diff options
| -rw-r--r-- | src/ffts_trig.c | 164 |
1 files changed, 115 insertions, 49 deletions
diff --git a/src/ffts_trig.c b/src/ffts_trig.c index 514a1e5..883d0c5 100644 --- a/src/ffts_trig.c +++ b/src/ffts_trig.c @@ -33,44 +33,110 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #include "ffts_trig.h" /* 1/(2*cos(pow(2,-p)*pi)) */ -static const FFTS_ALIGN(16) unsigned int half_secant[66] = { - 0x00000000, 0x3fe00000, 0x00000000, 0x3fe00000, 0x00000000, 0x3fe00000, - 0x00000000, 0x3fe00000, 0x00000000, 0x3fe00000, 0x00000000, 0x3fe00000, - 0x00000001, 0x3fe00000, 0x00000005, 0x3fe00000, 0x00000014, 0x3fe00000, - 0x0000004f, 0x3fe00000, 0x0000013c, 0x3fe00000, 0x000004ef, 0x3fe00000, - 0x000013bd, 0x3fe00000, 0x00004ef5, 0x3fe00000, 0x00013bd4, 0x3fe00000, - 0x0004ef4f, 0x3fe00000, 0x0013bd3d, 0x3fe00000, 0x004ef4f3, 0x3fe00000, - 0x013bd3cd, 0x3fe00000, 0x04ef4f34, 0x3fe00000, 0x13bd3cde, 0x3fe00000, - 0x4ef4f46c, 0x3fe00000, 0x3bd3e0e7, 0x3fe00001, 0xef507722, 0x3fe00004, - 0xbd5114f9, 0x3fe00013, 0xf637de7d, 0x3fe0004e, 0xe8190891, 0x3fe0013b, - 0x9436640e, 0x3fe004f0, 0x9c61d971, 0x3fe013d1, 0xd17cba53, 0x3fe0503e, - 0x7bdb3895, 0x3fe1517a, 0x00000000, 0x00000000, 0x00000000, 0x00000000 +static const FFTS_ALIGN(16) unsigned int half_secant[132] = { + 0x00000000, 0x3fe00000, 0xc9be45de, 0x3be3bd3c, + 0x00000000, 0x3fe00000, 0xc9be45de, 0x3c03bd3c, + 0x00000000, 0x3fe00000, 0xc9be45de, 0x3c23bd3c, + 0x00000000, 0x3fe00000, 0xc9be45de, 0x3c43bd3c, + 0x00000000, 0x3fe00000, 0xc9be45de, 0x3c63bd3c, + 0x00000000, 0x3fe00000, 0xc9be45df, 0x3c83bd3c, + 0x00000001, 0x3fe00000, 0x4df22efd, 0x3c7de9e6, + 0x00000005, 0x3fe00000, 0x906e8725, 0xbc60b0cd, + 0x00000014, 0x3fe00000, 0x906e8357, 0xbc80b0cd, + 0x0000004f, 0x3fe00000, 0x0dce83c9, 0xbc5619b2, + 0x0000013c, 0x3fe00000, 0x0dc6e79a, 0xbc7619b2, + 0x000004ef, 0x3fe00000, 0xe4af1240, 0x3c83cc9b, + 0x000013bd, 0x3fe00000, 0x2d14c08a, 0x3c7e64df, + 0x00004ef5, 0x3fe00000, 0x47a85465, 0xbc59b20b, + 0x00013bd4, 0x3fe00000, 0xab79c897, 0xbc79b203, + 0x0004ef4f, 0x3fe00000, 0x15019a96, 0x3c79386b, + 0x0013bd3d, 0x3fe00000, 0x7d6dbf4b, 0xbc7b16b7, + 0x004ef4f3, 0x3fe00000, 0xf30832e0, 0x3c741ee4, + 0x013bd3cd, 0x3fe00000, 0xd3bcd4bb, 0xbc83f41e, + 0x04ef4f34, 0x3fe00000, 0xdd75aebb, 0xbc82ef06, + 0x13bd3cde, 0x3fe00000, 0xb2b41b3d, 0x3c52d979, + 0x4ef4f46c, 0x3fe00000, 0x4f0fb458, 0xbc851db3, + 0x3bd3e0e7, 0x3fe00001, 0x8a0ce3f0, 0x3c58dbab, + 0xef507722, 0x3fe00004, 0x2a8ec295, 0x3c83e351, + 0xbd5114f9, 0x3fe00013, 0xc4c0d92d, 0x3c8b3ca4, + 0xf637de7d, 0x3fe0004e, 0xb74de729, 0x3c45974e, + 0xe8190891, 0x3fe0013b, 0x26edf4da, 0xbc814c20, + 0x9436640e, 0x3fe004f0, 