1t; } else { /* near pi/2, use 24+24+24 bit pi */ z += quicksort_pio2_2; y[ 0 ] = z + quicksort_pio2_2t; y[ 1 ] = ( z - y[ 0 ] ) + quicksort_pio2_2t; } return ( -1 ); } } if ( ix <= 0x43490f80 ) { /* |x| ~<= 2^7*(pi/2), medium size */ t = quicksort_fabsf( x ); n = ( int ) ( t * quicksort_invpio2 + quicksort_half ); fn = ( float ) n; r = t - fn * quicksort_pio2_1; w = fn * quicksort_pio2_1t; /* 1st round good to 40 bit */ if ( ( n < 32 ) && ( ( int ) ( ix & 0xffffff00 ) != quicksort_npio2_hw[ n - 1 ] ) ) y[ 0 ] = r - w; /* quick check no cancellation */ else { unsigned int high; j = ix >> 23; y[ 0 ] = r - w; QUICKSORT_GET_FLOAT_WORD( high, y[ 0 ] ); i = j - ( ( high >> 23 ) & 0xff ); if ( i > 8 ) { /* 2nd iteration needed, good to 57 */ t = r; w = fn * quicksort_pio2_2; r = t - w; w = fn * quicksort_pio2_2t - ( ( t - r ) - w ); y[ 0 ] = r - w; QUICKSORT_GET_FLOAT_WORD( high, y[ 0 ] ); i = j - ( ( high >> 23 ) & 0xff ); if ( i > 25 ) { /* 3rd iteration need, 74 bits acc */ t = r; /* will cover all possible cases */ w = fn * quicksort_pio2_3; r = t - w; w = fn * quicksort_pio2_3t - ( ( t - r ) - w ); y[ 0 ] = r - w; } } } y[ 1 ] = ( r - y[ 0 ] ) - w; if ( hx < 0 ) { y[ 0 ] = -y[ 0 ]; y[ 1 ] = -y[ 1 ]; return ( -n ); } else return ( n ); } /* all other (large) arguments */ if ( ix >= 0x7f800000 ) { /* x is inf or NaN */ y[ 0 ] = y[ 1 ] = x - x; return ( 0 ); } y[ 0 ] = y[ 1 ] = x - x; /* dummy initialization */ return ( 0 ); /* doesn't happen for our input */ } /* k_cosf.c -- float version of k_cos.c Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ const float #else float #endif quicksort_C1 = 4.1666667908e-02f, /* 0x3d2aaaab */ quicksort_C2 = -1.3888889225e-03f, /* 0xbab60b61 */ quicksort_C3 = 2.4801587642e-05f, /* 0x37d00d01 */ quicksort_C4 = -2.7557314297e-07f, /* 0xb493f27c */ quicksort_C5 = 2.0875723372e-09f, /* 0x310f74f6 */ quicksort_C6 = -1.1359647598e-11f; /* 0xad47d74e */ #ifdef __STDC__ float quicksort___kernel_cosf( float x, float y ) #else float quicksort___kernel_cosf( x, y ) float x, y; #endif { float a, hz, z, r, qx; int ix; QUICKSORT_GET_FLOAT_WORD( ix, x ); ix &= 0x7fffffff; /* ix = |x|'s high word*/ if ( ix < 0x32000000 ) { /* if x < 2**27 */ if ( ( ( int ) x ) == 0 ) return ( quicksort_one ); /* generate inexact */ } z = x * x; r = z * ( quicksort_C1 + z * ( quicksort_C2 + z * ( quicksort_C3 + z * ( quicksort_C4 + z * ( quicksort_C5 + z * quicksort_C6 ) ) ) ) ); if ( ix < 0x3e99999a ) /* if |x| < 0.3 */ return ( quicksort_one - ( ( float ) 0.5f * z - ( z * r - x * y ) ) ); else { if ( ix > 0x3f480000 ) /* x > 0.78125 */ qx = ( float ) 0.28125f; else { QUICKSORT_SET_FLOAT_WORD( qx, ix - 0x01000000 ); /* x/4 */ } hz = ( float ) 0.5f * z - qx; a = quicksort_one - qx; return ( a - ( hz - ( z * r - x * y ) ) ); } } /* k_sinf.c -- float version of k_sin.c Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ const float #else float #endif quicksort_S1 = -1.6666667163e-01f, /* 0xbe2aaaab */ quicksort_S2 = 8.3333337680e-03f, /* 0x3c088889 */ quicksort_S3 = -1.9841270114e-04f, /* 0xb9500d01 */ quicksort_S4 = 2.7557314297e-06f, /* 0x3638ef1b */ quicksort_S5 = -2.5050759689e-08f, /* 0xb2d72f34 */ quicksort_S6 = 1.5896910177e-10f; /* 0x2f2ec9d3 */ #ifdef __STDC__ float quicksort___kernel_sinf( float x, float y, int iy ) #else float quicksort___kernel_sinf( x, y, iy ) float x, y; int iy; /* iy=0 if y is zero */ #endif { float z, r, v; int ix; QUICKSORT_GET_FLOAT_WORD( ix, x ); ix &= 0x7fffffff; /* high word of x */ if ( ix < 0x32000000 ) { /* |x| < 2**-27 */ if ( ( int ) x == 0 ) return ( x ); /* generate inexact */ } z = x * x; v = z * x; r = quicksort_S2 + z * ( quicksort_S3 + z * ( quicksort_S4 + z * ( quicksort_S5 + z * quicksort_S6 ) ) ); if ( iy == 0 ) return ( x + v * ( quicksort_S1 + z * r ) ); else return ( x - ( ( z * ( quicksort_half * y - v * r ) - y ) - v * quicksort_S1 ) ); } /* s_atanf.c -- float version of s_atan.