IRIX Base Documentation 2002 November

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SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) NNNNAAAAMMMMEEEE SSSSCCCCFFFFFFFFTTTT2222DDDD, DDDDZZZZFFFFFFFFTTTT2222DDDD, CCCCSSSSFFFFFFFFTTTT2222DDDD, ZZZZDDDDFFFFFFFFTTTT2222DDDD - Applies a two-dimensional real-to- complex or complex-to-real Fast Fourier Transform (FFT) SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS Single precision -> Single precision complex Fortran: CCCCAAAALLLLLLLL SSSSCCCCFFFFFFFFTTTT2222DDDD ((((_i_s_i_g_n,,,, _n_1,,,, _n_2,,,, _s_c_a_l_e,,,, _x,,,, _l_d_x,,,, _y,,,, _l_d_y,,,, _t_a_b_l_e,,,, _w_o_r_k,,,, _i_s_y_s)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt ssssccccfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ffffllllooooaaaatttt _s_c_a_l_e,,,, ffffllllooooaaaatttt *_x,,,, iiiinnnntttt _l_d_x,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_y,,,, iiiinnnntttt _l_d_y,,,, ffffllllooooaaaatttt *_t_a_b_l_e,,,, ffffllllooooaaaatttt *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt ssssccccfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ffffllllooooaaaatttt _s_c_a_l_e,,,, ffffllllooooaaaatttt *_x,,,, iiiinnnntttt _l_d_x,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_y,,,, iiiinnnntttt _l_d_y,,,, ffffllllooooaaaatttt *_t_a_b_l_e,,,, ffffllllooooaaaatttt *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; Double precision -> Double precision complex Fortran: CCCCAAAALLLLLLLL DDDDZZZZFFFFFFFFTTTT2222DDDD ((((_i_s_i_g_n,,,, _n_1,,,, _n_2,,,, _s_c_a_l_e,,,, _x,,,, _l_d_x,,,, _y,,,, _l_d_y,,,, _t_a_b_l_e,,,, _w_o_r_k,,,, _i_s_y_s)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt ddddzzzzfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ddddoooouuuubbbblllleeee _s_c_a_l_e,,,, ddddoooouuuubbbblllleeee *_x,,,, iiiinnnntttt _l_d_x,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_y,,,, iiiinnnntttt _l_d_y,,,, ddddoooouuuubbbblllleeee *_t_a_b_l_e,,,, ddddoooouuuubbbblllleeee *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt ddddzzzzfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ddddoooouuuubbbblllleeee _s_c_a_l_e,,,, ddddoooouuuubbbblllleeee *_x,,,, iiiinnnntttt _l_d_x,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_y,,,, iiiinnnntttt _l_d_y,,,, ddddoooouuuubbbblllleeee *_t_a_b_l_e,,,, ddddoooouuuubbbblllleeee *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; Single precision complex -> Single precision Fortran: CCCCAAAALLLLLLLL CCCCSSSSFFFFFFFFTTTT2222DDDD ((((_i_s_i_g_n,,,, _n_1,,,, _n_2,,,, _s_c_a_l_e,,,, _x,,,, _l_d_x,,,, _y,,,, _l_d_y,,,, _t_a_b_l_e,,,, _w_o_r_k,,,, _i_s_y_s)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt ccccssssfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ffffllllooooaaaatttt _s_c_a_l_e,,,, PPPPaaaaggggeeee 1111 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _l_d_x,,,, ffffllllooooaaaatttt *_y,,,, iiiinnnntttt _l_d_y,,,, ffffllllooooaaaatttt *_t_a_b_l_e,,,, ffffllllooooaaaatttt *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt ccccssssfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ffffllllooooaaaatttt _s_c_a_l_e,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_x,,,, iiiinnnntttt _l_d_x,,,, ffffllllooooaaaatttt *_y,,,, iiiinnnntttt _l_d_y,,,, ffffllllooooaaaatttt *_t_a_b_l_e,,,, ffffllllooooaaaatttt *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; Double precision complex -> Double precision Fortran: CCCCAAAALLLLLLLL ZZZZDDDDFFFFFFFFTTTT2222DDDD ((((_i_s_i_g_n,,,, _n_1,,,, _n_2,,,, _s_c_a_l_e,,,, _x,,,, _l_d_x,,,, _y,,,, _l_d_y,,,, _t_a_b_l_e,,,, _w_o_r_k,,,, _i_s_y_s)))) C/C++: ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt zzzzddddfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ddddoooouuuubbbblllleeee _s_c_a_l_e,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_x,,,, iiiinnnntttt _l_d_x,,,, ddddoooouuuubbbblllleeee *_y,,,, iiiinnnntttt _l_d_y,,,, ddddoooouuuubbbblllleeee *_t_a_b_l_e,,,, ddddoooouuuubbbblllleeee *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; C++ STL: ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>> ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>> iiiinnnntttt zzzzzzzzfffffffftttt2222dddd ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n_1,,,, iiiinnnntttt _n_2,,,, ddddoooouuuubbbblllleeee _s_c_a_l_e,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_x,,,, iiiinnnntttt _l_d_x,,,, ddddoooouuuubbbblllleeee *_y,,,, iiiinnnntttt _l_d_y,,,, ddddoooouuuubbbblllleeee *_t_a_b_l_e,,,, ddddoooouuuubbbblllleeee *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;; IIIIMMMMPPPPLLLLEEEEMMMMEEEENNNNTTTTAAAATTTTIIIIOOOONNNN These routines are part of the SCSL Scientific Library and can be loaded using either the ----llllssssccccssss or the ----llllssssccccssss____mmmmpppp option. The ----llllssssccccssss____mmmmpppp option directs the linker to use the multi-processor version of the library. When linking to SCSL with ----llllssssccccssss or ----llllssssccccssss____mmmmpppp, the default integer size is 4 bytes (32 bits). Another version of SCSL is available in which integers are 8 bytes (64 bits). This version allows the user access to larger memory sizes and helps when porting legacy Cray codes. It can be loaded by using the ----llllssssccccssss____iiii8888 option or the ----llllssssccccssss____iiii8888____mmmmpppp option. A program may use only one of the two versions; 4-byte integer and 8-byte integer library calls cannot be mixed. The C and C++ prototypes shown above are appropriate for the 4-byte integer version of SCSL. When using the 8-byte integer version, the variables of type iiiinnnntttt become lllloooonnnngggg lllloooonnnngggg and the <<<<ssssccccssssllll____fffffffftttt____iiii8888....hhhh>>>> header file should be included. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN SSSSCCCCFFFFFFFFTTTT2222DDDD/DDDDZZZZFFFFFFFFTTTT2222DDDD computes the two-dimensional Fast Fourier Transform (FFT) of the real matrix _X, and it stores the results in the complex matrix _Y. CCCCSSSSFFFFFFFFTTTT2222DDDD/ZZZZDDDDFFFFFFFFTTTT2222DDDD computes the corresponding inverse transform. PPPPaaaaggggeeee 2222 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) In FFT applications, it is customary to use zero-based subscripts; the formulas are simpler that way. First the function of SSSSCCCCFFFFFFFFTTTT2222DDDD is described. Suppose the arrays are declared as follows: Fortran: REAL X(0:ldx-1, 0:n2-1) COMPLEX Y(0:ldy-1, 0:n2-1) C/C++: float x[n2][ldx]; scsl_complex y[n2][ldy]; C++ STL: float x[n2][ldx]; complex<float> y[n2][ldy]; where _l_d_x >= _n_1, _l_d_y >= (_n_1/2) + 1. SSSSCCCCFFFFFFFFTTTT2222DDDD computes the formula: n2-1 n1-1 Y(k1, k2) = scale * Sum Sum [ X(j1, j2)*w1**(j1*k1)*w2**(j2*k2) ] j2=0 j1=0 for _k_1 = 0, ..., _n_1/2 + 1 _k_2 = 0, ..., _n_2-1 where: _w_1 = exp(_i_s_i_g_n*2*_p_i*_i/_n_1) _w_2 = exp(_i_s_i_g_n*2*_p_i*_i/_n_2) _i = + sqrt(-1) _p_i = 3.14159..., _i_s_i_g_n = +1 or -1 Different authors use different conventions for which of the