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Improve payne hanek (#210)
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This patch improves the Payne-Hanek reduction algorithm.
The restriction on the input domain of trig functions is all removed.
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@shibatch
shibatch committed Aug 16, 2018
1 parent 7f056e9 commit 86d5c2d
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Showing 12 changed files with 505 additions and 538 deletions.
8 changes: 4 additions & 4 deletions src/arch/helperadvsimd.h
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Original file line number Diff line number Diff line change
Expand Up @@ -185,7 +185,7 @@ static INLINE vint2 vtruncate_vi2_vf(vfloat vf) { return vcvtq_s32_f32(vf); }
static INLINE vfloat vcast_vf_vi2(vint2 vi) { return vcvtq_f32_s32(vi); }
static INLINE vint2 vcast_vi2_i(int i) { return vdupq_n_s32(i); }
static INLINE vint2 vrint_vi2_vf(vfloat d) {
return vcvtq_s32_f32(vrndaq_f32(d));
return vcvtq_s32_f32(vrndnq_f32(d));
}

/***************************************/
Expand Down Expand Up @@ -398,7 +398,7 @@ static INLINE vdouble vcast_vd_vi(vint vi) {
}
static INLINE vint vcast_vi_i(int i) { return vdup_n_s32(i); }
static INLINE vint vrint_vi_vd(vdouble d) {
return vqmovn_s64(vcvtq_s64_f64(vrndaq_f64(d)));
return vqmovn_s64(vcvtq_s64_f64(vrndnq_f64(d)));
}

/***************************************/
Expand Down Expand Up @@ -487,10 +487,10 @@ static INLINE vopmask veq_vo_vi2_vi2(vint2 x, vint2 y) {
return vceqq_s32(x, y);
}
static INLINE vopmask vgt_vo_vi2_vi2(vint2 x, vint2 y) {
return vcgeq_s32(x, y);
return vcgtq_s32(x, y);
}
static INLINE vopmask vgt_vo_vi_vi(vint x, vint y) {
return vcombine_u32(vcge_s32(x, y), vdup_n_u32(0));
return vcombine_u32(vcgt_s32(x, y), vdup_n_u32(0));
}
static INLINE vopmask visinf_vo_vf(vfloat d) {
return veq_vo_vf_vf(vabs_vf_vf(d), vcast_vf_f(SLEEF_INFINITYf));
Expand Down
4 changes: 2 additions & 2 deletions src/arch/helperneon32.h
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Original file line number Diff line number Diff line change
Expand Up @@ -161,9 +161,9 @@ static INLINE vint2 vandnot_vi2_vo_vi2(vopmask x, vint2 y) { return (vint2)vbicq
#define vsra_vi2_vi2_i(x, c) vshrq_n_s32(x, c)

static INLINE vopmask veq_vo_vi2_vi2(vint2 x, vint2 y) { return vceqq_s32(x, y); }
static INLINE vopmask vgt_vo_vi2_vi2(vint2 x, vint2 y) { return vcgeq_s32(x, y); }
static INLINE vopmask vgt_vo_vi2_vi2(vint2 x, vint2 y) { return vcgtq_s32(x, y); }
static INLINE vint2 veq_vi2_vi2_vi2(vint2 x, vint2 y) { return (vint2)vceqq_s32(x, y); }
static INLINE vint2 vgt_vi2_vi2_vi2(vint2 x, vint2 y) { return (vint2)vcgeq_s32(x, y); }
static INLINE vint2 vgt_vi2_vi2_vi2(vint2 x, vint2 y) { return (vint2)vcgtq_s32(x, y); }

static INLINE vint2 vsel_vi2_vo_vi2_vi2(vopmask m, vint2 x, vint2 y) { return (vint2)vbslq_u32(m, (vmask)x, (vmask)y); }

Expand Down
41 changes: 21 additions & 20 deletions src/libm-tester/tester.c
View file
Original file line number Diff line number Diff line change
Expand Up @@ -3520,7 +3520,7 @@ void do_test() {
fprintf(stderr, "sin : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_d(mpfr_sin, child_sin, d, 3.5);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracy_d(mpfr_sin, child_sin, d, 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_sin, child_sin, pow(2.1, i), 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_sin, child_sin, pow(2.16, i), 3.5);
for(i64=(int64_t)-1e+14;i64<(int64_t)1e+14 && success;i64+=(int64_t)1e+12) {
double start = u2d(d2u(M_PI_4 * i64)-20), end = u2d(d2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracy_d(mpfr_sin, child_sin, d, 3.5);
Expand All @@ -3532,7 +3532,7 @@ void do_test() {
fprintf(stderr, "sin_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_d(mpfr_sin, child_sin_u1, d, 1.0);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracy_d(mpfr_sin, child_sin_u1, d, 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_sin, child_sin_u1, pow(2.1, i), 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_sin, child_sin_u1, pow(2.16, i), 1.0);
