https://github.com/arsenm created https://github.com/llvm/llvm-project/pull/187666
This was originally ported from rocm device libs in efeafa1bdaa715733fc100bcd9d21f93c7272368, merge in more recent changes. >From 367d5abbf52fd709d2a8c8fbf3370d82dff60272 Mon Sep 17 00:00:00 2001 From: Matt Arsenault <[email protected]> Date: Thu, 19 Mar 2026 14:21:54 +0100 Subject: [PATCH] libclc: Update acos This was originally ported from rocm device libs in efeafa1bdaa715733fc100bcd9d21f93c7272368, merge in more recent changes. --- libclc/clc/lib/generic/math/clc_acos.cl | 2 + libclc/clc/lib/generic/math/clc_acos.inc | 231 ++++++++++++----------- 2 files changed, 122 insertions(+), 111 deletions(-) diff --git a/libclc/clc/lib/generic/math/clc_acos.cl b/libclc/clc/lib/generic/math/clc_acos.cl index 526ee3b17649f..df641a0ad6adb 100644 --- a/libclc/clc/lib/generic/math/clc_acos.cl +++ b/libclc/clc/lib/generic/math/clc_acos.cl @@ -9,10 +9,12 @@ #include "clc/clc_convert.h" #include "clc/float/definitions.h" #include "clc/internal/clc.h" +#include "clc/math/clc_ep.h" #include "clc/math/clc_fabs.h" #include "clc/math/clc_fma.h" #include "clc/math/clc_mad.h" #include "clc/math/clc_sqrt.h" +#include "clc/math/clc_sqrt_fast.h" #include "clc/math/math.h" #include "clc/relational/clc_isnan.h" diff --git a/libclc/clc/lib/generic/math/clc_acos.inc b/libclc/clc/lib/generic/math/clc_acos.inc index e036a998a65bd..32e007a542799 100644 --- a/libclc/clc/lib/generic/math/clc_acos.inc +++ b/libclc/clc/lib/generic/math/clc_acos.inc @@ -25,134 +25,143 @@ //===----------------------------------------------------------------------===// #if __CLC_FPSIZE == 32 +_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_acos(__CLC_GENTYPE x) { + // Computes arccos(x). + // The argument is first reduced by noting that arccos(x) + // is invalid for abs(x) > 1 and arccos(-x) = arccos(x). + // For denormal and small arguments arccos(x) = pi/2 to machine + // accuracy. Remaining argument ranges are handled as follows. + // For abs(x) <= 0.5 use + // arccos(x) = pi/2 - arcsin(x) + // = pi/2 - (x + x^3*R(x^2)) + // where R(x^2) is a rational minimax approximation to + // (arcsin(x) - x)/x^3. + // For abs(x) > 0.5 exploit the identity: + // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) + // together with the above rational approximation, and + // reconstruct the terms carefully. + + __CLC_GENTYPE ax = __clc_fabs(x); + + __CLC_GENTYPE rt = __clc_mad(-0.5f, ax, 0.5f); + __CLC_GENTYPE x2 = ax * ax; + __CLC_GENTYPE r = ax > 0.5f ? rt : x2; + + __CLC_GENTYPE u = + r * __clc_mad(r, + __clc_mad(r, + __clc_mad(r, + __clc_mad(r, + __clc_mad(r, 0x1.38434ep-5f, + 0x1.bf8bb4p-7f), + 0x1.069878p-5f), + 0x1.6c8362p-5f), + 0x1.33379p-4f), + 0x1.555558p-3f); + + __CLC_GENTYPE s = __clc_sqrt_fast(r); + __CLC_GENTYPE ztp = 2.0f * __clc_mad(s, u, s); + __CLC_GENTYPE ztn = __clc_mad(0x1.ddcb02p+0f, 0x1.aee9d6p+0f, -ztp); + __CLC_GENTYPE zt = x < 0.0f ? ztn : ztp; + __CLC_GENTYPE z = + __clc_mad(0x1.ddcb02p-1f, 0x1.aee9d6p+0f, -__clc_mad(x, u, x)); + z = ax > 0.5f ? zt : z; -_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acos(__CLC_GENTYPE x) { - // Some constants and split constants. - const __CLC_GENTYPE piby2 = __CLC_FP_LIT(1.5707963705e+00); - const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897933e+00); - const __CLC_GENTYPE piby2_head = __CLC_FP_LIT(1.5707963267948965580e+00); - const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(6.12323399573676603587e-17); - - __CLC_UINTN ux = __CLC_AS_UINTN(x); - __CLC_UINTN aux = ux & ~SIGNBIT_SP32; - __CLC_INTN xneg = ux != aux; - __CLC_INTN xexp = __CLC_AS_INTN(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; - __CLC_GENTYPE y = __CLC_AS_GENTYPE(aux); - - // transform if |x| >= 0.5 - __CLC_INTN transform = xexp >= -1; - - __CLC_GENTYPE y2 = y * y; - __CLC_GENTYPE yt = 0.5f * (1.0f - y); - __CLC_GENTYPE r = transform ? yt : y2; - - // Use a rational approximation for [0.0, 0.5] - __CLC_GENTYPE a = - __clc_mad(r, - __clc_mad(r, - __clc_mad(r, -0.00396137437848476485201154797087F, - -0.0133819288943925804214011424456F), - -0.0565298683201845211985026327361F), - 0.184161606965100694821398249421F); - - __CLC_GENTYPE b = __clc_mad(r, -0.836411276854206731913362287293F, - 1.10496961524520294485512696706F); - __CLC_GENTYPE u = r * MATH_DIVIDE(a, b); - - __CLC_GENTYPE s = __clc_sqrt(r); - y = s; - __CLC_GENTYPE s1 = __CLC_AS_GENTYPE(__CLC_AS_UINTN(s) & 0xffff0000); - __CLC_GENTYPE c = MATH_DIVIDE(__clc_mad(s1, -s1, r), s + s1); - __CLC_GENTYPE rettn = __clc_mad(s + __clc_mad(y, u, -piby2_tail), -2.0f, pi); - __CLC_GENTYPE rettp = 2.0F * (s1 + __clc_mad(y, u, c)); - __CLC_GENTYPE rett = xneg ? rettn : rettp; - __CLC_GENTYPE ret = piby2_head - (x - __clc_mad(x, -u, piby2_tail)); - - ret = transform ? rett : ret; - ret = aux > 0x3f800000U ? __CLC_GENTYPE_NAN : ret; - ret = ux == 0x3f800000U ? 0.0f : ret; - ret = ux == 0xbf800000U ? pi : ret; - ret = xexp < -26 ? piby2 : ret; - return ret; + return z; } #elif __CLC_FPSIZE == 64 -_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acos(__CLC_GENTYPE x) { - // 0x400921fb54442d18 - const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897933e+00); - // 0x3ff921fb54442d18 - const __CLC_GENTYPE piby2 = __CLC_FP_LIT(1.5707963267948965580e+00); - // 0x3ff921fb54442d18 - const __CLC_GENTYPE piby2_head = __CLC_FP_LIT(1.5707963267948965580e+00); - // 0x3c91a62633145c07 - const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(6.12323399573676603587e-17); +static _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_acos_identity_reduction( + __CLC_GENTYPE x, __CLC_GENTYPE r, __CLC_GENTYPE u, __CLC_GENTYPE z) { + __CLC_EP_PAIR s = __clc_ep_sqrt(r); + __CLC_GENTYPE zm = __clc_mad(0x1.dd9ad336a0500p+0, 0x1.af154eeb562d6p+0, + -2.0 * __clc_mad(s.hi, u, s.hi)); + __CLC_GENTYPE zp = 2.0 * (s.hi + __clc_mad(s.hi, u, s.lo)); + z = x < 0.0 ? zm : zp; + z = x == -1.0 ? 0x1.921fb54442d18p+1 : z; + z = x == 1.0 ? 0.0 : z; + return z; +} + +_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_acos(__CLC_GENTYPE x) { + // Computes arccos(x). + // The argument is first reduced by noting that arccos(x) + // is invalid for abs(x) > 1. For denormal and small + // arguments arccos(x) = pi/2 to machine accuracy. + // Remaining argument ranges are handled as follows. + // For abs(x) <= 0.5 use + // arccos(x) = pi/2 - arcsin(x) + // = pi/2 - (x + x^3*R(x^2)) + // where R(x^2) is a rational minimax approximation to + // (arcsin(x) - x)/x^3. + // For abs(x) > 0.5 exploit the identity: + // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) + // together with the above rational approximation, and + // reconstruct the terms carefully. __CLC_GENTYPE y = __clc_fabs(x); - __CLC_LONGN xneg = x < __CLC_FP_LIT(0.0); - __CLC_INTN xexp = __CLC_CONVERT_INTN( - (__CLC_AS_ULONGN(y) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64); + __CLC_S_GENTYPE transform = y >= 0.5; - // abs(x) >= 0.5 - __CLC_LONGN transform = __CLC_CONVERT_LONGN(xexp >= -1); - - __CLC_GENTYPE rt = __CLC_FP_LIT(0.5) * (__CLC_FP_LIT(1.0) - y); + __CLC_GENTYPE rt = __clc_mad(y, -0.5, 0.5); __CLC_GENTYPE y2 = y * y; __CLC_GENTYPE r = transform ? rt : y2; - // Use a rational approximation for [0.0, 0.5] - __CLC_GENTYPE un = __clc_fma( - r, - __clc_fma( - r, - __clc_fma(r, - __clc_fma(r, - __clc_fma(r, 