transforms, _i_s_i_g_n = +1 or _i_s_i_g_n = -1, is the forward or inverse transform, and what the _s_c_a_l_e factor should be in either case. You can make these routines compute any of the various possible definitions, however, by choosing the appropriate values for _i_s_i_g_n and _s_c_a_l_e. PPPPaaaaggggeeee 3333 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) The relevant fact from FFT theory is this: If you take the FFT with any particular values of _i_s_i_g_n and _s_c_a_l_e, the mathematical inverse function is computed by taking the FFT with -_i_s_i_g_n and 1/(_n_1 * _n_2 * _s_c_a_l_e). In particular, if you use _i_s_i_g_n = +1 and _s_c_a_l_e = 1.0 for the forward FFT, you can compute the inverse FFT by using _i_s_i_g_n = -1 and _s_c_a_l_e = 1.0/(_n_1 * _n_2). SSSSCCCCFFFFFFFFTTTT2222DDDD is very similar in function to CCCCCCCCFFFFFFFFTTTT2222DDDD, but it takes the real- to-complex transform in the first dimension, followed by the complex-to-complex transform in the second dimension. CCCCSSSSFFFFFFFFTTTT2222DDDD does the reverse. It takes the complex-to-complex FFT in the second dimension, followed by the complex-to-real FFT in the first dimension. See the IIIINNNNTTTTRRRROOOO____FFFFFFFFTTTT(3S) man page for more information about real-to-complex and complex-to-real FFTs. The two-dimensional analog of the conjugate formula is as follows: _Y_k_1, _k_2 = conjg _Y n1 - k, _n_2 - _k_2 for _n_1/2 < _k_1 <= _n_1 - 1 0 <= _k_2 <= _n_2 - 1 where the notation conjg(_z) represents the complex conjugate of _z. Thus, you have to compute only (slightly more than) half of the output values, namely: _Y_k_1, _k_2 for 0 <= _k_1 <= _n_1/2 0 <= _k_2 <= _n_2 - 1 See the NOTES section of this man page for information about the interpretation of the data types described in the following arguments. These routines have the following arguments: _i_s_i_g_n Integer. (input) Specifies whether to initialize the _t_a_b_l_e array or to do the forward or inverse Fourier transform, as follows: If _i_s_i_g_n = 0, the routine initializes the _t_a_b_l_e array and returns. In this case, the only arguments used or checked are _i_s_i_g_n, _n_1, _n_2, and _t_a_b_l_e. If _i_s_i_g_n = +1 or -1, the value of _i_s_i_g_n is the sign of the exponent used in the FFT formula. PPPPaaaaggggeeee 4444 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) _n_1 Integer. (input) Transform size in the first dimension. If _n_1 is not positive, the routine returns without calculating a transform. _n_2 Integer. (input) Transform size in the second dimension. If _n_2 is not positive, the routine returns without calculating a transform. _s_c_a_l_e Scale factor. (input) SSSSCCCCFFFFFFFFTTTT2222DDDD: Single precision. DDDDZZZZFFFFFFFFTTTT2222DDDD: Double precision. CCCCSSSSFFFFFFFFTTTT2222DDDD: Single precision. ZZZZDDDDFFFFFFFFTTTT2222DDDD: Double precision. Each element of the output array is multiplied by _s_c_a_l_e factor after taking the Fourier transform, as defined previously. _x Array of dimensions (_l_d_x, _n_2). (input) SSSSCCCCFFFFFFFFTTTT2222DDDD: Single precision array. DDDDZZZZFFFFFFFFTTTT2222DDDD: Double precision array. CCCCSSSSFFFFFFFFTTTT2222DDDD: Single precision complex array. ZZZZDDDDFFFFFFFFTTTT2222DDDD: Double precision complex array. Array of values to be transformed. _l_d_x Integer. (input) The number of rows in the _x array, as it was declared in the calling program. That is, the leading dimension of _x. SSSSCCCCFFFFFFFFTTTT2222DDDD, DDDDZZZZFFFFFFFFTTTT2222DDDD: _l_d_x >= MMMMAAAAXXXX(_n_1, 1). CCCCSSSSFFFFFFFFTTTT2222DDDD, ZZZZDDDDFFFFFFFFTTTT2222DDDD: _l_d_x >= MMMMAAAAXXXX(_n_1/2 + 1, 1). _y Array of dimension (_l_d_y, _n_2). (output) SSSSCCCCFFFFFFFFTTTT2222DDDD: Single precision complex array. DDDDZZZZFFFFFFFFTTTT2222DDDD: Double precision complex array. CCCCSSSSFFFFFFFFTTTT2222DDDD: Single precision array. ZZZZDDDDFFFFFFFFTTTT2222DDDD: Double precision array. Output array of transformed values. The output array can be the same as the input array, in which case, the transform is done in place and the input array is overwritten with the transformed values. In this case, it is necessary that the following equalities hold: SSSSCCCCFFFFFFFFTTTT2222DDDD, DDDDZZZZFFFFFFFFTTTT2222DDDD: _l_d_x = 2 * _l_d_y. CCCCSSSSFFFFFFFFTTTT2222DDDD, ZZZZDDDDFFFFFFFFTTTT2222DDDD: _l_d_y = 2 * _l_d_x. _l_d_y Integer. (input) The number of rows in the _y array, as it was declared in the calling program (the leading dimension of _y). PPPPaaaaggggeeee 5555 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD, DDDDZZZZFFFFFFFFTTTT2222DDDD: _l_d_y >= MMMMAAAAXXXX(_n_1/2 + 1, 1). CCCCSSSSFFFFFFFFTTTT2222DDDD, ZZZZDDDDFFFFFFFFTTTT2222DDDD: _l_d_y >= MMMMAAAAXXXX(_n_1 + 2, 1). In the complex-to-real routine, two extra elements are in the first dimension (_l_d_y >= _n_1 + 2, rather than just _l_d_y >= _n_1). These elements are needed for intermediate storage during the computation. On exit, their value is undefined. _t_a_b_l_e Array of dimension (_n_1 + _N_F_R) + (2 * _n_2 + _N_F) (input or output) SSSSCCCCFFFFFFFFTTTT2222DDDD, CCCCSSSSFFFFFFFFTTTT2222DDDD: Single precision array DDDDZZZZFFFFFFFFTTTT2222DDDD, ZZZZDDDDFFFFFFFFTTTT2222DDDD: Double precision array Table of factors and roots of unity. See the description of the _i_s_y_s argument for the value of _N_F and _N_F_R. If _i_s_i_g_n = 0, the routine initializes _t_a_b_l_e (_t_a_b_l_e is output only). If _i_s_i_g_n = +1 or -1, the values in _t_a_b_l_e are assumed to be initialized already by a prior call with _i_s_i_g_n = 0 (_t_a_b_l_e is input only). _w_o_r_k Array of dimension _n_1 + 4 * _n_2 SSSSCCCCFFFFFFFFTTTT2222DDDD, CCCCSSSSFFFFFFFFTTTT2222DDDD: Single precision array DDDDZZZZFFFFFFFFTTTT2222DDDD, ZZZZDDDDFFFFFFFFTTTT2222DDDD: Double precision array Work array. This is a scratch array used for intermediate calculations. Its address space must be different from that of the input and output arrays. _i_s_y_s Integer array dimensioned 0000........_i_s_y_s((((0000)))). An array that gives implementation-specific information. All features and functions of the FFT routines specific to any particular implementation are confined to this _i_s_y_s array. In the Origin series implementation, _i_s_y_s((((0000))))====0000 and _i_s_y_s((((0000))))====1111 are supported. In SCSL versions prior to 1.3, only _i_s_y_s((((0000))))====0000 was allowed. For _i_s_y_s((((0000))))====0000, _N_F====33330000 and _N_F_R====11115555, and for _i_s_y_s((((0000))))====1111, _N_F====_N_F_R====222255556666. The _N_F(_R) words of storage in the _t_a_b_l_e array contain a factorization of the length of the transform. The smaller value of _N_F and _N_F_R for _i_s_y_s((((0000))))====0000 is historical. They are too small to store all the required factors for the highest performing FFT, so when _i_s_y_s((((0000))))====0000, extra space is allocated when the _t_a_b_l_e array is initialized. To avoid memory leaks, this extra space must be deallocated when the _t_a_b_l_e array is no longer needed. The