for(i64=(int64_t)-1e+14;i64<(int64_t)1e+14 && success;i64+=(int64_t)1e+12) {
double start = u2d(d2u(M_PI_4 * i64)-20), end = u2d(d2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracy_d(mpfr_sin, child_sin_u1, d, 1.0);
Expand All @@ -3544,7 +3544,7 @@ void do_test() {
fprintf(stderr, "sin in sincos : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyX_d(mpfr_sin, child_sincos, d, 3.5);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracyX_d(mpfr_sin, child_sincos, d, 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracyX_d(mpfr_sin, child_sincos, pow(2.1, i), 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracyX_d(mpfr_sin, child_sincos, pow(2.16, i), 3.5);
for(i=1;i<10000 && success;i+=31) {
double start = u2d(d2u(M_PI_4 * i)-20), end = u2d(d2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracyX_d(mpfr_sin, child_sincos, d, 3.5);
Expand All @@ -3556,7 +3556,7 @@ void do_test() {
fprintf(stderr, "sin in sincos_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyX_d(mpfr_sin, child_sincos_u1, d, 1.0);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracyX_d(mpfr_sin, child_sincos_u1, d, 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracyX_d(mpfr_sin, child_sincos_u1, pow(2.1, i), 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracyX_d(mpfr_sin, child_sincos_u1, pow(2.16, i), 1.0);
for(i=1;i<10000 && success;i+=31) {
double start = u2d(d2u(M_PI_4 * i)-20), end = u2d(d2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracyX_d(mpfr_sin, child_sincos_u1, d, 1.0);
Expand Down Expand Up @@ -3632,7 +3632,7 @@ void do_test() {
fprintf(stderr, "cos : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_d(mpfr_cos, child_cos, d, 3.5);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracy_d(mpfr_cos, child_cos, d, 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_cos, child_cos, pow(2.1, i), 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_cos, child_cos, pow(2.16, i), 3.5);
for(i64=(int64_t)-1e+14;i64<(int64_t)1e+14 && success;i64+=(int64_t)1e+12) {
double start = u2d(d2u(M_PI_4 * i64)-20), end = u2d(d2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracy_d(mpfr_cos, child_cos, d, 3.5);
Expand All @@ -3644,7 +3644,7 @@ void do_test() {
fprintf(stderr, "cos_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_d(mpfr_cos, child_cos_u1, d, 1.0);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracy_d(mpfr_cos, child_cos_u1, d, 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_cos, child_cos_u1, pow(2.1, i), 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_cos, child_cos_u1, pow(2.16, i), 1.0);
for(i64=(int64_t)-1e+14;i64<(int64_t)1e+14 && success;i64+=(int64_t)1e+12) {
double start = u2d(d2u(M_PI_4 * i64)-20), end = u2d(d2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracy_d(mpfr_cos, child_cos_u1, d, 1.0);
Expand All @@ -3656,7 +3656,7 @@ void do_test() {
fprintf(stderr, "cos in sincos : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyY_d(mpfr_cos, child_sincos, d, 3.5);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracyY_d(mpfr_cos, child_sincos, d, 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracyY_d(mpfr_cos, child_sincos, pow(2.1, i), 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracyY_d(mpfr_cos, child_sincos, pow(2.16, i), 3.5);
for(i=1;i<10000 && success;i+=31) {
double start = u2d(d2u(M_PI_4 * i)-20), end = u2d(d2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracyY_d(mpfr_cos, child_sincos, d, 3.5);
Expand All @@ -3668,7 +3668,7 @@ void do_test() {
fprintf(stderr, "cos in sincos_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyY_d(mpfr_cos, child_sincos_u1, d, 1.0);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracyY_d(mpfr_cos, child_sincos_u1, d, 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracyY_d(mpfr_cos, child_sincos_u1, pow(2.1, i), 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracyY_d(mpfr_cos, child_sincos_u1, pow(2.16, i), 1.0);
for(i=1;i<10000 && success;i+=31) {