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ const float quicksort_atanhi[ ] = { #else float quicksort_atanhi[ ] = { #endif 4.6364760399e-01f, /* atan(0.5)hi 0x3eed6338 */ 7.8539812565e-01f, /* atan(1.0)hi 0x3f490fda */ 9.8279368877e-01f, /* atan(1.5)hi 0x3f7b985e */ 1.5707962513e+00f, /* atan(inf)hi 0x3fc90fda */ }; #ifdef __STDC__ const float quicksort_atanlo[ ] = { #else float quicksort_atanlo[ ] = { #endif 5.0121582440e-09f, /* atan(0.5)lo 0x31ac3769 */ 3.7748947079e-08f, /* atan(1.0)lo 0x33222168 */ 3.4473217170e-08f, /* atan(1.5)lo 0x33140fb4 */ 7.5497894159e-08f, /* atan(inf)lo 0x33a22168 */ }; #ifdef __STDC__ const float quicksort_aT[ ] = { #else float quicksort_aT[ ] = { #endif 3.3333334327e-01f, /* 0x3eaaaaaa */ -2.0000000298e-01f, /* 0xbe4ccccd */ 1.4285714924e-01f, /* 0x3e124925 */ -1.1111110449e-01f, /* 0xbde38e38 */ 9.0908870101e-02f, /* 0x3dba2e6e */ -7.6918758452e-02f, /* 0xbd9d8795 */ 6.6610731184e-02f, /* 0x3d886b35 */ -5.8335702866e-02f, /* 0xbd6ef16b */ 4.9768779427e-02f, /* 0x3d4bda59 */ -3.6531571299e-02f, /* 0xbd15a221 */ 1.6285819933e-02f, /* 0x3c8569d7 */ }; #ifdef __STDC__ float quicksort___atanf( float x ) #else float quicksort___atanf( x ) float x; #endif { float w, s1, s2, z; int ix, hx, id; QUICKSORT_GET_FLOAT_WORD( hx, x ); ix = hx & 0x7fffffff; if ( ix >= 0x50800000 ) { /* if |x| >= 2^34 */ if ( ix > 0x7f800000 ) return ( x + x ); /* NaN */ if ( hx > 0 ) return ( quicksort_atanhi[ 3 ] + quicksort_atanlo[ 3 ] ); else return ( -quicksort_atanhi[ 3 ] - quicksort_atanlo[ 3 ] ); } if ( ix < 0x3ee00000 ) { /* |x| < 0.4375 */ if ( ix < 0x31000000 ) { /* |x| < 2^-29 */ if ( quicksort_huge + x > quicksort_one ) return ( x ); /* raise inexact */ } id = -1; } else { x = quicksort_fabsf( x ); if ( ix < 0x3f980000 ) { /* |x| < 1.1875 */ if ( ix < 0x3f300000 ) { /* 7/16 <=|x|<11/16 */ id = 0; x = ( ( float ) 2.0f * x - quicksort_one ) / ( ( float ) 2.0f + x ); } else { /* 11/16<=|x|< 19/16 */ id = 1; x = ( x - quicksort_one ) / ( x + quicksort_one ); } } else { if ( ix < 0x401c0000 ) { /* |x| < 2.4375 */ id = 2; x = ( x - ( float ) 1.5f ) / ( quicksort_one + ( float ) 1.5f * x ); } else { /* 2.4375 <= |x| < 2^66 */ id = 3; x = -( float ) 1.0f / x; } } } /* end of argument reduction */ z = x * x; w = z * z; /* break sum from i=0 to 10 aT[ i ]z**(i+1) into odd and even poly */ s1 = z * ( quicksort_aT[ 0 ] + w * ( quicksort_aT[ 2 ] + w * ( quicksort_aT[ 4 ] + w * ( quicksort_aT[ 6 ] + w * ( quicksort_aT[ 8 ] + w * quicksort_aT[ 10 ] ) ) ) ) ); s2 = w * ( quicksort_aT[ 1 ] + w * ( quicksort_aT[ 3 ] + w * ( quicksort_aT[ 5 ] + w * ( quicksort_aT[ 7 ] + w * quicksort_aT[ 9 ] ) ) ) ); if ( id < 0 ) return ( x - x * ( s1 + s2 ) ); else { z = quicksort_atanhi[ id ] - ( ( x * ( s1 + s2 ) - quicksort_atanlo[ id ] ) - x ); return ( ( hx < 0 ) ? -z : z ); } } /* s_cosf.c -- float version of s_cos.