SSSSCCCCFFFFFFFFTTTT2222DDDDFFFF routine is used to release this memory. Due to the potential for memory leaks, the use of _i_s_y_s((((0000))))====0000 should be avoided. PPPPaaaaggggeeee 6666 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) For _i_s_y_s((((0000))))====1111, the value of _N_F and _N_F_R are large enough so that no extra memory needs to be allocated, and there is no need to call SSSSCCCCFFFFFFFFTTTT2222DDDDFFFF to release memory. If called, it does nothing. NOTE: _i_s_y_s((((0000))))====1111 means that _i_s_y_s is an integer array with two elements. The second element, _i_s_y_s((((1111)))), will not be accessed. NNNNOOOOTTTTEEEESSSS The following data types are described in this documentation: TTTTeeeerrrrmmmm UUUUsssseeeedddd DDDDaaaattttaaaa ttttyyyyppppeeee Fortran: Array dimensioned 0000........_n----1111 xxxx((((0000::::nnnn----1111)))) Array of dimensions (_m,_n) xxxx((((mmmm,,,,nnnn)))) Array of dimensions (_m,_n,_p) xxxx((((mmmm,,,,nnnn,,,,pppp)))) Integer IIIINNNNTTTTEEEEGGGGEEEERRRR (IIIINNNNTTTTEEEEGGGGEEEERRRR****8888 for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision RRRREEEEAAAALLLL Double precision DDDDOOOOUUUUBBBBLLLLEEEE PPPPRRRREEEECCCCIIIISSSSIIIIOOOONNNN Single precision complex CCCCOOOOMMMMPPPPLLLLEEEEXXXX Double precision complex DDDDOOOOUUUUBBBBLLLLEEEE CCCCOOOOMMMMPPPPLLLLEEEEXXXX C/C++: Array dimensioned 0000........_n----1111 xxxx[[[[_n]]]] Array of dimensions (_m,_n) xxxx[[[[mmmm****nnnn]]]] oooorrrr xxxx[[[[nnnn]]]][[[[mmmm]]]] Array of dimensions (_m,_n,_p) xxxx[[[[mmmm****nnnn****pppp]]]] oooorrrr xxxx[[[[pppp]]]][[[[nnnn]]]][[[[mmmm]]]] Integer iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision ffffllllooooaaaatttt Double precision ddddoooouuuubbbblllleeee Single precision complex ssssccccssssllll____ccccoooommmmpppplllleeeexxxx Double precision complex ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx C++ STL: PPPPaaaaggggeeee 7777 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) Array dimensioned 0000........_n----1111 xxxx[[[[_n]]]] Array of dimensions (_m,_n) xxxx[[[[mmmm****nnnn]]]] oooorrrr xxxx[[[[nnnn]]]][[[[mmmm]]]] Array of dimensions (_m,_n,_p) xxxx[[[[mmmm****nnnn****pppp]]]] oooorrrr xxxx[[[[pppp]]]][[[[nnnn]]]][[[[mmmm]]]] Integer iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]]) Single precision ffffllllooooaaaatttt Double precision ddddoooouuuubbbblllleeee Single precision complex ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> Double precision complex ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> CCCCAAAAUUUUTTTTIIIIOOOONNNNSSSS Transform sizes with a prime factor exceeding 22223332222----1111 are not supported for the 8-byte integer version of the library. In addition to the _w_o_r_k array, the FFT routines also dynamically allocate scratch space from the stack. The amount of space allocated can be slightly bigger than the size of the largest processor cache. For single processor runs, the default stack size is large enough that these allocations generally cause no problems. But for parallel runs, you need to ensure that the stack size of slave threads is big enough to hold this scratch space. Failure to reserve sufficient stack space will cause programs to dump core due to stack overflows. The stack size of MP library slave threads is controlled via the MMMMPPPP____SSSSLLLLAAAAVVVVEEEE____SSSSTTTTAAAACCCCKKKKSSSSIIIIZZZZEEEE environment variable or the mmmmpppp____sssseeeetttt____ssssllllaaaavvvveeee____ssssttttaaaacccckkkkssssiiiizzzzeeee(((()))) library