double start = u2d(d2u(M_PI_4 * i)-20), end = u2d(d2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracyY_d(mpfr_cos, child_sincos_u1, d, 1.0);
Expand Down Expand Up @@ -3715,7 +3715,7 @@ void do_test() {
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_d(mpfr_tan, child_tan, d, 3.5);
for(d = -1e+7;d < 1e+7 && success;d += 1000.1) checkAccuracy_d(mpfr_tan, child_tan, d, 3.5);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracy_d(mpfr_tan, child_tan, d, 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_tan, child_tan, pow(2.1, i), 3.5);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_tan, child_tan, pow(2.16, i), 3.5);
for(i=1;i<10000 && success;i+=31) {
double start = u2d(d2u(M_PI_4 * i)-20), end = u2d(d2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracy_d(mpfr_tan, child_tan, d, 3.5);
Expand All @@ -3728,7 +3728,7 @@ void do_test() {
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_d(mpfr_tan, child_tan_u1, d, 1.0);
for(d = -1e+7;d < 1e+7 && success;d += 1000.1) checkAccuracy_d(mpfr_tan, child_tan_u1, d, 1.0);
for(d = -1e+14;d < 1e+14 && success;d += (1e+10 + 0.1)) checkAccuracy_d(mpfr_tan, child_tan_u1, d, 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_tan, child_tan_u1, pow(2.1, i), 1.0);
for(i = 0;i < 920 && success;i++) checkAccuracy_d(mpfr_tan, child_tan_u1, pow(2.16, i), 1.0);
for(i=1;i<10000 && success;i+=31) {
double start = u2d(d2u(M_PI_4 * i)-20), end = u2d(d2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2d(d2u(d)+1)) checkAccuracy_d(mpfr_tan, child_tan_u1, d, 1.0);
Expand Down Expand Up @@ -4266,7 +4266,7 @@ void do_test() {
fprintf(stderr, "sinf : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_f(mpfr_sin, child_sinf, d, 3.5);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracy_f(mpfr_sin, child_sinf, d, 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_sin, child_sinf, pow(1.06, i), 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_sin, child_sinf, pow(1.092, i), 3.5);
for(i64=(int64_t)-1000;i64<(int64_t)1000 && success;i64+=(int64_t)1) {
double start = u2f(f2u(M_PI_4 * i64)-20), end = u2f(f2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracy_f(mpfr_sin, child_sinf, d, 3.5);
Expand All @@ -4278,7 +4278,7 @@ void do_test() {
fprintf(stderr, "sinf_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_f(mpfr_sin, child_sinf_u1, d, 1.0);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracy_f(mpfr_sin, child_sinf_u1, d, 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_sin, child_sinf_u1, pow(1.06, i), 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_sin, child_sinf_u1, pow(1.092, i), 1.0);
for(i64=(int64_t)-1000;i64<(int64_t)1000 && success;i64+=(int64_t)1) {
double start = u2f(f2u(M_PI_4 * i64)-20), end = u2f(f2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracy_f(mpfr_sin, child_sinf_u1, d, 1.0);
Expand All @@ -4290,7 +4290,7 @@ void do_test() {
fprintf(stderr, "sin in sincosf : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyX_f(mpfr_sin, child_sincosf, d, 3.5);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracyX_f(mpfr_sin, child_sincosf, d, 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracyX_f(mpfr_sin, child_sincosf, pow(1.06, i), 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracyX_f(mpfr_sin, child_sincosf, pow(1.092, i), 3.5);
for(i=1;i<10000 && success;i+=31) {
double start = u2f(f2u(M_PI_4 * i)-20), end = u2f(f2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracyX_f(mpfr_sin, child_sincosf, d, 3.5);
Expand All @@ -4302,7 +4302,7 @@ void do_test() {
fprintf(stderr, "sin in sincosf_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyX_f(mpfr_sin, child_sincosf_u1, d, 1.0);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracyX_f(mpfr_sin, child_sincosf_u1, d, 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracyX_f(mpfr_sin, child_sincosf_u1, pow(1.06, i), 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracyX_f(mpfr_sin, child_sincosf_u1, pow(1.092, i), 1.0);
for(i=1;i<10000 && success;i+=31) {
double start = u2f(f2u(M_PI_4 * i)-20), end = u2f(f2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracyX_f(mpfr_sin, child_sincosf_u1, d, 1.0);