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ float quicksort___cosf( float x ) #else float quicksort___cosf( x ) float x; #endif { float y[ 2 ], z = 0.0f; int n, ix; QUICKSORT_GET_FLOAT_WORD( ix, x ); /* |x| ~< pi/4 */ ix &= 0x7fffffff; if ( ix <= 0x3f490fd8 ) return ( quicksort___kernel_cosf( x, z ) ); /* cos(Inf or NaN) is NaN */ else if ( ix >= 0x7f800000 ) return ( x - x ); /* argument reduction needed */ else { n = quicksort___ieee754_rem_pio2f( x, y ); switch ( n & 3 ) { case 0: return ( quicksort___kernel_cosf( y[ 0 ], y[ 1 ] ) ); case 1: return ( -quicksort___kernel_sinf( y[ 0 ], y[ 1 ], 1 ) ); case 2: return ( -quicksort___kernel_cosf( y[ 0 ], y[ 1 ] ) ); default: return ( quicksort___kernel_sinf( y[ 0 ], y[ 1 ], 1 ) ); } } } /* s_sinf.c -- float version of s_sin.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ float quicksort___sinf( float x ) #else float quicksort___sinf( x ) float x; #endif { float y[ 2 ], z = 0.0; int n, ix; QUICKSORT_GET_FLOAT_WORD( ix, x ); /* |x| ~< pi/4 */ ix &= 0x7fffffff; if ( ix <= 0x3f490fd8 ) return ( quicksort___kernel_sinf( x, z, 0 ) ); /* sin(Inf or NaN) is NaN */ else if ( ix >= 0x7f800000 ) return ( x - x ); /* argument reduction needed */ else { n = quicksort___ieee754_rem_pio2f( x, y ); switch ( n & 3 ) { case 0: return ( quicksort___kernel_sinf( y[ 0 ], y[ 1 ], 1 ) ); case 1: return ( quicksort___kernel_cosf( y[ 0 ], y[ 1 ] ) ); case 2: return ( -quicksort___kernel_sinf( y[ 0 ], y[ 1 ], 1 ) ); default: return ( -quicksort___kernel_cosf( y[ 0 ], y[ 1 ] ) ); } } } /* s_fabsf.c -- float version of s_fabs.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ /* fabsf(x) returns the absolute value of x. */ #ifdef __STDC__ float quicksort___fabsf( float x ) #else float quicksort___fabsf( x ) float x; #endif { unsigned int ix; QUICKSORT_GET_FLOAT_WORD( ix, x ); QUICKSORT_SET_FLOAT_WORD( x, ix & 0x7fffffff ); return ( x ); } /* s_scalbnf.c -- float version of s_scalbn.c. Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* ==================================================== Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ==================================================== */ #ifdef __STDC__ const float #else float #endif quicksort_two25 = 3.355443200e+07f, /* 0x4c000000 */ quicksort_twom25 = 2.9802322388e-08f; /* 0x33000000 */ #ifdef __STDC__ float quicksort___scalbnf( float x, int n ) #else float quicksort___scalbnf( x, n ) float x; int n; #endif { int k, ix; QUICKSORT_GET_FLOAT_WORD( ix, x ); k = ( ix & 0x7f800000 ) >> 23; /* extract exponent */ if ( k == 0 ) { /* 0 or subnormal x */ if ( ( ix & 0x7fffffff ) == 0 ) return ( x ); /* +-0 */ x *= quicksort_two25; QUICKSORT_GET_FLOAT_WORD( ix, x ); k = ( ( ix & 0x7f800000 ) >> 23 ) - 25; } if ( k == 0xff ) return ( x + x ); /* NaN or Inf */ k = k + n; if ( ( n > 50000 ) || ( k > 0xfe ) ) /* overflow */ return ( quicksort_huge * quicksort___copysignf( quicksort_huge, x ) ); if ( n < -50000 ) /* underflow */ return ( quicksort_tiny * quicksort___copysignf( quicksort_tiny, x ) ); if ( k > 0 ) { /* normal result */ QUICKSORT_SET_FLOAT_WORD( x, ( ix & 0x807fffff ) | ( k << 23 ) ); return ( x ); } if ( k <= -25 ) /* underflow */ return ( quicksort_tiny * quicksort___copysignf( quicksort_tiny, x ) ); k += 25; /* subnormal result */ QUICKSORT_SET_FLOAT_WORD( x, ( ix & 0x807fffff ) | ( k << 23 ) ); return ( x * quicksort_twom25 ); } /* Written by J.T. Conklin . Public domain. */ /* isinff(x) returns 1 if x is inf, -1 if x is -inf, else 0; no branching! */ int quicksort___isinff( float x ) { int ix, t; QUICKSORT_GET_FLOAT_WORD( ix, x ); t = ix & 0x7fffffff; t ^= 0x7f800000; t |= -t; return ( ~( t >> 31 ) & ( ix >> 30 ) ); }