0xe2b34b50, 0x3c8091ab, + 0x9c61d971, 0x3fe013d1, 0x6ce01b8e, 0x3c7f7df7, + 0xd17cba53, 0x3fe0503e, 0x74ad7633, 0xbc697609, + 0x7bdb3895, 0x3fe1517a, 0x82f9091b, 0xbc8008d1, + 0x00000000, 0x00000000, 0x00000000, 0x00000000, + 0x00000000, 0x00000000, 0x00000000, 0x00000000 }; /* cos(pow(2,-p)*pi), sin(pow(2,-p)*pi) */ -static const FFTS_ALIGN(16) unsigned int cos_sin_pi_table[132] = { - 0x00000000, 0x3ff00000, 0x54442d18, 0x3e0921fb, 0x00000000, 0x3ff00000, - 0x54442d18, 0x3e0921fb, 0x00000000, 0x3ff00000, 0x54442d18, 0x3e1921fb, - 0x00000000, 0x3ff00000, 0x54442d18, 0x3e2921fb, 0x00000000, 0x3ff00000, - 0x54442d18, 0x3e3921fb, 0xffffffff, 0x3fefffff, 0x54442d18, 0x3e4921fb, - 0xfffffffe, 0x3fefffff, 0x54442d18, 0x3e5921fb, 0xfffffff6, 0x3fefffff, - 0x54442d16, 0x3e6921fb, 0xffffffd9, 0x3fefffff, 0x54442d0e, 0x3e7921fb, - 0xffffff62, 0x3fefffff, 0x54442cef, 0x3e8921fb, 0xfffffd88, 0x3fefffff, - 0x54442c73, 0x3e9921fb, 0xfffff621, 0x3fefffff, 0x54442a83, 0x3ea921fb, - 0xffffd886, 0x3fefffff, 0x544422c2, 0x3eb921fb, 0xffff6216, 0x3fefffff, - 0x544403c1, 0x3ec921fb, 0xfffd8858, 0x3fefffff, 0x544387ba, 0x3ed921fb, - 0xfff62162, 0x3fefffff, 0x544197a1, 0x3ee921fb, 0xffd88586, 0x3fefffff, - 0x5439d73a, 0x3ef921fb, 0xff62161a, 0x3fefffff, 0x541ad59e, 0x3f0921fb, - 0xfd885867, 0x3fefffff, 0x539ecf31, 0x3f1921fb, 0xf621619c, 0x3fefffff, - 0x51aeb57c, 0x3f2921fb, 0xd8858675, 0x3fefffff, 0x49ee4ea6, 0x3f3921fb, - 0x62161a34, 0x3fefffff, 0x2aecb360, 0x3f4921fb, 0x88586ee6, 0x3feffffd, - 0xaee6472e, 0x3f5921fa, 0x21621d02, 0x3feffff6, 0xbecca4ba, 0x3f6921f8, - 0x858e8a92, 0x3fefffd8, 0xfe670071, 0x3f7921f0, 0x169b92db, 0x3fefff62, - 0xfcdec784, 0x3f8921d1, 0x6084cd0d, 0x3feffd88, 0xf7a3667e, 0x3f992155, - 0xe3796d7e, 0x3feff621, 0xf10dd814, 0x3fa91f65, 0xa3d12526, 0x3fefd88d, - 0xbc29b42c, 0x3fb917a6, 0xcff75cb0, 0x3fef6297, 0x3c69a60b, 0x3fc8f8b8, - 0xcf328d46, 0x3fed906b, 0xa6aea963, 0x3fd87de2, 0x667f3bcd, 0x3fe6a09e, - 0x667f3bcd, 0x3fe6a09e, 0x00000000, 0x00000000, 0x00000000, 0x3ff00000 +static const FFTS_ALIGN(16) unsigned int cos_sin_pi_table[264] = { + 0x00000000, 0x3ff00000, 0xc9be45de, 0xbbf3bd3c, + 0x54442d18, 0x3df921fb, 0xbb77974f, 0x3a91a390, + 0x00000000, 0x3ff00000, 0xc9be45de, 0xbc13bd3c, + 0x54442d18, 0x3e0921fb, 0x54a14928, 0x3aa19bd0, + 0x00000000, 0x3ff00000, 0xc9be45de, 0xbc33bd3c, + 0x54442d18, 0x3e1921fb, 0xb948108a, 0x3ab17cce, + 0x00000000, 0x3ff00000, 0xc9be45de, 0xbc53bd3c, + 0x54442d18, 0x3e2921fb, 0x4be32e14, 0x3ac100c8, + 0x00000000, 0x3ff00000, 0xc9be45de, 0xbc73bd3c, + 0x54442d18, 0x3e3921fb, 0x2c9f4879, 0x3ace215d, + 0xffffffff, 0x3fefffff, 0x6c837443, 0x3c888586, + 0x54442d18, 0x3e4921fb, 