Expand Down Expand Up @@ -4378,7 +4378,7 @@ void do_test() {
fprintf(stderr, "cosf : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_f(mpfr_cos, child_cosf, d, 3.5);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracy_f(mpfr_cos, child_cosf, d, 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_cos, child_cosf, pow(1.06, i), 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_cos, child_cosf, pow(1.092, i), 3.5);
for(i64=(int64_t)-1000;i64<(int64_t)1000 && success;i64+=(int64_t)1) {
double start = u2f(f2u(M_PI_4 * i64)-20), end = u2f(f2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracy_f(mpfr_cos, child_cosf, d, 3.5);
Expand All @@ -4390,7 +4390,7 @@ void do_test() {
fprintf(stderr, "cosf_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_f(mpfr_cos, child_cosf_u1, d, 1.0);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracy_f(mpfr_cos, child_cosf_u1, d, 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_cos, child_cosf_u1, pow(1.06, i), 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_cos, child_cosf_u1, pow(1.092, i), 1.0);
for(i64=(int64_t)-1000;i64<(int64_t)1000 && success;i64+=(int64_t)1) {
double start = u2f(f2u(M_PI_4 * i64)-20), end = u2f(f2u(M_PI_4 * i64)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracy_f(mpfr_cos, child_cosf_u1, d, 1.0);
Expand All @@ -4402,7 +4402,7 @@ void do_test() {
fprintf(stderr, "cos in sincosf : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyY_f(mpfr_cos, child_sincosf, d, 3.5);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracyY_f(mpfr_cos, child_sincosf, d, 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracyY_f(mpfr_cos, child_sincosf, pow(1.06, i), 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracyY_f(mpfr_cos, child_sincosf, pow(1.092, i), 3.5);
for(i=1;i<10000 && success;i+=31) {
double start = u2f(f2u(M_PI_4 * i)-20), end = u2f(f2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracyY_f(mpfr_cos, child_sincosf, d, 3.5);
Expand All @@ -4414,7 +4414,7 @@ void do_test() {
fprintf(stderr, "cos in sincosf_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracyY_f(mpfr_cos, child_sincosf_u1, d, 1.0);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracyY_f(mpfr_cos, child_sincosf_u1, d, 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracyY_f(mpfr_cos, child_sincosf_u1, pow(1.06, i), 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracyY_f(mpfr_cos, child_sincosf_u1, pow(1.092, i), 1.0);
for(i=1;i<10000 && success;i+=31) {
double start = u2f(f2u(M_PI_4 * i)-20), end = u2f(f2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracyY_f(mpfr_cos, child_sincosf_u1, d, 1.0);
Expand Down Expand Up @@ -4458,9 +4458,10 @@ void do_test() {
//

fprintf(stderr, "tanf : ");
checkAccuracy_f(mpfr_tan, child_tanf, 70.936981201171875, 3.5);
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_f(mpfr_tan, child_tanf, d, 3.5);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracy_f(mpfr_tan, child_tanf, d, 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_tan, child_tanf, pow(1.06, i), 3.5);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_tan, child_tanf, pow(1.092, i), 3.5);
for(i=1;i<10000 && success;i+=31) {
double start = u2f(f2u(M_PI_4 * i)-20), end = u2f(f2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracy_f(mpfr_tan, child_tanf, d, 3.5);
Expand All @@ -4472,7 +4473,7 @@ void do_test() {
fprintf(stderr, "tanf_u1 : ");
for(d = -10;d < 10 && success;d += 0.002) checkAccuracy_f(mpfr_tan, child_tanf_u1, d, 1.0);
for(d = -10000;d < 10000 && success;d += 1.1) checkAccuracy_f(mpfr_tan, child_tanf_u1, d, 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_tan, child_tanf_u1, pow(1.06, i), 1.0);
for(i = 0;i < 1000 && success;i++) checkAccuracy_f(mpfr_tan, child_tanf_u1, pow(1.092, i), 1.0);
for(i=1;i<10000 && success;i+=31) {
double start = u2f(f2u(M_PI_4 * i)-20), end = u2f(f2u(M_PI_4 * i)+20);
for(d = start;d <= end;d = u2f(f2u(d)+1)) checkAccuracy_f(mpfr_tan, child_tanf_u1, d, 1.0);
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