routine. See the mmmmpppp(3C), mmmmpppp(3F) and ppppeeee____eeeennnnvvvviiiirrrroooonnnn(5) reference pages for more information on controlling the slave stack size. For pthreads applications, the thread's stack size is specified as one of many creation attributes provided in the pthread_attr_t argument to pppptttthhhhrrrreeeeaaaadddd____ccccrrrreeeeaaaatttteeee(3P). The stacksize attribute should be set explicitly to a non-default value using the pppptttthhhhrrrreeeeaaaadddd____aaaattttttttrrrr____sssseeeettttssssttttaaaacccckkkkssssiiiizzzzeeee(3P) call, described in the pppptttthhhhrrrreeeeaaaadddd____aaaattttttttrrrr____iiiinnnniiiitttt(3P) man page. Care must be exercised if copies of the _t_a_b_l_e array are used: even though a copy exists, the original must persist. As an example, the following code will nnnnooootttt work: #include <scsl_fft.h> float x[256][129]; scsl_complex y[256][65]; float table[(128 + 256) + (2*256 + 256)]; float work[128 + 4*256]; int isys[2]; isys[0] = 1; { float table_orig[(128 + 256) + (2*256 + 256)]; PPPPaaaaggggeeee 8888 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) scfft2d(0, 128, 256, 1.0f, (float *) x, 129, (scsl_complex *) y, 65, table_orig, work, isys); bcopy(table_orig, table, ((128+256)+(2*256+256))*sizeof(float)); } scfft2d(1, 128, 256, 1.0f, (float *) x, 129, (scsl_complex *) y, 65, table, work, isys); In this example, because _t_a_b_l_e__o_r_i_g is a stack variable that does not persist outside of the code block delimited by the braces, the data in the copy, _t_a_b_l_e, are not guaranteed to be valid. However, the following code will work because _t_a_b_l_e__o_r_i_g is persistent: #include <scsl_fft.h> float x[256][129]; scsl_complex y[256][65]; float table_orig[(128 + 256) + (2*256 + 256)]; float table[(128 + 256) + (2*256 + 256)]; float work[128 + 4*256]; int isys[2]; isys[0] = 1; scfft2d(0, 128, 256, 1.0f, (float *) x, 129, (scsl_complex *) y, 65, table_orig, work, isys); bcopy(table_orig, table, ((128+256)+(2*256+256))*sizeof(float)); scfft2d(1, 128, 256, 1.0f, (float *) x, 129, (scsl_complex *) y, 65, table, work, isys); EEEEXXXXAAAAMMMMPPPPLLLLEEEESSSS The following examples are for Origin series only. Example 1: Initialize the TTTTAAAABBBBLLLLEEEE array in preparation for doing a two- dimensional FFT of size 128 by 256. In this case, only the _i_s_i_g_n, _n_1, _n_2, and _t_a_b_l_e arguments are used; you can use dummy arguments or zeros for other arguments. Fortran: REAL TABLE ((128 + 256) + (2*256 + 256)) INTEGER ISYS(0:1) ISYS(0) = 1 CALL SCFFT2D (0, 128, 256, 0.0, DUMMY, 1, DUMMY, 1, & TABLE, DUMMY, ISYS) Example 2: XXXX is an array dimensioned (0...128, 0...255), and YYYY is a complex array dimensioned (0...64, 0...255). The first 128 elements of each column of XXXX contain data; for performance reasons, the extra element forces the leading dimension to be an odd number. Take the two-dimensional FFT of XXXX and store it in YYYY. Initialize the TTTTAAAABBBBLLLLEEEE array, as in example 1. PPPPaaaaggggeeee 9999 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) Fortran: REAL X(0:128, 0:255) COMPLEX Y(0:64, 0:255) REAL TABLE ((128 + 256) + (2*256 + 256)) REAL WORK(128 + 4*256) INTEGER ISYS(0:1) ISYS(0) = 1 CALL SCFFT2D(0, 128, 256, 1.0, X, 129, Y, 65, TABLE, WORK, ISYS) CALL SCFFT2D(1, 128, 256, 1.0, X, 129, Y, 65, TABLE, WORK, ISYS) C/C++: #include <scsl_fft.h> float x[256][129]; scsl_complex y[256][65]; float table[(128 + 256) + (2*256 + 256)]; float