0x0005f376, 0x3acd411f, + 0xfffffffe, 0x3fefffff, 0x4df22ef1, 0xbc8de9e6, + 0x54442d18, 0x3e5921fb, 0x9937209e, 0xbaf7b153, + 0xfffffff6, 0x3fefffff, 0x906e88aa, 0x3c70b0cd, + 0x54442d16, 0x3e6921fb, 0xfe19968a, 0xbb03b7c0, + 0xffffffd9, 0x3fefffff, 0xdf22ed26, 0xbc8e9e64, + 0x54442d0e, 0x3e7921fb, 0x8d1b6ffb, 0xbaee8bb4, + 0xffffff62, 0x3fefffff, 0x0dd18f0f, 0x3c6619b2, + 0x54442cef, 0x3e8921fb, 0x7f2b20fb, 0xbb00e133, + 0xfffffd88, 0x3fefffff, 0x0dd314b2, 0x3c8619b2, + 0x54442c73, 0x3e9921fb, 0x619fdf6e, 0xbb174e98, + 0xfffff621, 0x3fefffff, 0x3764acf5, 0x3c8866c8, + 0x54442a83, 0x3ea921fb, 0xf5b2407f, 0xbb388215, + 0xffffd886, 0x3fefffff, 0x20e7a944, 0xbc8e64df, + 0x544422c2, 0x3eb921fb, 0x7b9b9f23, 0x3b5a0961, + 0xffff6216, 0x3fefffff, 0x52ee25ea, 0x3c69b20e, + 0x544403c1, 0x3ec921fb, 0x4df6a86a, 0xbb5999d9, + 0xfffd8858, 0x3fefffff, 0xd8910ead, 0x3c89b20f, + 0x544387ba, 0x3ed921fb, 0x0809d04d, 0x3b77d9db, + 0xfff62162, 0x3fefffff, 0x438d3925, 0xbc8937a8, + 0x544197a1, 0x3ee921fb, 0xa5d27f7a, 0xbb858b02, + 0xffd88586, 0x3fefffff, 0x94b3ddd2, 0x3c8b22e4, + 0x5439d73a, 0x3ef921fb, 0xf8a3b73d, 0xbb863c7f, + 0xff62161a, 0x3fefffff, 0x7ea469b2, 0xbc835c13, + 0x541ad59e, 0x3f0921fb, 0xb8cee262, 0x3bae9860, + 0xfd885867, 0x3fefffff, 0x23a32e63, 0xbc77d556, + 0x539ecf31, 0x3f1921fb, 0xfcd23a30, 0x3b96b111, + 0xf621619c, 0x3fefffff, 0xbbbd8fe6, 0xbc87507d, + 0x51aeb57c, 0x3f2921fb, 0x4916c435, 0xbbca6e1d, + 0xd8858675, 0x3fefffff, 0x54748eab, 0xbc879f0e, + 0x49ee4ea6, 0x3f3921fb, 0x744a453e, 0x3bde894d, + 0x62161a34, 0x3fefffff, 0xb1f9b9c4, 0xbc6136dc, + 0x2aecb360, 0x3f4921fb, 0x7e566b4c, 0x3be87615, + 0x88586ee6, 0x3feffffd, 0xf173ae5b, 0x3c81af64, + 0xaee6472e, 0x3f5921fa, 0x284a9df8, 0xbbfee52e, + 0x21621d02, 0x3feffff6, 0xebc82813, 0xbc76acfc, + 0xbecca4ba, 0x3f6921f8, 0x7bcab5b2, 0x3c02ba40, + 0x858e8a92, 0x3fefffd8, 0x1883bcf7, 0x3c8359c7, + 0xfe670071, 0x3f7921f0, 0xfe6b7a9b, 0x3bfab967, + 0x169b92db, 0x3fefff62, 0xc81fbd0d, 0x3c85dda3, + 0xfcdec784, 0x3f8921d1, 0xbe836d9d, 0x3c29878e, + 0x6084cd0d, 0x3feffd88, 0x4556e4cb, 0xbc81354d, + 0xf7a3667e, 0x3f992155, 0x091a0130, 0xbbfb1d63, + 0xe3796d7e, 0x3feff621, 0x2e24aa15, 0xbc6c57bc, + 0xf10dd814, 0x3fa91f65, 0x0d569a90, 0xbc2912bd, + 0xa3d12526, 0x3fefd88d, 0x378811c7, 0xbc887df6, + 0xbc29b42c, 0x3fb917a6, 0xd26ed688, 0xbc3e2718, + 0xcff75cb0, 0x3fef6297, 0x2a361fd3, 0x3c756217, + 0x3c69a60b, 0x3fc8f8b8, 0xb9ff8d82, 0xbc626d19, + 0xcf328d46, 0x3fed906b, 0x10231ac2, 0x3c7457e6, + 0xa6aea963, 0x3fd87de2, 0xd3d5a610, 0xbc672ced, + 0x667f3bcd, 0x3fe6a09e, 0x13b26456, 0xbc8bdd34, + 0x667f3bcd, 0x3fe6a09e, 0x13b26456, 0xbc8bdd34, + 0x00000000, 0x00000000, 0x00000000, 