0.0000482901920344786991880522822991, - 0.00109242697235074662306043804220), - -0.0549989809235685841612020091328), - 0.275558175256937652532686256258), - -0.445017216867635649900123110649), - 0.227485835556935010735943483075); - - __CLC_GENTYPE ud = __clc_fma( - r, - __clc_fma(r, - __clc_fma(r, - __clc_fma(r, 0.105869422087204370341222318533, - -0.943639137032492685763471240072), - 2.76568859157270989520376345954), - -3.28431505720958658909889444194), - 1.36491501334161032038194214209); - - __CLC_GENTYPE u = r * MATH_DIVIDE(un, ud); - - // Reconstruct acos carefully in transformed region - __CLC_GENTYPE s = __clc_sqrt(r); - __CLC_GENTYPE ztn = __clc_fma(-2.0, (s + __clc_fma(s, u, -piby2_tail)), pi); - - __CLC_GENTYPE s1 = - __CLC_AS_GENTYPE(__CLC_AS_ULONGN(s) & 0xffffffff00000000UL); - __CLC_GENTYPE c = MATH_DIVIDE(__clc_fma(-s1, s1, r), s + s1); - __CLC_GENTYPE ztp = 2.0 * (s1 + __clc_fma(s, u, c)); - __CLC_GENTYPE zt = xneg ? ztn : ztp; - __CLC_GENTYPE z = piby2_head - (x - __clc_fma(-x, u, piby2_tail)); - - z = transform ? zt : z; - - z = __CLC_CONVERT_LONGN(xexp < -56) ? piby2 : z; - z = __clc_isnan(x) ? __CLC_AS_GENTYPE((__CLC_AS_ULONGN(x) | - (__CLC_ULONGN)QNANBITPATT_DP64)) - : z; - z = x == 1.0 ? 0.0 : z; - z = x == -1.0 ? pi : z; + __CLC_GENTYPE u = r * __clc_mad(r, __clc_mad(r, __clc_mad(r, __clc_mad(r, + __clc_mad(r, __clc_mad(r, __clc_mad(r, __clc_mad(r, + __clc_mad(r, __clc_mad(r, __clc_mad(r, + 0x1.059859fea6a70p-5, -0x1.0a5a378a05eafp-6), 0x1.4052137024d6ap-6), 0x1.ab3a098a70509p-8), + 0x1.8ed60a300c8d2p-7), 0x1.c6fa84b77012bp-7), 0x1.1c6c111dccb70p-6), 0x1.6e89f0a0adacfp-6), + 0x1.f1c72c668963fp-6), 0x1.6db6db41ce4bdp-5), 0x1.333333336fd5bp-4), 0x1.5555555555380p-3); + + __CLC_GENTYPE z = __clc_mad(0x1.dd9ad336a0500p-1, 0x1.af154eeb562d6p+0, + -__clc_mad(x, u, x)); + +#ifdef __CLC_SCALAR + if (transform) + z = __clc_acos_identity_reduction(x, r, u, z); +#else + __CLC_GENTYPE identity = __clc_acos_identity_reduction(x, r, u, z); + z = transform ? identity : z; +#endif return z; } #elif __CLC_FPSIZE == 16 -_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acos(__CLC_GENTYPE x) { - return __CLC_CONVERT_GENTYPE(__clc_acos(__CLC_CONVERT_FLOATN(x))); +_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_acos(__CLC_GENTYPE x) { + // Computes arccos(x). + // The argument is first reduced by noting that arccos(x) + // is invalid for abs(x) > 1 and arccos(-x) = arccos(x). + // For denormal and small arguments arccos(x) = pi/2 to machine + // accuracy. Remaining argument ranges are handled as follows. + // For abs(x) <= 0.5 use + // arccos(x) = pi/2 - arcsin(x) + // = pi/2 - (x + x^3*R(x^2)) + // where R(x^2) is a rational minimax approximation to + // (arcsin(x) - x)/x^3. + // For abs(x) > 0.5 exploit the identity: + // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) + // together with the above rational approximation, and + // reconstruct the terms carefully. + + __CLC_GENTYPE ax = __clc_fabs(x); + + __CLC_GENTYPE rt = __clc_mad(-0.5h, ax, 0.5h); + __CLC_GENTYPE x2 = ax * ax; + __CLC_GENTYPE r = ax > 0.5h ? rt : x2; + + __CLC_GENTYPE u = r * __clc_mad(r, 0x1.828p-4h, 0x1.52p-3h); + + __CLC_GENTYPE s = __clc_sqrt_fast(r); + __CLC_GENTYPE ztp = 2.0h * __clc_mad(s, u, s); + __CLC_GENTYPE ztn = __clc_mad(0x1.ea8p+0h, 0x1.a3cp+0h, -ztp); + __CLC_GENTYPE zt = x < 0.0h ? ztn : ztp; + __CLC_GENTYPE z = __clc_mad(0x1.ea8p-1h, 0x1.a3cp+0h, -__clc_mad(x, u, x)); + z = ax > 0.5h ? zt : z; + + return z; } #endif _______________________________________________ cfe-commits mailing list [email protected] https://lists.llvm.org/cgi-bin/mailman/listinfo/cfe-commits