work[128 + 4*256]; int isys[2]; isys[0] = 1; scfft2d(0, 128, 256, 1.0f, (float *) x, 129, (scsl_complex *) y, 65, table, work, isys); scfft2d(1, 128, 256, 1.0f, (float *) x, 129, (scsl_complex *) y, 65, table, work, isys); C++ STL: #include <complex.h> #include <scsl_fft.h> float x[256][129]; complex<float> y[256][65]; float table[(128 + 256) + (2*256 + 256)]; float work[128 + 4*256]; int isys[2]; isys[0] = 1; scfft2d(0, 128, 256, 1.0f, (float *) x, 129, (complex<float> *) y, 65, table, work, isys); scfft2d(1, 128, 256, 1.0f, (float *) x, 129, (complex<float> *) y, 65, table, work, isys); Example 3: Take the inverse FFT of YYYY and store it back in XXXX. Note that the leading dimension of _X must be increased to 2 * _l_d_y. The scale factor 1.0/(128.0*256.0) is used. Fortran: REAL X(0:129, 0:255) COMPLEX Y(0:64, 0:255) ... PPPPaaaaggggeeee 11110000 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) CALL CSFFT2D(-1, 128, 256, 1.0/(128.0*256.0), Y, 65, & X, 130, TABLE, WORK, ISYS) C/C++: float x[256][129]; scsl_complex y[256][65]; csfft2d(-1, 128, 256, 1.0f/(128.0f*256.0f), (scsl_complex *) y, 65, (float *) x, 130, table, work, isys); C++ STL: float x[256][129]; complex<float> y[256][65]; csfft2d(-1, 128, 256, 1.0f/(128.0f*256.0f), (complex<float> *) y, 65, (float *) x, 130, table, work, isys); Example 4: Perform the same computation as in example 2, but equivalence the input and output arrays to save storage space. In this case, a row must be added to X, because it is equivalenced to a complex array. Use the 8-byte integer version of SCSL. Fortran: REAL X(0:129, 0:255) COMPLEX Y(0:64, 0:255) EQUIVALENCE ( X(0, 0), Y(0, 0) ) REAL TABLE ((128 + 256) + (2*256 + 256)) REAL WORK(128 + 4*256) INTEGER*8 ISYS(0:1) ISYS(0) = 1_8 CALL SCFFT2D(0_8, 128_8, 256_8, 1.0, X, 130_8, & Y, 65_8, TABLE, WORK, ISYS) CALL SCFFT2D(1_8, 128_8, 256_8, 1.0, X, 130_8, & Y, 65_8, TABLE, WORK, ISYS) C/C++: #include <scsl_fft_i8.h> float *x; scsl_complex y[256][65]; float table[(128 + 256) + (2*256 + 256)]; float work[128 + 4*256]; long long isys[2]; isys[0] = 1LL; x = (float *) &y[0][0]; scfft2d(0LL, 128LL, 256LL, 1.0f, x, 130LL, (scsl_complex *) y, 65LL, table, work, isys); PPPPaaaaggggeeee 11111111 SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) SSSSCCCCFFFFFFFFTTTT2222DDDD((((3333SSSS)))) scfft2d(1LL, 128LL, 256LL, 1.0f, x, 130LL, (scsl_complex *) y, 65LL, table, work, isys); C++ STL: #include <complex.h> #include <scsl_fft.h> float *x; complex<float> y[256][65]; float table[(128 + 256) + (2*256 + 256)]; float work[128 + 4*256]; long long isys[2]; isys[0] = 1LL; x = (float *) &y[0][0]; scfft2d(0LL, 128LL, 256LL, 1.0f, x, 130LL, (complex<float> *) y, 65LL, table, work, isys); scfft2d(1LL, 128LL, 256LL, 1.0f, x, 130LL, (complex<float> *) y, 65LL, table, work, isys); Example 5: Perform the same computation as in example 2, but assume that the lower bound of each Fortran array is 1, rather than 0. No change is needed in the subroutine calls. Fortran: REAL X(129, 256) COMPLEX Y(65, 256) CALL SCFFT2D(0, 128, 256, 1.0, X, 129, Y, 65, TABLE, WORK, ISYS) CALL SCFFT2D(1, 128, 256, 1.0, X, 129, Y, 65, TABLE, WORK, ISYS) SSSSEEEEEEEE AAAALLLLSSSSOOOO IIIINNNNTTTTRRRROOOO____FFFFFFFFTTTT(3S), IIIINNNNTTTTRRRROOOO____SSSSCCCCSSSSLLLL(3S), CCCCCCCCFFFFFFFFTTTT(3S), CCCCCCCCFFFFFFFFTTTT2222DDDD(3S), CCCCCCCCFFFFFFFFTTTT3333DDDD(3S), CCCCCCCCFFFFFFFFTTTTMMMM(3S), SSSSCCCCFFFFFFFFTTTT(3S), SSSSCCCCFFFFFFFFTTTT3333DDDD(3S), SSSSCCCCFFFFFFFFTTTTMMMM(3S) PPPPaaaaggggeeee 11112222