0x00000000, + 0x00000000, 0x3ff00000, 0x00000000, 0x00000000 }; int @@ -187,13 +253,13 @@ ffts_generate_cosine_sine_pow2_32f(ffts_cpx_32f *const table, int table_size) FFTS_ASSUME(log_2 > 1); offset = 32 - log_2; ct = (const ffts_cpx_64f*) - FFTS_ASSUME_ALIGNED_32(&cos_sin_pi_table[4 * offset]); - hs = (const double*) &half_secant[2 * offset]; + FFTS_ASSUME_ALIGNED_32(&cos_sin_pi_table[8 * offset]); + hs = (const double*) &half_secant[4 * offset]; /* initialize from lookup table */ for (i = 0; i <= log_2; i++) { - w[i][0] = ct[i][0]; - w[i][1] = ct[i][1]; + w[i][0] = ct[2*i][0]; + w[i][1] = ct[2*i][2]; } /* generate sine and cosine tables with maximum error less than 0.5 ULP */ @@ -208,8 +274,8 @@ ffts_generate_cosine_sine_pow2_32f(ffts_cpx_32f *const table, int table_size) /* skip and find next trailing zero */ offset = (log_2 + 2 + ffts_ctzl(~i >> (log_2 + 2))); - w[log_2][0] = hs[log_2] * (w[log_2 + 1][0] + w[offset][0]); - w[log_2][1] = hs[log_2] * (w[log_2 + 1][1] + w[offset][1]); + w[log_2][0] = hs[2 * log_2] * (w[log_2 + 1][0] + w[offset][0]); + w[log_2][1] = hs[2 * log_2] * (w[log_2 + 1][1] + w[offset][1]); } mid_point: @@ -264,13 +330,13 @@ ffts_generate_table_1d_real_32f(struct _ffts_plan_t *const p, FFTS_ASSUME(log_2 > 2); offset = 34 - log_2; ct = (const ffts_cpx_64f*) - FFTS_ASSUME_ALIGNED_32(&cos_sin_pi_table[4 * offset]); - hs = (const double*) &half_secant[2 * offset]; + FFTS_ASSUME_ALIGNED_32(&cos_sin_pi_table[8 * offset]); + hs = (const double*) &half_secant[4 * offset]; /* initialize from lookup table */ for (i = 0; i <= log_2; i++) { - w[i][0] = ct[i][0]; - w[i][1] = ct[i][1]; + w[i][0] = ct[2*i][0]; + w[i][1] = ct[2*i][2]; } /* generate sine and cosine tables with maximum error less than 0.5 ULP */ @@ -297,8 +363,8 @@ ffts_generate_table_1d_real_32f(struct _ffts_plan_t *const p, /* skip and find next trailing zero */ offset = (log_2 + 2 + ffts_ctzl(~i >> (log_2 + 2))); - w[log_2][0] = hs[log_2] * (w[log_2 + 1][0] + w[offset][0]); - w[log_2][1] = hs[log_2] * (w[log_2 + 1][1] + w[offset][1]); + w[log_2][0] = hs[2 * log_2] * (w[log_2 + 1][0] + w[offset][0]); + w[log_2][1] = hs[2 * log_2] * (w[log_2 + 1][1] + w[offset][1]); } } else { for (i = 1; i < N/4; i++) { @@ -323,8 +389,8 @@ ffts_generate_table_1d_real_32f(struct _ffts_plan_t *const p, /* skip and find next trailing zero */ offset = (log_2 + 2 + ffts_ctzl(~i >> (log_2 + 2))); - w[log_2][0] = hs[log_2] * (w[log_2 + 1][0] + w[offset][0]); - w[log_2][1] = hs[log_2] * (w[log_2 + 1][1] + w[offset][1]); + w[log_2][0] = hs[2 * log_2] * (w[log_2 + 1][0] + w[offset][0]); + w[log_2][1] = hs[2 * log_2] * (w[log_2 + 1][1] + w[offset][1]); } } |
